## Superallowed Gamow-Teller decay of the doubly magic nucleus 100Sn

This is the second Nature paper I am a co-author of! The first one was about the nucleus 92Pd and this one is about the nucleus 100Sn, both in a similar region of the nuclear chart. This new paper even got a short survey in the journal, that I have written more about here. Before I get into details about what we did, let me quote the editor’s summary:

“Gamow–Teller (GT) transitions are an important feature of radioactive beta decay, which is relevant to many astrophysical processes. Yet the strength of GT transitions is difficult to find experimentally, because beta-decay studies can generally see only a fraction of the total GT strength. Theory suggests that the GT transition in the short-lived ‘doubly magic’ tin isotope 100Sn is likely to be unusually accessible to study. (In a doubly magic nucleus, both the proton and neutron shells are full and therefore relatively stable.) Christoph Hinke and colleagues now report measurements of this exotic nucleus in a milestone experiment in which 259 100Sn nuclei were produced, a factor of ten more than observed in any previous experiment. The half-life is 1.16 ± 0.20 seconds, and the GT strength is the largest yet measured in nuclear beta decay, confirming this as a ‘superallowed’ transition. The work establishes 100Sn as a model for nuclear-shell-structure calculations and is relevant to the understanding of nuclear processes in stellar explosions and for studying neutrino properties.”

OK, this sounds very fancy but threre is two main points in this that I think is interesting and that I will tell about in some more detail. One of them is the Gamow–Teller transitions, named after the two famous physicists George Gamow and Edward Teller. The second point is the so called log(ft) value, which is basically the half-life of the nucleus. Of course, these two conceps are related to each other as a high transition strength implies a short half-life, and vice versa.

Anyway, the experiment was one of the first experiments I participated in as a doctoral candidate. It was done at GSI using fragmentation of a high-energy 124Xe beam on a beryllium target. The details of this is not really important, more than the beam hits the target at a high energy, gets smashed to pieces and the pieces we are interested in gets selected from a cocktail of different nuclei in the same region.

What makes 100Sn interesting then? Well, I would say for several reasons, but since this was a β-decay study I will focus on these aspects. When a nucleus β decay it can in principle do this in two different ways. One of these ways is that a positron–neutrino pair is emitted with parallel spin, which is the Gamow–Teller transition I have mentioned earlier. The other way is that a positron–neutrino pair is emitted with anti-parallel spin, which is called a Fermi transition, named after the famous physicist Enrico Fermi. Now, why would we care about the difference between these? The reason is simply that since the Gamow-Teller transition changes the spin of the nucleus, these transitions are more sensitive to the underlying nuclear structure. The problem with the Gamow-Teller transitions is that it is quite difficult to study, since the decays are distributed over many final states. The good thing about 100Sn is that the Gamow-Teller transition is predicted to be very clean. The reason fort this is a heavy, doubly magic nucleus where the protons and neutrons are moving with high angular momentum and that there is a large energy gap to the neighbouring nuclei. By measuring the β-decay energy-distribution we can find how strong this transition is.

If this transition is strong, which this paper shows it is, it give the nucleus very particular life-time properties. As I stated earlier, a high transition probability gives a short life-time of the nucleus. This is the mysterious log(ft) value. The value is given as a logarithm, and the “f” in this case is a correction to the life-time that comes from the energy of the transition. A high energy transition has a shorter life-time, but by including this “f”, we can remove this dependency in our studies. Taking all this into account, the nucleus 100Sn should have one of the smallest log(ft) values found in nature. And, as we found in our experiment, it actually does.

Ther have been some other attention to this paper as well over the internet, see for example:

The Technische Universität Münchens press release, Tin-100, a doubly magic nucleus, also published in ScienceDaily, as Soon After the Big Bang, Heavier Elements Emerge, and in PhysOrg, as Tin-100 produced in key nuclear physics experiment. Also the University of Surrey made a press release, Doubly Magic nuclear physics answers fundamental questions about the universe, followed by a brief post in the Blog of the Isotopes, The Nature of Tin-100.

