James Smallcombe: There we go and is MAC your zoom windows, can you move that out the way a little bit.
James Smallcombe: And then I will say thank you again for joining us MAC and please tell us.
Mack Atkinson: Okay, thanks for the introduction James.
Mack Atkinson: So, today I want to i'm happy to be presenting for this.
Mack Atkinson: Interesting lockdown series i'll be talking about nuclear matter and sort of the connection between VI in nuclear matter sort of revisiting some of the.
Mack Atkinson: Some of the information that we have about it so, what are the fundamental properties of nuclear matter that we think of as nuclear physicist well to me there's there's two big ones number one is the saturation density of nuclear matter that is the density which nuclear matter, saturates.
Mack Atkinson: is about point one six inverse for me cute.
Mack Atkinson: The second property is the energy at that saturation point which is said to be about minus 16 and movie.
Mack Atkinson: So where do these values come from, why do we say that these are the values for the density and energy.
Mack Atkinson: And how does this relate to find out nuclei or rather how to find out nuclei help determine these numbers for us.
Mack Atkinson: In particular, in this in this talk i'm going to be focusing on this this binding energy of nuclear matter here at minus 16 new movie.
Mack Atkinson: and actually i'll just go ahead and give you the claim of the whole talk is that this value is a doesn't is not necessarily minus 16 a movie so now i'm going to proceed to try to convince you of this claim.
Mack Atkinson: Just a brief outline of how I will do this is a.
Mack Atkinson: I will discuss nuclear matter that more obviously these two numbers.
Mack Atkinson: Then I, in order to sort of address this problem with my own technique so in briefly introduce some Greens function formalism.
Mack Atkinson: As well as a model, I use, which is the disperse of all optical model and, finally, with all that machinery laid out i'll discuss binding energy densities, and how they really help us help me understand this connection to nuclear matter.
Mack Atkinson: Okay, so.
Mack Atkinson: Nuclear saturation this saturation density.
Mack Atkinson: it's there's evidence of nuclear saturation from a lot of different measurements, one of which is just the simple nuclear charge radius of nucleus, you see as as the number of nuclear weapons increases that the the radius.
Mack Atkinson: increases proportional at one third, or in other words, the volume just increases with a meaning that.
Mack Atkinson: You know the the nuclear ones that are in the nucleus reach some sort of saturation point where they don't get more dense rather the volume just starts to grow.
Mack Atkinson: Right, so this is sort of evidence of nuclear saturation or something like you know acts like water, which is why there's this liquid drop model.
Mack Atkinson: For for nuclei.
Mack Atkinson: So.
Mack Atkinson: getting a bit more detailed with it, you can actually.
Mack Atkinson: Look at the nuclear charts density through elastic electron scattering experiments on nuclei you can extract the nuclear charges D from these cross sections.
Mack Atkinson: And so, this is what i'm showing here just to get a picture of what's going on the.
Mack Atkinson: series a handful of nuclei.
Mack Atkinson: where you can see that they you know their varying sizes, obviously, but the near the near the interior of the nucleus, and the core they all.
Mack Atkinson: hover around a certain density, and this is the saturation density i've put this dashed line here to show where this point one six is, and you can see that everything is hovering around that more or less.
Mack Atkinson: So i'm.
Mack Atkinson: that's the story of the saturation density, as I see it, so, then how the saturation energy, where do we get that number so first.
Mack Atkinson: We need to.
Mack Atkinson: discuss this empirical mass formula developed by beta and by saker in the 1930s, where you.
Mack Atkinson: it's an empirical formula, where you plug in the number of nucleotides the number of protons forgiven nucleus and out out gets your binding energy so here's a binding energy versus a sort of plot to show that this empirical formula does.
Mack Atkinson: remarkably well to describe nuclei across the heart, where this line corresponds to the equation, you see here and the dots correspond to the experimental.
Mack Atkinson: values of the binding energies for these various nuclei.
Mack Atkinson: Okay, so, then, how does this connect to nuclear matter.
Mack Atkinson: Well, if we wanted to apply this equation to nuclear matter there's a number of terms that we can throw away so first in nuclear matter, there is no cool on force because no matter is a.
Mack Atkinson: You know this fictitious substance and we want it, where it's designed only to analyze the nuclear interaction so there's no cool i'm forced to get in the way.
Mack Atkinson: In this theoretical constructs so this cool on term doesn't contribute also, this is an infinite matter so that means there's no surface.
Mack Atkinson: So there's surface term from finite nuclei also doesn't contribute we're also going to be considering symmetric nuclear matter for the most part in this talk.
Mack Atkinson: So all of these terms are now cancel it out, so all that's left is this volume term.
Mack Atkinson: This is where this extrapolation happens where you claim that the the binding energy, nuclear matter is this AV parameter from this empirical mass formula that being minus 16 MTV.
Mack Atkinson: So just to.
Mack Atkinson: bring up a figure in the mind about the about nuclear matter said there's many calculations of nuclear matters, starting from a nuclear on nuke on interaction.
Mack Atkinson: And what what all these calculations have is an energy versus density plot where you will see a minimum at some point in this plot in this the minimum corresponds to the saturation point so you can see here in this figure on the left.
Mack Atkinson: The squares the red squares correspond to a.
Mack Atkinson: Self because it's a Greens function calculation and all these all these mini bio methods are using this Oregon.
Mack Atkinson: interaction.
Mack Atkinson: where you can see the the red squares they seem to have.
Mack Atkinson: The saturation density at the minimum about at point one six while the saturation energy is is you know closer to minus 11 or minus 12 which is.
Mack Atkinson: You know less bound and then minus 16 MTV whereas if you will get the brookner hard to fork in the the dots are the broken vader Goldstone in the triangles they get the energy about right, but their saturation density is a bit too high.
Mack Atkinson: And so, something that you know, the fact that both the density and energy cannot be reproduced in a new chromatic calculation is a very common feature is it's actually quite difficult to reproduce both of these simultaneously from a from a calculation in nuclear matter.
Mack Atkinson: and
Mack Atkinson: So this is a sort of the the picture of nuclear matter here.
Mack Atkinson: And so you know we're using nuclear matter calculations, I guess.
Mack Atkinson: As a sort of test test space for nuclear nuclear interactions and, ideally, you want to see the saturation point reproduced by a given new client new client interaction to to feel more confident about said interaction.
Mack Atkinson: So it's important to have a you know a good.
Mack Atkinson: A good saturation point to shoot, for I guess, but what I want to convey from this slide is that this.
Mack Atkinson: Energy for the saturation point that we claim to be minus 16 MTV is determined empirically by empirically I mean in a model dependent way we're setting an equal to a parameter of an empirical mass formula, so this seems a bit.
Mack Atkinson: Less ideal than I would I would hope first this sort of fundamental quantity to be coming from somewhere else.
Mack Atkinson: And, as I showed in the last slide this the saturation density, on the other hand, is determined more closer to experiment in that you know you can really see this.
Mack Atkinson: The density in the interior is is really around point one six inverse for me cube is not coming from some parameter of the densities, so I would claim that the density and in a nuclear matter calculation it's more important to reproduce this this saturation density than it is to reproduce.
Mack Atkinson: This minus 16 movie because it's less well determined.
Mack Atkinson: So um with that now that i've sort of introduced the whole idea of what i'm investigating, I will now.
Mack Atkinson: sort of discuss the method that I use to sort of investigate what's going on here so that involves the single particle propagator or the the minibar Greens function so.
Mack Atkinson: that's what i'm showing here in this equation at the top of the page.
Mack Atkinson: Where there's the the first expression or the first term in the expression is the the particle part where you add a particle and you remove one and look at the probability amplitude of this process.
Mack Atkinson: And then you can also look at the opposite situation where you remove a particle and then add it back.
Mack Atkinson: So this this object has a lot of interesting information baked into it.
Mack Atkinson: which you can already see from this expression, first of all an easy one to see is the poles of this Greens function correspond to the excitation energies of the a plus one and a minus one systems.
Mack Atkinson: Also, the numerator for for these given excitation energies or extension states correspond to the transition probability to these expectations at a given energy this transition this numerator is also known as a special function, and you can just sort of.
Mack Atkinson: extract this sexual function from the Greens function by just taking the imaginary part of the expression.
Mack Atkinson: And it has a very close connection with experiment.
Mack Atkinson: was so i'm showing a quick example here in the bottom right or, this is a.
Mack Atkinson: excitation energy spectrum, from a calcium 40 prime P experiment, where an electron comes in hits calcium 40.
Mack Atkinson: hits a proton in their strong enough to eject it so that you result your your resulting nucleus is potassium 39 so what we're looking at here is an excitation spectrum of that potassium 39 in for the equals to state which that corresponds to the.
Mack Atkinson: sort of the D3 have orbital and calcium 40 getting knocked out so in pramod naive independent particle model, you would expect, only to see this one bar that's had zero and all the strength to be there, however, from this sexual function from this.
Mack Atkinson: excitation spectrum, you can see their strength out at a higher expectation energies, so this is just a.
Mack Atkinson: Quick glimpse into the minibar correlations going on, and this is all all just straightforwardly comes from this Greens function.
Mack Atkinson: So this objects really interesting, but how do you calculate it the expression, I have at the top of the page is pretty complicated, I would say to try it and.
Mack Atkinson: To try and calculate in this form, so you can use perturbation theory to derive the dyson equation for the Greens function which i'm showing dogmatically in the right side of the page.
Mack Atkinson: Where the double line corresponds to this full Greens function I showed in the last slide the single line is a free propagator.
Mack Atkinson: which corresponds to just the kinetic energy and our formalism so that's known the single line is known and then there's also this new object in here the the Sigma star, which is the irreducible so.
Mack Atkinson: This so if energy is a one body.
Mack Atkinson: One body object one body potential, which contains all possible interactions of your system, so you can you can start from using two and three body.
Mack Atkinson: forces and even higher body forces and then diagram magically you form this one body object using using the free propagator is in the diagrams with the with your interactions so in this one body potential really contains all the information you need about your system.
Mack Atkinson: To get the single body propagator.
Mack Atkinson: So this, so the, the problem is now moved to using the dyson equation, the problem of finding the Greens function is really boiled down to finding the this irreducible self energy.
Mack Atkinson: So this is a one body of potential which describes the system fully, and so this sounds a lot like an optical potential.
Mack Atkinson: So one one way of trying to solve the these equations is to parameter eyes this self energy.
Mack Atkinson: In the same way that optical potential is i've been parameters for decades now to describe elastic.
Mack Atkinson: scattering of nuclear weapons on nuclei so.
Mack Atkinson: We do the same thing here we pram tries to self energy with the volume term a surface term and a spit orbit term furthermore we're using the same functional forms that have been that have done so well these optical potentials for the decades.
Mack Atkinson: So when.
Mack Atkinson: One thing we add to this, though, is you know the expressions that have been writing or have a nonlocality depends on our and our prime.
Mack Atkinson: And so we explicitly introduce or bacon this nonlocality using this beta parameter to really control how off diagonal this our potential will be we do it using this gaussian form.
Mack Atkinson: So.
Mack Atkinson: You know, we all know that potential is do pretty well at describing differential cross sections at positive energies, but how do they do, how can this formalism.
Mack Atkinson: also described negative energy observable like let's say the charges dense to your binding energy so because we were linking this all through this.
Mack Atkinson: Many body theory Greens functions, we can use this dispersion relation, we know that the self energy satisfies the following dispersion relation where the real part of self energy is.
Mack Atkinson: at any given energy let's say positive or negative energy is determined by a disperse of integral of the imaginary part of the self energy.
Mack Atkinson: In both positive and negative energy domains, so this is a really powerful constraint.
