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James Smallcombe: There we go. Okay, so right now.
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James Smallcombe: Please tell us if we can do all the physics happening here.
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Ragnar Stroberg: All right, I'll jump right in. Then
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Ragnar Stroberg: Thanks everyone for
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Ragnar Stroberg: Coming to the talk, virtually and I probably want to thank James for the invitation. I know it's early enough, but I'm not sure yet but
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Ragnar Stroberg: Probably. Thanks. And I'll say, James. The, the answer the question is probably no. But maybe what you go to the top to the practices. And so I'm going to talk about doing
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Ragnar Stroberg: Nuclear Physics thing, specifically in English structure ab initio and assume that most of you have heard about
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Ragnar Stroberg: Ab initio theory that's been having a become a lot more prominent in the last, say, two decades, but I'm also assuming that a large portion of you are experimentalists and so I'm going to spend a good amount of time at the beginning, trying to give some concepts.
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Ragnar Stroberg: Some, some people may think of an issue in terms of just blasting stuff on supercomputers, you know, lots of power.
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Ragnar Stroberg: And while there are big computers that are used. That's not really what I want to focus on here. I want to focus on the ideas which I think are really interesting. So I will jump in here.
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Ragnar Stroberg: The basic plan is that I'll give some kind of background night is an effective field theory and similarity. We're almost a group. So these are kind of the ideas that have made a lot of the progress possible. It's also not stuff that I did it. Was it happened larger before I came around
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Ragnar Stroberg: But I'll try to summarize it for you. I'll talk about the valence space in medium FRG. So that's the the method that I work on again try to keep it conceptual but there will be some equations.
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Ragnar Stroberg: And then I'll look at some results applications of these. So some specific nuclear physics cases.
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Ragnar Stroberg: The drip lines look at some Jamar Teller quenching story there and some recent progress towards calculating heavy glad
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Ragnar Stroberg: I've listed here. All the collaborators on these projects so that I don't forget later.
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Ragnar Stroberg: Okay, so just to begin. What do we mean when I say ab initio and the original phrase evolutional came from quantum chemistry where I think
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Ragnar Stroberg: It's the earliest definition that I saw was that it's an exact solution to an exact problem which maybe make sense in chemistry where you just have to say the coolest interaction.
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Ragnar Stroberg: That works. QED. But in nuclear physics that, of course, makes no sense at all.
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Ragnar Stroberg: There's no way of exactly solving any of these equations and even writing down the problem is not, you can't do it. Exactly. There's no such thing. So can't do that.
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Ragnar Stroberg: So what we'll go with here is that you need to start with realistic degrees of freedom and realistic was also historical used by
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Ragnar Stroberg: Prior to have an issue of theory. But what I mean by realistic here.
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Ragnar Stroberg: Is that if you have some theory that has a one buddy piece of jewelry piece, for example.
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Ragnar Stroberg: The one body piece should actually describe one of the body is that you're talking about. So if you say you're using protons are one body piece should actually describe a proton.
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Ragnar Stroberg: To buddy piece should enter that should describe the interaction of say to protons to class. So it should reproduce scattering as what I mean by realistic.
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Ragnar Stroberg: And then the other important issue is uncertainty quantification. This is essentially
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Ragnar Stroberg: How we're rewriting the exact solution. We're saying I'm certainly quantification, you're never going to solve it. Exactly. That doesn't. We don't even know what that means in our context.
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Ragnar Stroberg: But you should have some estimate of what is left out. So you know how precise your calculation is those are the goals.
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Ragnar Stroberg: Okay, so now this is essentially we can split this into two main areas here. So we're solving the many buddy non relativistic Schrodinger equation H size equity. SIGH
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Ragnar Stroberg: And the trouble is that we need to figure out what he is. So that's writing down what our Hamiltonian and figuring out the potential and for that.
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Ragnar Stroberg: We will use Carol effective field theory and I'll spend a little bit of time talking about this and then we need to solve the equation. And to do that we use.
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Ragnar Stroberg: Some many buddy methods, some ammunition. Anybody methods of which there are a number here.
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Ragnar Stroberg: I'll say the top two on this list quantum Monte Carlo and know course Jamal are
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Ragnar Stroberg: Probably the best in terms of being able to control the uncertainties. You have a very good estimate of your uncertainty, but they also are the most expensive and they scale.
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Ragnar Stroberg: Exponentially with the system sizes and so they can't really be extended very far. The next three of them, maybe even more or next for
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Ragnar Stroberg: Scale Poland know mailing so that they can be extended further up it's possible to calculate beyond save the P show, but there's a lot more effort needs to go into understanding the, the precision of the calculations.
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Ragnar Stroberg: Okay, so start with talking about the nuclear interaction. And here's just kind of a cartoon on the right. The of our we have longer distances, kind of a, an attractive potential and there's a minimum and then it short distances some
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Ragnar Stroberg: Repulsive hardcore, and this is his pictures been around for a very long time.
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Ragnar Stroberg: From a conceptual point of view, there's a lot of trouble that happens down at the short distances. So if you think about this potential as had usually was the case.
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Ragnar Stroberg: Last couple decades as due to exchange of Muslims long distance part you can think of an exchange of piloting or to pine exchange and it shorter distances, you're exchanging vector. And that sounds like rose or a mega and
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Ragnar Stroberg: Even more as you get to shorter distances. The problem is that there's lots of marathons in the particle data group book and a lot of them have poorly known
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Ragnar Stroberg: Properties, like the mass or a couple into the nucleus and they are very short, they live so they have very large widths and becomes very quickly poorly defined
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Ragnar Stroberg: Another problem here is that as you get down to, you know, about half of me or lower you convert that into a relative momentum that you approach the pie on production threshold so that even just the concept of what a potential means is kind of lost because to think of a potential
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Ragnar Stroberg: As the whole of your two objects at a certain distance and the energy of holding them at that distance or the work you have to do to bring them to that distance. But now if you hold them close enough that you can make pions
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Ragnar Stroberg: It doesn't even make sense what the energy is because you have plans flying out that distance. So everything kind of breaks down there and to make it worse.
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Ragnar Stroberg: Of course, when you actually have some sort of the potential blows up to infinity, like this, you run into divergent integrals. When you actually want to solve the equations. So we need to think about this picture.
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Ragnar Stroberg: So what we're going to do is use the effective field theory and this is going to be just not quite handily that a cartoonish picture.
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Ragnar Stroberg: So consider you want to do something at low energies or long wavelengths. Let's read here and you want to know about some physics that happens it short distances. So there's some short distance feature.
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Ragnar Stroberg: Of size are which I'll call f of x. So that's about function is. But we only have a long wavelength Pro. So here cave, a small number. That's the way to number
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Ragnar Stroberg: So we want to evaluate some sort of a new role like this that will come up. Lucky go scattering or something we can expand
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Ragnar Stroberg: This into the icon next to a tailor series expansion and pull up with stuff that doesn't depend on x. And what you'll see here's will have an integral over F and then weighted by various powers of x.
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Ragnar Stroberg: And that integral doesn't depend on k which is the wavelength of our pro. In fact, so this integral here is just a number.
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Ragnar Stroberg: And the next integral. So x f of x will be a number and it will have a character because of this X waiting here they'll have some characteristic size are which is the size of the system and x squared. And we'll, we'll have some characteristic size of our square
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Ragnar Stroberg: So these numbers here are dimensional and they are called low energy constants. So that's just an integral over all the stuff that we don't really know it short distance and the results don't depend on the details of the f of x, they just depend on that integral on the wall energy constant
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Ragnar Stroberg: And so this
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Ragnar Stroberg: We can we can basically do this as tissue expansion and it'll be fine. As long as we go up to some breakdown scale lamb to be which is going to be one over. So there are factors of h bar in converting this is a momentum scale. This is a link scale.
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Ragnar Stroberg: So as long as. So here we have k squared r squared as long as that's small, then we can truncate this finite order. So the only need a couple of numbers to describe what this process is. And so, converting our until lambda, we have now an expansion in K over lambda. So, Linda is the breakdown
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Ragnar Stroberg: So this is nice. We don't need to know what's going on at very short distance only no need to notice the integral over this. And in fact, you could cook up several different functions, f of x that had the same integral
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Ragnar Stroberg: And by proving it long wavelength, we wouldn't be able to tell the difference.
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Ragnar Stroberg: OK, so now getting back to the nuclear interaction, same kind of an idea, want to think about what are these scale so that we can have some sort of small scale big scale.
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Ragnar Stroberg: So that we can do an expansion and we were thinking about this in terms of pilots change row exchange.
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Ragnar Stroberg: We're going to look at the mass of the pie on the massive rose mega and massive the nuclear and here was the case means this is the ferry momentum in nuclear matter. So this gives you an idea of the typical male mentor that are in nuclei.
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Ragnar Stroberg: And we can see very quickly that
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Ragnar Stroberg: This gave me a small compared to these other masses. So that, that's good, but the payoff classes even smaller. We're not going to be able to
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Ragnar Stroberg: treat that as a small number. So what we end up doing is we're going to be doing a double expansion in momentum and the pan mass over these heavy scales.
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Ragnar Stroberg: Okay, so here's a strategy as you write down every operator, you can come up with involving new clowns and pions as long as it consistent with cemeteries like angular momentum and translational endurance and so on. Parody this
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Ragnar Stroberg: Organized them and powers of momentum or a pie mass divided by breakdown scale, which is going to be somewhere up here to some power and it will truncate at some finite power new so that gives us a finite number of times.
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Ragnar Stroberg: And then because there is divergent integrals, we need to cut off the integral at short distance
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Ragnar Stroberg: And then finally, we just need to fit these low energy Constance that encode all of the short distance information we can fit it to data or we can fit it to say a lattice QC calculation, although in the end.
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Ragnar Stroberg: That should reproduce data to. So what's it on practices we fit those low energy concepts to data. And so we have just a few numbers that characterize everything going on short distances that would calculate now.
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Ragnar Stroberg: Okay. And so now organizing and powers of that small scale over a large scale. We have a leading order next deleting order next next deleting order, next, next, next to each order. So there's
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Ragnar Stroberg: An increasing number of diagrams and the theory and it becomes increasingly complicated, but that's how you want to organize it. The idea is that these higher order terms are less important, and hopefully the become sufficiently unimportant before they become too painful to deal with.
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Ragnar Stroberg: also point out that at the lower two orders. We only have two nuclear force and as you go higher than incomes a treatment plan for us in the form of course. So, so we'll come back to that.
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Ragnar Stroberg: OK, so now I'm going to move on to the solving of the shorter equation. And there's been a lot of progress in this over the last decades. This is a
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Ragnar Stroberg: New cloud with the red squares are showing ab initio calculations and so 2009 or stuff, mainly in the P shell and over the last decade, till recently.
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Ragnar Stroberg: gone all the way up and get calculations mass 110 isotopes. And all of these. So it's been kind of explosion and really changed the landscape of what can be done have initial a large reason for this has been the concept of SRT or similarity or normalization discuss next year.
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Ragnar Stroberg: So the basic idea of similarity. We're normalization group are trying to solve the shorter equation. So we have our Hamiltonian and we partition and arbitrarily or
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Ragnar Stroberg: As a into a diagonal piece and then off diagonal piece and this is
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Ragnar Stroberg: Doesn't need to be specifically going on and off, Dave, I just kind of characterize is the part that is easy to do live is a dagger and the part we don't want to deal with is the off day. So you can think about this as a matrix. So the red is the diagonal. Move it as the off day ago
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Ragnar Stroberg: We've we perform a unitary transformation. So it's just a change of basis and we choose our unitary transformation. So this off diagonal piece goes to zero.
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Ragnar Stroberg: If we're able to do that. So then this is shows the unitary transformed Hamiltonian these bits are zero. Now we have some sort of a smaller subspace, who can solve the problem and it makes it tractable.
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Ragnar Stroberg: And because this transformation is unitary what a Unitarian contribution does is it preserves the eigenvalues of the operator here the Hamiltonian so that preserves the energies and it will also preserve all the other items.
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Ragnar Stroberg: Okay, so it's great book. If we need to then know where the unitary transformation is so the strategy is to parameter is is unitary transformation with appropriate what's called a flow parameter s. That's a just a time like number is a single number.
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Ragnar Stroberg: And we define how the unitary transformation changes with so the differential equation. So the change in our transformation with respect to s.
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Ragnar Stroberg: Is given by an operator Ada acting on the entire transformation we call data generator and the only requirement for maintain it unitary, it is that it's anti permission or if it's real than at symmetric
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Ragnar Stroberg: And so just by doing the chain rule. You can take this derivative here and
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Ragnar Stroberg: Plugging admitting it above you can find a flow equation for your Hamiltonian. So this tells you how your Hamiltonian will change with this flow parameter and it just in terms of a commentator
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Ragnar Stroberg: Of the Hamiltonian with the generator chosen so you're free to choose the generator
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Ragnar Stroberg: And a different choice of generator will take you along a different path in the space of possible theories but because everything is unitary here, they will all give you the same answer. In the end, and so the game is to choose a generator that makes your life easier.
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Ragnar Stroberg: So here in the interest of time, I will skip this. I will come. I can come back to you if people really want to hear about this is basically just an example of a two by two system shine how this works. You have a series of unitary transformations
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Ragnar Stroberg: Each of these Hamiltonian. This is unitary equivalence of gives the same answer. But you in the end you can make the problem simpler, so I can come back to it.
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Ragnar Stroberg: So the first application of the similarity or normalization group was interesting that that short range.
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Ragnar Stroberg: Repulsive core in the interaction which syndicated over here is causes trouble from anybody methods because if articles can't get close to one another. They have to know how to avoid each other and they become correlated and have to not be in the same place at the same time.
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Ragnar Stroberg: So rather than looking at this and position space. If we look at this in momentum space. This is what, for example, one particular channel.
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Ragnar Stroberg: Are going to be taking potential looks like and then momentum space. The thing that causes the trouble is the off diagonal bits here which
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Ragnar Stroberg: Connect long or mentor to have momentum. So if you have, say, some low moment of state. The short range repulsion will launch your particles into momentum state. And this makes it hard to solve the problem.
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Ragnar Stroberg: So we'd like those to go. That's the update on peace. We don't want and turns out to in that particular case, a very useful choice for ADA is the commentator of the kinetic energy with the potential energy. That's because the kinetic energy and momentum space is diag and so if the
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Ragnar Stroberg: Potential were to look like the kinetic energy. Basically, if it's diagonal, which is the shift that we want, then these would commute, so that the generator Ada would be zero and
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Ragnar Stroberg: The Hamiltonian doesn't change the basically the Hamiltonian will change to the extent that the potential doesn't look DAG. And so what this does is it suppresses the off DAG pieces.
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Ragnar Stroberg: Okay, so there's a lot on the slide. I just want to make it. Let's start out on the top panel here. So this is now applying s RG similar to normalization group to
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Ragnar Stroberg: Do different potentials are on the team, and in three in three yellow Cairo potential
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Ragnar Stroberg: And on the left side, this is basically the, the original potential. And as we go to the right, where we're flowing and solving this differential equation and softening the potential
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Ragnar Stroberg: It becomes useful to instead of us as flow parameter s to write things in terms of lambda, because that gives you a momentum scale and tells you kind of how the range of a mentor that are connected on the off day
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Ragnar Stroberg: So up here. This is a hard potential. And as we saw, we see that the at short distances. What was a very hard wrinkles propulsive core
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Ragnar Stroberg: Is softened and soften and softened and so now there's no repost repulsive core at all. This is much easier to solve with many buddy method.
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Ragnar Stroberg: And because this is a unitary transformation. It gives exactly the same answers for the hardest interaction in the softest interaction that they're equipped
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Ragnar Stroberg: And we can look at this again in momentum space. And we can see that indeed the potential is driven to a bandana.
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Ragnar Stroberg: And I'll on the right here we have the wave function of the dude Iran.
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Ragnar Stroberg: So the black line there is with the initial potential has that repulsive core. And so you have this kind of wound sorry wound at the center of the Deuteronomy due to their impulsive core
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Ragnar Stroberg: And as you soften it, you see that that wound at the center goes away. And now to the junior glands overlap.
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Ragnar Stroberg: And this more looks. Looks like I mean field kind of a picture but wave functions aren't observable and that all of the observable is in this are unchanged. So what we get basically here is that we get the same answers, but it's much easier to solve them anybody but
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Ragnar Stroberg: There's always an issue of that there's no free lunch when you're solving these problems. And so the price we pay here for making the problem simpler, is that we induce many body forces. This is the initiative that comes around, inevitably,
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Ragnar Stroberg: When you eliminate some degrees of freedom or eliminate modes that you will induce from anybody forces. So for example, if we have a diagram like this on the left.
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Ragnar Stroberg: Where we excite some intermediate delta excitation that we don't want to deal with Delta's we want to not have those in our theory, this needs to be converted into a three by force. Same thing happens if we want to eliminate I mentioned modes. This gets converted into a three by force.
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Ragnar Stroberg: And so right here we can see it a try. Thompson others is a three buddy problem and we can see that if we only
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Ragnar Stroberg: We only worried about to buddy forces as we soften. Now we start getting the wrong answer. And that's because we've industry by forces.
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Ragnar Stroberg: If we include the industry, but it forces the results is independent of the scale. So it is unitary yeah
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Ragnar Stroberg: Of course, that's not what the right answer is the right answer is down here. And that's because we need to include three forces from the get go, because the the Carol potentials have through it forces.
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Ragnar Stroberg: Okay, so I should basically to summarize this idea and take it of potential from Cairo live TV presents to channel challenges we get a short
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Ragnar Stroberg: Distance kind of repulsive core mission is hard to solve and we have three buddy forces and FRG lets us trade those short range repulsive potentials for three forces and so terms to problems into just one ball.
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Ragnar Stroberg: Okay, so now the because we now have just the problem of three way forces a large part of the anybody problem is going to be concerned with dealing with the fact that they have this three forces so
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Ragnar Stroberg: We do this, what's now solving them. Anybody problem, not just a two or three a problem. And here we'll go to the in medium similarity are normalization. Now, this is for solving them. Anybody shooting.
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Ragnar Stroberg: And that strategy we use for dealing with three buddy forces which are painful to deal with in general, it's called normal ordering
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Ragnar Stroberg: We choose a reference state until call here a fine not so that's just a guess for the way function should look like. And we then
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Ragnar Stroberg: Average three buddy force over all of the nuclear arms in the core and that gives us a number, it's a zero body piece of the Hamiltonian
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Ragnar Stroberg: If we average two legs over the core plus one outside of this reference state and gives us an effective one buddy potential. And likewise, we can get an effective to buddy potential and then there'll be some residual three buddy potential that we can't reduce for
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Ragnar Stroberg: And the nice thing about this is that, to the extent that those first three terms carry most of the physics we can throw away the residual three body terms will call the IMS energy to approximation because we only keep up the two buddy operators and this makes things much more tractable.
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Ragnar Stroberg: So the more detailed strategy here that we're going to follow is called the valence space and medium s RG and and
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Ragnar Stroberg: The motivation here is that historically the show model is a very good model for a lot of nuclear physics of the problem is that
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Ragnar Stroberg: It's not a controlled model in the sense that there's some sort of an approximation made and we don't know exactly how good that should be or how to make it. But
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Ragnar Stroberg: But we would like to map things on the show model because those are called relevant degrees of freedom.
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Ragnar Stroberg: The idea is that we have some inner core, we have a balanced space for the new clients are active and up above that there's some excluded space for the new villains are not allowed to be
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Ragnar Stroberg: So here we now define as we split it into the Hamiltonian into DAG on and off diagonal an update on the bad part we don't like. So that will be anything that spoils the
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Ragnar Stroberg: whole picture. So anything that causes an excitation out of the core or anything that causes an excitation into this excluded space. We don't want those because those spoiler.
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Ragnar Stroberg: So for example, you could take the generator to be the commentator of DAG on and off diagonal. And what this will do is this. If the off day or in part, zero, this is zero and it doesn't change the only changes to the extent that that commentators on zero
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Ragnar Stroberg: We can solve the surgery flow equation. And as we solve the off diagonal pieces will be driven to zero. So, these unpleasant bits are driven to zero. And so then we can just agonizing the valence space in this then looks exactly like a standard show model calculation.
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Ragnar Stroberg: And there's one additional aspects that
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Ragnar Stroberg: interest of time, I won't spend too much on but the essential point is that as you add more and more particles into the reference
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Ragnar Stroberg: The, the nave picture of using your reference as your core for your normal ordering this becomes a less good guess of what the way function actually is. And so it becomes more efficient to
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Ragnar Stroberg: Instead, you have your reference states the thing they use for number ordering leak into the valence space. So now you have a separate concept of a core and a reference state. And this allows you better capture the three forces within the space.
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Ragnar Stroberg: And you can just see here the
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Ragnar Stroberg: Is actually now some some data. And this is to demonstrate the benefit of that last step.
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Ragnar Stroberg: So I'm plotting as a function of a binding energy for oxygen calcium isotopes. And there's a bunch of different avenues methods all using the same input interaction. So they should be getting the same result.
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Ragnar Stroberg: And everything does except for this blue curve, which as you add more and more particles you get over binding.
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Ragnar Stroberg: And that's the the old way of doing this, where you use the core as a reference. If instead you allow the reference state to leak into the valence space and to account and
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Ragnar Stroberg: Implicitly for those imbalance through buddy terms it fixes everything up and everybody agreed. So that is red curve is the method that I'll be talking about using for now.
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Ragnar Stroberg: Agrees with all of these other many buddy methods where they can be applied some oxygen, lots of these many buddy methods can be applied to oxygen.
