James Smallcombe: Okay, so I think that's everything. So I will now hand over to Pete. Thanks very much.
isacker: Okay, thank you very much for this introduction
isacker: With the invitation to
isacker: Talk here.
isacker: So good afternoon, and for some of you, I think. Good evening, because some people from India are connected. So this afternoon or now I will talk about the structure of multiple forms and looking at
isacker: So this is an outline of my talk. So I will say a few things about the motivation. Most of the talk, I will deal with the schematic model of optical forums.
isacker: Appropriate for doubly magic Nokia, and then at the end, I will say something about extensions to optimize frankly I in maybe. Well, I won't have to take the time to converse in the magic nuclear
isacker: Okay, so
isacker: Okay.
isacker: So then the direct reason for that, I became interested in optical forms is actually some experimental work at Ghanian. And so this is an experiment that was done on
isacker: lead towards seven, in particular, dying to measure of measuring the half life of a 19 half minus state in which the case to 13 of plus state. And so this is a very large et value be a value of 40 wise convenience. And so this
isacker: Sort of is similar to what happens in lead to await in lead to eight, and that is very well known. So the first excited state of lightweight to t minus. And so in the case
isacker: Either strongly with a strong VT to the ground state of lightweight. And so in this case it's 34 ways cup units. And so this sort of
isacker: Made me interested in this problem. And so I did some calculations for for for for my experimental colleagues trying to interpret the results of their experiments.
isacker: Now this is this is published. So this paper is published. I'm not really going to talk about this particular case, I would like
isacker: To concentrate on a more simple case, namely what happens in lightweight and how you can describe the collectivity of the team mind state in lightweight
isacker: Now, so it's published the the experiment on lead towards seven in actually one thing that sort of when
isacker: He made in my mind about this paper is that there was a referee coughed, and he ended his book, which was not very flattery.
isacker: With the sentence that the his also is not even wrong in a sort of some of my collaborators Mike authors. They thought that this was a sort of a compliment. And so I had to explain to them that this was not really the case in that
isacker: So,
isacker: Therefore, he had grave problems with this page. But anyway, he got published in the end, and
isacker: So you can look it up. I mean, it's a case of a whole couples to an octagon. For now, more gentle. This is my direct reason why I got invested in into this problem.
isacker: But let me frame. The whole problem a little bit more general and let you let me remind to you.
isacker: How collective states are described in nuclei. And this has to do with a surface parameter ization which is written here in terms of spherical harmonics and then some shape variables alpha London you
isacker: And this actually this is not proper to nuclear physics. This goes back to all the work by lot rally in the 19th century, where he tried to describe
isacker: The vibrations of an incompressible liquid dog. And so that is the parameter ization used in this is then also the parameter ization that was adopted by nuclear physicists in the 1950s, I guess, in order to
isacker: Describe the nucleus as an incompressible quantum liquid top. And so if you go now go to the different Lucy polite issue. Start with lambda equals zero. So that's a compression. Whoa, that's very high energy
isacker: So that's not be the elephant to learn low energy physics that we're considering here.
isacker: Monday equals one is a translation. So that's a dipole degree of freedom, but
isacker: For the overall movement of a nucleus. This is a translation. So that's not an intrinsic deformation, but it's it's a spurious state actually that has to be
isacker: It wouldn't be their initial model calculation, but you have to eliminate it. This is the famous elimination of spurious states in the show more like you have to do.
isacker: Then
isacker: The next with the polarity is the quadruple degree of freedom is very well known and is very important in nuclei. And then the one that I will talk about here in this talk is the next one so Landy equals three pocketable degree of freedom. So that is
isacker: Something which is also rather frequently on countered in nuclei. And so you have sort of two manifestations of the optimal degree of freedom. It can be a vibration or it can be a static octopus Live Nation. And so the vibration. Then you have your nucleus in a spherical
isacker: equilibrium state, but it will vibrate into the optical degree of freedom as as he schematically indicated
isacker: Or you can have a static occupying the formation of your nucleus, for instance, in your bounce it and then this default shape can then rotate around the y axis which is perpendicular to the axis of symmetry and so was not so long ago so
isacker: Nature paper on this business.
isacker: About the observation of static optical information in
isacker: Radio mice.
isacker: Now this is the classical description of collective states of collective for lumps on in October informed states. And if you want to learn about this. This is really described
isacker: This is really described in detail in the second volume of both the Moto song which really these in detail about the concept of funnel and how it is applied to collective expectations in nuclear
isacker: And so the reason why another interest in this work is because this concept of full non in nuclear is equal. Currently it's putting to doubt.
isacker: And so there are several publications on this, but here I site, two of them. So one is a publication by the
isacker: Tokyo group. So this is like a high level Tucker and his collaborators. So that's the reason. Physical Review Letters, where he does some model again creations.
isacker: And so where he claims that I mean what defines me shell model calculation, it's really different from the classical picture.
isacker: Of beta and gamma vibrations that is adopted by both remote console. So that's one example. Another. Another example is Paul Gannett
isacker: And collaborators and in this case in this paper. It's a collaboration with a theoretical physicist or the radius would be beyond mean field calculations and so they studied
isacker: Cadmium isotopes, and they claim that can minimize the dogs were usually considered as very good examples of spherical vibrators
isacker: When they claim that we did experiments they observe a breakdown of the quadruple vibrational picture in these isotopes. So, these
isacker: These classical pictures that we know from Boeing and model some in that have been discussed in detail in their book. The second volume.
isacker: These are now putting doubt. And so my question in this focus. What about optical forms. So how are they calculate it microscopically and
isacker: Is the phone on picture that you proposed for quadruple vibrations. Is this applicable for optical Buffon's or not. So that is sort of the central question they would like to address in the store.
isacker: Now, how can you do this. And so my
isacker: My sort of microscopic approached by microscopic approach. I mean a shell model approach. And so what you have to do in the shell model picture of
isacker: Of octopus expectations is in. So I will discuss always with a reference to with reference to lead to it. And these are the orbitals that are relevant.
isacker: For a discussion of optical degrees of freedom, lightweight. So you have the new term orbitals below 126 and above 126 126 26 is the shell gap for the neutrals.
isacker: And for the protons at to which the show the gap. And so for her realistic description channel model description of an optical phone on state.
isacker: You need to consider the expectations below and above.
isacker: These shadow gaps. Okay. And in order to do so, what you need. You need to Kim boots, namely, first of all, you need the single particle energies of these orbitals.
isacker: And this can be extracted from the data and that has been done some 20 years ago by my, my colleague for gallium movies environment in this paper.
isacker: Okay. And next, what you need is an interaction between the neutrons, the portals and the new term photons. Okay. And this one can find a possible interaction from this kind of system in the paper by Alex brown also some 20 years ago.
isacker: And so what I should say that this is
isacker: It's not a complicated interaction in the sense that if you limit yourself to particle whole one particle one whole expectation. So you lift.
isacker: I am new to them over port from these orbitals into the higher line or Beatles, then you have something like 5050 possible combination. So you have to finalize a 50 by 50 matrix. And I think it's 4141 or something.
isacker: So that's not a simple, it's not complicated. However, what comes in is this 35,002 body matrix elements because you have a rather large
isacker: Orbital space for the neutrons and for the portals. So it is a rather large complicated interaction that you have to consider in order to do such a calculation.
isacker: Okay, let me say something about the structure of this problem.
isacker: So this is a little bit of formula.
isacker: And this is this is generic. I mean I discuss it here for lead to wait. But it's a generic t minus state in any
isacker: W magic McCreery so it could be consumed forward to oxy and 16 for instance will apply the same thing. So what you have
isacker: Is. First of all, you can have particle whole expectations for the neutrons. So you lift a neutron from these orbitals into the higher line.
isacker: And this I will the note by new new minus one. Okay. And you can do the same thing for the protons. So you leave the proton from below 82 two above 82 so that's a particle extension for the port.
isacker: In these expectations by themselves. So the neutron particle whole expectations they interact to the neutral. Neutral interaction and practical education for the portal. They interact the Portal. Portal.
isacker: So these are determined determined by the like nuclear interaction. Now in that's a little bit counter intuitive. So he has a new term particle excitation
isacker: Here you have a broken particle excitation in these can interact to the neutron proton interaction. So a lot. This is a new term.
isacker: Expectation that support on expectations, you would say, I mean this is doesn't conserve particle number, but it does. And this is sort of a property.
isacker: Of particle own expectations. If you want to learn more about this. This is described in detail in actually the first form you have more models on the reason appendix, which deals in detail about particle whole expectations.
isacker: So this is the matrix that you have to die, analyze and here you see the structure and how the different interactions come in to this problem. Okay, if you do these diarization you will find a low line t minus states the lowest t minus states in it will be sort of
isacker: A superposition of particle whole expectations for the neutrons and particle expectations for the portal switch it symbolically like
isacker: Okay, so this is this gives you an idea of how to do this calculation and what are the different interactions in how to, how do they appear into this problem.
isacker: Okay, so now what you can do. And this gives more insight on those, as I said, this is a small matrix. It's this particular case 4141 so it's
isacker: It's absolutely trivial to do this calculation. It gives you some insight to do this calculation in two steps. And you say, well, first I want to determine
isacker: My phone on my octopus form for the neutrons in for the protons separately. Right. And then I will let them interact by the neutral important interaction. So this is sort of a two stage problem.
isacker: Of this
isacker: Calculation. So you say first, well I determine my
isacker: Neutral octave optical for them. And this is only the neutral. Neutral interaction that we defined my new to have multiple for the same thing for the protons.
isacker: defines my total non critical for them. So then I have a lowest state for the neutrons lowest t minus state for the potent and then a mix them.
isacker: To the neutron proton interaction, right. And this is a two by two matrix, right. So this is not the exact problem exact problem is, as I said,
isacker: The straightforward boat for diarization of this matrix. This is sort of a two stage problem where is first define neutron and put on
isacker: Optical forums and then you let let the mix by the neutron proton interaction and he advantage of this is that you
isacker: Have the different interactions that come in at different stages of this problem. Now, I haven't shown here that this is a good approximation so on on has to verify whether this approximation is actually a good approximation to the full problem that you do by brute force.
isacker: Okay. So now instead of doing this complicated calculation with the 35,000 matrix elements.
isacker: What I would like to present to you is a schematic.
isacker: And I call this an ad phenom schematic model. This is a little, a little joke mean people know do lots of ab initio calculations and I'm always confirmed by people
isacker: Even heifer Eason tell me, why don't you do an initial calculation from the sword for that system.
isacker: And so this is not my approach. What I would like to do is sort of develop models that are certainly they are schematic when they give you an idea of where you should go to. So this is not from the beginning, but is
isacker: It with some kind of a goal in mind that you construct a schematic model. So let me explain my schematic model that I developed for optical forums.
isacker: I do to approximations. Actually, first of all, I forget about the single particle structure below and above. I mean, what I mean is it collects
isacker: All the levels from the neutrons and protons below the shell and gaps into one level.
isacker: In her collapse all the levels in a single particle energies into one single particle energy above Michigan. So I have two parameters that come in, namely, it shouldn't get for the neutrons initial gap for the portals. So that's the first
isacker: Approximation. So this is sort of a degenerate single particle levels approximation. And then the other thing I do is I take a surface delta interaction SDI.