Mack Atkinson: That really controls the self energy over both positive and negative energy domains What this means is that this ensures that both bounded scattering quantities are simultaneously described using this self energy.
Mack Atkinson: This is where this is the whole idea of this purse of optimal model, and this is the, this is what I use so to get get this a bit more concrete here's just a.
Mack Atkinson: Simple schematic of how this is done so have some initial set of parameters from this initial set of parameters construct a heart to fork potential and the imaginary part of the self energy.
Mack Atkinson: apply this dispersion disperse of integral I showed in the last slide and then after this is done, the the full self energy is is ready for calculations so, then you calculate all the variables that are included in your Chi Square.
Mack Atkinson: use an algorithm to minimize this guy squared by altering parameters until a minimum is reached, and then, once wants to Chi square has been minimized, then I can feel confident that self energy that the accurate describes your system is found.
Mack Atkinson: So, to give more concrete example here's how it's done for calcium 40, for example, so what's included in the fit.
Mack Atkinson: First Thursdays.
Mack Atkinson: differential cross sections for elastic scattering of protons and neutrons on calcium 40 were in these figures, the the lines correspond to the deal and best fit and the the dots correspond to experimental data and these each different line corresponds to a different energy.
Mack Atkinson: And the energies range from 10 and maybe up to about 200 MTV for these cases, also include is the analyzing power which which it really gives a handle on the spin orbit aspect of the potential.
Mack Atkinson: Also, the proton reaction cross section, it is very important in.
Mack Atkinson: really helping to determine the.
Mack Atkinson: imaginary part of the self energy gives a real good handle on that we also have the neutron total cross section, as well as a neutron reaction cross section so.
Mack Atkinson: All these parts that i'm showing so far for positive energy data, but I, you know sort of promised you that this could also calculate negative energy observable.
Mack Atkinson: As it can and so here is the charged in steel, which is also included in the fit So you can see that both scattering and balanced state data.
Mack Atkinson: can be reproduced using a single self energy so now that all this data is reproduced I can take the self energy and apply it to more interesting situations.
Mack Atkinson: So this has been done for calcium 40 calcium 48.
Mack Atkinson: and led to a weight.
Mack Atkinson: So just as a quick example of one of the things you can do with with this self energy that's now constrained is I could calculate the neutron skin, for example, so that's the difference between the root mean square radius of the neutrons vs Ruby square rate.
Mack Atkinson: And this is an interesting quantity, because it it's really sensitive to the the symmetry energy.
Mack Atkinson: Symmetry energy part of the nuclear equation of state, because this really tell us about how I guess.
Mack Atkinson: What configurations are optimal to minimize your energy when you when you're thinking about the difference between the number of neutrons and protons.
Mack Atkinson: So this is also relevant towards not only just it's interesting to have a better understanding of this nuclear equation and state, but it also applies to neutron stars, the.
Mack Atkinson: The radius of neutron stars is really highly correlated with this this symmetry energy and also this the neutron skin, so that you know, once the self energies are our constrain then it's a pretty simple thing to calculate these neutron skins using using myself energies.
Mack Atkinson: So this Furthermore, so this has been investigated by various theoretical calculations, but it's also.
Mack Atkinson: You know, been observed experimentally.
Mack Atkinson: In various different ways, the most model independent way is this a parody violating electron scattering experiment which is this P REX at Jefferson lab and this this pure X two more precise experiment was has.
Mack Atkinson: already been run for about two away and in just in October at the.
Mack Atkinson: dmp meeting of the APS, we there was a presentation about where they presented their results of this lead skin so i'll go ahead and show that here, so the pure X two results are in this.
Mack Atkinson: Vertical band.
Mack Atkinson: That I have this large vertical band.
Mack Atkinson: where you can see, you know it ranges from about Point two 2.35 for the for this experiment or result also shown in this figure.