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Ragnar Stroberg: Fewer can be applied to the calcium chance but the
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Ragnar Stroberg: MSR gene variant space formulation, can you claim wherever a show model calculation can be applied. So this means that where the other methods can be applied, we agree, but now we're not restricted to the same cases that they're
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Ragnar Stroberg: Spectroscopy is also possible, because it's basically a showman method at that point. And it turns out that you get results without any adjustable parameters that look pretty comfortable with.
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Ragnar Stroberg: Phenomenology. So that's the USD be here is phenomenology. The black curves are experiments and then blue curse. Here are the famous calculation.
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Ragnar Stroberg: With the three levels.
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Ragnar Stroberg: Okay, I'll skip that point as well. And of course, if we just look at a deviation from experiments RMS deviation from experiments in the SD shelf just kind of a
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Ragnar Stroberg: Benchmark here on the far right is phenomenology. This is the gold standard USD has great RMS we're not quite there yet, but you can see the improvement of just taking their interaction.
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Ragnar Stroberg: And applying the MS RG be reduced deviation substantially. And so while USD is better at reproducing these spectroscopy. It's also fit directly to this with something like 40 or 50 parameters. Whereas here, the IMS energy calculation has not
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Ragnar Stroberg: Okay, so now we're moving on more into physics.
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Ragnar Stroberg: Here we in this cactus paper here in 2017 we make the realization, I guess, other people have made it in a realization. A couple cases but realized that there was a particular interaction that had been around for six or seven years that
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Ragnar Stroberg: Now that we're able to do calculations of large swath of nuclear I realized that it did a great job of reproducing binding energies for a lot of nucleus. So that's this 1.8 2.0 em interaction in purple here and it's sitting right on top of the data for the most part.
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Ragnar Stroberg: So the other interactions that are shown here are also caramel derived interaction and the different numbers correspond to different cut offs us to regulate out the short distance physics.
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Ragnar Stroberg: And ideally, your results should not depend on the way in which you regulate our short distance physics because that's just an artifact of the theory.
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Ragnar Stroberg: And here we can see that it actually does. So this means that there's something going wrong with the details of how we're regulating things
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Ragnar Stroberg: So this is basically a bad sign. So, so there's something that wasn't understood there. However, it seems that in this case for the 1.8 2.0 maybe two or three bad things cancelled out or whatever managed to be done there.
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Ragnar Stroberg: It works out remarkably well. It seems to have done the right thing. So two or three and wrongs make a right here. So you can think that maybe it's just binding energy look good and other things go badly.
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Ragnar Stroberg: But even say open show includes like sulfur the binding energies look great and separation energies, even at a more detailed scale things look very nice. So it's definitely capturing the physics.
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Ragnar Stroberg: And so if we have
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Ragnar Stroberg: Something that can reliably reproduce separation energies without any adjusted parameters. So, this this interaction was fit with only input from
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Ragnar Stroberg: Two, three, and four, buddy. David nothing beyond killing for. So this seems to have a great predictive power we can start to think about what can we actually use this to predict the drip lines.
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Ragnar Stroberg: So the drip lines.
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Ragnar Stroberg: On Sam and neutron side the neutron drip line is the nucleus where it the last bound nucleus were any you had another neutron IT, JUST FALLS RIGHT OFF, so I'm showing here results for calcium
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Ragnar Stroberg: In the black lines or the experimental separation and energy. So here's one neutron separation energy. Here's a tune john separation and agree the red dots are the calculation.
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Ragnar Stroberg: And they can see it does a very nice job of sitting on top of the calculation and we can go out here and we can save it haha when the separation energy goes to zero. That's the drip line. And so we see that there's a. This is the drip line right here at ankles 40 so the calcium 60
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Ragnar Stroberg: Course
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Ragnar Stroberg: We're not doing a an exact calculation. We're doing it a an ab initio calculation. And so if we want to say is that a significant dip below zero. Is that meaningful there because there's some precision on this calculation, we need some theoretical Air Force.
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Ragnar Stroberg: So ideally, what we do is all what I discussed earlier we truncate our Cairo interaction at some order effect estimate the effect of higher orders.
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Ragnar Stroberg: And say evaluate that many by truncation. So the fact that we were throwing away three and four buddy forces afternoon on the ordering
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Ragnar Stroberg: Introduces somewhere. It's a good approximation. That's not a perfect approximation. So if we kept three buddy forces. Oh, if you kept forgetting forces that should change the answer.
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Ragnar Stroberg: We want to be able to estimate how much of a change that is and then ideally we propagate all of the different sources of error with full covariance to get a final Erica.
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Ragnar Stroberg: We don't have the machinery to do that yet. And because there's clearly something wrong with the Carolyn put at the beginning, just the fact that there's this regular independence.
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Ragnar Stroberg: This is kind of an old interaction, actually. So it's not even done at consistently at a given Cairo order this procedure doesn't actually make sense for the current case.
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Ragnar Stroberg: So what we're going to do instead is we're going to have a model for our uncertainty or for our error and this may seem
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Ragnar Stroberg: Unusual or seeing ad hoc, but this is actually whenever you quote uncertainty. This is what you're doing us. You have a model for your uncertainty.
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Ragnar Stroberg: That will, in general, involve a systematic piece which can may be different depending on whatever parameters are available and there will be a piece that you treat is random. So if you do an experiment and you
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Ragnar Stroberg: Give some, you know, error bars, what you're doing is you're saying that you model the some part of your experiment as a random variation but you don't have any control and you try to control for all systematics but at some point or something that
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Ragnar Stroberg: So we're going to try to do that. And so we need to figure out what systematic should there be
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Ragnar Stroberg: And to think about this, we can think about what is it, since this interaction does such a great job reproducing experiment. One thing about where does it fail. So that will give us a hint about where the system XR
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Ragnar Stroberg: So one thing we do know is that for this interaction radio come out too small. So that's uploaded here for a number of posts show isotopes.
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Ragnar Stroberg: This is the charge radio and so the black dots are experiment and the purple dots are this interaction. And we see that we come out a little bit too small. So something like 4% too small for the radio.
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Ragnar Stroberg: Radio very directly on the separation energies, we're just interested in energies, but this should have some effect because something's going wrong here.
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Ragnar Stroberg: And so you can think and just even in a meaningful picture if you squeeze the meaning field together. What this will end up doing is it spreads out the single particle spectrum.
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Ragnar Stroberg: And so you can just in a infinite. Well, kind of a picture. This is what a single particle energy level look like the ice level.
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Ragnar Stroberg: Looks like that. So there's a kinetic energy and potential energy from the wealth gap.
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Ragnar Stroberg: And now if we change the radius a little bit and principal. Maybe we bring the wealth depth down a little bit so that the overall binding energies are still preserve
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Ragnar Stroberg: The change in our single particle energies will be just taking a derivative here we get a minus two times the change in the radius and
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Ragnar Stroberg: Times that single particle energy. Again, that's just from taking a derivative and RE. RE expressing it in terms of a single particle energy. And then there's a variance variation in the potential. And actually, that should cancel out in here.
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Ragnar Stroberg: So what we predict here is that the error due to this radius, being a little bit too small.
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Ragnar Stroberg: If we plot it as a function of a single particle energy should be linear with this slope. And then with some offset and that offset should be naked.
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Ragnar Stroberg: And since we know what the error and the radius is it's 4% so it's too small, too small. So, that gives his mind science. So we should have the slope of this line should be 8% and
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Ragnar Stroberg: To reasonable approximation, the single particle interviews are the separation energies.