isacker: Right, and that's in terms of instead of those 35,000 matrix elements, I can know Biomet guys my interaction in terms of
isacker: For Constance, namely the state of the neutral. Neutral need direction. So this is an ageless vectors think because you have like practical. So it's only the eyes of vector component of the interaction that comes in, you have the Portal. Portal into action. So that's the highest effective
isacker: Bottom part only interaction. And then you have the neutron proton interactions or the international work between the two spaces.
isacker: In that as a nicer scale in a nicer vector component. So you can parameters. The whole problem in terms of for
isacker: Standby meters of your interaction and be sure at the end I will sort of analyze what how good is this the approximation in terms of the realistic shareable calculation that I started out with.
isacker: OK, so now let me tell you a few words about this how this schematic calculation of the schematic model can be solved. I will not go into the technical details.
isacker: The only thing I would like to say that I mean, so we do this in this two step.
isacker: Procedure. Right. So first we will determine the structure of the new term in the portal for rooms separately in the separate spaces for the neutron particle whole expectations and for the bottom article holic cetaceans
isacker: Okay, this index of all here. It can I do for neutrons who equals new offer bottom so it goes by.
isacker: Okay, and what is important is that if you consider a surface delta interaction, then this matrix. So, this is your Hamiltonian matrix or the matrix for the interaction.
isacker: Right, this is a sum of two separate matrix basis, actually. So an n by n matrix normally is n times n plus one over to come elements. If it is separable.
isacker: Or if it can be written as a sum of two separate mobile matrices, then you can write it in terms of vectors within components, two vectors within component and he's vectors are if
isacker: N G here in there just n numbers in these numbers. It happens that you can write in terms of TJ symbols. Now if you remember your, your course on linear algebra.
isacker: If you diagonal is a sum of two separable matrices, actually what you think will find in this isn't exactly so you will find that all the eigenvalues. Our zeal except
isacker: In the
isacker: Non Z or Agha values. They can be obtained from the finalization of a two by two matrix. So, this is an exact
isacker: Solution of the octopus problem right for an SDI, of course, for a surface don't interaction with degenerate single particle energies.
isacker: And so what you see here is that you have a low
isacker: Energy
isacker: T minus state. In the case of an optical. I mean, I did here in general shape, but I will apply for Jacob stage. So for an octagon.
isacker: Night till you have a low line and this will be our collective minds and then you have an highlight mode, right, which is a high energy like this is a tie entity. This one is a low energy
isacker: The position of those modes is determined by distinct of the neutral. Neutral interaction. If you look at the neutral octopus for them.
isacker: And by the bottom, bottom into action. If you look at the bottom optical phone
isacker: And then these mics by this of diagonal matrix element, but actually you can do better than that because you can show that this of the younger matrix element. It's either zeal.
isacker: Or he's very small this is shown here. If you have was he wanted oscillator shelled closures and if you consider multiple states or state we
isacker: Buy t minus in momentum t, then this of diagonal matrix is exactly zero. It's a some sort of TJ symbols. So that means that if you apply this for oxygen 16 for instance of calcium
isacker: This of diagonal matrix element is the exactly the you and your connective optical for non state is exactly the energy of it is exactly given by by by this quantity
isacker: Now for lead to wait. You don't have. I don't want to consolidate a shell closures, of course, you have this enormous chunk closures.
isacker: But then you can show that this, this quantity is very much smaller than the difference of the two. So if I go back here. This you take the difference this of diagonal matrix elements is very much smaller. And so this can be neglected. So you've neglected.
isacker: And then you consider only the lowest collective state. So the result of all this is that if you do this approximation of surface that the interaction and no
isacker: Degenerate single particle energies, then you find neutron and bottom.
isacker: Optical four months, which have this structure, right. It's an approximation its exact for calcium 14th of June 16th is our motivation for lead to eight.
isacker: But as I will show in a moment is fairly good and these components here. They're just TJ symbols that are written here, what proportion to to create a sequence. Okay, so how good is this. Well, this is the example of like to wait so I look, look at the structure of the the
isacker: The optical fallen from the bottom.
isacker: So I do a full calculations or Boutros calculation with the surface delta interaction.
isacker: He generated single particle energies. And then my components are given by this like bars and you see what is written here.
isacker: Are the different components of my object bone phone for instance this component would be if you excite a bottom from the defiant have
isacker: Into the p one half. Here we excite the proton from the G seven half into the p one half in trouble.
isacker: So these are, I believe there are 17 possible component for the bottom optical phone. And so this is calculated. First of all, with this.
isacker: Immediately I mean with this boot. First one, just by diarization and, secondly, which is three, Jason. And you see that these
isacker: Correspondences nearly exact to there is a slight difference in this slight differences because you're dealing here with like to eat. So the monkeys are not Armani constellations, but this has been Ahmed or which oscillator shells on it then.
isacker: It's likely giving advice to a difference. And so that's the same study for the new term. So in this case you have slightly more components, but they do agree with this.
isacker: Surface. So this is not a surprise. Actually, this is just a confirmation that my exact solution or my almost exact solution of my schematic model is is a is a reasonable approximation.
isacker: Okay, what I should stress here also, that I look at the science, the science are very important in this business, of course.
isacker: The overall size of your way function, we cannot fix, but one you fix the sign of one component, then the relative science or the signs of all the other components, they fall
isacker: Right. And the same is contained, of course, in the AJC move in this same agrees with what you find from your numerical calculation that's very important because that brings me to the second
isacker: Aspect of a phenomenon structure in a nucleus. So the first aspect of this form of structure is that you have a fragmented.
isacker: Structure so that and so
isacker: Fragmented structure. So you see here we have lots of components. And so they are sort of
isacker: Dave. Of course not. Equally important, but they all contribute to the structure of this team by mistake.