Mack Atkinson: Is the the deal m results for both calcium 48 which is this y axis, I have, and that led to eight, which is the X axis, so you can see that the the box, where the deal m calculates the neutron skin.
Mack Atkinson: isn't very good agreement with the pure to resolve, and let me just emphasize that the neutron skin was not used in our fits at all we.
Mack Atkinson: The only things were in the fate were essentially what I showed in the last few slides so also include in this plot our nuclear DNA T results as as well as a couple of cluster is all for calcium 48 so clearly, this is a really interesting.
Mack Atkinson: Quantity that a lot of different methods go about trying to calculate in the deal when.
Mack Atkinson: Does pretty well reproducing the T REX to result in in the future of cx will be measured so it'll be really interesting to see to add that, to this pot see if the deal and falls within the range of T REX and see rick simultaneously.
Mack Atkinson: Okay, with that.
Mack Atkinson: I now get back to the matter at hand.
Mack Atkinson: Which is the this nuclear matter binding energy puzzle that I have constructed so.
Mack Atkinson: In addition to to the the charge density the binding energy is also included in the film for for the soap energies, and this can be calculated from the Greens function using this make dog guzzi energy some rule.
Mack Atkinson: So just here's a table showing the deal and values versus the experimental values and just to show that we've constrained it about as good as it can be given the empirical model we have.
Mack Atkinson: So from these binding energies, I can define a binding energy density, just as this volume integral of a of the energy density, should we should give us divine energy.
Mack Atkinson: that's what i'm showing in this figure on the right, this figure has a lot going on in it so i'll take it, step by step, so.
Mack Atkinson: First, in red is the just the the matter density of, so this is for calcium 40 didn't label that but now you know this is for calcium 40.
Mack Atkinson: The the red is just the matter density so just to give you what the density profile looks like for this nucleus also notice that the you know the label the y axis.
Mack Atkinson: is not just the energy density, but it's also multiplied by this four pi R squared factor, so that we can really see what's contributing to this integral to the total energy.
Mack Atkinson: So in blue is the.
Mack Atkinson: Is the binding energy density, this is the object that i'm introducing here in the equation, but i've also split it up into.
Mack Atkinson: potential energy contributions, where the kinetic is in the orange and the potential energies and black, so the you know, showing this, along with the matter density shows that the energy energy density really just follows the the shape of the the matter density.
Mack Atkinson: And also.
Mack Atkinson: Now the the final thing of this block is the the points.
Mack Atkinson: So these points correspond to nuclear matter calculations using self consistent Greens function using three different interactions the triangles being the CD bond the circles being are going to be a team and the squares being in three oh.
Mack Atkinson: So.
Mack Atkinson: it's striking that these nuclear matter calculations actually.
Mack Atkinson: match quite well with the deal em in.
Mack Atkinson: A finite nucleus, this indicates to me that the binding energy density is a pretty good way of.
Mack Atkinson: Comparing with nuclear matter results.
Mack Atkinson: And finally.
Mack Atkinson: I want to point out that so it's the integral of this object of this figure that gives a toll binding energy and.
Mack Atkinson: Note that so near near zero in the interior of the nucleus, has the the smallest contribution to the total binding energy, and this is sort of an obvious statement to make because it's weighted by our square so of course being closer to zero.
Mack Atkinson: will make it less important, however, this this has an implication because it's it's in the interior, the nucleus, and the core that.
Mack Atkinson: That the nucleus is the most nuclear matter like because remember that's where the nucleus that's where the nucleus all saturate to this nuclear saturation point.
Mack Atkinson: So I would I would claim that this interior, is the most sensitive to nuclear matter, however, as i've said, the core the nucleus men, we contributes to the total binding energy, so this implies to me.
Mack Atkinson: That.
Mack Atkinson: The total binding energy of a nucleus is not a super good constraint for the energy of nuclear matter because.
Mack Atkinson: Again, the part of the nucleus, which is the most nuclear manner, like is contributing the least to the the total binding energy.
Mack Atkinson: So, with that in mind.
Mack Atkinson: I guess first I need to briefly mention something here, so this energy some role that in the deal and that's used to calculate this binding energy.
Mack Atkinson: it's actually assuming there's No three body force so of course this this sounds wrong because, obviously, there is a very important three body aspect to the nuclear force i'm not claiming that that's not the case here, I simply.
Mack Atkinson: and presenting this slide to convince you that this will not affect the arguments that i'm making towards this binding energy.
Mack Atkinson: of nuclear matter so in order to sort of convince you that i'll show you a couple ab initio calculations that we're done using variation of Monte Carlo.
Mack Atkinson: And this Oregon be 18 to body interaction policy your banner 10 three body interaction, so you can see very similar energy density plot for carbon 12 here.
Mack Atkinson: Where it's split up in the same sort of way, except the the matter density is not normalized in the same way, it was before that's why it looks way smaller than the rest.
Mack Atkinson: and
Mack Atkinson: So you know you see the energy density and blue and now there's this new line in Gray, which is the three body.
Mack Atkinson: Energy three body interaction energy density, so you can see it's it's quite small number one number two, of course, it still has no contribution in the core so it won't change that.
Mack Atkinson: argument and number three it's it's you know the same shape essentially as the rest of the energy density, so it really won't be affecting anything that we've seen in the past, so far to for your investor, you know, to make sure it's not justice urbana 10 that that shares this property.
Mack Atkinson: We use these various Cairo interactions developed by Maria purely.
Mack Atkinson: In these Norfolk interactions So you can see that they're all quite small and they're all very similar to each other in shape and everything else, and then, even if you look at the energy density using these different three body interactions it's it's quite similar among them all.
Mack Atkinson: Okay.
Mack Atkinson: With that in mind.
Mack Atkinson: We can we can take it one step further and sort of look at the energy in the as a function of radius in the nucleus.
Mack Atkinson: So a good.
Mack Atkinson: candidate for the doing this has led to a weight.
Mack Atkinson: Because it's such a large nucleus it's got such a large interior, where the density is is relatively constant, so we can make this approximation, where the energy is a function of radius is ratio, the energy density to the matter density.
Mack Atkinson: So you can see in this figure.
Mack Atkinson: For lead to eight, the blue band represents the deal and calculation of lead to eight, and this is the energy as a function of radio, so what one would expect is that the energy.
Mack Atkinson: In in the interior, in the first two to four Fermi have led to await should be about the value of nuclear saturation energy, because this is because of the density is also at nuclear saturation so since the matter is that saturation point you would expect the energy to also be there.
Mack Atkinson: Now that the dashed line that I have on the spot represents the.
Mack Atkinson: What energy, you would expect from the empirical mass formula, I guess, from from the same sort of arguments made for the saturation energy except.
Mack Atkinson: Of course, led to a is not a symmetric nucleus, therefore, we have to correct for this asymmetries not by now, including this asymmetry term So you see it's about a bit less than mine 16 maybe maybe 15 or something.
Mack Atkinson: But you can see, however, that the the deal and calculation is is above less bound in this value.
Mack Atkinson: And furthermore, the is arguably 18 which I showed in the in the figure few slides back for the new chromatic calculations which has the correct saturation density, but you can see, like in that figure, we can see that the saturation energy is much less bound, however.
Mack Atkinson: When when viewed in this way it's not.
Mack Atkinson: It doesn't seem so wrong that it's westbound because again like i've been arguing this whole time that the binding energy is not as well constrained by this empirical mass formulas, as one would think.
Mack Atkinson: So.
Mack Atkinson: i've also done this for for the other nuclei fits of course it's not as ideal for those cases, because they're much smaller, so the the range whether density is constant it's a lot smaller.
Mack Atkinson: Nevertheless, I did it.
Mack Atkinson: And you can see a you know there's a wide range of values going on here among the different nuclei and so you can sort of think of the spread as a sort of uncertainty and in my calculations of.
Mack Atkinson: Of what this energy should be and, furthermore, you can see that they're all consistently above this minus 16 movie canonical value, so this this all sort of.
Mack Atkinson: ties back into to this idea that this saturation energy is not necessarily minus 16 MTV.
Mack Atkinson: So i'd like to summer is my talk with.
Mack Atkinson: Few things so this canonical value of the saturation energy it's determined empirically from the mass formula in that a very model dependent way it comes from the a parameter that we've set in this equation in this in this particular functional form that was chosen to describe nuclei.
Mack Atkinson: And then couple that with the fact that, if you will get the binding energy density, the core of the nucleus.
Mack Atkinson: minimally contributes to this total buying energy and the again the core of the nucleus is where we see the nuclear on saturate so this implies to me that the that.
Mack Atkinson: The total binding energy isn't a great constraint for the for nuclear matter in general, therefore, this empirical mass formula is not a great constraints to this sort of extrapolation from the empirical mass formulas is a bit suspect to me.
Mack Atkinson: My binding energies are consistent with self assess the Greens function calculations which.
Mack Atkinson: gives me more confidence in their validity and finally again i'll put this claim up that the value of the saturation energy is not necessarily 16 me be.
Mack Atkinson: And with that i'd like to thank my collaborators at Washington university.
Mack Atkinson: argonne national lab and university sorry, and of course try out for for the research resources they provide.
Mack Atkinson: And thanks for listening and i'll take some questions now.
James Smallcombe: Thank you very much back.
James Smallcombe: So yeah, as I said at the start, if you got your questions, please do go in in that reactions menu on windows or MAC and I think it's still in the.
James Smallcombe: Participants menu on Linux find that raise hand button.
James Smallcombe: If you've got your questions or go into the chat window and get typing in the.
James Smallcombe: phil absolutely please go.
Philip Adsley: Hello i'm so you're talking about that direct to results, which is obviously very interesting but lots of people um.
Philip Adsley: it's from what I understand pyrex to result doesn't agree with some other determinations for the neutron skin and.
Philip Adsley: I think that also some of the astrophysical observations suggest less compact more compact a current Member.
Philip Adsley: That suggest a small and neutrons can I was wondering how your your bottom edge is exactly the same as the the T REX to results, so you you're doin really excludes a smaller.
Philip Adsley: neutron skin or.
Mack Atkinson: yeah so the.
Mack Atkinson: Yes, I am.
Mack Atkinson: Yes, I saw that paper out on the archive.
Mack Atkinson: Discussing the how yeah the pure actual result really throws a wrench in in most of these other astrophysical observations and things it's pretty interesting and also yeah the yeah some ideal result as I guess smaller uncertainty, you know reality is probably a bit larger.
Mack Atkinson: Even but.
Mack Atkinson: yeah it definitely it would.
Mack Atkinson: My results would be excluding a smaller skin, so it would imply a stiffer equation of state, I would say, and you know the the duo results are constrained by.
Mack Atkinson: The data I showed where we're using both scattering and balanced state data to constrain this self energy and we found actually in our when we're analyzing.
Mack Atkinson: You know what which data really helps to constrain this neutron radius the most it's this neutron total react, the neutron total cross section is.
Mack Atkinson: It can be sensitive to the neutron skin because again this dispersion relation is really pulling strength between the negative and positive energy domains, and so this.
Mack Atkinson: The neutron total cross section at large energies seems to give some sensitivity to that so you know in it the all the.
Mack Atkinson: Nuclear eft calculations only have bounced state information to help constraining them, so I guess we're pulling from a bit more data to help us to constrain what's going on.
Mack Atkinson: yeah.
Philip Adsley: Okay, thank you, and thanks to the top is very interesting.
James Smallcombe: Because more questions George I believe your first if you'd like to go ahead with your question.
George O'Neill (York): I am i'm going back to the fitting process.
George O'Neill (York): And how do you make sure that you're not.
George O'Neill (York): A dream anymore interesting.
Mack Atkinson: yeah that's not.
Mack Atkinson: um.
Mack Atkinson: With with human input I guess yeah there's definitely this algorithm doesn't like.
Mack Atkinson: You know, I have to look at the fit at the end of the algorithm and see what it looks like make sure the parameters aren't in some physical range and then you sort of alter alter things alter the inputs, in that way.
George O'Neill (York): Okay, so you're not just reading a script blindly and then.
Mack Atkinson: yeah no no that it'd be nice if if I had something that could do that, but no, it takes takes a lot of human input as well.
James Smallcombe: And jack please guide your question.
Jack Henderson: I guess related to that and say.
Jack Henderson: Actually, related to both the previous questions will go in reverse order and.
Jack Henderson: So there's a lot of the DRM has a huge number of parameters right so.
Jack Henderson: yeah there's also the question of.
Jack Henderson: correlations I seem to remember hearing.
Jack Henderson: That from someone that there was some slightly more sophisticated methods being used to investigate the correlations.
Mack Atkinson: Yes, so there's a culprit.
Mack Atkinson: is working with the deal, am using instead of the sort of this minimization algorithm i'm doing he's doing a more he's using.
Mack Atkinson: Markov chain Monte Carlo methods.
Mack Atkinson: Which which helped to give the correlations between parameters and such so he's.
Mack Atkinson: he's taking the do em and yeah really.
Mack Atkinson: honing in on on how the parameters are interacting with each other.
Jack Henderson: Does it have any major impact on the answer is.
Mack Atkinson: Yes, i'd say the uncertainties are a bit larger when you analyze it in that way, but the so he he did you know, using his different fit fitting method, I guess, also he fit calcium.
Mack Atkinson: And our neutron skins are in agreement with each other, you know, using both methods we're getting these large neutron skins but yeah I would say, using using that different Markov chain Monte Carlo method that the error bar will be a bit larger than then is reported with my method.
Jack Henderson: Because, to come back to the neutral skin, I mean how you've got quite a stock discrepancy with the punisher stuff for the 48 calcium, and they I think do really quite well with the other kind of correlated.
Jack Henderson: observable is like the diaper polarize ability, so they seem to reproduce that with the car battlefield three derived of initial methods so is there, can you reconcile those two is that an understanding you've got for why there's a discrepancy.
Mack Atkinson: um I mean I guess so i'll have a bias perspective that you know it's a larger skin and the deal and has it correct so um.
Mack Atkinson: I know that the it's my understanding of the couple of clusters, sometimes has problems reproducing radio.
Mack Atkinson: It could have to do with the interaction they're using this getting re normalized and softened.
Mack Atkinson: yeah I can't really.
Mack Atkinson: I don't know what.
Mack Atkinson: What I could say about reconciling them but I.
Jack Henderson: I feel that it's nothing it's a large neutron skin.
Mack Atkinson: It will be a large one, I guess, but you know, hopefully in a couple years see REX will have a result for us, so we can.
Mack Atkinson: Because yeah there's that's a more interesting case I guess from a theoretical perspective because there's there's right this ab initio result of a series of calcium 48 so it'll be really interesting to see what's going on there with calcium.
Jack Henderson: Okay that's fine this thanks very much.
James Smallcombe: Okay, great.
James Smallcombe: I don't see any other raised hands at this point, I used to like say if you're having trouble with the raise hand button and you are welcome to unmute yourself.
James Smallcombe: and ask any remaining questions.
James Smallcombe: I also don't see anything in the chat window.
James Smallcombe: Okay, it looks like we don't have any other questions so we'll call it close there, I will say thank you again MAC for getting up early and giving us a great talk.
Mack Atkinson: yeah thanks for the invitation I enjoyed myself.
James Smallcombe: i'm most welcome and Thank you everyone for coming and enjoy the talk to come back again next time Monday first of March, it will be 3pm GMT.
James Smallcombe: As always in will have Alejandro are gonna talk about total absorption measurements for reaction applications so have a good week and i'll see you then bye for now.
Thanks.