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Ragnar Stroberg: So what we can do is we can plot the separation that residual the error and the separation energy. So that's theory minus experiment.
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Ragnar Stroberg: Versus the calculated separation energy we expect align with the slope of 8% and that's actually exactly what we find your. So here I'm planning residual of the
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Ragnar Stroberg: Neutron separation energy to neutron separation and energy proton separation and energy into proton separate efficient energy for a bunch of different isotopes wherever the data is available, up to beyond calcium 60
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Ragnar Stroberg: And sure enough, if you look at the slope of this line. It's about 8% and the opposite is indeed negative and it's 8% for all of them. So this gives us some confidence that this is a source of
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Ragnar Stroberg: There's some physical. My name is cup of causes some systematic error. And it actually turns out to be the leading source of systematic error.
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Ragnar Stroberg: And we'd like to correct for that. So we have this line and we can correct for it. And now there's some scattered about the line and that we treat as a random number. It basically is a Gaussian scattered about that line.
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Ragnar Stroberg: So these bands. The line, the band here was actually obtained by doing a Gaussian or not guessing sorry basie and
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Ragnar Stroberg: Uncertainty Quantification. But it turns out to be very similar to if you had just that it would align and then model the residuals as a Gaussian. And that's because we have lots of data. And so in the end basie and kind of just tells you what the data says
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Ragnar Stroberg: Okay, so now we have that random error with it with the systematic shift. So now this is again the calcium separation energies. But now we have a an uncertainty band.
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Ragnar Stroberg: And because we have that systematic that and certainly band is not necessarily centered on our calculation. So you see up here.
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Ragnar Stroberg: For very neutron poor systems, we actually expect that we're over predicting the separation interview. So our century central value is lower than the point now here at neutron rich
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Ragnar Stroberg: It's the other way around. We expect that we're predicting too low or too small of a separation energy. And so essentially gets pushed up and we are we have some way
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Ragnar Stroberg: And so now we can
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Ragnar Stroberg: We have some error bands and now you can actually see here that yeah we have some probability for it to be bound in some probability for to not be down so we can take this for a single isotopic chain so that you touch your thoughts are what I was showing you here.
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Ragnar Stroberg: And these are now the proton separation energies. And so going along the esoteric chain, the probability to be bound is on the bottom.
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Ragnar Stroberg: Is the probability to be bound with respect to one day trial on a mission to new transmission one proton emission and proton admission. So that's just the integrated probability to be above that dashed line.
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Ragnar Stroberg: Multiply for each of these pounds and that's what's showing down here it goes between zero and one. And in the middle here everything is well above that line. So we have a probability of one to be bound and as we go out and cross below the the
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Ragnar Stroberg: Threshold there and now the probability to be bound drops off to zero and we even have some audio and staggering here from the one neutron separation.
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Ragnar Stroberg: We can do that, not just for calcium and what for, as I said everything up to calcium and a little bit beyond
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Ragnar Stroberg: And put it all into a single plot. And that's what's shown here. So the squares represents the probability bound. So a red is essentially in the middle third of the likelihood. So this these are kind of marginal cases.
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Ragnar Stroberg: Things that are blue are very likely to bounce above 95% chance to be about things that are white are below 5% very unlikely to be bad.
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Ragnar Stroberg: And I've also overlaid the last the conversion drip lines where they are known, and if not known than the last known nucleus. And so you can go along and see that
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Ragnar Stroberg: It does a pretty good job of reproducing where the drip lines are going to be and
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Ragnar Stroberg: Because it's probabilistic sometimes, you know, we have a toss up here and say it lithium 13 it's we'd say, maybe it's found, maybe it's not. But we don't have a precision to say
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Ragnar Stroberg: But at least now we know that we don't have the precision to say
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Ragnar Stroberg: And specifically out here at calcium before we would have said that the drip line was there at calcium 60 now even say that. Is he gone out basically all the way out to calcium 70, at least for the odd ones. It's based it's more or less a toss up it's equally likely balanced or unbalanced.
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Ragnar Stroberg: So it's interesting. It's interesting information know and I kind of in terms of thinking about what experiments should be done.
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Ragnar Stroberg: I guess it's now a matter of philosophy because he it now tells you that
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Ragnar Stroberg: This is we don't have good information from the theory. So if you want to know. Calcium is balanced, you probably need to do the experiment.
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Ragnar Stroberg: On the other hand, if you do the experiment and you find that if you don't find that it's unbound that doesn't really then come back and inform the theory. Because it, it was just as likely either way.
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Ragnar Stroberg: So it's a matter of philosophy about whether this tells you, you really should measure calcium or you shouldn't bother Council.
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Okay.
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Ragnar Stroberg: I have some time left. So I want to talk. Also, but another
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Ragnar Stroberg: Kind of say breakthrough that happened in the last couple years because of these methods all coming together.
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Ragnar Stroberg: So there's adjusting this long standing problem of quenching and gamma Teller beta decay essential issue is that you, you have a beta decay, which comes to the spin flip and I suspend flip
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Ragnar Stroberg: So this is the operator for gamma Teller beta decay. And if you do shell mental calculations and plug in this sigma towel operator and compare it to the experimental
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Ragnar Stroberg: Beta decay rates you find the theory consistently over predicts the strength of those transitions. So predicts lifetimes, or too short.
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Ragnar Stroberg: So it's been floated down here is the theoretical gamma Teller matrix element in the experimental gamma telling matrix element. And if they agree they should lie along the diagonal White was x, but instead. There's the slope of point seven and that's reflecting the
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Ragnar Stroberg: Theory over predicting the strength. Historically, it was suggested that this is due to a quenching of GA. The, the axial vector coupling constant to should be changed in medium.
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Ragnar Stroberg: But we want to address this ab initio without having to just phenomenal logically quench paramor so the the microscopic picture of what's going on here.
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Ragnar Stroberg: There are two main explanations. One is that if you're doing a shell model calculation. You're ignoring correlations or expectations outside of the bounce base. So you can have two particles excite up
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Ragnar Stroberg: Way up to some higher line state and then beta decay from there and neglecting that will end up
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Ragnar Stroberg: You basically over predict the size of the matrix. Because of this, this is some missing physics. There were ready to deal with that because
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Ragnar Stroberg: The way we would treat that as we can consistently evolve the transition operator with our same energy flow equation to account for those expectations implicitly so that then
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Ragnar Stroberg: we normalize is the transition operator. So we now have a operator that x in the valence base but accounts for execution outside of space.
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Ragnar Stroberg: The other explanation historically about this quenching was that there's non nuclear degrees of freedom, going on to the marathon's lying around. There's new Clancy excited to delta resonances. And those need to be taken into account as well.
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Ragnar Stroberg: And within Kyle effective field theory, all of those can be categorized as true by currents. So here is the idea is that basically you maybe do some
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Ragnar Stroberg: pion exchange. And right at that same vertex, where the pipeline is absorbed by the nucleus, there's a there's a beta decay there and what's going on in that blob is maybe we're making a delta, maybe we're exciting to some high momentum states.
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Ragnar Stroberg: It's all lumped into a low energy constant and really convenient that those low energy Constance actually also show up in the three buddy force. So,
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Ragnar Stroberg: Once we've fit our three buddy for us to say the trade time
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Ragnar Stroberg: We don't have any additional parameters for these two buddy currents. So all that the physics that's going on inside that little block.
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Ragnar Stroberg: Is also the physics that's going on inside three buddy forced. And so to be consistent. We have no choice. We have the parameters fixed so we can put all of this together.
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Ragnar Stroberg: And we did. And on the left is a calculation of 10 100 which is a very good case for looking at gamma telling the case because it's double the magic. So it's accessible. For example, a couple cluster theory.
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Ragnar Stroberg: But it also has a very strong gamma tiller transition. And so if you have a single a very strong single transition, you can really get at this question. Whereas if you had a small transition that was do
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Ragnar Stroberg: Lots of different cancellations between components, it kind of muddies the water. So this is a nice clean case to look at. And so it's over on the left here.
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Ragnar Stroberg: The bottom half is as other calculations and Sharma kind of calculations are done, but on the top, we have several different Carol interactions.
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Ragnar Stroberg: And I'll computed with the metrics on this computer with couple cluster. And so this blue diamond. Here is the extreme single particle model.
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Ragnar Stroberg: And so if you just do a couple of cluster calculation. So that then ads and correlations without doing currents that takes you to do open symbols here.
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Ragnar Stroberg: So there's a there's an effect of doing correlations. But now you include to buddy currents and shifts it further down, and this is now on the region where the experiment. Actually, it's so that's encouraging.
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Ragnar Stroberg: We can also go and work and say the official because we can generate the show model interactions.
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Ragnar Stroberg: And what's this is that same plot of this before with theory versus experiment and
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Ragnar Stroberg: If we don't do I am I am so G and we don't go to buddy currents and get these orange symbols and that's lying on the slope here, which is about seven, eight, which is what is found in phenomenology.
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Ragnar Stroberg: So now we do that is our G to account for correlations and we get the red symbols. So we move back towards the experiment, the line. And now we include to buddy currents at moves even further back towards the experiment one
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Ragnar Stroberg: And within the scattered. This is more or less consistent and it sort of depends on specifically which interaction will use, but we would all of them. We see the same behavior and it takes it most of the way back to one.
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Ragnar Stroberg: Okay, so one last thing I've seen some descriptions of this saying okay we've solved that the answer is that it was currents and that's not entirely true. It's more subtle than that. And this is explained here in this figure, which takes a little bit of looking at
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Ragnar Stroberg: So this is again a couple cluster calculations of 10 100 with all the same different interpret these different actions that were in the previous plot.
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Ragnar Stroberg: And what you can do is you can do just the correlation. So that's doing a couple of cluster calculation. And so that's this symbol with the top half filled in.
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Ragnar Stroberg: Or you can turn on, just to buddy currents or you can turn on books. And that's the Philip symbols here and
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Ragnar Stroberg: You can see is that
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Ragnar Stroberg: Either way, if you just turn on the currents or you just turn on the correlations and a lot of cases, like for example, here you get
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Ragnar Stroberg: More than half of the effect with the first thing you do, and less afterwards. What this means is not, it's not just a simple some
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Ragnar Stroberg: Of correlations and to buddy currents that are distinct. There's interplay between the two. So the correlations affect how the two buddy currents impact result and vice versa.
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Ragnar Stroberg: And another thing we look at is that these numbers here is one point a to point out to point to correspond to the cut off their use.
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Ragnar Stroberg: And if we use different cut offs that can shift things between correlations being important and currency important
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Ragnar Stroberg: And so he was kind of just little sketch of what's going on here. Remember, we're cutting off the very short distance physics because of the divergences
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Ragnar Stroberg: And I think thinking about it in this way, we're making some sort of a partitioning artificial partitioning between long distance physics and short distance physics.
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Ragnar Stroberg: But the long distance PHYSICS STILL leaks all the way into the short distance physics. So it's, there's some cut off where we're calling parts of saving you know paying exchange.
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Ragnar Stroberg: Or kind of parts of that short distance physics. And so as you move that cut off what you call long and short changes, but there are some or shouldn't change.
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Ragnar Stroberg: And so that's why if we look at and say these different interactions with different cut offs, the breakdown is different, but the result is not so different.
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Ragnar Stroberg: Okay, so this is the last thing I want to talk about in the last minute or two, and this is the progress towards going to having a clear I showed earlier prettier plot of this that we're making progress up into the beyond the official in even the some calculations in 10
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Ragnar Stroberg: But I like to then make the leap and go out here to the foreign and calculate lead to await
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Ragnar Stroberg: There are physics reasons why we actually want to be interested in led to a went, but also the developments needed to do that will allow us to reach a large swath of a child.
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Ragnar Stroberg: And so the limit. The thing that's kept us from doing that in the past is again three buddy forces in this case this is more just a computational issue is that the storage for all of the three running matrix elements, you need to catch it at that high is just really painful.
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Ragnar Stroberg: What we usually do is we don't keep all possible three by three matrix elements, but we make we work in an oscillator basis and we make a cut on the quantum numbers of the oscillator states that enter into these matrix elements. So that makes the number of matrix elements manageable.
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Ragnar Stroberg: And so here as a function on that cut, you can see the storage requirement and it grows like that.
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Ragnar Stroberg: And so here's a typical cut off of where people are usually comfortable with a 500 gigabyte file of matrix elements that you need to load into memory.
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Ragnar Stroberg: So historically people have stopped around a cut of 18 and that's there. And that's not big enough to go to lead but through some
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Ragnar Stroberg: trickery, especially this idea that we only need a subset of all of these metrics elements and so that we don't
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Ragnar Stroberg: compute anything that we don't need in the end. And that actually substantially reduces the file size.
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Ragnar Stroberg: And there's some other tricks in terms of angular momentum coupling came into this to make us manageable. But in the end, this reduction now means that for the same file size we can reach further out. And this allows us to, you know, reach far enough to converge heavier up
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Ragnar Stroberg: So I'm showing on the left here is now led to a weight. The ground state calculated as a function of this cut on three bloody terms. So, in principle, they should be going to infinity. So you don't have any
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Ragnar Stroberg: artifact of this truncation.
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Ragnar Stroberg: And the previous limit is this dashed line here and you can see that as you increase it. If you stop the 18. You have no idea what the actual answers.
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Ragnar Stroberg: But we now push it all the way up to 28 and we have a model for how this should converge. And so we can then extrapolate the last few MTV. And so now we have a converged calculation of level.
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Ragnar Stroberg: I think probably the coolest thing that we can do this and that is going on. And I'm actually really excited about this is that
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Ragnar Stroberg: What we're working on all this stuff. A couple cluster guys at Oakridge in Gothenburg.
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Ragnar Stroberg: Working on medical subspace projected couple cluster which is essentially a an emulator for their expensive couple, couple cluster calculations which allows them to do a few couple cluster calculations for given
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Ragnar Stroberg: Parameters of the Hamiltonian and then they can simulate or emulate many more calculations with different values of the input Hamiltonian parameters. So like changing the low energy Constance they can predict or emulate what they would have done with a couple of cluster calculation.
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Ragnar Stroberg: With those new parameters. So now, this allows you to very cheaply scan through the parameter space of the input Hamiltonian
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Ragnar Stroberg: And so what was done here is they just took around the the best fit Hamiltonian which is what we're using on the left hand side.
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Ragnar Stroberg: And they kind of just scan in a hyper tube of parameter space and see what they get. So this is the ground state energies on the x axis. And here is the neutron skin thickness, which is interesting in context of the
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Ragnar Stroberg: nuclear matter and neutron star physics. And you can see that there's a kind of a limited range of plausibility of, you know, as you very all these parameters.
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Ragnar Stroberg: Your answer only Verizon this limited range and and the really cool thing moving forward is that instead of just kind of scanning along a hybrid queue.
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Ragnar Stroberg: You can actually select parameters based on how well they reproduce. For example, scattering data.
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Ragnar Stroberg: And so we can have. We can generate a heat map of properties of lead weighted by are constrained by scattering news so we can connect the 200 particle system with the two particles system in a statistically meaningful way.
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Ragnar Stroberg: Okay, so, and now on to my last slide. And when they say two, three minutes over, and I'm going to finally address the question that I mentioned in the title slide a question of can we do everything have an issue.
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Ragnar Stroberg: And so far from what I've just mentioned, it's looking like closed and open shell systems between a those tools that do run all the way up to and beyond. That's 200 can be reached.
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Ragnar Stroberg: And for valence space methods.
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Ragnar Stroberg: Bit. Now the limiting factor is becoming the shell mold dimension. So if you want to go out into the active science, you can drive a shell model interaction, but then you can't agonize it because the space is absolutely enormous. This is the same issue that standard Shama will run into
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Ragnar Stroberg: So then there are maybe solutions moving forward to solving that one is to use a not just a direct legalization of that show model Hamiltonian, but using a stochastic demonization. So this is the idea behind a Monte Carlo show model which is already
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Ragnar Stroberg: Being used with more phenomenal logical interactions, but using microscopically or ab initio derived interactions could
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Ragnar Stroberg: Be a nice application of this. Alternatively, once you get out to say the active minds of the rare earths.
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Ragnar Stroberg: Show model may not be the correct degrees of freedom to us and said we should be using shapes. And so that's an alternative approach we call the medium generator coordinate method that's being developed.
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Ragnar Stroberg: So far, we can do electroweak observed rules, those, those are nice. Although collective observable is like he choose are still challenging for them. Anybody methods. I'll point to these papers. If you want to learn more about that.
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Ragnar Stroberg: Something else you might want to do is direct reactions. And that's still a work in progress, but at the moment. There's no insurmountable obstacle to being able to do that.
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Ragnar Stroberg: So there's other questions. Okay. Should we
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Ragnar Stroberg: Because in general these calculations are expensive. So is it worth doing this. So there are disadvantages to doing things at Michelle, namely that it's expensive, and you get lots of numbers that come out so it can be hard to interpret
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Ragnar Stroberg: I would argue that for moderately a sophisticated phenomenology. You also get lots of numbers that come on. So like for large scale shell model. It can also be hard to interpret. But that's still something to consider.
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Ragnar Stroberg: Other issues that you get lower percent lower precision and a limited range of applicability, but I would say, with the cut caveat that
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Ragnar Stroberg: You do an ab initio calculation. If you do it properly, it tells you that what precision is and it tells you what its range of applicability is because you have a breakdown scale.
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Ragnar Stroberg: Phenomenology in principle has some precision and some range of applicability. It just doesn't tell you what it is.
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Ragnar Stroberg: Until the advantages are you get theory error bars and you can get a handle on the small scale. Scale dependence, so that you can actually have a
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Ragnar Stroberg: More informed concept of what is an observable. That is actually meaningful and what is just a kind of a theory artifact depending on exactly how you set up your theory.
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Ragnar Stroberg: So I would say for a lot of cases, we should maybe not for all cases because it is expensive, but I think it's really exciting in the next couple of years, what will be able to do with admission. So I will stop there and say thank you for your time.
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James Smallcombe: Thank you very much.
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James Smallcombe: So do we have any questions right now, then please if you again. Go to the participants menu and use the little raise hand button there.
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Or if you want to type your questions into the text box.
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James Smallcombe: Well, people are thinking, did you want to go out. We've got one for Philip, Philip
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Philip Adsley: And I would turn on my my video. No one wants to see that.
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Philip Adsley: I have what's potentially a really dumb question, as you were talking about the the gamma Teller transitions and concentrating on strong individual transitions.
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Philip Adsley: I was wondering if there's has there been any investigation of, say, the gamma Teller resonance or or the splitting of strength and D do is to has been a do you reproduce those behaviors.
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Ragnar Stroberg: There has not yet.
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Ragnar Stroberg: Then investigations and that's
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Ragnar Stroberg: Partially because we doing, looking at the gamma Teller resonance, you're doing this with a charge exchange reaction, right, not, not a
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Ragnar Stroberg: Week decay. And so there you actually have to then if you're doing this at an issue, you have to treat the reaction.
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Ragnar Stroberg: And so that makes it a little bit more complicated. So the beta decay and charge exchange.
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Ragnar Stroberg: At the at the absolute leading order. If you're assuming that everything is just a one page. In exchange, they both reduced down to a sigma towel operator. But if you want to understand things like say quenching
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Ragnar Stroberg: The equivalent of the two buddy currents that come in here are three body forces. So in what you would need to do and and
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Ragnar Stroberg: I plan to do. I'm interested in doing is doing these charge exchange reactions and including the effect of three.
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Ragnar Stroberg: Forces, which should be analogous to this needs to be currents and I expect there should be some question effect, but it's not obvious that it will be exactly the same. So, this will be interesting.
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James Smallcombe: OK. And then we have a request for you to go back to the slide you skipped with your example of the realization
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Excellent.
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James Smallcombe: And after that.
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Ragnar Stroberg: My computer is working very hard. I'm not sure why. Okay.
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Ragnar Stroberg: So I can just
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Ragnar Stroberg: step through it or
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James Smallcombe: Yeah, go through the question.
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Ragnar Stroberg: I have to
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Ragnar Stroberg: Go, but OK. So imagine you have a Hamiltonian which is just a two by two matrix.
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Ragnar Stroberg: So you have diagonal pieces like anything about these a single particle energies and an off day or piece which is a potential which mixes the two and to solve that problem. You should to analyze the two by two matrix.
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Ragnar Stroberg: Alternative is that you can make this choice for the generator. So it's got a minus sign there. So this is anti formation.
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Ragnar Stroberg: And if you now take the commentator ADA. Ah, so that's just this matrix with that matrix, you multiply both ways. You get a commentator. This is what comes out.
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Ragnar Stroberg: So now you have a differential equation DH ds is equal to this. So he looks is like this form, and all of these parameters are so dependent. So it's a
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Ragnar Stroberg: Differential equation of a two by two matrix. So each individual element there.
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Ragnar Stroberg: Is a differential equation. And because of you know the end started the same thing. You basically have three differential equations. So looking
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Ragnar Stroberg: Say the lower left V and it's derivative is minus p. So, you have a differential equation here.
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Ragnar Stroberg: DVD S is minus V and we immediately know how to solve that. It's just an exponential. So what this tells us is that the off diagonal piece of that two by two matrix is suppressed exponentially with the flow parameter. And that's plotted over here. So we have s s suppress exponentially.
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Ragnar Stroberg: We also have flow equations for epsilon one up some of these are like our single particle energies.
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Ragnar Stroberg: Flowing single particle energies. And so if we integrate those because we can just plug in the solution here.
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Ragnar Stroberg: This is what the solution looks like for those. So we see that they change for a while and then as the suppressed sufficiently they kind of just level act.
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Ragnar Stroberg: And what's being flooded here, it's just because there's only three parameters you can plug it in three dimensional space. So that's this is just a bunch of time or you know points in S as we go along. It follows this trajectory. So each point here.
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Ragnar Stroberg: Is a two by two matrix that if you diagnosed, you'd get the same answer what the parameters in the matrix are different. So this is all unitary equivalence
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Ragnar Stroberg: And as you get down to here. We're now in the the epsilon went on to plane which is where VS is zero. So that's where we want to be in the end, because now it's even easier to solve the problem, because you just read off the answer.
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Ragnar Stroberg: So that's the basic idea.
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James Smallcombe: Great, then we go. Another question was if you can go forward to slide to slide 14
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James Smallcombe: karat from the text question desert how we just find the physics while softening softening the Newtonian nuclear nuclear interaction as you already said in disadvantage ab initio gives low precision.
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Ragnar Stroberg: So the lower precision does not come from this. So the lower precision.
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Ragnar Stroberg: Comes from
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Ragnar Stroberg: You are not fitting your interaction directly to the data that you're trying to predict. So example if I want to do it. That's phenomenal logical show model and you're fitting
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Ragnar Stroberg: exactly two spectroscopy in the St shell, you're going to get a good rubric reduction of spectroscopy in the St show
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Ragnar Stroberg: Whereas here, you're doing an order by order expansion. And so if you trunk. It's a third order, there is some higher order error that you're making
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Ragnar Stroberg: So that's just what I mean by
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Ragnar Stroberg: Law or precision in that sense.
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Ragnar Stroberg: But this is related to the this the suffering.
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Ragnar Stroberg: Your question.
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James Smallcombe: Yes. So I think we've got a follow up from the same person in slide 17 as you mentioned in the introduction ab initio calculations is now done around 800
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James Smallcombe: For almost 10 isotopes. And as this person's knowledge and it's rain sometimes X tastings occur excluded mobile space. Although these expectations are important to highlight each state's. So is there any chance to consider this. So, excluding these because you've limited your space.
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James Smallcombe: Patreon. If you agree in your chat window you can see
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Ragnar Stroberg: Me a chat window, maybe
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Ragnar Stroberg: So,
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Ragnar Stroberg: So you've got
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James Smallcombe: X Titans can occur and excluded model space, which are important to the higher energy space. So I guess.
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James Smallcombe: Is the question of can you expand your space to the order up this exclusive
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Ragnar Stroberg: Okay, so if you wanted this is if I could maybe a restate that if you restrict to event space that you know that limits the size of your homework space that limits the number of
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Ragnar Stroberg: Hagen states that you can get. And that you're in the state that you're interested in, may not be among the agent states that are described within that nowadays.
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Ragnar Stroberg: So that's absolutely true. And if you wanted to get more states are different states, in principle, yes, you need to change your balance space.
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Ragnar Stroberg: There's a paper out recently. I don't have a reference here for
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Ragnar Stroberg: Talking up Miyagi is the lead author on working on extending valence spaces.
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Ragnar Stroberg: There are technical issues that come about, which are related to the old problem of the company true problem.
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Ragnar Stroberg: And that's because you're trying to push states out that are lower energy than states, you're trying to pull him. So there are technical difficulties there. But in certain cases that can be done.
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James Smallcombe: Okay. I hope that answers that question.
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James Smallcombe: Do we have any other questions for
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Mark
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Please go ahead.
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Hey,
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Praveen C Srivastava: Hey, yeah. So everyone questions. So are you also planning to study forbidden bit addictive. It didn't become a Sunday. So me
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Ragnar Stroberg: So didn't pay
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Yeah.
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Ragnar Stroberg: I don't have immediate plans.
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Praveen C Srivastava: To do it. Yeah, okay.
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Ragnar Stroberg: It could be done. It could also be interesting, but not not in the immediate future. Okay.
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Ragnar Stroberg: Did Mark
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James Smallcombe: Mark. Mark, do you want to go ahead, you're not muted, but we can't hear you.
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James Smallcombe: Okay, so having some technical difficulties, if I'm not
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James Smallcombe: Able to hear me.
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James Smallcombe: A little bit quiet.
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Ragnar Stroberg: Just shout.
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Ragnar Stroberg: It maybe you're covering your microphone.
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Mark Spieker: Here is that you hear me now.
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Mark Spieker: Okay, perfect. Sorry for that delay our Ragnar he he cites showing the differential quantities. When you discuss the separation energies.
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Mark Spieker: And how you had to adjust your model. You also shelled the absolute energy of the ground states where for the oxygens enlightened nuclei, you actually had a fairly good for production.
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Mark Spieker: And then for the costumes, as well as for the left which which you showed later you had some deviation
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Mark Spieker: In terms of the absolute energies. Now, if you look at the differential quantities.
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Mark Spieker: Like the new trend separation energies and the two Newton separation energies, it looks like this is just a shift which he observing, which is cancelled out once you look at differential quantities.
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Ragnar Stroberg: I should make the caveat here that this interaction, but I'm showing this slide.
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Ragnar Stroberg: Is not the one that was use in later slides.
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Ragnar Stroberg: So this one.
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Ragnar Stroberg: Has it tends to overbuying is ego heavier in mass. So you can see here, calcium is over bound by at MTV or something like this. So, yes, you may catastrophic Lee bad
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Ragnar Stroberg: Whereas, okay. So you can see here now with this purple interaction.
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Ragnar Stroberg: It's basically nailing calcium
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Mark Spieker: OK, so the problem inlet for the over binding that you observe is something else. So
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Oh,
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Mark Spieker: The interaction also needs to be worked on assistant interaction problem, as well as to something else.
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Ragnar Stroberg: So I would say two things. First, this is I didn't mention this, but this is this is just a third over perturbation theory.
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Ragnar Stroberg: And from what we've seen is that doing an energy calculation we actually pushes it up a little bit, relative to turn over provision theory, but also okay this deviation is something like 4050
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Ragnar Stroberg: Something like that me be out of 1600 and 80
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Mark Spieker: That's not too bad. So
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Ragnar Stroberg: Yes, if you are to propagate like okay we're worried about the convergence, not, not to get that really high precision there. But I mean, because if you propagate.
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Ragnar Stroberg: Cairo uncertainty. So if you look over on the right hand side here.
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Ragnar Stroberg: Look at the x axis. So that's if you just wiggle the parameters in the interaction. What kind of arranged in binding energies, you get so this is 1000 and maybe this is 2018 yeah you can get that easily. So there's there's certainly some fine tuning at that level of
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Ragnar Stroberg: You know that many particles, you should really look at this in terms of binding energy perfectly
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Mark Spieker: Okay, thanks.
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James Smallcombe: Okay. Do we have any other questions for right now, I
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James Smallcombe: Don't see any hands.
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James Smallcombe: Anyone who can't raise their hand. Who wants to unmute and ask a question, please go ahead
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But
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James Smallcombe: I think we have exhausted our audience for now. So I say, Thank you very much, Ragnar
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James Smallcombe: Thank you. And thank you all for joining us for this talk, I do hope that you can come back for our other talks. If you come back on Monday. Same time 3pm BST.
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James Smallcombe: We've got David O doll from the University of west of Scotland, who's going to be talking to us about measurements of low energy dipole strength in extra nuclei, which I believe is
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James Smallcombe: Worth their magical in Nature paper for actually doing in their lap in Paisley. So let's come back to that on Monday. So thank you all for joining us. And thank you, right now the back now.