isacker: The second feature of this phone is that it should be coherent and so what does that mean that is illustrated here. So if you know this is for the gotten optical form.
isacker: And so you look at the transition of the lowest t minus states to the ground state. And so now you look at the different
isacker: Components of this transition. So if you write in terms in terms of the different particle whole contributions, you see that their own constructive and I didn't force this, this comes automatically out of the calculation. So this is just a product of
isacker: TJ symbols and then the appropriate matrix element for the three
isacker: The three transition matrix element and you see them all of them have the same sign, and they all contribute construct. If you do the transition. And so that is one
isacker: That he's one white one talks about a collective transition and the same story of course for the quadruple transition. And it's the same story from the the
isacker: Pupils phone on for the new terms right you see many components, but of course different insights with the size the sign of all those components x constructively.
isacker: And this is an important property and I go back a little bit to the structure of my matrix. I mean, what I discussed here was the structure of this, this, this.
isacker: This optimal state here. But what I argued, or what comes out of this two by two matrix is an order.
isacker: Three minus states at high energy. And so you should you should look at the structure of that state as well and you see it is equally fragmented. It is also written in terms of of
isacker: TJ symbols, but a little bit different ones then if you look at the the fragmentation of this highlighting archetypal state.
isacker: Is is the same, or it's equally fragmented. However, if you look at the collective structure, you see that here it is not coherent at all. So the
isacker: The different contributions are out of phase in this i don't i don't know what one should call this this is over a normal collective or even an anti collective states because they sort of they refused to work in incoherence
isacker: With each other. So if I'm actually in a bad mood, I would like to call this a French collective transition because it sort of
isacker: It is fragmented in in in go here. And so, and the same story for the neutral collective and the collective states of this is a neutral next cetacean at high energy
isacker: And you see there is not coherence between the different components. Okay, so this is the first stage. I mean, I have put in guidelines neutral. Neutral to actually put a button to action for my surface delta interaction. And so now I would type come to the next stage.
isacker: Namely, what about the neutron bottom interaction. So I take my octopus phone on for the neutrons. My optical phone for the for the buttons in a mixed them by the neutron proton interaction. Okay.
isacker: In that can be done actually almost analytically. So now you have a two by two matrix and that you have to die, analyze, because this, this mixing is another he booked in you see
isacker: I will not explain this formula on the bottom here, but you see all the parameters that I mentioned in the beginning they now appear in this problem. So first of all,
isacker: You have to the shell gap for the new towards the shell gap for the protons, you have the neutral. Neutral interaction.
isacker: Stand the proton vote on interactions, think, and then for the new to important interaction you have the ICO scale live in the age of factors things. And this can all be determined and politically. This is new and this is by, you don't have to worry. These are some silver
isacker: PJ symbols which can be calculated and actually is in here is the beta oscillator shell so you can find a simple expression for this is of diagonal matrix elements in this interaction matrix and the matrix and
isacker: So if you put all of that together. So the solution. The whole sort of the schematic mode. So this is my genetic expression for an octopus photo.
isacker: So you have beautiful particle whole expectations, hold on particle expectations. They are mixed with these coefficients alpha and alpha phi
isacker: In these alpha and alpha by they appear if you die, analyze this two by two matrix. And if you have done that you have completely determined the structure of your optical phone because these geez, they are simple.
isacker: DJ symbols. Okay, so that now you can put everything together and compare with your surface that interaction.
isacker: The full calculation. So in black is the full calculations or the brute force calculation of my 41 by 41 matrix that I realize I determine destruction of of your phone knows in in Luke is the TJ symbols.
isacker: So my analytic calculations correspondences almost
isacker: Exact. So now, I mean, yo. You say, Well, okay, but this is service delta. And this is the can excellent article energies. What about the realistic and how does that
isacker: Compare with this ideal for lunch structure.
isacker: That you determine in your schematic mode.
isacker: Okay, so let's do that. And so here is the result. And this is a disaster. You see,
isacker: There are some components that are in phase and then there are other components that have a different phase. And that's so
isacker: That's the first result that I obtained and so then you say, what is oh my god what is happening. Okay.
isacker: And this is a good lesson, actually, because if you do a show model calculation you should be aware of the face convention that you're using.
isacker: And you using your face convention in two different ways. First of all, you're using a certain channel model code in this show model code.
isacker: will assume a certain face convention and, secondly, you will use some matrix elements. So to body matrix elements in these two by two matrix elements. They are derived
isacker: Reading the certain fears convention and what you should make sure is that the face convention of your body matrix elements are consistent with the face convention of your code.
isacker: And that is an important and if you if you don't do that. Okay. Your energy calculation will be okay. But your, your transition calculation will be completely
isacker: Wrong. If you are not using a consistent face.
isacker: Face convention and so that is what happened here. And so then if I adapt my realistic to body matrix element in such a way that agrees with the face convention, but I used in order to get my components. This is what I did. Okay, so everything now.
isacker: It's
isacker: Consistent, at least in inside, of course, to be sure, there are differences because now I use the realistic.
isacker: Interaction. So that's obviously not a surface delta into action. But you really read that at least the faces are consistent and also the fragmentation structure is momentous satisfy this is still with
isacker: With degenerate single particle energies. If you know do the real realistic calculation as as Morrissey Raymond would have done it, or as a knowledge bomb would have done it. This is the reason that you get you obtain in in comparison still always with this.
isacker: TJ simple calculation and you see that is still it's a fragmented structure.
isacker: Right, some of the components are much larger than in your ideal phone and some of them are much smaller and that is what you should expect if you take non degenerates in the park.
isacker: Okay, so that's
isacker: The comparison with the artistic
isacker: Shambala calculation. However, a sort of
isacker: A glossed over something. Namely, I immediately showed you the result of my entire list the realistic calculation.
isacker: For the full calculation. So I immediately compare the food calculation. When I compared the, the, the final octopus phone with what I get in my god im a schematic moment.
isacker: So let's do the calculation, a little bit on the comparison with the realistic calculation in the schematic model a little bit more careful. Right. And let's do it. Also in two stages.
isacker: And you will see that is actually a bit of a surprising result, I know you've obtained the so called the deconstruction
isacker: Of my new term for known and you will see why I call it the construction in the moment. So this is a call. What I obtained in what I showed you, if you do surface. They'll thing to action degenerates single particle energies almost perfect in Cleveland. So now I take my realistic.
isacker: Interaction degenerate single particle energies okay agreement is less, but it's still reasonable and then I take a non degenerate single particle energies.
isacker: And then it becomes a little bit more problematic because you see a few very strong pics and then for the rest of it is essential in class.
isacker: And this is even more so for the bottom octopus formal. So this was the nice result gets a little bit late for a mistake interaction, but it is really not such a collective structure because you have one strong component, maybe a second one and then the rest is history class so
isacker: What I show here is that if you actually just considered the little Newton and the gluten. Gluten interactions, you do not update
isacker: octave ball new to inform once in optical proton for notes and that's that brings me to
isacker: What I would call an ontological question ontology, if you remember your philosophy is deals with questions of existence. Okay. And so what I've shown is that if you do
isacker: A live show model calculation. It confirms the validity or the approximate validity of the concept of them are critical for them.
isacker: But not have the separate neutral and problem occupy conformance these do not seeming do not exist separate and so that is my ontological question, do the neutral in the bottom multiple forms actually exist separately is not
isacker: A question without interest. I mean I quoted a recent paper. So this is by is the golden goose or I don't know where I know people from also from
isacker: From I ll from Canada. Okay. But so in they they discuss low lying optical eyes affected expectations in these interviews in this is Victor excitation this you should
isacker: Understand as a as I
isacker: Hear that, if you do this two by two matrix with a new term optical phone in the proton optical phone. They are mixed by the neutron proton interaction. And so you will have
isacker: Two states coming out of that I discussed, especially the the symmetric, the lowest combinations. So that's a major scale and expectation. If you this
isacker: Is not properly. And so then the, the anti semitic or the mixed symmetric combination of the optical formal
isacker: For the neutrons and for the bulletins, this is called of sometimes called the eyes of an expectation. So, but can you really talk about in as a victim cetacean if the new term in a boat on logical forms actually do not exist separately. So that's, that's my
isacker: ontological question which I will try to answer here. I think they do exist.
isacker: But it's it's a bit paradoxical docs.
isacker: I have doxey Kali, namely, they do exist, not because of the neutral. Neutral in the Portal. Portal interactions separately, but because of the neutron proton
isacker: Action. Actually, the new term gotten interaction generates the collective structure of the optimal performance, but at the same times it couples the
isacker: Neutron in the octopus forms and so it will define a symmetric combination in the mix symmetry combination of
isacker: Okay, now I have talked for about three quarters of an hour, so I will
isacker: make a few remarks about old mass nuclei this i'm not discuss in so much detail, but it's sort of what I'm now interested
isacker: And so it still, it's an interesting question. I think it goes back to the, the question I raced in the beginning about the phone on like structure. And in this particular case, I mean, does the octopus.
isacker: Phone on a DNS it full on like structure if you part couple of particle on a whole to such a formal and so this is actually
isacker: A problem which is discussed, if you look at this book by book and what was on the second volume, there are pages and pages.
isacker: Of discussion on this problem where they will. I mean, this is called particle vibration copying so they will. I mean, sort of, discuss this.
isacker: This problem in terms of how do I, couple of particle or home to vibration in this particular example that I would like to discuss how do you copy it to an octave for me.
isacker: Okay, so I will discuss this, not with the example that I started out with. In the beginning, name it to seven, but I will discuss it for two main lead
isacker: Because this is also the example that is discussed in detail in the book Bible and so just to give you an idea of what is the spectroscopy of lead to nine. So it has a grand state, which is a nine half plus state and this is predominantly
isacker: A single particle expectation. So it's a dominant one neutron in the gene. I'm half or at night and the other state which is important for the story that I would like to develop here is the 15 half minus state.
isacker: So that is predominantly again it's
isacker: A particle state. And in this case, you excite your you have your neutral. Sorry. You have your neutral in the orbital with which is the date was 15
isacker: Or but it's a bit more complicated than that. And so if you wish to learn about this. You have to read the book Moto moto so because we're in Madison, say, well,
isacker: But this line have plus
isacker: State, it's actually it is
isacker: A particle in Jeannine half but it can also be a Newtonian
isacker: Half coupled to an octopus formal and these two expectations, they will be strongly coupled by this particle vibration coplin matrix element and the same team for the 15 half minus. So, okay, fine. The lowest expectation will be
isacker: Newtonian Jake was 54 day 15 have that there will be strong coupling with a neutral in Jeannine half couple to report form. And again, you have enough diagonal matrix element that couples. These two expectations and so
isacker: What in this collective particle vibration copying model what what what both a motor some behave is
isacker: Something I mean a simple relation between this is copying.
isacker: matrix elements actually this analyze this analysis, you can you can do English homework. And so what you have to do initial one
isacker: Is ok you consider one neutron expectations. I mean there's just neutrons in in in the different orbitals that are available for the neutron. Okay.
isacker: But you can also do to neutral or to particle one whole expectations so then you can have a neutron excitation in a particle whole exited either of the new terms of the products. And so this is
isacker: Let's say a shampoo bottle basis, which I will call the full sermon basis, of course, it's the truncation. It's the truncation to
isacker: Particle expectations and to particle one horn expectations and this problem can be done. I mean, it gives us two matrices of the order of a few hundred
isacker: They mentioned, so it's it's not such a big problem. And so then you can check, to what extent this particle vibration copying model.
isacker: Is present in the shin model. And for instance, you can calculate what is the nature of this company matrix.
isacker: Right. So, this you can you can view this two by two matrix as a sort of a truncation of the
isacker: Actual model space of one particle expectations when to particle one Horlicks cetaceans, so that would be the, what I call the function mobile space.
isacker: And this is his donkey the diversion extreme can claim version of it, namely the two by two matrix. Ensure you can ask yourself the question, to what extent these two by two matrix.
isacker: mimics the fulfillment problem that you can calculate with realistic interaction that that's what I show in the next transparency. So this is the analysis.
isacker: Of the nine half plus states. Okay so 900 plus states. So I have in my schematic. I mean, my particle vibration coupling model. I have two states first excited nine have the second ticket nine have the energies are indicated to buy the Purple Arrows right
isacker: Right, and then I can calculate the overlap of this state in the particle vibration with the Food Channel, the state. Why can I do that.
isacker: Because in this case I have an optical for known which is coupled. I mean, which, of which I know the structure because I just determine the structure of it for lead to eight I copied it to
isacker: The Jake was 15 half I can get to the nine
isacker: To nine have bus excitation in soap. I have all the ingredients to do the calculation of my two by two matrix, but now in
isacker: As as a truncated version of the full sample calculation and then you can calculate the overlap of your particle
isacker: State copy to an octopus for them. And here the overlap section. So this is very large overlap, it's it's close to 100% is like something like 95% these r squared and Richardson.
isacker: And so you see this is actually this is not very surprising because this is the ground state of led to align this as we said is essentially a particle excitation
isacker: single particle expectation. And this is, of course, this is contained in this chromatic model. This is this expectation. Okay.
isacker: And this is contained in this model and you see the overlap is very like what is more significant.
isacker: Is that the second excited state in the shell moment in the future model calculation. It is indeed the t minus and oxygen on coupled to Jake was 15
isacker: That comes out of the flu, someone will calculate full in the sense of one particle plus two particle one whole expectations and you see here, these, these
isacker: These are the components of the
isacker: The state in the full shall mold that. Sorry. These are the components of the state in the two by two matrix with the full time model components and you see these are another
isacker: Small. I mean, Edwin large scale in order to view these components. Same thing here, right, for the 15 half minus. So, this is essentially a single particle expectation, but this is this is the
isacker: Essentially, the second excited state in the full show model calculation is a section essentially a t minus couple to Jeannine half. So this sort of the same model analysis. This confirms the idea of boredom optimism for
isacker: The Occupy Wall.
isacker: Particle vibration or whole type relational model. So this is a more complete year you do it mean, what is the structure of the t minus couple to Gina in half. And you see that in all the States for all the
isacker: negative polarity states right this essentially the first excited state is a t minus couple to Jeannine have in in this problem, you, you really have to worry about spurious states.
isacker: Because the first excited state in your sham or the calculation will be schoolers. So you have to remove it. And if you do that, then the will, the physical first excited state is the state of an optical former couple to Gina have in this particular case.
isacker: Okay, so I think I conclude my my seminar here.
isacker: So I showed you a schematic model and so
isacker: You reduce your problem for the calculation of the optical to a two dimensional collective subspace. So you can show that if you use the surface delta interaction and and and
isacker: And degenerating particle energies then actually you you reduce exactly your problem, or almost exactly a problem to a two dimensional problem. So your collective subspace exists in
isacker: Two dimensions of space and this exists separate from the one particle hold space and this property is approximately found in a realistic shall model calculation. But this is only valid if you switch on
isacker: Completely the interaction. So the neutral. Neutral the Portal. Portal and the neutron proton interaction is actually the middle gotten into action that Diageo system to this.
isacker: conductive properties, much more than the neutral. Neutral in the Portland port on the directions separate
isacker: And then at the end, I showed you an example of the optical phone and he thinks it collective character in an organized. So this is sort of a little bit of variance of people now claiming that this, this
isacker: This
isacker: Analysis of both models and at least for the quadruple degree of freedom is sort of, it doesn't work properly. I mean, for the octave fall for norms, actually what I showed that
isacker: The this phone on character seems to work and even you can consider it for the non Muslim increase in this political validation coupling procedure or approach of both and Matson seems to be born out by realistic.
isacker: Said mama calculations, at least for for lead toward okay extensions so I discussed on mass nuclei.
isacker: What I would like to to do in this doing is to extend it to see me see my magic nuclei. So, so far, I discussed only
isacker: W magic nucleus, you can perhaps construct the schematic models of see my magic nuclei and then make it even a little bit more complicated by copying and not particle to it. And this is a case of interest to some color collaborators in
isacker: The West got his university. So this is the case of it terbium one
isacker: Determine which I think some
isacker: In one other interesting state is a question is, how well are two optical four states he realized in nuclear, this was a question that was discussed by Alex brown
isacker: In this paper that I showed at the beginning with some 20 years ago and I think it would be perhaps of interest to address this question in this schematic approach. Perhaps this can learn something about
isacker: The nature of to octopus expectations in in in nuclear. Okay. So I will stop here and I tell thank you for for your attention.
James Smallcombe: Thank you very much. P. That was a
James Smallcombe: Very interesting person there because I particularly appreciated the inclusion of the face convention issue that was a very satisfying to see that.
James Smallcombe: So do we have any questions, then I see we've got a couple of people joining in with the digital clapping appreciating talk
James Smallcombe: But if you've got a question. Now, if you'd like to go to the participants menu and use the raise hand button and then also if you if you don't have like phone you can type in the chat box adult. Do you want to go ahead with your question.
James Smallcombe: So,
James Smallcombe: To unmute yourself.
isacker: You don't is from sorry
Zsolt Podolyak: Sorry. Now you can hear us.
James Smallcombe: Yes, yes.
Zsolt Podolyak: Yes, yeah. I forgot to unmute myself.
Zsolt Podolyak: Very nice. And he showed how complex how the structure of the octo portfolio and how complicated it and in many papers, only the data as equal delta j Wesley.
Zsolt Podolyak: Particle full pads are emphasized, but it seems that in your calculation. The other bands are also very important.
isacker: Yes. Maybe this this was also a surprise for me again maybe yes and that's let's go to the most basic one.
isacker: I guess this is maybe
isacker: The most. Can you see it or should I put in
Zsolt Podolyak: I can see the first one is already not entirely equal data.
isacker: Yes, exactly. Yeah.
isacker: This, this was a surprise to me too, and
isacker: Maybe here it is more important.
isacker: Not even so when in
isacker: So,
isacker: They all contribute in its it's not obvious to me that this delta L is the most important
isacker: Okay, right, I mean that that comes out of the calculation.
Zsolt Podolyak: Okay.
James Smallcombe: Okay, Marcus. You want to go ahead with your question.
Marcus Scheck: Rather comment to the previous question.
Marcus Scheck: Joy what you meant was the steady delta change equals three.
Marcus Scheck: And then shell configuration.
Marcus Scheck: By know Pete has basically the one h bar omega come to
Marcus Scheck: Configuration that also makes in the octopus for known have an open shell loop loose, but in open Shelby would address rather this delta delta change, which is the most important component
Macy.
Marcus Scheck: Place can be justified by simply okay and by speech a symbols.
Marcus Scheck: Because there's preference over this other possible configuration with delta t equals three delta x equals one.
isacker: So because because I mean my
Marcus Scheck: In an open shot nucleus, we would, of course, lower Slide three minus configurations
isacker: Yes.
Marcus Scheck: They say created by the sub shells with delta chiclets three
isacker: And then we have a see what you mean is
isacker: That is it to
Marcus Scheck: lightspeed has no
Marcus Scheck: Limited himself to the Bourne age ball McCoy's today.
isacker: So your point is that I mean if you then look at one oscillators shun
isacker: Yeah, new at the octopus within that it just so happens and delta x equals C or the deal. Well, not the only ones, but certainly I mean the most dominant once
Marcus Scheck: You're at the system energetically favorite because of the
Marcus Scheck: Speech a symbol.
isacker: But in this case, certainly it's it's it's not obvious. Like if to as would be tell delta x equals three.
isacker: Which is
Marcus Scheck: Collected is
isacker: not large enough to listen.
Marcus Scheck: But a foreign looks in the other couplings, but if you want peace and joy it I can send you something that a
Marcus Scheck: Guided in a bedroom is for me.
Okay.
Zsolt Podolyak: Yeah, okay.
Marcus Scheck: It was to comment that though that we were talking about two different things. Development space.
Marcus Scheck: And one H bottle McCall
Okay.
Okay, when
James Smallcombe: You get to another question. Then we have a mark.
Mark-Christoph Spieker: Thanks a lot for your talk. Pete
Mark-Christoph Spieker: I hope you can hear me.
Mark-Christoph Spieker: Regarding the realistic Sharma calculation that you use from Alex brown
isacker: Is
Mark-Christoph Spieker: I know that he does cast, including cross check citations show so to particle to whole excitations to the lead to a ground state.
Mark-Christoph Spieker: And when discussing phone ons Polly blocking is always an important topic. And since we're just looking at the matrix elements here. I'm wondering whether
Mark-Christoph Spieker: They change when you include the two particles to whole configurations in the lead to a crown state and then you actually block some slots. Just because you basically have two particles in them now.
Yes.
isacker: I agree with that. Of course, I mean this this would make it more complicated. So that's why I didn't do it, but I guess for the ground state. This, this has been. I mean, this would be an important
isacker: Yeah, this, this would be an important elements that they should add in. So that's what I also mentioned at the end. I mean, looking at the
isacker: Two phone on structure, it would in instead of just limiting yourself to one particle one whole, you have to go to to practical to whole
isacker: Hopefully not more than that. And so the two particles to whole for the t minus, of course, it would have little influence but for the ground state, it would have influence and it would lead to problems that okay you say that is blocking
isacker: I think it will be nice for me to study this within the schematic model and see what something
isacker: reasonably simple can be said about the nature of this blocking the other thing. I mean, I read this paper by by Alex Brown, of course.
isacker: In the other thing which surprised me a little bit was the statements about which octopus and double optical forms, he found in the shell model in which he didn't found and
isacker: You see what I know from quadruple foremost is that the quality performance. I mean, the double for notes with low spin. They're not so well realized in. I mean, empirically, you see that many problems, whereas the high
isacker: For non state. So four plus two for non state or the six plus three for non state for quantity performance. They're reasonably well realized in I mean never collective structure in what Alex said
isacker: For the optical four months. It seems to be the opposite way. I mean, the low spins were reasonably well found
isacker: To. I mean, they had to octopus for non character zero plus, whereas the six plus did not have at all. This double or triple for so that's also a question that
isacker: Raised my interest in reading newspaper. But I mean, you're certainly right one should put in the the the particle to whole expectation and look at what happens with the ground state correlations. And this something I
isacker: I don't know what it's reasonably simple
isacker: When I can do it in the schematic mobile, but this is something which I would like to try
Mark-Christoph Spieker: And I ask another quick question, since we were talking about the to finance states.
isacker: Was
Mark-Christoph Spieker: Is there any chance that you can use your schematic model and the act in that region.
isacker: Or yes, yes, it's a generic model.
isacker: Because
Mark-Christoph Spieker: I think even
isacker: More interesting when we can. When I have done it for for a W matic nucleus.
Mark-Christoph Spieker: Yes.
isacker: So now if you go to acting lights mean for the phone, nuclear, that's a different story. So, this I will not be able to say something maybe for semi magic. Okay.
isacker: Then I can but I'm trying for the moment. Also, in, in collaboration with now has seen trying to do some generalizations this, I'm afraid. This will, it will remain on a schematic level so
Thanks.
James Smallcombe: Seeing our seniors unmute
James Smallcombe: Himself, did you have a comment on that nursery.
S Nara Singh Bondili: Was wondering, I mean, what is the main difference that PhD or finding between that's a lead region on the on the IBM pleasure.
S Nara Singh Bondili: For exam.
S Nara Singh Bondili: Yeah, in terms of contribution current contributions.
isacker: Or
isacker: Yeah, well I i'm not not there yet. I mean, so your question is what happens if I put in
isacker: Now,
isacker: Particles. I mean, if I if I go away from a W magic MacPherson okay you know and in the work we do together.
isacker: What you do is you put 10 particles in certain orbits and we tried to describe the optical by sort of freezing those particles in particular, or it's a very systematic
isacker: Approach. I don't know. I don't. It might work for the t minus expectation that I think might be still reasonable. I doubt it will
isacker: Work.
isacker: For Hire line. I mean, if you look down at the band which is constructed on top of the t minus i would doubt that you can reliably describe
isacker: The nature of those bands in it. You used to doing the full calculation as, for instance.
isacker: Find
isacker: Some simple features.
S Nara Singh Bondili: Yeah, I think in the future, maybe even is a German name is also optical support supposed to be so.
S Nara Singh Bondili: I think even the even the last item epi
S Nara Singh Bondili: There are some more night lighter neatly also
isacker: And maybe we should do that more it's easier to do.
S Nara Singh Bondili: Yeah.
Okay.
James Smallcombe: Okay. Do we have any other questions.
James Smallcombe: Mark, you've got another one for us.
Mark-Christoph Spieker: Let's see if I may. Um, so, Pete, you mentioned
Mark-Christoph Spieker: That people started questioning the collectivity of the quarter quote phone
isacker: Yes.
Mark-Christoph Spieker: As far as I understand, people didn't question the collectivity or credit card activity for the first phone on the one phone on state but like to phone on Marty phone on states.
Mark-Christoph Spieker: Or intrinsic excitation spurred on some shape coexisting configuration.
isacker: With
Mark-Christoph Spieker: The main problem in the work of call was that you have this features of shape coexistence and the cadmium isotopes, which might mix with
Mark-Christoph Spieker: The more pure Marty phone on states and therefore diminish their phone on character.
Mark-Christoph Spieker: I'm wondering whether you'd expect something similar for the optical states because, especially in the spirit and UK it. Now, if you don't talk about
Mark-Christoph Spieker: Let's but something else like the 10 or, for instance, the doctor performance would be at high energies and usually the shape coexisting state state, they have found at lower energies expect that the finance will be affected by other structures. The okta performance.
isacker: Will
isacker: Will you would be looking for negative polarity states. I'm not so sure whether they are many ways to make t minus state mean in the in the quadruple problem.
isacker: You have, of course, you have a zero plus quadruple I mean to for non state, right. Enjoy. You have many ways to make zero buses and that's actually the first
isacker: coexisting state that you can think of will be zero plus so many ways of making alternative and then you have to worry about whether it makes us or not. So I think this problem might be less important. I'm just guessing.
isacker: I don't know, but I think it would be less prominent problem for the optical form then then probably both
isacker: On the whole, I think that the collectivity, this is something I learned from this study that productivity of the optical for new sort of better than what you see for for the portfolio. So the four walls of the new see a few components that contribute, but not in this case.
isacker: 3040 components and they're not small.
isacker: Is important in one of the commentary. I hate on your comment is, it's true that the question the nature of the
isacker: They don't question. Sorry for the spherical vibrated they don't question the nature of the first 414 different phone
isacker: With the Christian the nature of the first four months excitation in the form Nokia, namely a better vibration the gamma rays, and so they really the fundamental vibration which is good.
isacker: And I think that's a it's an interesting question in
isacker: Terms of relations by the they
isacker: They are well done. And He analyzes and we find something different from what we know from
isacker: Certainly something to follow and also experimental on so the pin down experiments and probe whatnot, the other
isacker: Great.
James Smallcombe: Okay. Do we have any other questions.
isacker: So I've still got a
isacker: Sense.
James Smallcombe: So if anyone wants to unmute themselves if unable to use the raise hand button and just
James Smallcombe: If not, I think that's a lot, in which case I will say thank you very much to Pete for another great talk.
James Smallcombe: To all of you for joining us and before, before I let you all go, I'll do my plug for the next talks.
James Smallcombe: Particularly if you're interested in this topic we've got a talk next Monday by David all university of west of Scotland, which is an experimental talk, it's relevant to all shapes.
James Smallcombe: So to come back for that. But before that, on Friday. We've got to talk by Ragnar Spielberg, University of Washington. Another theory talk
James Smallcombe: asking, can we do nuclei. What can we do all of nuclear physics ab initio so that's that's the next plenary session on Friday. Of course, we also have the student towards do encourages students to come to those on Wednesday.
James Smallcombe: So that's the end of the plug. So once again, thanks for joining us. And thank you very much speed. Okay.
isacker: See you. I hope we