## Nuclear physics: Symmetrical tin

In the same issue of Nature as the 100Sn paper, a short survey about the importance of the nucleus 100Sn was also published. Therefore, I have decided to split the post about 100Sn into two; one that goes into more detail about the results in the 100Sn paper, and one that outlines the special properties of 100Sn in a more general way. This is the more general one. Since a lot of the interesting physics in this short survey is explained very well, I will include several quotes from this paper.

The, what is the properties of this nucleus and what is the big deal about it? It all comes back to the magic numbers. A magic number, in nuclear physics, is basically certain numbers of protons and neutrons where the nucleus is more tightly bound. This is a basic property of the nuclear force and the magic numbers are 2, 8, 20, 28, 50, 82 and 126. In other words, oxygen, with eight protons, is a tightly bound nucleus and 16O, with eight protons and eight neutrons, is even more tightly bound.

“One would expect that symmetrical doubly magic nuclei, which have an equal magic number of protons and neutrons, would follow the magic number sequence, and this is indeed the case for light nuclei: those of helium (4He), oxygen (16O) and calcium (40Ca). However, because of the repulsion between protons, the line of stable nuclei in the nuclide chart veers away from the symmetry line, as ever more neutrons are required to bind heavier nuclei. [...] Therein lies the particular attraction of 100Sn: it is at the same time doubly magic and at the edge of the nuclear landscape. Many long-standing questions about this oddball are now beginning to be answered. For example, is it really doubly magic and simple in structure?”

Now, 100Sn is not easy to produce and study. In the GSI experiment, about 250 of them were produced in total. This can be compared to the earlier experiments that, altogether, produced about an order of magnitude less, that is around 25 of them. So this is a great achievement indeed. With these statistics it was possible to study how this nucleus decays. There is a large energy difference between 100Sn and 100In (the nucleus it decays to) and the transition is expected, and now also found to, be very pure. Thus, it is one of the best testing ground for the nuclear shell model. Or, as the short survey states:

“The results of the authors’ experiment represent a giant step compared with previous attempts to study 100Sn. [...] As always happens with scientists, once they have been given a taste of a new delicacy, they crave more. Other laboratories have joined the race and are working to improve on the GSI 100Sn production rates. They include: the Radioactive Isotope Beam Factory in Wako, part of Japan’s RIKEN national network of labs, which has recently synthesized 100Sn nuclei; SPIRAL2 at the heavy-ion accelerator GANIL in France; and the Facility for Rare Isotope Beams at Michigan State University. These facilities will produce this remarkable nucleus, as well as many others, in even larger quantities. Deciphering the emergent properties of 100Sn, and of other nuclei located far from the stability line on the nuclide chart, should lead scientists towards a fuller understanding of the nuclear force.”

Yes, that’s where I am now: The Radioactive Isotope Beam Factory in Wako, part of Japan’s RIKEN national network of labs. And we have another run of 100Sn that is preliminary scheduled at the end of this year, maybe in December. So I’m in a really great position to help out the continuing study of this nucleus. Hopefully we will be able to reach 10 times higher intensity, which would mean that the 250 nuclei produced in GSI will be 2500 nuclei here at RIKEN. This amount of 100Sn could really give exciting information about what is going on in this region.

## Algorithms for pulse shape analysis using silicon detectors

Pulse shape analysis of output signals is a hot topic in instrumentation development for nuclear and particle physics detectors. Since we are reaching further and further out into the unknown our tools are getting, relatively, more and more blunt. We have to find some way to sharpen them so we more carefully can study rarely occuring exotic processes. And studying the pulse shapes out from the detectors is a good way to squeese extra power from our intrumental tools. This is, for example, one of the basic ideas behind the AGATA detector array and the new neutron detector array. But, as shown in a newly published paper, this can also be done for silicon detectors.

What the authors of this paper want to do is to study proton-rich nuclei that decay by emitting protons or alpha particles. They do not only want to find these decays, but also measure the energies. In a normal situation without pulse shape analysis you would get, from a silicon detector, an output that is proportional to the energy deposited in the material. But if there are several decays like, in their example, when the nucleus 109Xe decays to 105Te that decays to 101Sn this does not work. You would just get a total energy that is the sum of these two decays. But by looking at the pulse shape it is possible to distinguish these decays by the small time difference between them.

What the authors have done is to develop a couple of algorithms to fit an average pulse shape to the experimental data. In the case of two pulses from two alpha decays, they have used two average pulses together in the fit. The result, as seen in the picture above, looks great. In the bottom right corner is the pulse from two decays stacked on top of each other. The single pulse, of course, does not work so well. But the fit with two pulses is almost indistinguishable from the real data. In this way they can not only find that there were two alpha particles that decayed, but also find the energies of these two particles. This kind of technique will hopefully be valuable in the future when we want to understand nuclear physics far out in the unknown regions of radioactive nuclei.

## Compton polarimetry with a 36-fold segmented HPGe-detector of the AGATA-type

The reason it is important to measure polarization is that this can give us unique insight into the nature of the γ rays emitted, if they are of electric or magnetic nature. The first question at this point, I guess, is what is the difference between an electric or a magnetic γ ray? Should they not be the same since the electromagnetic force is one? The answer to this question is polarization. A wave can be polarized if the direction of propagation and the direction of vibration is different. Since the room has three spatial dimensions (not considering the black magic of string theory), you have the propagation and the vibration in two directions and nothing in the third. If you switch the two directions of “vibration” and “nothing” you also switch between electric or magnetic wave.

The second question is why this is important in nuclear physics? The answer to this is spin and parity. A γ rays of a specific type can only connect certain combinations of spin and parity with each other. An electric γ ray can connect some spin- and parity states, while a magnetic γ ray can connect other spin- and parity states. This means that if we know the spin and parity of one state, but not the other, we can measure the type of γ rays emitted, their polarization, and from this find the spin and parity of the unknown state.

In practice this is done based on the fact that electric and magnetic polarized γ rays have different probabilitys to scatter in different angles when they hit the detector. The standard way to do this is to have three detectors: one in the center, on on top and one on the side. If the γ ray first hits the center detector, we can count the number of times similar γ rays scatter to the top detector and the number of times they scatter to the side detector. These numbers should then be different for electric and magnetic γ rays.

Now, with the AGATA detector array, we have a whole new possibility to do this. Since AGATA is divided into several segments, we do not need to have three detectors arranged as described above. Instead we can look at the scattering within a single detector. Plus, by adding more detectors we can increase the detection power of polarized γ rays significantly. A study of how well this works in practice is what is described in the article this post is reviewing.

## Monte Carlo simulation of a single detector unit for the neutron detector array NEDA

There is a lot of activity in instrumentation for nuclear physics these days. The reason for this is the construction of several advanced accelerator facilities for radioactive ion beams. One of these projects that are ongoing is the neutron detector array NEDA at SPIRAL2, which is also the focus of a recently published paper. But before I discuss the NEDA detector, I would like to share a qoute from the Greek poet Callimachus, Hymn 1 to Zeus. This quote is also the origin of the name for this detector array.

“Lifting her great arm she [Rhea] smote the mountain [Mount Ithome] with her staff; and it was greatly rent in twin for her and poured forth a mighty flood. Therein, O Lord, she cleansed thy [the baby Zeus'] body; and swaddled thee, and gave thee to Neda to carry within the Kretan (Cretan) covert, that thou mightst be reared secretly: Neda, eldest of the Nymphai who then were about her bed, earliest birth after Styx and Philyre. And no idle favour did the goddess repay her, but named that stream Neda; which, I ween, in great flood by the very city of the Kaukonians, which is called Lepreion, mingles its stream with Nereus, and its primeval water do the son’s sons of the Bear, Lykaon’s daughter [Kallisto] drink.”

But enough with the Greek poetry already, let’s return to the NEDA detector. There are many aspects that are relevant when designing a new neutron detector array. Some of these are the geometry of the detector array, the electronics and readout that will be used in the neutron detector (actually, my first paper was about digital electronics algorithms for neutron detectors), but also the properties of the detector cell itself. The newly published paper is about the detector cell aspects.

To test different detector properties in physics, it is quite common to do Monte Carlo simulations of the setup. This means that one designs (a simplified version of) the detector and the radiation to be detected in a computer and then let these two interact with each other. The interaction is selected by random, based on the probabilities for different possible interactions, and the radiation is tracked on its path through the detector. Then it is easy to change the computer model of the detector and see how this affects the performance. This, of course, requires a good understanding of the physics processes involved. So a good thing to do is to copy a detector design that is already available in the lab and make sure that the computer gives the same results as the real life stuff. I will not go into the details of the simulation verification and the effects of changing the geometry here, but I recommend reading of it in the paper itself.

Another important aspect of the detector design is also what material that is used for the detector. In out case, we want to use a liquid organic scintillator as detector material. This means, in principle, a hydrocarbon liquid similar to benzene. The material that has been more or less standard in these kind of arrays is called BC-501A, manufactured by the Bicron company. The exact formula for this material is kind of a company secret, and I don’t know it, but it is basically hydrogen and carbon. One open question, however, about the material was whether it might be better to use deuterium instead of hydrogen in the mix. There has been some indications that the deuterium based scintillator, BC-537, might be a better choise because it would be better at determining the energy of the neutron. The DESCANT neutron detector array (in its design phase) at TRIUMF is based on this idea. The simulations in this paper, however, shows no real improvement in using a deuterated liquid scintillator. But more detailed experimental tests on both types of detectors are ongoing and these might change the picture, even if the preliminary results are somewhat discouraging.

## AGATA – Advanced Gamma Tracking Array

The massive AGATA paper has finally been published. The work I did on AGATA was one of the parts of my PhD thesis. The other two parts being the collective nuclear structure around 170Dy and development of neutron detectors. However, the AGATA detector array is a huge effort made by many people, so I will try to describe the features of the detector here.

When studying the structure of atomic nuclei, their emission of γ radiation are a very useful thing. The energies of these γ rays can tell us the shapes of the nuclei, how stiff they are, if they are rotating, how the particles are flying around them and a lot of similar things. However, to see this we need good detector instruments, especially for short-lived radioactive nuclei that quickly decay into something else.

A common material for studies of γ rays is high-purity germanium crystals. Germanium is a semiconductor material with characteristics that makes it possible to measure the γ-ray energies with a high precision. This has been used for many years, where big assemblies of many crystals have been built, that can detect as much of the radiation as possible. But, there are problems with this as well. For example, often the radiation does not leave all of its energy but leave the detector to go somewhere else. Also, the crystals are quite big, which means that if the nucleus is moving with a high speed, the Doppler effect makes it more difficult to sort out the energy of the γ ray, since we need to know the angle between the γ ray and the nucleus, and a large detector will not tell us that very precisely. All of these problems can be solved by segmenting the crystal into smaller pieces, but there is still a problem. If many γ rays hit the detector, it is difficult to know which segments belong together and which segments do not.

To carry out this difficult task we first of all need to know where the γ rays have hit the detector more precisely. Sure, we know which segment that we read the information from, but this is simply not enough for us. There are some tricks to get this information by looking at the voltage pulse from the crystal. For example, the closer to the centre of the crystal the hit was, the faster the voltage pulse will rise, simply because the distance the information need to travel is shorter than if the hit was in the outer part of the crystal. Now we know how close to the centre the crystal was hit, but we can also know where in the sides this happen. Since a hit in the crystal will create an electromagnetic field this will be seen also in the segments next to the hit one. By comparing the sizes of this influence between these segments, information about where the hit was can be determined quite accurately.

When we now know the details about every hit in the crystals we can use this information to reconstruct the tracks through the entire assembly. Since we know that most of the γ rays are bouncing around through the so-called Compton effect, we can do some calculations about what the energies should be and compare this to the measured energies. If we try this several times we will, sooner or later, find a matching track and we know how the γ ray has travelled. The information we have gotten out of this quite lengthy procedure is the energy of the γ ray and the angle it was emitted. And now we are ready to do some nuclear physics. To summarize:

For more information about AGATA you can visit the AGATA detector array on Facebook, the official AGATA webpage or the webpage of the AGATA Collaboration Council.

## Zeros of 6-j symbols: Atoms, nuclei, and bosons

The fundament of small-scale physics, like nuclear physics and particle physics, is a what is called quantum mechanics. And one of the fundamental quantities of quantum mechanics, in terms of nuclear and particle physics, is what is called angular momentum. Angular momentum in quantum mechanics can, in principle, be provided in two ways. Either is can be via particles spinning around their own axis (although this is a very simplified picture), so called spin, or by particles orbiting some reference point, so called orbital angular momentum.

This sounds simple enough, right? But, what happens if we want to add these angular momenta together? If we, for example, have a neutron and a proton that are bond together in a deuterium nucleus? In this case we might have a proton with spin 1/2 and a neutron with spin 1/2 pointing up, and if we want the deuteron to have spin 1 pointing up there is only one way to do it. We have $1/2\uparrow + 1/2\uparrow = 1\uparrow$. On the other hand, if we want the deuteron to have a spin pointing neither up or down there are two ways to do it: $1/2\uparrow + 1/2\downarrow = 1$ or $1/2\downarrow + 1/2\uparrow = 1$.

In nature both of these ways are equally probable, which is quite obvious. A mathematical way to write this relation is $|1,0> = \sqrt{1/2}|1/2,1/2;1/2,-1/2> + \sqrt{1/2}|1/2,-1/2;1/2,1/2>$. This might look a bit complicated, but it is really not. Basically it says that the deuteron has a total of spin 1, of which an nothing is pointing up (or down). This can be realized in half (1/2), the square root is because probabilities have to be summed in squared, of the cases by the proton having a total spin of 1/2 of which 1/2 is pointing up while the neutron has a total spin of 1/2 of which 1/2 is pointing down. In the other half (1/2) of the cases by the proton having a total spin of 1/2 of which 1/2 is pointing down while the neutron has a total spin of 1/2 of which 1/2 is pointing up. These values of $\sqrt{1/2}$ are called the Clebsch–Gordan coefficients for a given system, after the mathematicians Alfred Clebsch and Paul Gordan.

Now, I have used a quite simple example where it is obvious that the probabilities are the same, but for more complex systems it is not always so obvious. For example, if we want to combine a particle with spin 3/2 and a particle with spin 1 into a system with spin 5/2 where 1/2 of these are pointing up we would probably have to go to a table of Clebsch–Gordan coefficients to sort this situation out.

These Clebsch–Gordan coefficients can be written in different ways. One quite common way in nuclear physics is to write them as so-called Wigner 3-j symbols. A Wigner 3-j symbol is not exactly the same as the Clebsch–Gordan coefficients, but they are clearly related. A Wigner 3-j symbol will answer the question: What is the probability of a spin j1 particle, where m1 of this spin is pointing upwards, and a spin j2 particle, where m2 of this spin is pointing upwards, to couple to a system of spin j, where m of this spin is pointing upwards. This is written as
$\left( \begin{array}{ccc}j_{1} & j_{2} & j \\m_{1} & m_{2} & m \end{array} \right)=W_{3j},$
or, for the two examples in this post
$\left( \begin{array}{ccc}1/2 & 1/2 & 1 \\1/2 & -1/2 & 0 \end{array} \right)=\sqrt{1/6},$ and $\left( \begin{array}{ccc}3/2 & 1 & 5/2 \\1/2 & -1 & 1/2 \end{array} \right)=\sqrt{1/20}.$
Note that the difference between the Clebsch–Gordan coefficients and the Wigner 3-j symbols is that the Wigner 3-j symbols give the chance out of the total possible combinations of these particles, while the Clebsch–Gordan coefficients only give the probability out of a given state.

Now that the basics of Wigner 3-j symbols are covered I think it might be time to see what happens of we look at more complex systems. There are several kinds of situations where more than two angular momenta are involved in a physical system.

For example, instead of having a deuterium nucleus we could have a tritium nucleus where three different particles have different spin. Or we could have the case where one of the components of the system is not standing still, but moving around, giving rise to an orbital angular momentum.

If we take a look at the tritium nucleus, we have a system with two neutrons and one proton. Each of these particles will have 1/2 in spin: j1, j2 and j3. But not just this, they can also couple to each other in different ways. The two neutrons might couple to each other and create a system with spin J12, while a neutron and a proton might also couple to each other and give rise to a system with spin J23. Finally these particles might couple together and give rise to a system with spin J. The probability of these possibilities are conveniently summarized in the Wigner 6-j symbol as
$\left\lbrace \begin{array}{ccc}j_{1} & j_{2} & J_{12} \\j_{3} & J & J_{23} \end{array} \right\rbrace=W_{6j}.$
Lets do something concrete with this information. What is the chance that we have a tritium nucleus where the two neutrons, j1 and j2, couple to 0, while the proton, j3, and the neutron, j2, couples to 1 and the total system couples to 1/2? According to the Wigner 6-j symbols this is
$\left( \begin{array}{ccc}1/2 & 1/2 & 0 \\1/2 & 1/2 & 1 \end{array} \right)=\sqrt{1/4}.$

Not so bad, right? By just playing around with the limits of J12, J23, and J it is possible to calculate the Wigner 6-j symbols and get the probabilities for different configurations of the tritium nucleus and from see the structure of the three-nucleon system. Of course, this is very simplified as it first assumes that there is no difference between neutrons and protons. Secondly it assumes that no orbital angular momentum is relevant for the tritium nucleus. But we have a good starting point for experimental studies of tritium!

We could from this, for example, compare the nucleus to 3He and see if there is any difference between neutrons and protons. And we could compare the configurations with calculations where the orbital angular momentum is present to study this aspect. So already from this simple model and simple system several experimental questions have emerged for us to further investigate. It is science at its finest!

Now, since I have mentioned orbital angular momentum already, maybe I should say a couple of words about this as well. So far I have mostly been concerned with the spins of the particles, but we can also have particles that are moving around.

I will take aluminium as an example, to be specific 28Al, a nucleus that has 13 protons and 15 neutrons. To a first approximation this nucleus will have an odd proton (actually a proton-hole) that is moving around with an orbital angular momentum of 2, and an odd neutron that is not moving around. It might seem complicated, and not entirely correct, but let’s accept this for the moment. How do we couple these two particles with each other?

Well, the proton (hole), j1, will have a spin of 1/2, the same as the neutron, j2. Furthermore the proton (hole) will have an orbital angular momentum, jl, of 2. We know that the ground state, J, of 28Al has a spin of 3. How can we couple the spins of the particle-hole pair, Jjj, and the spin-orbit angular momentum of the proton (hole), Jls, to give this ground state spin? One possibility, and the chance of this, is
$\left( \begin{array}{ccc}j_{1} & j_{2} & J_{jj} \\j_{l} & J & J_{ls} \end{array} \right)=\left( \begin{array}{ccc}1/2 & 1/2 & 1 \\2 & 3 & 5/2 \end{array} \right)=\sqrt{1/18}.$
Of course, this is a very simplified model, but also here we get a nice starting point for further experimental study. For example, we could study the spin-orbit coupling further. That is, the coupling between spin and orbital angular momentum.

So far, I have discussed systems where only two or three angular momenta needs to be coupled. However, for most of the atomic nuclei this is not applicable. Basically due to the assumption that, so far, at least one of the particles does not have any orbital angular momentum. But in the most common situation the case is that we have two particles that both have a spin and that both are moving with respect to each other. That is, we need to couple four angular momenta. To do this, we can use the… *drum roll* … Wigners 9-j symbols!

I think that the basic concept of these symbols should be quite clear at the moment, so I think I will just skip right away to their definition,
$\left\lbrace \begin{array}{ccc}j_{1} & j_{2} & J_{12} \\j_{3} & j_{4} & J_{34} \\J_{13} & J_{24} & J\end{array} \right\rbrace=W_{9j}.$

The meanings of the different j should be quite obvious at the moment? They small j are the spins and the orbital angular momenta of the particles, while the large J are their coupling. The bottom-right J is the total spin of the system. OK? Then I guess we have enough knowledge to move to the forefront of nuclear structure research at the moment: 100Sn!

No, lets not do that, let’s go to 100In instead, which is basically 100Sn with one proton (hole) and one extra neutron, both of which are in the g9/2 orbital. Without going into too much details of the shell model, the g9/2 orbital means that the particle has an orbital angular momentum, l, of 4 and the spin-orbit coupling to this angular momentum is 9/2. Our knowledge of 100In tells us that its ground state spin is 6 or 7. Let us assume it is 6. Using this knowledge, we have only three possibilities:
$\left\lbrace \begin{array}{ccc}1/2 & 4 & 9/2 \\1/2 & 4 & 9/2 \\0 & 6 & 6\end{array} \right\rbrace=\sqrt{2/8775}\approx 0.015,$
$\left\lbrace \begin{array}{ccc}1/2 & 4 & 9/2 \\1/2 & 4 & 9/2 \\1 & 5 & 6\end{array} \right\rbrace=\sqrt{4/19305}\approx 0.014,$
$\left\lbrace \begin{array}{ccc}1/2 & 4 & 9/2 \\1/2 & 4 & 9/2 \\1 & 7 & 6\end{array} \right\rbrace=-\sqrt{7/1579500}\approx -0.0021.$

Hey! Already we have some predictions! We predict that the proton (hole) and the neutron should be mixed with about 50% spin-spin coupling to spin 0 and about 50% coupling to spin 1. We also predict that the orbital angular momentum of these should couple to either 5 or 6. Of course, this picture is very simplified, but still.

With all this discussion above, how does this relate to the title of the post? Well, in a recent paper by Zamick and Robinson, the non-trivial zeroes of the Wigners 6-j and Wigners 9-j symbols are studied. These zeroes provides some nice explanations about recent results from the g9/2 shell, that I used as an example above, but also relates these zeroes to phenomena about atoms and bosons. These Wigner coefficients are definitely a fundamental quantity of the quantum mechanics that describes the world on the smallest scales. I will finish this post by a quote from the authors themselves:

“By putting all these results in one place we hope we have conveyed the beautiful unity that pervades the problem of missing states.”

## High-spin isomers in 96Ag: Excitations across the Z=38 and Z=50, N=50 closed shells

One of the first nuclear physics experiments, that have been mentioned several times before, I participated in has just come out with a new paper. This is definitely a very productive experiment, with a very productive analysis group. So far they have managed to publish data on 94Pd, 98Cd, 96Cd as well as several conference proceedings.

So, what is the news this time? Well, I have mentioned the thing with nuclear isomers earlier in this blog. In that post I also discussed the famous 94Ag briefly. And now three more isomers have been found in 96Ag, one of them being a core-excited isomer. These core-excited states are a nice well to dig deeper into the nuclear shell model. The shell model, basically, describes single protons and neutrons outside of so-called closed shell. Or layers. Once a layer is full, it is considered solid, and the only thing that matters for the physics is the single particles outside of the solid core.

But this is not true, as clear by the core-exited states, like the newly discovered one in 96Ag. Studying these kind of states can, thus, give very interesting information about the subtle details of the nuclear shell model.

Another interesting note about this topic is that the paper High-spin μs isomeric states in 96Ag by A. D. Becerril et al., from the National Superconducting Cyclotron Laboratory at Michigan State University, was published as a Rapid communication in the same issue of Physical Review C. The nice thing about these two papers being published simultaneously is that we both saw the same isomeric state, with the same energy, in 96Ag as them. The even nicer thing is that we saw more, two more isomeric states. Furthermore, we could measure the lifetime of this isomer to 100 μs, while the other experiment was not sensitive to this and needed higher statistics and longer collection times.

I think both papers are very nice work and it is great to see how science is made when different experimental collaborations both compete and complement each other. Verifying each others results and competing about publishing interesting data first creates a living scientific community.

## Conceptual design and infrastructure for the installation of the first AGATA sub-array at LNL

The AGATA Demonstrator is currently running and taking data at Laboratori Nazionali di Legnaro. Well, it has actually done so for a time now, starting with the first commissioning experiment in March 2009 and several physics runs after that. I actually sitting here in Legnaro at the moment, waiting for our beam time on Wednesday to start for an experiment that I hope will confirm or reject my findings in 170Dy, followed directly by a similar experiment to study the actinides uranium and thorium. Both of these experiments will be very exciting for me as the first will test one of the fundamental parts of my Ph.D. thesis. The second one was an idea I got when I was working on 170Dy. It turned out that the Köln group had not only gotten the same idea, but also started working on it. Thus, instead of continuing this work myself, I decided to join in on their experiment.

This recent paper that has been published describes the installation of AGATA at Laboratori Nazionali di Legnaro. It is an interesting piece of work, and the first time (I think) someone cites me by name in a publication: “The first commissioning that evaluates the position resolution of the array has been published by Söderström and collaborators [10]. How cool is that?

However, no γ-ray detector is complete on its own. Even if it is possible to do physics with only a γ-ray spectrometer (data from the commissioning experiment still under analysis here), there are usually many other detectors connected to the γ-ray detector to get a complete picture of the reactions and provide invaluable information for the analysis. A couple of these systems are listed in the paper this post is about, and I thought it would be nice to discuss them a bit.

The most important of these ancillary detectors it the magnetic spectrometer PRISMA. This is a complex piece of machinery weighting over 40 tons, I learned during lunch, which is intended to find the reaction products in the experiment. The complexity of this spectrometer is too large to go into details about in a post like this, but it is a very nice setup containing a quadrupole and a dipole magnet to separate reaction products from each other as well as a system of different detectors to measure the mass, the element, the speed and the direction of the different fragments from the reaction.

Another often used ancillary detectors is the heavy-ion detector DANTE. This detector is smaller than PRISMA and basically consist of a number of microchannel plate detectors. The idea is to increase the limited efficiency of PRISMA, but the drawbacks are that much of the information that is obtained in the complex PRISMA setup will not be available. As always, there are pros and cons.

The γ-ray detector array HELENA is a complementary Barium fluoride (BaF2) for fast detection of high-energy γ-rays. It is a quite useful tool for, such as, studies of isomers, giant- and pygmy resonances as well as order-to-chaos transitions in atomic nuclei.

The Cologne plunger for grazing reactions is yet another possible ancillary device. A plunger detector is typically used for life-time measurements of excited states. The principle is both simple and smart. Basically, a nucleus is moving with high speed and the plunger consist of a small piece of metal that slows the nucleus down. If the nucleus decays before slowing down the Doppler shift of the γ ray will not be affected by the plunger. If, however, the nucleus decays after slowing down the Doppler shift of the γ ray will be affected by the plunger. Thus, the same γ ray will give rise to two different peaks, showing the chance that the nucleus decays before the plunger. By varying the distance from the target to the plunger, one can quite accurately measure the life time of the excited state in this nucleus.

Finally, the last ancillary detector mentioned in this recent paper is TRACE, a highly segmented Si-pad telescope detector modules. This detector is designed around a standard way to discriminate between light charged particles by measuring the energy loss in two different detector layers. The principle is quite like parts of the PRISMA detector system, and it is the same as I used in my Masters thesis many years ago.

These are some of the detector possibilities to use with AGATA. For more information about AGATA you can visit the AGATA detector array on Facebook, the official AGATA webpage or the webpage of the AGATA Collaboration Council.