# Nuclear shapes and collectivity investigated using lifetime measurements and γ-ray spectroscopy

Joa Ljungvall

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Joa Ljungvall. Nuclear shapes and collectivity investigated using lifetime measurements and γ-ray spectroscopy. Nuclear Experiment [nucl-ex]. Université Paris Saclay, 2020. tel-03862484

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
Nuclear shapes and collectivity investigated
using lifetime measurements and γ-ray
spectroscopy

Joa Ljungvall

February 28, 2020
# Contents

I A Short Introduction 3

II Nuclear shapes and coexistence investigated using lifetime measurements and γ-ray spectroscopy 7

1 Nuclear shapes, shape coexistence, collectivity, and their observables 8

2 Nuclear Structure Physics at the end of my PhD 12

3 What has happened in the field since my PhD? 14

4 Nuclear structure between now and the end of my life... 30

5 High resolution γ-ray spectroscopy 37

5.1 The High-Purity Germanium detector 37

5.2 AGATA 38

5.2.1 The AGATA detectors 38

5.2.2 Detector modeling, characterization and PSA basis generation 42

5.2.3 Pulse-shape analysis 44

5.2.4 Gamma-ray tracking 48

5.2.5 Monte Carlo simulations 49

5.2.6 Performance of AGATA as of today (February 28, 2020) 50

5.2.7 What should we do to improve AGATA? 52

6 Measuring picosecond lifetimes of excited states in nuclei 54

6.1 Lifetime measurements using Recoil Distance Doppler Shift with AGATA at Legnaro and GANIL 65

6.2 Future developments for Recoil Distance Lifetime measurements and the Oups family in particular 66

III Appendices 119

7 Selected publications 120

7.1 Shape Coexistence in Light Se Isotopes: Evidence for Oblate Shapes 120

7.2 Onset of collectivity in neutron-rich Fe isotopes: Toward a new island of inversion? 125

7.3 The Orsay Universal Plunger System 130

7.4 Investigation of high-K states in $^{252}$No 137
<table>
  <tbody>
    <tr>
      <td>7.5</td>
      <td>Musett: A segmented Si array for Recoil-Decay-Tagging studies at VAMOS</td>
      <td>149</td>
    </tr>
    <tr>
      <td>7.6</td>
      <td>Magnetism of an Excited Self-Conjugate Nucleus: Precise Measurement of the g Factor of the 2<sub>1</sub><sup>+</sup> State in <sup>24</sup>Mg</td>
      <td>162</td>
    </tr>
    <tr>
      <td>7.7</td>
      <td>Measurement of lifetimes in <sup>62,64</sup>Fe, <sup>61,63</sup>Co, and <sup>59</sup>Mn</td>
      <td>168</td>
    </tr>
    <tr>
      <td>7.8</td>
      <td>Experimental determination of reference pulses for highly segmented HPGe detectors and application to Pulse Shape Analysis used in gamma-ray tracking arrays</td>
      <td>180</td>
    </tr>
    <tr>
      <td>7.9</td>
      <td>B(E2) anomalies in the yrast band of <sup>170</sup>Os</td>
      <td>193</td>
    </tr>
    <tr>
      <td>7.10</td>
      <td>Performance of The Advanced GAmma Tracking Array at GANIL</td>
      <td>202</td>
    </tr>
    <tr>
      <td>7.11</td>
      <td>Pulseshape calculations using the AGATAGeFEM code and applications</td>
      <td>216</td>
    </tr>
    <tr>
      <td>7.12</td>
      <td>Extended Geant4 simulations of the AGATA spectrometer</td>
      <td>230</td>
    </tr>
    <tr>
      <td>7.13</td>
      <td>OASIS ANR</td>
      <td>238</td>
    </tr>
    <tr>
      <td>7.13.1</td>
      <td>Proposal's context, positioning and objective(s)</td>
      <td>239</td>
    </tr>
    <tr>
      <td>7.13.2</td>
      <td>Project organization and means implemented</td>
      <td>246</td>
    </tr>
    <tr>
      <td>7.13.3</td>
      <td>Impact and benefits of the project</td>
      <td>253</td>
    </tr>
    <tr>
      <td>8</td>
      <td>List of Publications</td>
      <td>255</td>
    </tr>
    <tr>
      <td>9</td>
      <td>Shape of the rare-earth nucleus <sup>136</sup>Sm via sub-barrier Coulomb excitation</td>
      <td>267</td>
    </tr>
    <tr>
      <td>9.1</td>
      <td>Proposal (as sent to the GANIL PAC)</td>
      <td>267</td>
    </tr>
    <tr>
      <td>9.2</td>
      <td>Experiment, a two stage rocket into the void</td>
      <td>275</td>
    </tr>
    <tr>
      <td>9.2.1</td>
      <td>Report on test experiment for E614</td>
      <td>275</td>
    </tr>
    <tr>
      <td>9.2.2</td>
      <td>The E614 experiment</td>
      <td>288</td>
    </tr>
    <tr>
      <td>10</td>
      <td>Lifetime measurements using the RDDS method after incomplete fusion</td>
      <td>297</td>
    </tr>
    <tr>
      <td>10.1</td>
      <td>Proposal (as sent to the ALTO PAC)</td>
      <td>297</td>
    </tr>
    <tr>
      <td>10.2</td>
      <td>Experiment and outcome</td>
      <td>306</td>
    </tr>
    <tr>
      <td>10.2.1</td>
      <td>Target issues</td>
      <td>306</td>
    </tr>
    <tr>
      <td>10.2.2</td>
      <td>Problems encountered during the experiment</td>
      <td>306</td>
    </tr>
    <tr>
      <td>10.2.3</td>
      <td>Results and Conclusions</td>
      <td>306</td>
    </tr>
  </tbody>
</table>
# Part I

## A Short Introduction
A "Habilitation à Diriger des Recherches (HDR)” is, in my mind, the recognition that the scientist in question has reached a level so that the scientist can in a meaningful way supervise the work of a student. I profit from the occasion to write my HDR to convince myself, and hopefully a few others, that this is indeed my case. Most of this knowledge consist of well established facts, on which the present day front-line research is based. I have tried to assure myself that I have some understanding of both the established facts as well as the present frontiers by summarizing theoretical methods, experimental achievements, and developments in this HDR. This means that the about 60 pages of text I have written for this HDR do not only treat what I have done. I expect the selected and included publications to cover most of that. The text written for the HDR is more general, and written with the goal to expand my horizon a bit. This also explains why the text treating the techniques surrounding Recoil Distance Doppler Shift methods and all technical issues around AGATA are rather short. My publications on the subjects are sufficiently detailed, and included.

The HDR beginning with the foundations of "Nuclear shapes and..." discussed in chapter 1. In chapters 2 and 3 the developments in the field since the end of my PhD thesis (May 2005) are treated. Here chapter 2 is a short snapshot of the status in 2005 and chapter 3 an interleaved description of how the field advanced and more in-depth looks, found in boxes, on topics which I have worked on. A final chapter 4 tries to position me in the future of nuclear structure research. As I have been involved in the study of nuclei of all mass ranges, both neutron rich and proton deficient nuclei, and studying both collective as well single particle aspects of nuclear excitations I feel a very short summary of this here is in its place. I think it makes reading the rest of the HDR easier. So in figure 1 I've summarized what I have done the years 2005-2019 by marking the regions in the Segré chart of nuclei where the studied nuclei are located. Topics typical this period are present, with focus on shell evolution in exotic nuclei and shape coexistence. Worth noting is also the long excursion into the terrain of heavy and super heavy nuclei. Although divided into four color-coded groups, to give the main theme for the experiment and the following publication, there is a common theme; The interplay between the terms of the Hamiltonian keeping nuclei spherical and states "single particle" like and parts driving different correlations in nuclei.

As I have worked with the development of AGATA, and the exploitation of AGATA, for the last 15 years chapter 5 is devoted to a short description of high resolution γ-ray spectroscopy and γ-ray tracking. Also here the idea to keep a coherent text about the generalities and boxes filled with contributions from me. There are also publications that relate to the "AGATA topic" in the included publications. Together with the chapter 6 covering the use of so-called "Plunger devices" for measuring picosecond lifetimes and g-factors of excited states, these two chapter also provides an outlook to the means that I think will be used to achieve the objectives as described in chapter 4. Again, to give an overview aiding in reading the rest of the HDR, my involvement in the development of instrumentation for nuclear-structure physics studies, not including the work done during my thesis, is summarized in figure 2. The top row illustrates what is my large involvement in the development of the Advanced GAmma Tracking Array, AGATA. I've been working with detector characterisation, modelling of detectors, pulse-shape analysis, and simulations and characterisation of the complete AGATA. In parallel with this work I've developed and coordinated the use of the Orsay Universal Plunger System in different version for use at the ALTO facility, and in two slightly different versions for use at GANIL together with the VAMOS spectrometer or the DIAMANT/NEDA setup.
<figure><img src="image_2.png" /><figcaption>Figure 1: Nuclear chart showing an overview of my activities with nuclear structure physics</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>Figure 2: Instrumentation related activities, a) represents AGATA detector characterisation, b) pulse-shape analysis, c) characterisation and simulation of AGATA, d) is the Orsay Universal Plunger System (OUPS) Mk I, e) OUPS Mk II, f) OUPS MKIII</figcaption></figure>
In most scientists career there are also the experiments that did not quite give a
result, but might still have something in them to learn from... I have decided to profit
and include some of this material in this manuscript, to leave a written trace of the
work done and the possibility to not do the same mistakes in the future. Two such
experiments are described in the chapters 9 and 10. These two chapters are in my
mind more documentation than a part of this HDR.
Part II

Nuclear shapes and
collectivity investigated using
lifetime measurements and
γ-ray spectroscopy
Chapter 1

Nuclear shapes, shape
coexistence, collectivity, and
their observables

Nuclei that are at closed shells develop non-spherical matter distributions. As the un-
derlaying Hamiltonian is invariant under rotation this is an example of spontaneous
symmetry breaking. The splitting of degenerate orbitals by the deformation, lowering
some in energy whereas others increase in energy, allows to lower the total energy
if the orbitals that were degenerate at spherical shape were not fully filled. This is
in analogy with the Jahn-Teller effect as stated for atomic systems. Quadrupole de-
formed examples of nuclear shapes are shown in figure 1.1.

<figure><img src="image_4.png" /><figcaption>Figure 1.1: Examples of nuclear shapes. To the left a spherical shape. In the middle a triaxial shape where all three axes of the spheroidal shape are different, and finally to the right a prolate shape.</figcaption></figure>

It is the breaking of the rotational symmetry that allows for excitations by rotating
the nucleus. As mentioned this can be considered as an example of spontaneous sym-
metry breaking and the rotational excitation corresponds to the Goldstone modes.
This is however not really enough if one wants to phrase nuclear rotations in this
language as Goldstone modes for broken global symmetries are "mass less", i.e. they
require zero energy to be excited. This is not observed as it would corresponds to de-
generate rotational bands in nuclei. It is possible to make an analogy between nuclear
rotations and the Higgs mechanism [1], providing a formalism that tackles this prob-
lem. By writing the nuclear Lagrangian as a one dimensional (the only independent
coordinate is time) field theory where the nuclear quadrupole vibrations φ (a vector of
five elements φ₂, φ₁, φ₀, φ₁, φ₂) are interpreted as fields. As spherical symmetric
potential up to order four in the fields $\phi$ is combined with a kinetic energy term that is half of the square of the time derivative of $\phi$. By adding a second order term to the potential the possibility of spontaneous axial symmetry breaking is created, as is the case for the scalar field associated to the Higgs field. By imposing a local gauge symmetry on this system, i.e. demanding it to be invariant under rotations with a time-dependent angle $\theta(t)$ a gauge field is needed to maintain the symmetry, which can be identified with the angular velocity $\omega$ of the rotating nucleus. This gives a Lagrangian of the form:

$$ \frac{1}{2} |D_t \phi(t)|^2 - \frac{\mu^2}{2} |\phi|^2 - B(\phi \times \phi \times \phi) - C |\phi|^4 \quad (1.1) $$

where $D_t$ is the covariant derivative $\partial_t - i\omega(t)L$, L the angular momentum operator. By setting $\mu^2$ negative, as is done for the Higgs field, the vacuum gets a non-zero expectation value, axially symmetric deformation in our case. By developing the field $\phi_0$ around this expectation value and inserting in into the Lagrangian 1.1 it can be shown how the fields $\phi$ couples to the "gauge field" $\omega$, and generates its mass, in this case inertia. For the electro-weak case this corresponds to the Z and W bosons acquiring masses via the Higgs field, where "our" $\phi$ is the Higgs field and $\omega$ corresponds to the mass-less gauge fields that becomes Z and W bosons.

Staying within the view of the nucleus as a deformed object the most used model is the Bohr-Mottelson model of collective excitation in nuclei [2]. In this model it is assumed to be possible to write the wave function of the nucleus as a product of a function depending on only the orientation of the nucleus in space (Euler angles) and a function describing the shape of the nucleus: A spheroid object that can rotate as well as vibrate. This is a very successful model that provides us with the language used to describe collective excitation in nuclei, and its success is the rationalisation for discussing the shape of nuclei in an "internal reference system", i.e. body-fixed. It has however no direct connection to the nuclear many-body problem when this is thought of as a solution in terms of mixed single particle states to a many-body Hamiltonian (although it can be derived using the Coordinate Generator Method and use parameters calculated from, e.g., mean-field calculations and hence connecting the results to more microscopic models [3]).

Microscopic approaches to calculate properties of nuclei applicable all over the nuclear chart are the Energy Density Functionals. In the nuclear case they have emerged from Hartree-Fock like calculations. Because of the need for density dependent terms in the interactions to produce good results they are better called "Nuclear Density Functional Theories". A, at the limit of being excessive, simplification of these methods is that they as a first approximation aim to describe the true solution of the quantum system as a product of non-interacting single particles wave functions by minimizing the energy calculated from these single particles states (to be precise, the particle densities given by these single particle states) in a self consistent way. The "self consistence" means that the density given by the single-particle wave functions generates a potential that reproduces the single-particle wave functions. This way a large fraction of two (and more) body interactions can be absorbed into a one-body potential which allows a good description of the physics while remaining in single particle basis. As this is not done in an infinite basis that would allow an exact description, these correlations give wave functions that no longer preserve the symmetries of the Hamiltonian, i.e. the symmetries are broken. Examples are that of translation symmetry (wave function located in space), rotation symmetry (wave function has a preferred axis in space), and particle number conservation (wave function does not
have a sharp particle number). To compare observables such as transition rates with
experimental data these symmetries should be restored. This is done via "projection"
methods. Staying in the scope of extreme simplification "projecting" is constructing
a wave function which is the superposition of the symmetry breaking wave function
transformed in all possible ways in accordance with the symmetry that should be
restored. This generates by construction a wave function that has the wanted sym-
metry. It can also be shown that it is possible to find a weighting function that allows
both this symmetry and minimizes the energy [3]. This weighting function is given
by expanding it in functions that are eigenfunctions of the symmetry in question and
then minimizing the total energy based on the variation principle. This is a speciali-
sation of the Coordinator Generator Method also used to include beyond mean-field
correlations [3, 4, 5].

The interacting shell model also gives useful descriptions of deformed and/or col-
lective nuclei. The possibility to calculate deformed nuclei in a spherical basis, with as
only symmetry breaking that of translation symmetry, was in the early days of nuclear
structure not given and the connection between geometrical models and shell model
calculations not clear. Such a connection was given explicitly by Elliot [6, 7]. Hav-
ing notices that the Harmonic Oscillator plus a specific quadrupole-quadrupole form
of the nucleon nucleon interaction follows a SU(3) symmetry he explicitly showed
how to find the irreducible representations of this SU(3) within the SU(N) group. The
SU(3) is here as an intermediary step to find the irreducible representations of the
R(3) on the reduction of SU(3), i.e. the angular momenta included in each SU(3) irre-
ducible representations. Here it was shown that the L values found had the correct
$L(L + 1)$ energy dependence on. He further showed that the SU(3) wave functions
corresponded to > 90% of the wave functions of full diagonalisation. This of course
suggests that the in-medium nuclear interaction is quite well described by a mean
field and quadrupole interaction. In a second paper it was demonstrated how, from
an intrinsic state labeled by its SU(3) quantum numbers and with given quadrupole
moment, but not good angular momentum, rotational bands can be constructed using
projection on good angular momentum. This provides the connection between an in-
trinsic state with a shape (for each SU(3) irreducible representation) and the rotational
band. The SU(3) symmetry is not valid for heavier nuclei as the spin-orbit interaction
breaks the degeneracy of the harmonic oscillator shells and hence the states needed
to span the representation no longer have the same energy. For heavier nuclei the so-
called pseudo spin symmetry generates levels that are close to degenerate allowing the
use of pseudo-SU(3) to single out important configurations. It has also been realised
that a large fraction of the "true" wave function can be given by only including only
$\Delta j = 2$ sequences in harmonic oscillator shells (referred to as quasi-SU(3) [8]). This
can also be traced back to the dominance of monopole and quadrupole components
of the effective nuclear interaction. The combination of pseudo- and quasi-SU(3) has
found applications both as guide to truncate model spaces and as a tool to explain the
results of large-scale nuclear shell model calculations.

All collective states found in nuclei are not "rotational", and excitations in the form
of vibrations are also found. Different types of collective excitations are differentiated
by model independent quantities such as the ratio of excitation energies and transition
probabilities as well as the coherence in, from models, extracted values of quadrupole
moments. When moving from structures described as single particle states towards
more collective structures the typical behaviour in an isotopic or isotonic chain is that
of passing over an region of "vibrational behaviour" before entering a regime of static
deformation and an yrast band in the form of a rotational sequence of states. This
change in structure, i.e. single particle towards collective, does not only come with
changing number of nucleons but also with excitation energy, i.e., how the nucleons
distributed over different orbitals in a nucleus. This gives rise to "shape coexistence"
in nuclei [9, 10]. It can be defined as states at similar energy but very different struc-
tures. The canonical region for shape coexistence is around lead with shape staggering
in Mercury isotopes and several known excited 0+ states in neutron deficient lead iso-
topes. A modern view is that shape coexistence manifests itself not only close to the
classic "magic numbers" but at all places where rapid changes in collectivity is seen
in the Segré chart. Shape coexistence is a phenomena that offers stringent tests of nu-
clear models as small changes in the relative energy between the coexisting structures
have large effect on some nuclear observables. Here the observables are not so much
the excitation energies but rather lifetimes of excited states and Coulomb-excitation
cross sections. If the basic spectroscopic information for a nucleus is well enough
known lifetimes and Coulomb-excitation cross sections give model-independent val-
ues for electromagnetic transition elements, e.g. ⟨*I*<sub>*f*</sub>||*M*(*E*/*ML*)||*I*<sub>*i*</sub>⟩ where *I*<sub>*f*</sub> ≠ *I*<sub>*i*</sub>
in the case of life times whereas Coulomb-excitation gives the possibility to extract
also the sign and magnitude of diagonal matrix elements (i.e. transitions between dif-
ferent m states). The transition strengths are readily compared to calculations from
different models and offer a larger sensitivity than just comparing the energy of the
levels with calculations. Another interesting concept, presented by Kumar [11], is
that of quadrupole sum rules. If one knows at least the few lowest transitional and
diagonal matrix elements this gives an invariant definition of quantities that can be
put into correspondence with absolute deformation, triaxiality, γ-softness etc. This
way a extraction of nuclear deformation without reference to a specific nuclear model
can be made.
## Chapter 2

# Nuclear Structure Physics at the end of my PhD

The material for this section is mainly drawn from the NuPECC Long Range Plan of 2004 [12], an admittedly biased sampling of publications between 2000-2005 in the Nuclear Sciences References [13], and with my contribution a posterior as a very strong weighting factor. The paragraph on the state on nuclear structure theory is my ten-line vision of what is written by Bender at al. [4], Caurier et al. [14], and Dean et al. [15].

In the beginning of this millennium the open questions in the nuclear structure fields where summarized by the European community as:

1. The limits of bound nuclei in terms of Z,N, and A.

2. The Z/N dependence of the nuclear force.

3. How does collectivity emerge.

4. How are nuclei built from the particles of the standard model?

With these larger questions in mind, or with the language of physics: assuring a non-zero projection on the hyperspace spanned by these large questions smaller tangible questions can be asked for which single experiments can add a part of the answer. Some of the "hot" subjects at the turn of the century, fueled by fundamental questions as well as new experimental opportunities, were:

* The evolution of "the magic numbers" when moving away from stable nuclei. First seen in the island of inversion in neutron-rich nuclei with masses around 20-30 amu, experimental techniques allowed the investigation of this phenomenon both for heavier nuclei as well with higher precision for lighter nuclei and closer to the drip lines. The weakening of N=8, 20, 28, 40 and 50 was seen and the development of or suggestion of new "magic numbers" such as N=16 or N=32 found. Examples are the mapping of the first "island of inversion" [16, 17], investigation of the N=40 [18] sub-shell closure. There was intensive work trying to approach the N=50 shell closure [19, 20]. Many of the observation are understood as rooted in monopole part of the tensor interaction [21, 22].
* Closely connected to shell-evolution but to some extent viewed as subject of it-self is that of shape, shape-evolution and shape coexistence. Regions of interest related to shape coexistence were neutron deficient lead nuclei, nuclei around the N=Z Se and Kr isotopes [23, 24]. But also close to the N=60 Zr and Sr iso-topes [25, 26]. Super deformation as well as exotic shapes transitions ("Jacobi" shapes) were also often present in discussions.

* The combination of high-performance separators, high-beam intensities and large γ-ray spectrometer arrays allowed for an important push forward in the spectroscopy of very heavy nuclei. Spectroscopy in these lighter nuclei was viewed as giving access to orbitals that are crucial for the island of stability. Prompt and decay spectroscopy nuclei such as $^{253,254}$No [27, 28], $^{250}$Fm [29] are performed.

* The question of three-body forces, and to what extent they are needed and how to include them in nuclear structure calculations is discussed [30, 31, 32].

* Efforts to see and characterise $^{100}$Sn using different experimental techniques [33, 34].

* Is there a strong T=0 n,p pairing? This question was investigated using spec-troscopy of high-spin states in N~Z nuclei [35, 36] as well as using mass mea-surements [37].

* Isospin non-conserving interaction terms, probing the charge symmetry and charge independence of the nucleon-nucleon interaction. The rather large push forward in this topic came as a direct consequence of the technical development on the γ ray spectrometer side and on shell-model calculations. This is described in detail by Bentley et al. [38].

On the theoretical side, as of the middle of the first decade of this century, the combined development of computer power and algorithms to solve the numerical problems, had allowed both energy density functional based theories and the inter-acting shell model to better understand and separate the "many-body" aspect of the problem and the "interaction" aspect of the problem. For neutron-rich nuclei the role on the monopole part of the effective interaction of the tensor component is pointed out. For the shell model exact solution for light nuclei clearly showed the need for, at least, a 3-body force in order to reproduce both excited states and the total binding energies. Further more, efficient truncation schemes based on the quadrupole domi-nance in nuclear structure allowed meaningful calculations of even super deformation in a interacting spherical shell model.

The different versions of energy density functional methods (Relativistic, Skyrme, and Gogny and all versions of them) had started to extensively use what is often re-ferred to as "beyond the mean field", i.e. the restoration of symmetries or phrased a bit differently: provide wave functions with sharp quantum numbers where a sym-metry suggests the quantum numbers should be sharp. As such they provide good spectroscopic description over all of the Segrè chart. However, although not obvi-ously the right thing to compare, single particle energies from mean-field calcula-tions were not always those deduced from experiments and the rapid (as interpreted) shell-quenching seen in exotic light nuclei was not reproduced.
Chapter 3

What has happened in the
field since my PhD?

Where have we made progress in our understanding of the nucleus since 2005? These
almost 15 years of time correspond to about 10 % of the lifetime of the nuclear physics
subject. A small but non negligible fraction. A simple way is to compare the content
of the NUPECC Long range plan from 2004 [12] with that one of 2017 [39]. Although
phrased differently it stands clear that the "large" questions that were open when I
finished my thesis in large remains unanswered, or to be more precise, only a bit more
answered then they were in 2004. This does however not mean, as contradictory as it
might sound, that no progress has been made. What it means is that nuclear physics
is an old, and rather successful field forcing us to work hard for every increase in our
understanding of the nuclei.

Before exploring the experimental advances and my contributions to these, I give
my version of the development in the theory we use to interpret data and claim under-
standing with. During the this period substantial progress has been made in theoreti-
cal nuclear structure physics. Ab initio methods have been added to the nuclear shell
model and energy density functional based nuclear structure theory methods. These
models today give the solution to the "many-body" problem leaving us with the prob-
lem of finding the correct form of the nuclear interaction [40]. The ab initio label is
typically given to nuclear models that use an interaction fitted on nucleon-nucleon
and nucleon-nucleon-nucleon data and that uses controlled and systematically im-
provable approximations [41]. Today the interaction are often derived from Chiral
effective field theory [42] where only a few constants taking care of unresolved high-
energy physics are fitted to few-nucleon data. These interaction can then be used
"as is" or after having been made "softer" using similarity transformations (that in it-
self induced multi-body interactions). Examples of ab-initio methods are the No Core
Shell Model (NCSM) that solves the full A body system with a truncation at high en-
ergies [43]. This is viable to somewhere around oxygen isotopes. Other often used
method for semi-magic nuclei are the Coupled Cluster methods [44], the in-medium
similarity normalisation group [45], Quantum Monte Carlo methods [46], and nuclear
lattice effective field theories [47, 48]. Examples of recent application (I will not dif-
ferentiate between them) of ab-initio is in the calculation of ¹¹Be [49]. The problems
in resolving the ordering of the lowest states in ¹¹Be is linked to the interactions used.
The distribution the neutron matter in light N isotopes was addressed by Bagchi et
al. [50]. Here ab-initio calculations do a overall good job but fail to reproduce the evolution of the neutron skin as a function of neutron number. Ab-initio, and the coupled cluster method in particular, have been extensively used to interpret data on Calcium isotopes [51, 52]. Results concerning the quenching of the coupling between the weak force and the nucleon [53] have been presented as well as wealth of more shell structure oriented work [52, 54, 55]. Common for the ab-initio methods are that they are not yet as good as more phenomenological methods in terms of reproducing observables (absolute errors in energies are in the order of some to a few percent) and the conclusion that, as stated earlier, the low-energy limit of the strong interaction still is not fully understood.

The scientific basis for and the technical aspects of the interacting shell-model has not changed a lot the last 15 years and papers such as [8, 14, 32, 56, 57] and [58] still gives a good description of the field. However, the increased computer capacity together with refinements of algorithms used so solve the diagonalisation has allowed the user of larger and larger spaces, in some cases including more than 10¹⁰ states. With these increased valances spaces new shell model interactions have been developed such as LNPS [59], PFSDG-U [60], SDPFMU-DB [61], and A3DA [58].

For the energy density functionals (this is based on the review of Grasso [5]) the connection to Density Functional Theories used in atomic and molecular physics has been closely investigated (e.g. Messud al. [62]) showing that "our" use of energy functionals can be considered as sound (the unknown nuclear interaction stops us from calling what we do DFT, this in difference with atomic and molecular physics). With the importance of the tensor force having been shown for shell evolution investigations on its influence on mean-field calculations have been done (see [63] and references therein). A tensor terms seems needed but its actual impact is difficult to find as the fitting procedure used when constructing the energy functionals includes important aspects of the tensor interaction even without an explicit tensor term. Based on (failed) efforts to improve the classical energy density functionals [64] the community has tried to find new functional forms more closely connected to the nucleon-nucleon interaction, e.g. [65], or by including higher order derivatives of the density without direct connection to the bare nucleon nucleon force. The redefinition of the functional forms used in EDF calculations also comes from their use in beyond-mean field calculations. This is from both the possibility for double counting correlations as well as pathologies found when restoring broken symmetries using the coordinator generator method [66, 67, 68]. Beyond-mean field methods are now able to tackle even odd systems such as ²⁵Mg [69] with descent success but also here there are deficiency pointing to the need for other energy functionals.

Experimentally the question of shell evolution, i.e. the appearance of new shells closures and the disappearance of others has been thoroughly investigated. Staring at low masses the investigations of the "first" spin-orbit shell gap N,Z=6 where a combination of experimental methods and ab-initio calculations using modern 2N and 3N nuclear forces based on chiral effective field theory [70], showed that there indeed is such a gap. The last stable oxygen isotope ²⁴O is also suggested to be double magic with Z=8 and N=16 as new magic number [71]. This shell closure is driven by the same 3N forces that is used to explain "the oxygen anomaly", i.e. the low number of stable neutron-rich oxygen isotopes [72]. Moving towards heavier nuclei there are suggestions of "tensor force driven" new shell closures in neutron-rich calcium isotopes [73]. It has been shown that ⁷⁸Ni is a doubly magic nucleus. Based on experimental data and calculations performed with several state-of-the-art nuclear theory models it is concluded that there is a low laying deformed structure in ⁷⁸Ni, i.e. shape coexistence,
although higher in energy than the first excited $2_1^+$ state [74]. This results excludes $^{78}$Ni from the island of inversion in the region. The last known doubly magic nucleus without known excited states is $^{100}$Sn. However, $\beta$-decay studies suggest that it is indeed a good doubly magic nucleus [75]. A longstanding question regarding the tin isotopes, the asymmetric collectivity around the neutron mid-shell with a surprisingly large B(E2)'s approaching $^{100}$Sn has been given an explanation [76] using the Monte Carlo Shell Model. For neutron-deficient tin isotopes the quadrupole correlation energy for protons in the $1\pi g_{7/2}$ can compete with the pairing, something that is not true from N=66 and the expected typical seniority like nuclei reappear. The magicity of $^{132}$Sn was confirmed in a transfer reaction study performed at Holifield radioactive beam facility, this by comparing deduced spectroscopic factors with that of $^{208}$Pb [77].

## Island of inversion at N=40 and beyond

Neutron-rich nuclei with Z close to the last harmonic-oscillator magic number (28) attracted interest as there are sub-shell closures at N=34,36 [78, 79] and a weakening of the N=40 harmonic oscillator shell moving away from the Z=28 Ni isotopes. From the second half of the first decade of this century there is a consensus that the increased collectivity when removing protons from nickel is the result of an increase in the numbers of neutrons in the $1\nu g_{9/2}$ orbital as the result of the decreased gap between it and the $1\nu f_{5/2}$ orbital. This rapprochement of orbitals is a result of the tensor force [21, 22] between protons in the $1f_{7/2}$ and neutrons in the $1f_{5/2}$ and $1g_{9/2}$ orbitals. The monopole part of the tensor force is attractive between protons and neutrons having anti-parallel spins (i.e. $1\pi f_{7/2}$ and $2\nu p_{1/2}$, $1\nu f_{5/2}$) and repulsive when the spins are parallel (i.e. $1\pi f_{7/2}$ and $1\nu g_{9/2}$). This way removing protons in the $1\pi f_{7/2}$ orbital decreases the gap between the $1\nu g_{9/2}$ and the $2\nu p_{1/2}$, $1\nu f_{5/2}$. This removes the (weak) N=40 gap. With the no N=40 gap quadrupole correlations energy can be gained by as both protons ($1\pi f_{7/2}$-$2\pi p_{3/2}$) and neutrons ($1\nu g_{9/2}$-$2\nu d_{5/2}$) have active quadrupole partners.

The iron isotopes $^{60-64}$Fe spans N=32-36 and are therefore of interest to address questions concerning the onset of collectivity close to N=40 and the question of N=32,34 sub-shell closures. An experiment was performed at GANIL using the EXOGAM $\gamma$-ray spectrometer for $\gamma$-ray detection coupled to the VAMOS spectrometer for event-by-event identification of the reaction product. The Cologne compact Plunger device [80] was used in inverse kinematics with a $^{238}$U beam impinging on a $^{68}$Ni target. A magnesium foil was used as a degrader in the plunger. This was a pioneering experiment that was carefully prepared by extensive simulations. The experiment, performed during autumn 2008, was successful and measured the lifetime of the first $2_1^+$ states in $^{62-64}$Fe, and confirmed the lifetime of the $2_1^+$ state in $^{60}$Fe. The results showed clearly that not only the $1\nu g_{9/2}$ is populated as protons are removed from Ni, but also the $2\nu d_{5/2}$ orbital, being a part of the quasi-SU(3) scheme. The paper [81], cited 86 times as of February 28, 2020, is included as an appendix 7.2. Results, including $^{66}$Fe, from MSU collaborated the conclusions [82].

The same experiment gave rise to exploitable data for the Cobalt isotopes $^{63,65}$Co. Lifetimes for yrast $9/2-2_1^-$ states where measured as well as for the
$3/2_1^-$ state in $^{63}$Co. Using these Dijon et al. [83] investigated if the $9/2_1^-$ states can be seen as a state with the structure $|(1\pi f_{7/2})^{-1} \otimes 2_1^+(\text{Ni})|9/2 >$ and the $3/2_1^-$ states as $|1\pi f_{7/2} \otimes 2_1^+(\text{Fe})|3/2 >$ as suggested by energy systematic. The conclusion is that this is not the case, and that such a simple model does not correctly capture the physics. An experiment with the same setup aiming at measuring lifetimes in $^{70,72}$Ni was also performed in 2010. Unfortunately the $2_1^+$ and $4_1^+$ in $^{72}$Ni were out of reach and the $2_1^+$ in $^{70}$Ni was known. Lifetimes in odd $^{69,71}$Zn isotopes could however be measured [84]. The conclusion was that low-laying states in these nuclei can not be considered as a single neutron coupled to the even-even core and that to correctly describe them calculations need a valence space larger than $2p_1 1f_{5/2} 1g_{9/2}$.

The first experiment performed with AGATA@GANIL, for which I was one out of two spokespersons, was a continuation of the work performed on moderately neutron-rich iron nuclei. The aims of the experiment were very ambitious: Remeasuring the lifetimes of the $2_1^+$ states in $^{62,64}$Fe using $\gamma\gamma$ coincidences, measuring yrast lifetimes up $6^+$ in the $^{62,64,66}$Fe isotopes and finally to measure the g-factor of the $2_1^+$ states in $^{66}$Ni and the iron isotopes. This was believed to be possible thanks to the increase in efficiency of AGATA as compared to EXOGAM and improvements in the detection system of VAMOS. The physics goal of the experiment was to investigate to what extent the collectivity in the iron isotopes was developed by looking at the variation of B(E2) in the yrast band, and address questions regarding shape coexistence in the neutron-rich irons [85]. Compared to the ambitions the outcome of the experiment is not impressive. The reasons for this is however understood and identified:

* Instead of the 33 AGATA detectors that should have been installed an average of only 19 detectors could be used.

* The beam intensity that was possible on the target was one third of what had been achieved in 2008, at least in part because the shorter distances needed because of the shorter lifetimes of the higher laying states in the yrast band.

* Time was lost debugging both AGATA and VAMOS as this was the first real experiment. An example is the increased load on the entrance detector in VAMOS because of the elastic scattering on the Mg degrader foil.

The data was analysed in collaboration between me and a student at the University of Oslo, Malin Klintefjord. Lifetimes for the $4_1^+$ states in $^{62,64}$Fe were extracted, together with $11/2_1^-$ states in 61, 63Co and $^{59}$Mn. The resulting transition strengths were compared to large scale shell model calculations as well as beyond mean-field calculations. These results strengthen our understanding of the region, in particular the limit of the onset of the "island of inversion" close to N=40. The shell model calculations are in good agreement with experimental data whereas the beyond mean field calculations does not suggest a structural change close to N=40. The beyond mean field calculations suggest more of a vibrational structure for the neutron-rich irons. Details are found in Klintefjord et al. [86], also included as appendix 7.7.
Considerable experimental effort has also been invested in neutron-rich nuclei close to N=40, and even more moving towards N=50 during the second decade of the century [85, 87, 88, 89, 90, 91, 92, 93, 94, 95]. At the same time large theoretical efforts have been made, using shell models calculations [59, 96, 97, 60], interacting boson models [96], and different beyond mean field calculations [98, 99]. This body of work consolidates the idea of a N=40 island of inversion build on the same mechanism as the N=20 island of inversion, i.e. the lowering of intruder configurations by the strong quadrupole interaction in the residual proton-neutron interaction. In figure 3.1 this is illustrated for <sup>64</sup>Cr with the differences in occupation numbers for spherical orbits when performing a full Symmetry Conserving Configuration Mixing beyond-mean-field calculations and spherical mean-field calculations. The increased population of the 1νg<sub>9/2</sub> and 2νd<sub>5/2</sub> is a clear illustration of the quadrupole coupling and the usefulness of the quasi-SU(3) scheme for truncating shell model calculations. The strong connection between shape coexistence and "islands on inversion" has also been emphasized.

<figure><img src="image_5.png" /><figcaption>Figure 3.1: Illustration of the structure of the ground state of <sup>64</sup>Cr, located in the center of the N=40 island of inversion. The difference between the occupation numbers for spherical orbits calculated with the SCCSM method and the occupation numbers for the same orbits when using spherical HFB or HF (normal filling) approximations. Figure taken from Rodríguez et al. [99].</figcaption></figure>

THE island of island of inversions is the one centered around <sup>32</sup>Mg. This region of the nuclear chart is rather well explored but high-precision g-factor measurements of the 2<sup>+</sup> states in the magnesium chain is missing. At CSNSM we have, together with A. Stuchbery of Australian National University, put in place a program to move towards the measurement of g-factors in the first island of inversion. A proof of principle experiment was performed using the OUPS at the ALTO facility, also giving exciting physics results [100]. The technique, Time Dependent Recoil-In-Vacuum modified for radioactive beams [101], is based on the hyperfine interaction between a 1s electron and the nuclear spin. As the magnetic field at the nuclear site for a 1s electron can be calculated from first principles the g-factor can be measured with, in principle, only statistical errors. A second experiment in this line of investigations was performed at ISOLDE in the end of 2017. The goal was to measure the g-factor of the 2<sup>+</sup> state in <sup>28</sup>Mg by the TDRIV technique and Coulomb excitation of the state in interest. The analysis was started as a part of the PhD of Amar Boukhari, for which I was co-supervisor. A part from being a stepping stone
towards the island of inversion it is quite possibly a sensible amount of "in-
truder" configuration to be found already in $^{28}$Mg, something that a g-factor
measurement is very sensible to.

The last 15 years there has been considerable progress made in our knowledge
about how the nuclear shape evolves as Z,N, and/or excitation energy. It has been
shown that shape coexistence is a rather generally occurring phenomenon. This has
been possible, to a large extent, thanks to radioactive beam facilities such as REX
ISOLDE, MSU/NSCL, GANIL, and RIKEN. For evolution of collectivity, shapes, and
shape coexistence electromagnetic transition strengths and moments are key observ-
ables and it is therefore not surprising that the larger body of the experimental data
is from Coulomb excitation measurements and lifetime measurements using plungers
or fast timing.

Already in quite light nuclei examples of how shape and shape evolution is closely related to shell closures and shell evolution are found. In $^{30,32}$Mg excited $0_1^+$ states have been studied proving shape coexistence, the lighter isotope have a spherical ground state [102] whereas the heavier of the two has a deformed ground state and a what seems to be rather complicated excited $0^+$ state [103]. This shape coexistence is created by the same mechanism that gives rise to the island of inversion. Shape coexistence is also found close to the N=28 shell closure, e.g., neutron-rich Sulfur isotopes where the deformed structure gains quadrupole correlation energy. A combination of a smaller N=28 shell closure and the change of relative positions for the $2\pi s_{1/2}$ and $1\pi d_{3/2}$ allowing $\Delta l = 2$ excitation for both protons ($1\pi d_{5/2}$-$1\pi s_{1/2}$) and neutrons ($1\nu f_{7/2}$-$2\nu p_{3/2}$). This is driven by the monopole part of the tensor force [104, 105, 106].

A classical region for the study for nuclear shape, is that of revisited region of germanium isotopes. The stable $^{72}$Ge was Coulomb excited, using the γ-ray tracking array GRETINA to detect the γ rays. The result of this experiment, showing the interest in improving precision on old measurements using knew tools, show that $^{72}$Ge can be understood on the simple picture of two mixed triaxial bands [107].

The often studied region around the nucleus $^{68}$Ni has also given examples of shape coexistence in the nuclei $^{66-70}$Ni. This is well described by shell model calculations [108, 109]. With these examples shape coexistence has been found for all proton shell closures. For the neutron-rich Ni nuclei, which is unusual, shape coexistence has been suggested close the doubly magic $^{78}$Ni (but also in $^{68}$Ni) [74]. In $^{79}$Zn a deformed isomer was investigated using laser spectroscopy and based on the magnetic moment it is speculated that one should include not only the $2\nu d_{5/2}$ orbital but also the $3\nu s_{1/2}$ orbitals beyond the N=50 shell closure [110] in order to correctly describe this in shell model calculations. In $^{84}$Ge a large $B(E2;2^+_1 \rightarrow 0^+_1)$ is found. This is explained as a consequence of the impact on the pseudo-spin partners (in this case the $1\pi f_{5/2}$ and $2\pi p_{3/2}$) from the change of the binding potential. This leaves the $1\pi f_{7/2}$ unaffected in agreement with observations [111], and an alternative explanation to that of the monopole part of tensor part of the nucleon nucleon interaction.

Shape coexistence at the N=Z line

Nuclei with N~Z~36 are located in a region where the shape of nuclei show
rapid changes with both the number of protons, number of neutrons, and
with the excitation energy. Noticeable examples are oblate ground states
in $^{68}$Se [35] and shape-evolution and shape coexistence in light Kryptons
[23, 112, 113]. This is understood in terms of the competing deformed shell
gaps in the region, and have been addressed using different theoretical ap-
proaches such as the excited VAMPIR [114], axial beyond mean-field using
the Skyrme interaction [115], and triaxial beyond mean-field using the Gogny
force [116]. In figure 3.2 examples for axial and triaxial beyond-mean field cal-
culations in the region are shown. The axial calculations by Bender et al. use
particle number and angular momentum projected HFB states as generator
functions for the generator coordinator method (CGM [3]), with the weights
for each projected configuration found with by solving the Hill-Wheeler-
Griffin equation. This corresponds to first solving the mean-field equations
(dashed line in left top of figure 3.2) followed by projection on good angu-
lar momentum (solid lines) and finally allowing mixing of different intrinsic
$\beta_2$ generating the physical states. This is illustrated by the labeled states in
the upper left panel and by the curves in the lower left panel of figure 3.2.
<figure><img src="image_6.png" /><figcaption>Figure 3.2: Axial and triaxial calculations for $^{74}$Kr. Figure from Bender et al. (left) [115] and Girod et al. (right) [116]. The top row shows, with dashed line in the case of axial calculations, the energy for the mean field for $^{74}$Kr. Below are shown the collective wave functions for the physical states.</figcaption></figure>

In the approach of Girod et al. the CGM is combined with the Gaussian overlap approximation (GOA), generating an eigenvalue problem looking like an Hamiltonian where the masses and potential ("masses" include both the moment of inertia for rotation as well as collective masses for vibrations) are calculated from the solutions of constrained HFB calculations. This eigenvalue problem is then solved using a set of basis functions that have the correct symmetries imposed giving, i.e., restoring angular momentum as a symmetry to allow calculations of transition strengths and other spectroscopic quantities.
Experimental and theoretical work agreed rather well on the oblate ground state in $^{68}$Se. Giving the similarity in moment of inertia found for the ground-state band in $^{70}$Se and $^{68}$Se it was a surprise when Coulomb excitation measurements [117] performed at REX-Isolde suggested that the ground state of $^{70}$Se is prolate. A prolate ground state deformation for $^{70}$Se was also deduced from Coulomb Energy Differences by Nara-Singh et al. [118]. Based on the experience gained by the nuclear structure group at Saclay with neutron deficient Krypton isotopes we proposed an experiment to remeasure lifetimes in the yrast band of $^{70,72}$Se as these lifetimes are crucial for the interpretation given by Hurst et al. [117]. The experiment was performed at INFN Legnaro with the GASP [119] $\gamma$-ray spectrometer and the Cologne plunger device [120] using the reaction $^{40}$Ca($^{36}$Ar,$\alpha$2p)$^{70}$Se to populate the states of interest. The experiment showed that the lifetimes of the $2_1^+$ state in $^{70}$Se from Heese et al. [121] were wrong. As these lifetimes were used by Hurst et al. to conclude on the shape this finding changes the interpretations, and the ground state of $^{70}$Se is found to be oblate rather than prolate. The need of considering triaxial degrees of freedom was highlighted. This is described in detail in the publication "Shape Coexistence in Light Se Isotopes: Evidence for Oblate Shapes" [122], see section 7.1.

After 2008 the activity in this region of the nuclear chart has continued to be high. A multitude of experiments have been performed, mainly at fragmentation facilities [123, 124, 125, 126, 127, 128, 129, 130]. Calculations using microscopic-macroscopic models [131], shell model calculations [132, 133, 134], different version of Beyond Mean Field calculations [116, 135, 136, 137] as well as calculations based on the IBM models with its parameters extracted from Constrained HFB [138] have been performed. What has clearly come out of this work is that close to N=Z line triaxial deformation should be taken into account. For $^{70}$Se and $^{70}$Kr there is also a need for more data to see if the rather complex situation could be given a "simpler" shape coexistence explanation. Apart from the increased sophistication in the Beyond Mean Field calculations I like the concept of "shape entanglement" [132].

Nuclei around Z=40, N=60, i.e. $^{100}$Zr, have been of interest for a long time. This because of the spectacular decrease in the energy of the $2_1^+$ state when passing from N=58 to N=60 for the strontium and zirconium isotopes. As the Z=40 can not be considered a shell closure the mechanism for such a rapid change was for long not well understood. Recent data give example of shape coexistence deduced from Coulomb excitation measurements [139], lifetime measurements [140, 141], and in-elastic electron scattering [142]. The increase in collectivity has been explained using Monte Carlo Shell Model calculations [143], and is due to what has been dubbed "type-II shell evolution" where the promotion of protons impacts the effective single particle energies of the neutrons via the tensor force allowing the build up of quadrupole collectivity. The region of a sudden increase in collectivity at N=60 is limited by Z>36 [144]. Dudouet et al. also presents an interesting parallel between the Z~24 N=40 and Z=40 N~60 regions giving an explanations that corresponds to what is seen for chromium and iron isotopes close to N=40. In short one needs more than 36 protons to activate the quasi-SU(3) space ($g_{9/2}$, $d_{5/2}$, $s_{1/2}$). More recent work looking at the spectroscopy of $^{98,100}$Kr moderates the conclusion that the deformed structures found in Sr and Zr are not present in Kr. These structures are present at higher energies, i.e.
shape coexistence [145].

The classic region of shape coexistence and shape evolution is neutron deficient lead and mercury isotopes. Continuous experimental and experimental efforts are made, with as an example the study of shape coexistence in mercury isotopes [146, 147]. Marsh et al. extend the measurements of averaged squared charge radii and explains the staggering seen for $^{180-186}$Hg as the result of competition between quadrupole correlation energy and pairing, where the "correlation energy" wins for odd neutron mid-shell nuclei due to blocking by the unpaired neutron.

## Shape and collectivity in neutron deficient Os isotopes

The region of neutron deficient nuclei in proximity of the shell closure Z=82 shows a large number of examples of shape coexistence [9], making it an interesting region for nuclear structure research. A good example is that of $^{186}$Pb with three $0^+$ states close in energy [148]. Other nuclei in the region where shape coexistence have been shown are neutron deficient Polonium, Mercury and Platinum isotopes. The shape coexistence in this region is viewed as the result of proton excitation across the Z=82 shell gap [9], giving rise to highly deformed structures which are brought down in energy via the increased number of n-p interactions available in such configurations. This also explains why the intruder states are lowest in energy for a half full N=82–126 neutron shell. Lifetime measurements in Pb [149, 150, 151], Po [152], Hg [153, 154], and Pt [155] isotopes have corroborated this understanding of the shape coexistence phenomena. The model-independent measurements of the B(E2) values in the yrast bands have given firm experimental evidence for several low-energy configurations that are highly mixed at low spins. Beyond mean-field calculations support this picture [156], although the idea of "simple band mixing" is an oversimplification.

The question of shape coexistence in light osmium isotopes has been addressed several times over the last few decades [157, 158, 159]. Spectroscopy in $^{170-173}$Os and lifetime measurements in the yrast band of $^{172}$Os are discussed in terms shape coexistence described by three-band mixing or particle alignment. More recent work concerning neutron deficient Os isotopes such as $^{162}$Os [160, 161], including a lifetime measurement of the $17/2^+$ state in $^{167}$Os [162], give evidence for a shape transition from prolate deformed via $\gamma$ soft nuclei to spherical shapes close to the N=82 shell gap. For $^{168}$Os shape coexistence is a possible explanation for observations [160].
<figure><img src="image_7.png" /><figcaption>Figure 3.3: Transition strengths for the $4_1^+$ → $2_1^+$ and $2_1^+$ → $0_1^+$ for $^{166}$W [163], $^{168}$Os [164], $^{170}$Os, and $^{172}$Pt [165].</figcaption></figure>

To try to clarify the question of shape coexistence in $^{170}$Os an experiment was performed during 2012 to measure lifetimes in the yrast band of $^{170}$Os using the ORGAM array and the OUPS [166] (see "OUPS box") at the ALTO facility $^a$. Excited states in $^{170}$Os were populated using the reaction $^{142}$Nd($^{32}$S, $4n$)$^{170}$Os. The target, evaporated onto a 2 mg/cm$^2$ thick Ta foil facing the beam, was made of isotopically enriched $^{142}$Nd and had a thickness of 1 mg/cm$^2$. A 5 mg/cm$^2$Au thick foil was used as a stopper for the fusion-evaporation fragments. The experiment, a part of the post-doc project of Alain Goasduff, was successful and the data analysis was performed within the two years of the post-doc. However, as a paper was started do be drafted in 2014 it stood clear that the results that we had found were difficult to explain as the collectivity decreased from the $2_1^+$ state to the $4_1^+$ state, which was not supported by the beyond-mean-field calculations performed for the publication. This problem combined with the end of the post-doc of Alain Goasduff and my increased involvement in preparing and executing the first campaign of AGATA@GANIL led to that the osmium paper was put a side, without being forgotten. As a set of surprising results, shown in figure 3.3, from the same region showing the same anomaly as $^{170}$Os in the yrast band were published [163, 164, 165] a renewed effort was made to finish the publication for $^{170}$Os [167], see appendix 7.9. Looking at the energy systematics of the lowest yrast and yrare levels of the osmium isotopes, see figure 3.4, there is the increase in excitation energy moving away from the middle of the N=83-126 shell. Also seen is an indication that the $0_2^+$ state will be above the $2_2^+$ state in $^{170}$Os. Calculations give in general a too stretched energy spectrum, and in particular too high laying $0_2^+$ states. There is however nothing that could explain the decrease of the $B(E2; 4_1^+ \rightarrow 2_1^+)$ transition strength seen moving from $^{172}$Os to $^{170}$Os. Cederwall et al. [165] suggests that the explanation is to be found in a transition into a seniority like phase at N=92. The high collectivity of the $2_1^+$ states and their conformity to systematics in the region are not properly given a satisfactory explanation in a seniority like scheme.
<figure><img src="image_8.png" /><figcaption>Figure 3.4: Energy systematics for the lower states in osmium isotopes. Beyond-mean-field calculations performed using the Symmetry Conserving Configuration Mixing method are also shown. The calculations were performed by T. R. Rodríguez.</figcaption></figure>

Looking at the nuclei in the region showing the unusually low $B(E2; 4_1^+ \to 2_1^+)$ one can observe, see figure 3.3, that while the $B(E2; 2_1^+ \to 0_1^+)$ are different and in agreement with the distance to shell closures (N=82 and Z=82) the $B(E2; 4_1^+ \to 2_1^+)$ values are rather constant. An explanation to the low $B(E2; 4_1^+ \to 2_1^+)$ value found in $^{170}$Os could have been that the $4_1^+$ is not a part of the same band as the $2_1^+$ state. However, the SCCM calculations do not support such a scenario. For $^{44}$S [168], such a scenario was found i.e. that the $4_1^+$ state is of single particle character and is produced by the alignment of a pair of nucleons. In figure 3.5 calculations expanded by performing PN-VAP including cranking and by extending the range of triaxial quadrupole deformations to $-60^\circ < \gamma < 120^\circ$ as done in Ref. [168] are shown. Such a single-particle state would manifest itself in these calculations by a minimum present for the PES calculated with $J_c = 4$ (third row in figure 3.5) not present for $J_c = 0, 2$. As no such minima are found the calculations are not capable of explaining the low $B(E2; 4_1^+ \to 2_1^+)$ value.

<footnote>ªA comment in the proposal that in the future it could be possible to perform Coulomb ex-citation of Os isotopes at Spiral2 using the S3 spectrometer could deserve a comment but I will not...</footnote>
<figure><img src="image_9.png" /><figcaption>Figure 3.5: Potential energy surfaces for <sup>170</sup>Os generated by Variation After Particle number projection followed by projection on good angular momentum. This for four different rotational frequencies used for the cranking. Calculations by T. R. Rodríguez.</figcaption></figure>

The unusually low B(E2; 4<sup>+</sup><sub>1</sub> → 2<sup>+</sup><sub>1</sub>)'s found in the region around <sup>168</sup>Os raise questions. Are we looking at a common cause failure in the lifetime measurements? Is there yet to be understood new physics? Effort will surly be devoted to answering these questions despite the experimental difficulties given that these nuclei are for the moment only accessible via fusion-evaporation reactions making if difficult to try to measure the transition strengths using Coulomb excitation <sup>b</sup> or to populate non-yrast low-laying states in the reactions.

A nuclear physics highlight related to shapes in the last decade was the discovery of permanent octupole in <sup>224</sup>Ra [169]. Similar work on Radon isotopes has also been performed showing that although they perform octupole vibrations no static octupole deformation is seen [170]. Apart from the intrinsic interest in "exotic" nuclear deformations static octupole is of interest because their application in the search for static permanent electric-dipole moments. This is an indicator of physics beyond the standard model and nuclear structure physics enters via the Schiff moment (e.g. [171]).

The era of measuring the shape of very heavy nuclei has also arrived. With the help of a Penning trap connected to the SHIP separator at GSI the mean squared radius (or the difference with respect...) of the nobelium isotopes <sup>253,253,254</sup>No [172] were measured together with the magnetic dipole moment for <sup>253</sup>No [173]. The authors compare their results with energy-density functional calculations that are giving good

<footnote><sup>b</sup>Coulomb excitation at S3 would not have been without interest...</footnote>
agreement between calculated and measured deformation.

Prompt spectroscopy of very-heavy and superheavy nuclei

Starting with the prediction from the 1960's [174] of an island of stability for superheavy nuclei around Z=114 and N=184, intensive experimental work to synthesis and/or find so-called super heavy nuclei has been performed. This work has mainly been divided between the synthesises of superheavy nuclei to explore the limits of the table of isotopes and the spectroscopy of lighter heavy nuclei. The often stated goal of spectroscopy of very-heavy and super-heavy nuclei is to benchmark theoretical models as close as possible to the predicted island of stability. It is hoped that this way reliable predictions for the next magic proton and neutron numbers can be made. This is illustrated by an example taken from Dobaczewski et al. [175] shown in figure 3.6 where the single-particle levels, as given by relativistic mean-field calculations, for different deformations are shown. By comparing experimental determination of the ordering of the nuclear levels with such calculations at experimentally determined deformation the quality of the theoretical description can be scrutinized. The experimental determination of particle configuration in these very-heavy and superheavy nuclei can in some cases be done by prompt γ-ray spectroscopy using recoil- and/or recoil-decay tagging (for description of these methods see [176] and references therein). In such studies so-called K isomers [177] provide very pure configuration and hence excellent data for theory bench marking. Such an isomer and the rotational band built on top of it in $^{252}$No was studied in an experiment at the Accelerator Laboratory of the University of Jyväskylä. Here the configuration of the $8^-$ isomer was determined to be spin singlet two-quasi neutron state with the configuration $7/2^+[624]_ν ⊗ 9/2^-[734]_ν$ [178]. In close relation to this I also worked with the MUSETT segmented Si array for Recoil-Decay-Tagging studies at VAMOS [179].
<figure><img src="image_10.png" /></figure>

Figure 3.6: Illustration of the development of deformed shell gaps for $^{254}$No as calculated using the NL1 and NL3* covariant EDFs. Figure taken from Dobaczewski et al. [175].

The experimentally determined deformed shell gaps of Z=100 and N=152 [176] for deformation of about $\beta_2$ = .3 are not yet correctly reproduced [175].

Starting at around the turn of the century, there has been an impressive collection of experimental data on heavy- and superheavy nuclei as well as progress in the production of superheavy nuclei. Today the element Z=118 is the heaviest nuclei that has been synthesized and its and the decay chains of Z=117 have been extensively studied proving not only existence of the isotopes but also allowing insights to shell structure from Q values and showing the need of using x-rays to identify the Z [180, 181, 182, 183, 184, 185].

A large extension of the spectroscopy of lighter nuclei has also been achieved. Here K isomers have been used to determine the orbital ordering in heavy nuclei. The limited number of possible ways to create the K-isomers allows for good comparisons between theory [186, 187] and experiments. It has also been suggested that K isomerism might offer longer lived states for superheavy nuclei than the ground states of the same nuclei [188]. K isomers are useful for assigning spin and parity to states is the prompt spectroscopy of odd nuclei [189, 190], but to move forward it seems as a new generation of γ-ray spectrometers, such as AGATA, is needed. For this reason most prompt spectroscopy has been performed on even-even heavy and superheavy nuclei. These studies have helped to confirm the existence of deformed shell closures at Z=100 and N=152. An example is that of $^{256}$Rf [191]. A recent review
of in-beam γ-ray spectroscopy is given by Theisen et al. [192]. Spectroscopy after α decay is much used to determine the nuclear structure and also useful for assigning spin and parities to states allowing careful comparison with theory. It is found that theory often fail to reproduce the correct level ordering [193]. The question of where the next spherical shell closures are located remains open as the microscopic nuclear models still fail to reproduce spectroscopic data for lighter nuclei Z~100-108 and N~150-160 and the extrapolation to heavier system therefore remains shaky.
## Chapter 4

# Nuclear structure between now and the end of my life...

The general questions and open subjects are described in length in the NUPECC 2017 long range plan [39]. I will not repeat those here but instead explain how I see my involvement, using γ-ray spectroscopy and the measurement of collectivity, in the work of answering these questions. The focus will be on using Doppler Shift methods (in combination with Coulomb excitation). With this I do not make a statement about the merits of different techniques or the importance of observables, I just stay close "to home". I will also take me the freedom to be generous in the sense that no strict feasibility filter will be applied. And, there is of course the assumption of the existence of a high-performance γ-ray spectrometer such as a 3–4π AGATA.

The open question in nuclear structure physics can be phrased as [39] (over stricken means I think that what I do have no direct relevance):

* How does the nuclear chart emerge from fundamental interactions?

* Where are the limits of stability and what is the heaviest element?

* How does nuclear structure evolve across the nuclear landscape and what shapes can nuclei adopt?

* How does the structure change with temperature and angular momentum?

* How to unify nuclear structure and reaction approaches?

* How complex are nuclear excitations?

* How do correlations appear in dilute neutron matter, both in structure and reactions?

* What is the density and isospin dependence of the nuclear equation of state?

The question about structure- and shape-evolution across the nuclear chart can be addressed with a few observables; the mass, the energy of the first excited state in even-even nuclei, and the reduced transition probability of the transition depop-ulating the first excited state. There is as well the spectroscopy of even-odd close to closed shell nuclei. The nuclei of great interest for which these observables are not
already measured (February 28, 2020), i.e. $^{60}$Ca, $^{100}$Sn, and nuclei close to the hard-to-get-to-region around $^{208}$Pb will be addressed by experiments performed in large-scale collaboration at facilities such as RIKEN, HFRIB, or FAIR using state-of-the art detectors such as AGATA and GRETA. While this is clearly some of the most important work there is to be done I do not see myself as a driving force in it. This because what attracted me to nuclear structure physics in the first place was the "medium sized science" of it.

What I have in mind of trying to do instead is to look for "exotic" states in less exotic nuclei in experiment that can be performed at medium sized or even small facilities (but assuming state of the art detection systems). The number of experimentally known lifetimes for non-yrast states is illustrated in figure 4.1 where nuclei with known lifetimes for the first and second 2+ and 4+ are shown, respectively. It can be seen that the known non-yrast states are closely clustered around stable nuclei. This reflects that the best way of exciting the non-yrast states are with low-energy Coulomb excitation and hence requires stable targets or post-accelerated radioactive beams. These levels give important information about the wave functions and hence are excellent for probing our understanding of the nuclear system. Non-yrast states will be accessible via low-energy Coulomb excitation at facilities like Spiral1, HEISOLDE, and SPES, using HPGe detectors such as AGATA or MINIBALL to detect $\gamma$ rays. The radioactive beams will also be combined with Plunger devices using non-conventional targets to allow transfer reactions in combination with the RDDS technique. These are also reactions that can be performed with high-intensity stable beams where powerful ancillary detector systems such as magnetic spectrometers and/or particle detectors adds large selectivity to select the reaction product. Near future possibilities include studies of non-yrast states around N=40,50 and also the region of shape change around $^{100}$Zr. This is a region of interest because it is accessible for calculations using the interacting shell model, mean-field methods and, although with less precision for the moment, in ab-initio calculations. To exemplify some physics cases from a letter of intent, for which I am the spokesperson, for the second AGATA at Legnaro campaign are given here:

Yrast and non-yrast states close to $^{68}$Ni is accessible using multi-nucleon transfer reactions with either heavy beams (targets) for yrast states in more neutron-rich nuclei or lighter beams (targets) for less neutron-rich species non-yrast states. Here the general goal would be to complete existing information on transition strengths.

* Transition strength of non-yrast and "high spin" states close to $^{68}$Ni.

Different versions of fission (fusion-fission, Coulomb induced fission etc) and multi-nucleon transfer reactions allow the population of nuclei around N=54 and N=86. These are regions with signs of substantial $\gamma$ softness or deformation. As spectroscopic information now is rather abundant the next step to better characterize these nuclei and challenge the theoretical description of them (accessible both with large scale shell model calculations and symmetry restored energy density functional theory calculations) is to measure transition strengths of at least a few of the yrast states.

* Transition strengths in the region of $\gamma$ softness N=54 and N=86.

Another observable is the g-factor, which is a sensitive probe of the occupation of orbitals. Recent work has shown how g factors probe the structure of $2_1^+$ states in the semi-magic tin isotopes [194]. Nickel shares with tin that it has a closed proton shell, and has a large number of bound isotopes, which allows the study of how nuclear
<figure><img src="image_11.png" /><figcaption>Figure 4.1: Illustration of how the number of datum decreases for non-yrast states and how they cluster around the valley of stability. The black crosses are new data from 2018-2019 from a quick search using NSR.</figcaption></figure>
structure develops as neutron orbitals are filled. As recent shell-model calculations have proven capable of reproducing both excitation energies and transition strengths in nickel and iron isotopes close to $^{68}$Ni, a natural next step would be to test them against g factor measurements. The picosecond scale lifetimes of the $2_1^+$ states in $^{66}$Ni and in $^{62-64}$Fe make it feasible to measure the g factors using recoil-in-vacuum methods. It should be recognized that the g factor measurements also depend critically on the lifetime of the state, and the alignment given in the reaction, which are not well known in advance. Vacuum deorientation effects must be evaluated in plunger-type lifetime measurements, making the determination of alignment and deorientation important also for estimating systematical errors in lifetime measurements. It is therefore important to explore the possibility to also extract the g factors from the lifetime data, along the lines of recent recoil in vacuum measurements on the neutron-rich Sn isotopes [194]. Multi-nucleon transfer reaction has proven capable of populating these moderately neutron-rich nuclei and the yrast states of interest. Here an AGATA covering a fairly large solid angle coupled to the PRISMA together with a Plunger device is an attractive setup for an attempts at measuring g factors in the region close to $^{68}$Ni.

* Measure g-factors close to $^{68}$Ni.

As amply discussed in this HDR intriguing results for the B(E2) strengths in the yrast bands for neutron deficient nuclei close to N=94 have been found the last few years [163, 164, 165, 167]. In this nuclei a lower $B(E2;4_1^+ \rightarrow 2_1^+)$ than the have been measured. $B(E2;2_1^+ \rightarrow 0_1^+)$ This observation has not yet a satisfactory theoretical explanation. As $^{170}$Os can be produced with a high cross-section in fusion evaporation reactions, dedicated studies of both pure spectroscopy and transition strengths of higher laying yrast and non-yrast offers a good laboratory for investigating this surprising loss in collectivity with spin. As the fusion cross section is dominated by fission in this region, the coupling of AGATA with the recoil filter detector would be beneficial to clean the $\gamma$-ray spectra. Also, the use of a Plunger with a degrader foil together with the RFD can be envisioned.

* In-depth investigation of $^{170}$Os.

I will finish my perspectives with a very ambitious and more worked out example. One of the experiments that I've proposed as a letter of intent with AGATA at several occasions is the measurement of lifetimes in the yrast band of $^{254}$No with the RDDS technique. Such an experiment would be a tour de force using a Plunger, a $\gamma$-ray spectrometer such as AGATA, and a separator for recoil-tagging of the $^{254}$No events. The motivation behind this experiment is that there are no measured absolute transition strengths for very heavy nuclei. There are theoretical predictions for B(E2) values in the yrast band of $^{254}$No[195] based on the relativistic density functional DD-PC1, which are presented in figure 4.2. The goal is then to measure another type of anchor point for nuclear theory trying to predict the stability of superheavy nuclei and states in superheavy nuclei. This to make the extrapolation more reliable (is such a thing as reliable extrapolation exists).

What I humbly suggest is to measure the lifetimes of excited states in ground-state rotational band in $^{254}$Nousing the RDDS technique with Oups plunger device coupled with a spectrometer such as VAMOS Gas Filled mode, the AGATA germanium array and the focal plane detector such as MUSETT [179].
<figure><img src="image_12.png" /><figcaption>Figure 4.2: The low-energy collective spectra of $^{254}$No calculated with the collective Bohr Hamiltonian based on the relativistic density functional DD-PC1 and a separable pairing force of finite range, compared to the experimental yrast sequences. The calculated B(E2) values, in Weisskopf units, refer to transitions depicted by arrows. Figure taken from Heenen et al. [195].</figcaption></figure>
Considering the population mechanisms and the very large conversion coefficients for such heavy and deformed nuclei one would expect that states above the $8_1^+$ or $10_1^+$ are our best candidates when using the RDDS technique. This is advantageous as the lifetime of the lower spin members in the yrast band possibly can be measured using other techniques ("charged plunger", "in-trap decay"), and we would have the possibility to investigate if the yrast states are pure rotational states or if there are variation in the intrinsic quadrupole moment in the yrast band.

The proposed experiment uses the fusion evaporation reaction $^{48}$Ca($^{208}$Pb, $2n$)$^{254}$No in inverse kinematics which will populate $^{254}$No with a cross section of about $2~\mu$b. In order to use the RDDS technique, and have sufficient recoil velocity to pass a gas-filled separator inverse kinematics is the only option. After the separation by the gas filled separator the evaporation residues will pass through a focal plane detection system to measure the energy loss and give a timing signal. The residues will finally be implanted in a focal plane detector, providing the energy, the position and implantation time information of both the recoiling nuclei as well as their subsequent decay. Using Recoil Decay Tagging and recoil gates, clean $\gamma$ spectra of the interested nuclei will be reconstructed. The long half life of the $^{254}$No nuclei (55 s) and its relatively high production cross section could make it beneficial to the Recoil Decay Tagging method in order to gain statistics.

<table><caption>Table 4.1: Experimental Parameters</caption><thead><tr><th>Reaction</th><th></th></tr></thead><tbody><tr><td>Target fronting</td><td>2mg/cm<sup>2</sup> <sup>nat</sup>Au</td></tr><tr><td>Target</td><td>0.5mg/cm<sup>2</sup> <sup>48</sup>Ca</td></tr><tr><td>Target Backing</td><td>0.5mg/cm<sup>2</sup> <sup>nat</sup>Au</td></tr><tr><td>Beam</td><td>16pnA <sup>208</sup>Pb</td></tr><tr><td>Degrader</td><td>5 mg/cm<sup>2</sup> <sup>nat</sup>Au<br>or<br>2 mg/cm<sup>2</sup> <sup>nat</sup>Mg</td></tr><tr><td>Rate and beam time estimates</td><td></td></tr><tr><td>Beam time request</td><td>Two effective weeks on target</td></tr><tr><td>Cross section to gsb</td><td>0.8&mu;b</td></tr><tr><td>Transmission of <sup>254</sup>No</td><td>80%</td></tr><tr><td>Efficiency MUSETT</td><td>50%</td></tr><tr><td>Efficiency AGATA</td><td>10%</td></tr><tr><td>Magnetic rigidity [B<sub>&rho;</sub>] in gas, Ghiroso [196]</td><td></td></tr><tr><td>Residues (<sup>254</sup>No)</td><td>1.78</td></tr><tr><td>Beam (<sup>208</sup>Pb)</td><td>1.64</td></tr><tr><td>Scattered degrader (<sup>nat</sup>Au)</td><td>1.59</td></tr><tr><td>Scattered Target <sup>48</sup>Ca</td><td>1.54</td></tr><tr><td>Scattered degrader (<sup>nat</sup>Mg)</td><td>0.900</td></tr></tbody></table>

I would suggest an experiment with a $0.5~\text{mg/cm}^2$ $^{48}$Ca target, made as a sandwich between $2~\text{mg/cm}^2$ gold upstream the target and $0.5~\text{mg/cm}^2$ gold downstream the target. Taking into account the energy loss in the front of the target, a beam energy of 1039 MeV would be needed, giving a center-of-target energy of 950 MeV. A degrader foil of $5~\text{mg/cm}^2$ gold or $2~\text{mg/cm}^2$ magnesium would be used at a short distance downstream from the target in order to slow down the reaction products recoiling from the target. The fusion-evaporation residues, i.e. $^{254}$No, will leave the target
with a velocity of about 8% of the speed of light. After the degrader the speed will be about 6% of the speed of light. This is a sufficiently large change to allow for peak separation when analyzing the RDDS data.

The first major challenges with such an experiment is the separation of the beam in the separator. This aspect has been investigated to some extent by C. Theisen while preparing the LOI that this paragraph is based on. In table 4.1 the expected magnetic rigidity of the different ion species are shown. The conclusion is that in a gas-filled separator such as the projected gas-filled VAMOS it would be possible to separate the wanted fusion-evaporation residues from other unwanted ions (beam, elastically scattered target and degraders etc.). The second important challenge for such an experiment would be that of the target itself. In order to protect the $^{48}$Ca from oxidation and to be able to stretch it would have to be sandwiched in gold. This is a technique that works well with light beams (e.g. it was use for lifetime measurements in $^{70}$Se [122] and $^{74}$Kr [112]). How such a target would withstand the heavy $^{208}$Pb is not clear.

If I convince myself all the problems can be solved and I try to make the most realistic simulation of the experiment the results are very promising. Using parameters for the reaction and efficiencies of the separator and focal-plane detection as given in table 4.1 for the basic kinematics. Further taking into account energy losses in target and degrader and straggling to refine the modeling of the peak shapes. Finally adding Coulomb excitation on the rather large amounts of gold, and a random $\gamma$-ray background (shape and amount calibrated on $^{254}$No spectra from Jyväskylä) to make give more realistic spectra. For $1\pi$ AGATA (max useful solid angle for RDDS in this case) and 48 hours of beam time these simulations suggest that we would have spectra like those shown in figure 4.3.

<figure><img src="image_13.png" /><figcaption>Figure 4.3: Simulations of the expected statistics for 48 hours of beam on target per distance. The simulation includes a background not coming from the gsb of $^{254}$No. For details, see text.</figcaption></figure>
Chapter 5

High resolution γ-ray
spectroscopy

The energy scale for the atomic nucleus is MeV. So when nuclei deexcite the excess energy is mostly emitted as γ rays. For particle-bound excitations in the nucleus the width of the energy level is small as compared to its energy and compared to the average level densities with identical quantum numbers (e.g. spin and parity). As a consequence high resolution γ-ray spectroscopy is a valuable tool for investing the structure at low excitation energy in atomic nuclei. Furthermore, as the angular momentum and linear polarisation of the emitted γ rays can be measured the spin and parity of the state emitting the γ ray can often be deduced. Using more advanced spectroscopic techniques transition strengths, magnetic moments, and quadrupole moments can also be measured.

The ultimate in high resolution is given by Bragg diffraction spectrometers such
as the GAMS [197] used with the high-flux reactor at Institut Laue-Langevin (ILL),
Grenoble, France. Here a resolution of a few ppm can be achieved, but with a very low
efficiency. This technique is used for performing complete spectroscopy, and lifetime
measurements using the GRID technique. The low efficiency prohibits its use when γγ
correlations are needed or in-beam experiments when heavy ions are used to populate
excited states in the nuclei of interest. Here detector systems with higher efficiency
are needed. If the demands on resolution is moderate, i.e. low γ-ray multiplicity
experiments and simple excitation schemes, highly efficient scintillator detectors such
as LaBr₃ or NaI are used with great success (e.g. DALI [198] and DALI2 [199] at
RIKEN). As the average γ-ray multiplicity in an experiment increases or nuclei with
more complex deexcitation schemes higher energy resolution is needed. This need is
addressed using semi-conductor detectors, and in particular High Purity Germanium
detectors. For more details on γ-ray spectroscopy see classic text books [200, 201].

**5.1 The High-Purity Germanium detector**

With an energy resolution of about 1-2 %, individual crystals up to 150% relative efficiency <fnref n="1" />, and a peak-to-total of 25% High-Purity Germanium detectors is the detector technology that gives the best compromise between energy resolution, peak-

<footnote n="1">¹Measured at a γ ray energy of 1332 keV and compared to a 2×2 inch NaI detector at 25 cm</footnote>
to-total, and efficiency for γ-ray spectroscopy. If combined with different techniques to increase the peak-to-total (anti-Compton shields, γ-ray tracking...) HPGe detectors make excellent building blocks for large detector arrays for detailed γ-ray spectroscopy. For a recent and comprehensive review of the technology advances and use of HPGe detectors see [202].

## 5.2 AGATA

The Advanced GAmma-ray Tracking Array [203] is a European project born at the end of the 1990s. It capitalizes on the advancements made with the Euroball [204], EXOGAM [205], and MINIBALL [206] HPGe detector arrays. With arrays such as Euroball the sensitivity limit for high-spin experiments with the optimization of high Peak-to-Total (Compton shields) and low multi-hit probability (large number of detector elements) had been reached. The main limitation comes from the loss of effective solid angle due to the BGO Compton Shields. In parallel HPGe detector arrays were optimized for reaction using radioactive beams, such as Coulomb excitation and single particle transfer reaction, where the emphasis was on high efficiency and Doppler Correction. Without Compton Shields the HPGe crystals are positioned very close to the target giving a high detection efficiency for reaction with low γ-ray multiplicity (« number of detector elements). However, as the recoil velocity in general is rather high a good Doppler Correction capability was needed forcing the development of segmented detectors and pulse-shape analysis [207].

Once segmented encapsulated HPGe detectors were a proven reality the step towards γ-ray tracking was not long. By tiling a $4\pi$ sphere in irregular hexagons it is possible to close pack coaxial tapered HPGe crystals covering more than 80% of the solid angle. To keep an acceptable peak-to-total an alternative Compton suppression have to be used, which is the γ-ray tracking. This is made possible by the position sensitivity of the highly segmented HPGe detectors. In the case of AGATA, and the sister project GRETA in the USA, 36 folded segmentation is used. The outer contact of the crystal is segmented six times longitudinally and six times along its depth axis. This is shown in figure 5.1 together with the not yet segmented crystal, a sketch of the AGATA triple cryostat and finally an encapsulated crystal. All 37 seven signals are continuously digitized and sent to FPGAs where energy and time information is extracted if the central contact energy, corresponding to the total energy deposited in the crystal, is above a threshold (typically 10-20 keV). In that case the energy, time, and about 1 µs of signal is sent forward to perform pulse-shape analysis where the γ-ray interaction positions are calculated. After this step the γ-ray hits are sent to event building and the actual γ-ray tracking. This is illustrated in figure 5.2.

### 5.2.1 The AGATA detectors

The individual AGATA detectors are made out of HPGe crystals that are 90 mm long and have a diameter of 80 mm. In AGATA, as can be seen in figure 5.2 there are three slightly different shapes for the crystals. There are referred to Red, Green, and Blur or as A, B, and C. To extract the best possible energy resolution from such complex detectors care has to be taken to correct for crosstalk between the channels inside one crystal (this is enough for AGATA, however if less care is taken when designing the front-end electronics there might also be crosstalk between crystals). A novel feature is the use of pulse shape analysis to correct for neutron-damage induced trapping to
<figure><img src="image_14.png" /><figcaption>Figure 5.1: AGATA HPGe crystal and cryostat. The shaped Germanium crystal before segmentation is shown in the upper left corner of the figure. In the lower left corner the encapsulated crystal is shown. On the upper right side the AGATA triple cryostat is shown. Finally, the lower right corner is showing the segmentation of the AGATA crystals.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure 5.2: Schematic view over the γ-ray tracking detector array AGATA. In the top left corner an AGATA crystal is hit by a γ-ray. Pulse shapes are shown in top right corner. The result of the PSA goes into the global frame for tracking, illustrated by the many AGATA crystals in the bottom right corner. Finally, the result of the tracking is a γ-ray spectrum, shown in the bottom left corner.</figcaption></figure>
recuperate the energy resolution. Many excellent publication exists describing these
detectors, cryostats [208], and calibration procedures used [209, 210, 211].

My contribution to Costumer Acceptance Testing and cross-talk
measurements

During my post-doc at CEA Saclay I was involved in setting up the AGATA
customer acceptance laboratory, shown in figure 5.3. I did participate in
mounting several crystals in single-crystal cryostats. In order to accept the
crystals a set of tests have to be performed. They included validation of the
energy resolution of all 37 channels and characterisation of the crosstalk in
the detector. The crosstalk is dominated by the capacitive coupling between
the segments and central contact. There is also a small coupling between seg-
ments. These couplings are removed by the calibration procedure in the case
of only one segment having a net charge, but generate a shift of the full en-
ergy peak in the case of multi-segment events, see figure 5.4. This has been
modeled with high accuracy by B. Bruyneel et al. [209]. The electronics of the
laboratory consisted of one analog channel used for reference measurements
and a 40 channel digital DAQ system based upon 10 TNT2 card [212], each
card measuring 4 channels. As a results of this timestamped events where
written into 10 different files that were sorted and time correlated offline.

<figure><img src="image_16.png" /><figcaption>Figure 5.3: Photo of the AGATA test
laboratory at CEA Saclay</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>Figure 5.4: Example of crosstalk mea-
surement of a AGATA crystal.</figcaption></figure>

In addition to participating in setting up the laboratory I also wrote the soft-
ware used for energy measurements and crosstalk characterisation. The soft-
ware time correlates the data from the different TNT2 cards, performs energy
calibration and creates ROOT trees [213] containing the calibrated and event-
build data. Histograms for characterisation of the detector in either so-called
singles or coincidence mode can also be created with the program. This soft-
ware is still used at CEA and IPHC (as in 2019).
### 5.2.2 Detector modeling, characterization and PSA basis generation

It was understood early on within the AGATA and GRETA projects that a key for performing PSA is the fidelity with which the pulse shapes from the highly segmented HPGe detectors can be modeled (or experimentally determined). If this condition is fulfilled one can expect a PSA that gives accurate position information, has some capability to estimate the number of interaction inside a single segment with net-charge, and delivers a good estimate on the error of the deduced position. In the AGATA collaboration this work was taken on with a two-legged approach. The first leg being simulations of the detectors and the second leg being detailed measurements of the detector response as function of interaction position, referred to as scanning. Examples of packages for pulse-shape calculations are MGS [214], JAZZ [215, 216], and ADL [217, 218]. Scanning of detectors have been performed and is performed at several location within the AGATA collaboration (amply treated in [219, 220, 221, 222, 223]). Careful characterisation of the electronics response and innovative techniques to measure the space-charge profiles based on capacitance measurements have given valuable information about the detectors [208, 209, 224, 225, 226, 227]. Within the AGATA community the work of adapting simulations to this body of experimental data has been performed using the ADL by B. Bruyneel et al. [217, 218] in the IKP Cologne group. The result of this work is used in the form of the pulse-shape data bases used for the PSA in the AGATA.

#### AGATAGeFEM - A Finite Element Method based signal modeling program.

In the beginning of 2006 I started an effort to develop a pulse-shape calculation code. The difference as compared to what existed and was used within the AGATA community was that the description of the geometry was to be exact within machine precision for the transport of charge carriers and when solving the Poisson and Laplace equations. Therefore an adaptive finite element methods was to be used so that any geometry can be adequately described. The program, named AGATAGeFEM, is written in C++ and leverage quite heavily both object orientation and the template features of C++ (but very little C++11). For the charge-carrier transport the ordinary differential equation solvers of the Gnu Scientific Library [228] were chosen. Typically a 4th order Runge-Kutta solver with adapted time step is used for the calculations. For describing the geometry two different version exist, one written in its totality by me and one that use the geometry packages of geant4. Earlier versions of the program used mainly a library called dealii [229, 230]. Dealii is a very flexible code that allows an iterative refinement of the FEM mesh in a very simple way. However, the mesh cell geometry is limited to quadrilaterals and hexahedra. This is for solving the partial differential equations very good choices. I did, however, not want to project down the solutions to a regular grid when using them in charge-carrier transport processes and calculations of the induced signals via the Shockley-Ramo theorem, the quadrilaterals and hexahedra are however challenging. Behind this is the idea that the refinement procedure tells where high granularity is needed and all projections to regular grids deteriorates this information. The problem is then that to find the correct cell in an irregular mesh one has to ask cells if a point belongs to
them or not. Hexahedra cells have boundaries that are curved making these
calculations quite flop intensive. As a result the first version of AGATAGeFEM
was capable of calculating about 2-3 pulse-shapes per second. While this is
enough to calculate a basis for use with PSA it is far from enough for using the
code in fitting of parameters used in the pulse-shape calculations or to use it
in a complete Monte Carlo simulation chain. I therefore moved the FEM part
of the program into using the libmesh library [231]. It uses tetrahedra with
each side defined by three points making the calculation whether a point is
inside a cell or not much faster. I further more restrained to the use of only
linear basis function in the solution. This way the code reproduced the results
from before but is almost a factor of 100 faster.

Other features of the AGATAGeFEM is that it is fully parallelized using both
threads and the MPI interface. Field calculations are parallelized by using one
MPI process per field that is calculated. If the libmesh library was built with
thread support further threads are used for each field. Pulse-shape calcula-
tions and χ² fitting of the parameters that enter into pulse-shape calculations
are also parallelized with a combination of threads and MPI. The χ² fitting is
based on the Minuit and Minuit2 [232] that comes with ROOT [213]. ROOT
has further been used to create an interface allowing calculating of both fields
and pulses. The fields and pulses can also be displayed inside the chosen de-
tector geometry from the ROOT interpreter interface (the cint and cling in-
terpreter). AGATAGeFEM has further a very simple server client mechanism
allowing other programs to ask the server to calculate pulse shapes.

All the needed miscellaneous codes for applying pre-amplifier response (de-
fined in time domain), cross talk, to re-sample pulse shapes, compare pulse
shapes, calculate pulse shapes from the output of the AGATA geant4 MC [233]
etc. are also included in the AGATAGeFEM.

Details can be found in a planned publication 7.11. As written in the OASIS
application (see section 7.13) the AGATAGeFEM code will be used in an effort
to improve our understanding of the detectors and where to concentrate our
efforts to improve the final result.

A method to scan the response as a function of position using an uncollimated
source was developed and tested using simulated pulse shapes (using MGS [214] and
AGATAGeFEM) and pulse shapes from the Liverpool scanning table [234, 235]. The
use of an "in-situ" method can help to solve many issues of the PSA as the pulse-shape
bases created includes effects such as crosstalk, time alignment between different seg-
ments etc.

In-situ determination of a pulse-shape basis for PSA

I initiated a project together with GANIL to test the ideas of Desesquelles et al. [234, 235] on source data taken at the GANIL site. The work was performed in close collaboration with two post-docs at GANIL, Hongjie Li and Caterina Michelagnoli.

The method proposed by Desesquelles et al. is based on finding experimental
estimators of the interaction position of a γ ray that can be calculated from
the pulse shapes. The estimators should have monotonous relations to the
coordinates of the interaction position. Having found such estimators re-
alistic simulations are performed giving the "true" distributions of interac-
tion positions from the $\gamma$ rays. The distribution of the experimental estimator
can then be matched with the simulated distribution of interaction positions.
This is done starting from one side of the simulated distribution and the dis-
tribution of the experimental estimator and demanding the fraction of total
area in the two distributions that coincide. This is illustrated in figure 5.5.

<figure><img src="image_18.png" /><figcaption>Figure 5.5: Example of matching the relative area for the simulated distribu-
tion and the distribution of the experimental estimator. The y axis ($f_r$) is the
experimental estimator for the radial coordinate. On the x axis the simulated
distribution of the radial coordinate of interaction points is given ($r$).</figcaption></figure>

This work is published, see Li et al. [236], and I refer to this paper for further
details.

5.2.3 Pulse-shape analysis

For γ-ray tracking to work a prerequisite is the correct determination of the positions
of the γ-ray interactions. Because of the finite distance needed for the energetic elec-
tron created to lose all of its energy a lower limit of a position resolution of about 1
mm is expected. This is to be (favorable) compared with the 5 mm FWHM resolution
needed for γ-ray tracking.
Many different methods for pulse-shape analysis (PSA) have been tried within the AGATA and GRETA community. In the AGATA community grid search (GS) [237], extensive GS [237], particle swarm minimization [215], matrix method [238], genetic algorithm [239], recursive subtraction [240], and neural networks (mainly for timing) [241] have been tried. The GRETINA (and GRETA) collaboration uses similar approaches, "With a realistic set of basis signals, signal decomposition is reduced to the task of fitting the waveform data, event-by-event, with the best possible linear combination of basis signals." [242]. In real life experiments, as of 2019, there is one big difference between how PSA is performed in the AGATA and GRETA collaborations: In the AGATA collaboration PSA allows for only one interaction point per segment, whereas the PSA done in the GRETA collaboration allows for more than one interaction in a segment. Comparing to Monte Carlo simulations the consequences of this are that within the AGATA community the number of interactions made by a γ-ray is underestimated whereas the GRETA collaboration overestimates this number [243]. This is one of the problems the OASIS ANR project tries to address. The OASIS ANR application is included as an appendix to this work, section 7.13.

The different approaches used all have in common that they compare a set of pulse-
shapes for known positions in the detectors with the experimental pulse shapes. A
metric of the type $\sum_i |y_i^{exp} - y_i^{bases}|^a$ is used. For $a = 2$ this is just the square
sum. The grid search codes of AGATA [237] has been shown to give the best result
with $a = 0.3$. This is indicative of the possibility to improve the bases used in the
PSA. As, in the beginning of 2019, no error estimates are made there is no need to
include an estimate of the noise on the experimental signals. Adding error estimates
is considered as an important step forward. Considerable efforts have been put into
estimating the performance of the PSA within both the AGATA [244, 245, 246] and
GRETA/GRETINA collaborations [247, 248]. The conclusions from these efforts are
that the resolution needed for γ-ray tracking is achieved. This is however a conclusion
that is somewhat contradicted by γ-ray tracking optimisations, discussed in detail in
section 2, taken from the ANR application for the project OASIS.

My efforts related to PSA in the AGATA project

In 2005 the first in-beam experiment with the AGATA symmetric triple cluster was performed. The goal of the experiment was to measure the position resolution for γ-ray interactions in the AGATA prototypes. The symmetric triple cluster consists of three 36 segmented symmetric HPGe crystals, and served as the prototype to the asymmetric triple clusters [208] used in AGATA today. Doppler Correction capabilities was chosen as the method to measure the position resolution. The experiment used a $^{48}$Ti beam with an energy of 100 MeV impinging on a 220 μg/cm$^2$ deuterated titanium target, with the reaction $^{48}$Ti(d,p)$^{49}$Ti populating excited states in $^{49}$Ti. Outgoing protons where detected in a double sided silicon strip detector, allowing for suppression of background from Coulomb excitation and the reconstruction of the direction of the outgoing $^{49}$Ti nucleus. A picture of the setup is shown in figure 5.6.
<figure><img src="image_19.png" /></figure>

Figure 5.6: Photo of the experimental setup used to measure the position resolution of the AGATA triple cluster prototype. To the left inside the target chamber the double sided silicon strip detector is visible with the AGATA triple cluster in the center of the picture. Picture taken from Recchia et al. [244].

The process of extracting the position resolution from such an experiment passes via Monte Carlo simulations of the experiment taking into account all other effects than the position resolution of the PSA. By varying the assumed position resolution for the γ-ray interactions the FWHM of the γ-ray peak of interest as a function of position resolution is created and compared to the experimental FWHM of the γ-ray peak of interest. This is described in detail in [244].

At the time of the experiment (Aug-Sep 2005) the signal bases used for the PSA were calculated using the MGS code [214] developed at Strasbourg. The work of analysing the data was shared between different groups in the AGATA collaboration. I took the responsibility to analyse the data using two different PSA approaches, the so called MINIBALL approach [206] and the matrix-inversion method [238].

In figure 5.7 the result for the grid-search algorithm presently used (with some modifications) is compared to the result from the MINIBALL and Matrix PSA algorithms. The MINIBALL algorithm can only be used for events with one net-charge segment, and it was used as a baseline reference. The Matrix algorithm developed by Desesquelles et al. [238] is based on the fact that an experimental signal can approximately be built up as a superposition of signals originating from fixed positions by giving a non-negative weight to each position. This problem is formulated as a matrix inversion problem solved using the non-negative least squares algorithm of Hanson and Lawson [249]. To further improve the signal-to-noise ratio a singular value decomposition is used. As can be seen in figure 5.7 the results are disappointing as compared to what was expected on the basis of the results on
simulated but realistic signals. The explanation is thought to be lack of fi-
delity for the basis of signals used. Given this and the improvements in the
signal bases, improved treatment of crosstalk, and determination of the t₀
that have been made [209, 217, 218, 224, 225, 226] a renewed effort concern-
ing the Matrix PSA is well worth considering. This is particularly true as it
provides event-by-event error estimates on the given interaction positions.

<figure><img src="image_20.png" /><figcaption>Figure 5.7: Comparison between different PSA methods used to analyse the data from the AGATA symmetric triple cluster test experiment performed at IKP Cologne in Aug-Sep 2005.</figcaption></figure>

As data from the Liverpool scanning table (see Dimmock et al. [250, 251] and references therein) became available I also tried the Matrix PSA using a pulse-shape data basis calculated using MGS on the data from the scanning table. This work, combined with efforts to try to coordinate work with PSA and detector characterisation was presented within the AGATA collaboration. It was decided that the DAQ of AGATA was to be based on the NARVAL [252]. As NARVAL is written in the programming language ADA an interface to allow the implementation of different algorithms in C (and hence C++) was defined by X. Grave (IPN Orsay) and J. Cresswell (University of Liverpool). Using this interface I created an architecture of a PSA base class on which any PSA algorithm class can inherit and be used together with the AGATA DAQ. The first, (and of 2019 still only fully) algorithm to be fully included in the AGATA DAQ was the grid search algorithm [237], with the first version implemented by me.

Using the code AGATAGeFEM (see publication in progress 7.11) I’ve also in-
vestigated the resolution for Grid-search methods and the Singular Value De-
composition methods as a function of noise and inclusion of differential and linear crosstalk. