Tzany Kokalova Wheldon: Alright, so it's three to five minutes past three. So we're going to start with today's load lockdown and social distancing seminars.
Tzany Kokalova Wheldon: It's a great pleasure and honor for me to introduce the today speaker and today we have Antonio Romero or Dr. Antonio, Marcus Romero, he has got the I up nuclear physics Book Award for 2019. This is our, our word early career researchers who is
Tzany Kokalova Wheldon: Not just a simple researcher, like me, but he's a theorist and he has got the Award for his fantastic work.
Tzany Kokalova Wheldon: On proton, neutron pairing during his PhD at the University of York, and afterwards. It's a great, great pleasure for me to let him speak before this a little bit of housekeeping, which means
Tzany Kokalova Wheldon: Us. I can see all of you are wonderful. So you have muted yourself you know very well what to do. Please stay like this until Antonio speaking and also afterwards.
Tzany Kokalova Wheldon: If you have questions, it will be great to ask your questions, please use the chat box to write them well and don't use stoking
Tzany Kokalova Wheldon: Or simply afterwards, please raise your hand into the chat section on will ask you to speak and ask your question. So questions are welcome. Thank you very much.
Tzany Kokalova Wheldon: We're also recording you have probably already seen the message. I can see it, you see in front of me.
Tzany Kokalova Wheldon: This is so that everybody else who had the moment. During another zoom meeting and or by whatsoever reasons they come not here. I'm done. You stoke will have these opportunity and do it. Thank you very much. I'm telling you, in your own time, please.
antonio: Okay well hello everybody, and thank you for, for joining us here at first I would like to thank thanks Annie and James for each invitation.
antonio: But also their up for considering me for this award. I am I am very honored. I'm very glad to have been considered for the recipient of this of this price.
antonio: So they talk, I'm going to do today is related to the PhD work that IP. The bucking the University of New York.
antonio: And it's related to them to the proton, neutron pairing coexistence, along with like particle pairing using millfield methods I would symmetry restoration techniques.
antonio: So first of all, let me introduce the University of York's nuclear theory group. So this group is is quite recent, I think it was created on 2015 so five years ago and
antonio: And it's the third group. Now, in the UK, along with the groups in in Manchester, then roughly regrouping Manchester and another one in, sorry.
antonio: So the leader of this group is my was my supervisor professor, Jessica. Jessica here. This is me, obviously.
antonio: We also had a lecturer and also my unofficial supervisor. Dr. Alessandra story.
antonio: And we had a postdoc working with us a PR Becker and working in with a shift moment she found out to Paul moment, there was a famous PRL that was like two years ago.
antonio: And he was working with fasting York and also we had to all their PhD students, but I'm sure that they will soon to be doctors. They return you're working with Jessica Alessandra with our they've all Hamiltonian and collected by citations in nuclei and Matthew Shelley working with Alessandro
antonio: About Bayesian analysis and other statistical methods applied to two nuclear so you can see where we were a very diverse group in the sense that we work on very different areas within nuclear theory structure theory.
antonio: This picture was taken. I would say, like, one year and a half ago. So since then, we had reselling corporations to the group. So when we have we have Paolo sorry need a new PhD student
antonio: Who will continue on the work that I that I left there, but at least we continued and also another academic another Pasta, pasta, a lot or hear me or not.
antonio: So I wanted to say that I'm really glad that I got the opportunity to study at York University and to work with this wonderful team.
antonio: With which I had discussions on a stocking almost every day and receiving positive feedback always so I feel like a part of this a war of these are up award also belongs to that.
antonio: OK, so now, with that being said, let's get into business. So first I will introduce the concept of bearing and the motivation behind behind the project behind this PhD project.
antonio: It would be followed by the theoretical techniques that we use to describe this parent correlations in nuclei. A which are based on the main thing description and beyond, beyond
antonio: Namely, meaning a restoration of the broken symmetries are violated by these meaningful description, it will be nothing too heavy a promise and with these
antonio: Techniques, we have a series of results that
antonio: We're going to show you. I'm going to show you, and then out of these results, we can extract some conclusions I finally
antonio: Okay, so
antonio: So for those of you who are not familiar with the concept of Barry, it is a phenomenon that is founding nuclei or what a nuclear or any
antonio: Or many other many belief systems for that matter. A by which burst of particles.
antonio: They, they couple in such a way that the reduce the total energy of the system. So they make the system more stable. They make the system more
antonio: More bound. A. So a nuclear arms. So a proton and neutron in nuclei. They orientate themselves in a space and also there is being as well to make a total composite correlated pair couple two to tango moment to equal to zero.
antonio: So this concept of pairing will sink in nuclei was introduced by boron models on in our, in our famous brief paper from the 60s, where they notice that the spectra of even are not nuclei, which is represented here by this schematic. This is not a real spectrum.
antonio: And they noticed that there was a large gap between the ground state. And the first extensively state of all even locally.
antonio: And moreover, they realized that these are spectra was very similar to this backdrop found in superconducting metals.
antonio: But in superconducting metals. At the time, there was another way to implement that theory that was very successful in describing this phenomena, which was the BCS theory, which I'm sure you have heard of
antonio: So the VCs theory rely upon the formation of the so called Cooper Paris. So you have a pair of electrons for our meals, which has been one half.
antonio: The spirit of electrons can couple totally spin CEO or one and therefore allowing the possibility of compensation and this is the
antonio: Next one. This is the principle of superconductivity or super fluidity in some in some systems in some superconducting metals. So Moto moto song said that the same thing can be happening in nuclei that could explain the spectra. So instead of
antonio: Electrons. We have protons and neutrons that can also capital to grow momentum equal to zero.
antonio: Now, the only difference between what is fun to be conducting methods which Cooper piers and what is funding nuclei.
antonio: Is that in order to form a couple pair you need some external forces you need immediate effects. You can only from a cooper in a review.
antonio: Because if you had two electrons in vacuum, they will only interact by by date repulsive cool um interaction. Therefore, they will not find occur because they don't like each other, they tend to repel each other.
antonio: So unit by rationale form on effects inside a medium in order to form a cooper however in in nuclei. This is not the case because we have a short range very attractive nuclear interaction. Therefore, there is a possibility that
antonio: That nucleus protons and neutrons can found bears, even in the vacuum not really nuclear matter of the nuclei that also happens, but also in the bathroom.
antonio: And this happens with the with the director on that uterine is a bounce state of a proton and neutron. So it's a it's a pair of a proton, neutron
antonio: And so with this idea of bearing in nuclei can be explain why the ground state of full even nuclei each other. We see a plus, because in and even system.
antonio: You have an even number of part because on the road coupled together.
antonio: Forming pairs of the angular momentum equal to zero. Therefore, if you sound, the total angular momentum for these pairs that resulting unreal momentum of the system of the nuclear will be also Cyril
antonio: While, on the other hand on the old system, there will always be a particle that it cannot be paradise will be alone. And therefore, the total a momentum of this state of the system will be dictated by the momentum of these old particle which can sit on a on a shell Jay with parity p
antonio: And
antonio: So,
antonio: In this, sorry. So this also explains why there is a large gap between the first on the within the ground and the first excited state.
antonio: And it's because we need to break one of these parents, you know, lead to excite and even nucleus, while on the other hand on the old system.
antonio: You only need to excite the source particle sitting there alone therefore allowing a low lying expectations and therefore a much more complex expect right
antonio: So, okay, there is bearing in nuclei. But can we can we find in a more powerful direct way base. For example, in the binding energy of nuclei.
antonio: Well, yes, actually, we can. I mean, this figure we plot a quantity that is called the three point indicator who's formalized given here and this
antonio: Is indicating the difference between the binding energy of a nucleus with an even number of neutrons and and I give me a number of protons set
antonio: A difference between this nucleus and the corresponding neighbors and we plug this quantity here as a function of the total number of particles n plus X number of problems on the number of electrons.
antonio: And we can immediately see what is called the alt even staggering effect, which is basically this see so behavior going up and down, up and down.
antonio: So the points that are on the top correspond to nuclei that happen even number of articles.
antonio: While, on the contrary, the points are at the bottom correspond to look at with an odd number of particles. Therefore, the split is telling us that a nuclear with an even number of articles are always more bound than the corresponding all neighbors.
antonio: So this is a very powerful indication that there is a pairing in nuclei based on an analysis of the binding energies. So this was done well, sorry. These are three so Topic Chains for things seen on and palladium.
antonio: And but but these can be found anywhere, in any other topic and then just for those of you who are curious, we have these three points here, which are can be considered outliers of the general trend.
antonio: But if you analyze it more closely, you can see that the number of neutrons hearing Palladium is a 50. So, this corresponds to a magic number and therefore on here they correspond to a number of nutrients equal to
antonio: Two would be so it's also a magic number. And therefore, we expect that they say these cases are going to be far away from the trend, because it's nuclei are going to be a rebound because their numbers they they balance Shirley's completely for
antonio: Okay. And so let me go farther. Let me go deeper in this concept of correlated pair, because when I started my PhD. I had the feeling that I didn't fully understand what was going on there.
antonio: And I think with the six sample here that I'm about to show you really made a clear picture in my head. So let's imagine
antonio: A shelf space. Let's imagine just a shell with L number equal to two. And so our system where particles can sit in with an equal to
antonio: And according to quantum mechanics five magnetic states minus two minus 1012 corresponding to the projection of these angular momentum.
antonio: A total of 10 particles can sit here. Let's consider just one species programs from iTunes or any other, but also by twist beans are not represented here.
antonio: And we choose to a forum for particles that can see in in any of these states of these magnetic states.
antonio: Now, if there is no is being Orbitz interaction or any other interaction that breaks the generosity of these mathematical states.
antonio: In principle, a particles can see anywhere there is not a state that is that is more preferred by a particle to say that any anyone else.
antonio: Therefore be FISA possible configuration of a full body says have a VR for for for the system that is as likely to happen as any other one because, in principle, but it's nothing that that we lower the at the energy particles are sitting anywhere else.
antonio: However, this is not what is found in nuclear apparently particles like to move in what is called time rubbers Orbitz. So, namely Orbitz with opposites angular momentum projection and spin production.
antonio: Why, because then they total angular momentum will be zero. You can see that it will be some all of these numbers, the totals for the zero nothing here. I mean here where it wasn't happening here.
antonio: So there is. So this is why we say that they form a correlated fair because they choose to move in certain states in order to make the total agreement to equal to zero.
antonio: So we so okay so we can see that there is there is like a preferred direction. Right. So you choose the system you choose for particles you
antonio: Do say okay, you can move anywhere here but particles are like intelligent and the direct to to move in time reverse Orbitz in order to make that moment to equal to zero.
antonio: So of course there's limitations to this, right, because we have, for example, Polly's exclusion principle two particles cannot cheat on the same mistake.
antonio: And also we're assuming that there is a there is degeneracy here. So if you
antonio: If you read this degeneracy. It is possible that there is a configuration that we lower the total energy, even when they're, they're not in pain for various organs, but this is that you have a picture that happens in an open in an open shell nucleus.
antonio: Okay, so what I was saying is that there is a preferred direction right so particles will move in the Angry Birds or weeks before any other possible configuration.
antonio: And it happens that in physics that anytime there is a preferred direction. There is a symmetry that is broken.
antonio: Imagine for example as here we're sitting on our chairs. We have a desk when you take something from your desk and you throw it away, then you will inevitably fall to the floor.
antonio: A disease because of gravity. Okay. But these these indicating that there is a preferred direction which is the vertical direction it goes down.
antonio: If you work in outer space and you take an object and just throw it away. This object will follow the direction for over an hour.
antonio: And this is indicating a in the surface of Earth that there is a development of a symmetry. So it's the translation of symmetry in this case.
antonio: So the same concept is happening here and they seem to we're breaking is the particle number symmetry. So, we will not have a nice integer number anymore telling us the, the number of particles. Yep, I will have an average number with some fluctuation some oscillations are on this number.
antonio: And this is a problem that will happen in BCS theories and in being filled theater. What I'm going to describe and that we need to address.
antonio: Okay. So after that, let me begin with the motivation of of my project. So okay, so in nuclear we have protons and neutrons. Right. So, in principle, we should expect
antonio: A proton comparing need from us from Paris, but also proton, neutron pair.
antonio: Howard this proton, neutron pairing correlations are usually neglected in most of the calculation, a new class structure.
antonio: And this has a PC calories on physical basis is because the Fermi surfaces. So they states of the lexical pie proton and
antonio: Neutron are very different are very far away and then they don't allow a huge an overlap between the states and therefore we don't expect to have
antonio: To form opportunity from her. However, this is no longer true in the region, with no credit chart where nuclear nuclear has around the same number of protons and neutrons around n equals said nope that
antonio: In this case, the Fermi surfaces are very similar if not the same. The and therefore these assumptions, no longer valid. You can find a proton, neutron pair, along with a light particles pair. So a proton proton or a neutral. Neutral Nazis don't NBC a schematic here.
antonio: However, so we should expect coexistence between proton, neutron purse broken proton and neutron from parents
antonio: However, the square assistance is quite elusive, and I quote, know symmetry and restricted meet the calculation of proximity comparing it with
antonio: With so speak on certain forms have been carried out. So this was your motivation, actually. So, we will start from scratch, we will build a meaningful implementation in order to describe this quick systems.
antonio: But also using symmetric restoration on top of this.
antonio: And since we are building everything from scratch. We need to start with a very simple simplistic and interaction to start with.
antonio: So for that interaction we choose these so eight algebraic model.
antonio: And if you're familiar, maybe with the A. So three model algebraic model that was used for the description of angular momentum at this is basically added mathematically it's the same HST Nathan mentions
antonio: So this is a model that is that has been used widely in the local community because he has an analytic solution.
antonio: So you can compare any of your methods with the exact results from this, from this model. So this model relies upon this pairing Hamiltonian here, which consists of two
antonio: Terms of to contribution. So on one hand you have this so better contribution, based on the on this pair creation articulation operators and this purse are coupled to total access being equal to one. That's why it's called I soap actor and total expenses.
antonio: So,
antonio: So maybe having described what is a sustained. So maybe, for those of you who are not familiar with this concept I suspicious. An additional quantum number.
antonio: For new plans that tell us if these certain nucleus at a particle is a proton or a neutral.
antonio: So, it brought in some new topics being one health we say that article have has ISIS being one health therefore having projections minus one half or one have telling us if that particle is a neutron or a proton.
antonio: So in that way in in instead of saying that we have a certain nucleus with a certain number of protons on certain number of neutrons, we said that we have a certain nucleus with a sad thing. So spin
antonio: And the assessment projection will tell us about the difference between neutrons and protons divided by two. So, we will know that it's just it's analogous
antonio: To the proton and neutron numbers in numbers, but he's just mathematically easier to treat them this way.
antonio: So if we have this actual vector pairs that are coupled to total ISIS being equal to one and therefore we have these three different projections minus one that will correspond to to
antonio: Protons a serial that we correspond opportunity and one that we correspond to a new frontier from her.
antonio: On the other hand, we have this term. The these exosphere contribution, based on the on the operator of these pair creation articulation operators.
antonio: That are I just cannot curse now exoskeleton, because we took our actual spring is equal to zero is football or soccer they spin triplet term where now we have obviously all the proton, neutron pairs with different orientations of this being projection
antonio: So the rest of the elements of the spring Hamiltonian is this coupling custom gene, which is not really relevant because you could always we scaled Hamiltonian by base a constant.
antonio: And these mixing parameter x, which is more interesting because he's a tuning parameter, they will tell us the relative competition between the spectrum. And it was clear contributions. So for example, if you have x equals one.
antonio: These term vanishes and you only have a sister contribution on the other way around. If x is equal minus one. These malicious and for money. So effects in between minus one on one, you have
antonio: Productive competition between the two specific sorry specific specifically for x equals zero and we have an equal strength in both interactions.
antonio: So, as I have said before we see some way to use model because the ground state energy and the corresponding wave function.
antonio: It can be obtained by the organizing this Hamiltonian here, so they can be obtained. Exactly. So any meaningful method that we're going to develop that can be directly compared to the exact results out of this month.
antonio: Okay, so let's start out with a meaningful description.
antonio: So we are going to use a heartfelt bubble you both approach, which is basically a generalization of the single particle heart we folk
antonio: Approach it I will happily study doing all quantum mechanics course but it to include this parent correlations
antonio: So, it relies upon the transformation from the single particle basis is bound by the operators creation. And here's some operators.
antonio: A dagger to the quasi particle basis, a beta a total transformation is keeping here. And because we're going from message to basis has to be unitary
antonio: So the question they should be a function built in this way, also called a quasi particle vacuum and what will serve as the ground, the state of our nucleus.
antonio: It will be defined as the as the way function that he said he highlighted by this policy party articulation operator.
antonio: Now you can immediately see that in this transformation from this to this basis we are mixing particles on hold because we're mixing operators related to the critical for particle
antonio: And the destruction of a particle or the creation of a whole therefore a particle number will be violated directly by the way function.
antonio: Because we're mixing particles on holes, but this is not ending here. You can also mix. Any other degree of freedom, for example, and we do. It's been an interesting
antonio: And therefore, as being an so spin symmetries while their respected by the pairing Hamiltonian that I have interviews before they will be broken, and they will need to be restored after
antonio: But this needs to be done because this is the this is the way where you can explore different possible potential configurations of the system.
antonio: So that we function that is building this way is very can be very complex. However, a solace theorem tells us that the way function of I'm even nucleus can be written
antonio: A proportionate to the exponential of all the parents consider in the system. So in our case it will be all these pairs that are considered in the pairing. So if Hamiltonian
antonio: So if we assign a number of parameters are kind of known to all of these pairs, then we can build the, the energy surface as the sandwich of the Hamiltonian with us back this way function and minimize it. And then when we minimize it. We will find
antonio: A number on around the state energy that we expect that it will be close to the exact result.
antonio: But not only that, but for these a minimum we should expect that the norms here of the ISIS of the proton, neutron proton proton and neutron. Your parents are kind of the same. And therefore, we can conclude that there is coexistence in the snow, please.
antonio: Okay, so, but before that we need to address the problem of breaking the cemeteries within these way function.
antonio: Because the way function that we are building are going to be. It's going to be a superposition of states with with quantum numbers in our case it would be particle numbers being an actual state.
antonio: And so yeah, so there will be two Asians and we, the results are not gonna be as good
antonio: As if you instead of using the word function you use these states with quantum numbers. So you can say, okay, so why don't you use this estate.
antonio: What problem is that you don't usually have these states from the beginning. In most of the calculation. Most of the time you don't. However, you always have a gap with function.
antonio: And you can extract from the subject. We will function in the state with the good quantum numbers good particle number spin and spin
antonio: This can be done. Sorry. This can be done by, by means of projection methods. So by the application of these operators that I'm not going to give the expression, maybe they'll need to be too heavy, but if you apply these operators.
antonio: Today to be with function, you could extract this estate with would quantum numbers and where we call their projected estate. This is not accepted state. If you sustain an approximation, but this is state we have concert symmetries.
antonio: Now with this a with this is state, you can compute now that project that energy
antonio: We've seen the suspect instead of the HF B wave function.
antonio: But now, at this point, we have a choice to make, because we can say okay
antonio: I have a chubby we function I build their the surface and then I minimize it. I find the optimal HTTPS state right and it's only at this point where I will restore the broken symmetries and
antonio: I will apply this projection operators and then we will obtain some energy. This is yes of course this is a valid method is called the projection after variation method because we minimize first we create and then we're starting to see metrics we project.
antonio: But also we can proceed the other way around. And this was a turning point in our, in our periods in my PhD, because you can
antonio: A construct that project that energy surface so you can apply the brilliant show operative restaurant asymmetries at all points considered in the energy surface or at least
antonio: At all the points considered along the path of gradient descent or any other minimization solver to go to the minimum, a decision was another method and you will find another optimal state and then you will find another energy
antonio: So which one of these methods will work better. Well, the variation of the projection should must what must work better. Always because all of these methods rely upon the variation of principle in quantum mechanics that tells us that
antonio: You don't know the exact way function, you almost never know. Like subway function. So you start with announcements.
antonio: If you compute the energy with these answers you will always have an upper bound to the exact energy
antonio: So this upper bound will be closer and closer to the Accept energy to accept result if the answer is closer and closer to the except we function.
antonio: And of course, using a wave function, which has a always seem to be restored is going to be a much better answers than using HTTP with function that that all these cemeteries are broken.
antonio: So because they accept we function, obviously we have all of these things that we've restored and we will see that in a in a second, that in this method is going to work much better.
antonio: Okay, yes. So no, sorry, let me just say something. And so, so okay so we should always use this method right
antonio: But the problem is is computationally very costly, because we need to apply these projection operators which are computationally costly to print them and because they involve integration over all the possible configurations of the of the system.
antonio: Of the symmetry generator. So, this usually around three dimensional intervals. So they are very costly to implement and computers are going to have a hard time trying to
antonio: win this calculation. So that's why this is usually not implemented in most of the release the calculation because of all the time.
antonio: They will take if not impossible and. However, since we're starting from a very simplistic method and a very simplistic interaction we could actually perform it. But it's not always doable.
antonio: Okay, so with that being said, let's go to to to see some results.
antonio: So in this first finger here I plot the plot the energies we scaled by these coupling custom D as a function of the mixing parameter x. That was in the apparent Hamiltonian. And I recall
antonio: That this was during the competition between the two scanner. So vector interactions. So if you go to the right, you will have a stronger so scary interaction. If you go to the left, we will have a stronger so back for interaction.
antonio: So we plot here the energies for the three different methods that I have described before, and we compare them to the to the to the exact results from this right model given by the solid line.
antonio: So we immediately say that the these variations, a prediction method works wonderful with the words. Wonderful. So the points are almost on top.
antonio: Of the except for souls, so there is only a difference or on x equals zero of around 1.5% but also I recall that the values affects their range of x was from minus one to one. So I have seemed here.
antonio: From minus 0.22 0.2 in order to see the difference that we will not see to the naked eye. If I use the full range.
antonio: A now the projection of the variation approach that's better than the HF B approach, of course, because we're restoring the symmetries.
antonio: But still the only difference is just apparently just a shift. So, but the shape of the curve is the same, right. So we just assume it's like as if you try to get this curve down
antonio: But it doesn't reproduce perfectly their behavior around x equals zero. So we're both a guideline selector interaction in the bedding Hamiltonian aren't the same.
antonio: So we should have kind of like a smooth hail here waiting here we have a very sharp it. So this is no were produced by using all the objection after variation approach me to go
antonio: To use the above approach. So okay, so we have described the energies. But what about the pairing persistence. This is what we wanted to do when we went to the square in the beginning.
antonio: And in this plot in this figure here we plot the SS killer norms. So basically the parameters then open the process of ISIS killer Paris in the way function.
antonio: And we plotted using data be method, whereas I'm showing up the mixing parameter using their kids we method for which it follows I steps like core
antonio: So, for I struggled so the interaction. We don't have access to our parents at all.
antonio: And for a stronger ISIS killer introduction, we only have so scared or Paris, because as a square norm is one that some of the ISO vector and this was killer nones has to be one because there's nothing else in the system.
antonio: So all the, you know, who each one very close around x equals zero, we can find a quick systems.
antonio: However, for the evaluation of the project should approach to have this very nice increasing curve.
antonio: Of this is killer norm as you increase x. So, this is telling us that there is click systems for all points for all values of x for all interactions are positive interactions.
antonio: Apart from the extreme limiting values of minus one and one where you only have a suitcase. So back to our people. So school. So back to interaction.
antonio: So this is what we wanted to see in the beginning. So we're really happy to see this figure, because we wanted to describe this. And we actually see that we can obtain this so
antonio: This was like a, like the breakthrough my PhD and or maybe breakthroughs too much of a word, but we wanted to see this. And we actually sought. So we're you can understand the feeling that we got when we saw this picture.
antonio: And what okay so we expect that we can port this technology of the meaningful method blast by each of their production approach for the restoration of broken symmetries using a much more realistic interaction, because this is completely independent of the of the interaction, but the
antonio: Realistic interaction. I should have structure setting is needed to see if we can observe respect sister is what
antonio: I'm okay. But what I have shown before are really a killer norms or kind of like the number of parents, but this is not really an observable, you cannot really measure them. Look at you can only see them.
antonio: However, there is a potential link between all of these theoretical methods and experiment, based on the different transfer. So the neutron. Again, it's about a pair of our proton and neutron
antonio: So it turns out that the neutron transfer is related to this d their creation operator.
antonio: And these the was a part of the Hamiltonian described double. Therefore, we can obtain the exact reduced metrics elements of this operator, but we can also thing this reduced metrics elements.
antonio: Using the usual me feel techniques and we can compare them again. So let's see what we obtain. And so this is neutral addition to a state with a bang a particle number a spin zero. And I just been t
antonio: In the, in the figure of the left we plotted for several bottles of the ISIS being of the total. So speaking of the system. So this with the notes. They put a mutual imbalance in the in the system.
antonio: But also for several particle numbers and we see again that the that the accuracy is quite remarkable because you cannot really tell that the points the symbols that correspond to orbit calculation.
antonio: Are really not on top of where they are really on top of the solid line which correspond to the exotic assault. So again, this is another proof of the great accuracy of this method.
antonio: On how we if we can
antonio: You know way be an experiment. And then we can maybe see something like this which is not exactly what is going to be found in our, in our lives from transfer reaction.
antonio: But if we can actually describe this. This results, we can infer that there is bearing consistency nuclei, because these theoretical method is telling us so
antonio: Um, okay. So with that, I would like to to go to their conclusions. And so really the main takeaway message that I wanted to
antonio: To convey here is that this elusive bearing coexistence between proton, neutron pairs. Unlike particle person can actually be described within meaningful methods that
antonio: Everybody likes I think because they can be used widely all along the local chart a but properly restoring the symmetry. Some by properly we mean using this variation after prediction approach, which takes a lot of competition on time.
antonio: So this is maybe at the moment, it's not quite realistic to do a full calculation using a realistic. Let's say density functional interaction at least dictionary structure setting but
antonio: It's not feasible. It's not doable but computers improve every year. So who knows, maybe it's not that I'm realistic in the near future.
antonio: Um, and then there's no hope, of course, or what they have said so this technology needs really to be ported
antonio: You synchronicity interactions on cello structure settings and this is the work that the new PhD students in New York power will be doing so we need to we need to stay tuned to see new resource to see what we have.
antonio: Okay, so, um, with that, I would like to thank my university again and the science and technology facilities Council, where my funding came from. And I also would like to thank you for your attention.
Tzany Kokalova Wheldon: Thank you. I thank you very much. Antonio, that was really very interesting and also quite educational as as an experimental is, I have to say I really appreciate it. You're
Tzany Kokalova Wheldon: In a way, rhetorical ability to explain some complicated concepts in simple terms, thanks a lot. So if there any questions, please. Now is the time to ask your questions as I said you can use the chat.
Tzany Kokalova Wheldon: And James is looking after the chat. So we're not going to meet that question, or you can just raise your hand.
Tzany Kokalova Wheldon: And I can see some raised hands already
So,
Tzany Kokalova Wheldon: In no particular order. I will start with yardstick.
Tzany Kokalova Wheldon: Okay, yeah, it's like if you would like to
Jacek Dobaczewski: Yours are clapping in recognition of the quality of that. Oh, sometimes presentation the race looks differently today.
Tzany Kokalova Wheldon: Oh apologetic, I am without
Tzany Kokalova Wheldon: My glasses to be on
Tzany Kokalova Wheldon: I can do see a blue hand. Yes, you're right.
Tzany Kokalova Wheldon: Well, I'm sure. Excited apologies for that. But anyway, so you're free to ask questions. If you want an hour probably just asked my question before people find where the right hands is
Tzany Kokalova Wheldon: So, Antonio,
Tzany Kokalova Wheldon: I you mentioned this at the beginning as well that you've used the so eight
Tzany Kokalova Wheldon: So I was just wondering if you can just explain just an easy question, in a way, if you can explain a little bit more which a dimensions and white.
antonio: Yes, well, because we want to describe a this is a scheduler is a better price of this a dimension is because we take and all of these possible pairs into consideration. So it is a dimension means that
antonio: We have all of these generators of this group. So it's really this algebraic model. So I don't I don't recall on top of my head all of these different operators, but
antonio: They were these so called PR creation, the installation as well. This was killer one the number operator. And I think he was the GM of teller or some as equal one, and he was being equal one operators.
antonio: So really, the dimension of the model is to take all of these possible PR creation and operators, but
antonio: This So wait, is various is completely similar to the so three A algebraic model that was describing Angra momentum that was taking us operators Ella square and or org a square. And he said,
antonio: So, in, in essence, these eight yes means it all, then all the possible generators of the group.
antonio: I don't know if that
Tzany Kokalova Wheldon: Thanks, you know,
Tzany Kokalova Wheldon: I was trying to calm myself.
Tzany Kokalova Wheldon: I noticed you find kind of like missing something there.
antonio: I go, Well, I do prefer to these paper here. Where do they solve everything. And I think if I recall correctly, there were like 28 different operators in this
antonio: In this algebraic model. So I don't recall them on top of my on top of my head.
antonio: But it's basically, it works. Mathematically it works the same. And they have the same how you say it structure constants that these computational relations as there is for three model is yes without different number with a different dimension.
Tzany Kokalova Wheldon: Thank you. So I i've read several papers. So I have a little bit of experience with so they although I'm an experimental is that quite good papers.
Tzany Kokalova Wheldon: When they're using. So 13 the clustering area which is my experimental area. So in this direction, if you don't mind me asking another short question. I just want to be sure that there is nobody
Tzany Kokalova Wheldon: Who wants to ask a question. I'm kind of like taking the space and the time and you like nuclear clustering. So what we showed there is quite exciting. So
Tzany Kokalova Wheldon: Enlightened certainly when I was seeing what you were showing the first thing, of course, was okay. Well, what about the alpha particle, because you have
Tzany Kokalova Wheldon: Two programs to neutrons and pairing there we know is very important. So, and how far you can go as well there. Have you tried already because, for me, the easily. The easiest to try will be something like alpha particle or brain to mate.
Tzany Kokalova Wheldon: With your small numbers.
antonio: So I don't know if you are aware of this, but there is also an alternative picture of this pairing correlation based on this quartet modeling.
antonio: Yes. Okay, so what we claim here and what we claim in the in the paper that we published is that these are really like two sides of the same coin.
antonio: Because for the cases of a equal, so I don't have the plot here, but for the cases of a equal for
antonio: A method that we use here who really nailed down to the to the accepted way functions that were also described by these a quarter the modeling formalism. So what we what we came here is that it's the same
antonio: Is yes to that by using these meaningful techniques you can add some spurious correlations when you increase the number of particles.
antonio: However, they wave function that we use is completely general while when we read these these papers in the court that the formalism.
antonio: And you need a specific way function because he has to be the exact one for all the possible Casey. So if you have an answer spinning balance or if you have
antonio: Um, well, I don't remember that. Or if you have like a BCS
antonio: Well documented over my head, but there were several papers and they and the difference was always in the way functional they were using
antonio: Well, in our case is completely general we have one way function one set of prediction operators and then it just depends on the quantum numbers that you want to project on
antonio: So, so we we know they claim they will not work as well as as our technique, but this technique can be applied everywhere.
antonio: That's the advantage of using this
Tzany Kokalova Wheldon: Thank you, sounds promising and also the fact that you converge is quite good now.
antonio: That's already that the convergence.
Tzany Kokalova Wheldon: In the fact that you have the same results you get to the same results.
Tzany Kokalova Wheldon: Is also good.
antonio: Yes. But again, this is a simplistic model. So we really need to to know what is happening in our, in our realistic calculation. But yes, but it's interesting.
Tzany Kokalova Wheldon: Thank you very much.
antonio: Thank you.
Tzany Kokalova Wheldon: You mentioned that somebody else will be working on this as well. And you yourself have moved already to a different area.
antonio: And yes, yes. I'm not working on this anymore. Yes. Okay.
Tzany Kokalova Wheldon: Thank you very much. So, um, any questions, just a second.
Tzany Kokalova Wheldon: I don't see at the moment. Anything but I don't have my glasses so
Tzany Kokalova Wheldon: James, please.
James Smallcombe: It seems everyone was quite satisfied what talk
Tzany Kokalova Wheldon: Okay, so if there are no other questions, I guess. I mean, it was a very clear talk and the subject is, as you said, very simple, but
Tzany Kokalova Wheldon: Complicated enough that probably some of our students may feel a little bit intimidated to ask something so if you have, if you have any questions, please. You can also contact James, or you can write to us. If you want to ask something later.
antonio: Otherwise, there's my email there.
Tzany Kokalova Wheldon: Or. That's very kind of you, Tony. Thank you very much, or you can contact directly Antonio and ask up, otherwise I will wish everybody a wonderful day.
Tzany Kokalova Wheldon: What a lovely way to start the Monday we deny stoke as well in the afternoon, and please tune up for the next one, next session or next docs, which is if I'm not wrong next week.
James Smallcombe: No, we actually we've got student talk on Wednesday, but that's hosted by Manchester. The undergrads also we've got a talk on Friday and the plenary session so that same time
Tzany Kokalova Wheldon: It's actually even better than I thought. Thanks. Hello, James.
Tzany Kokalova Wheldon: Thank you, Antonio,
Tzany Kokalova Wheldon: Thanks.
antonio: Yeah. Thank you. Thank you, everybody.
Tzany Kokalova Wheldon: everybody for joining us. Have a lovely day.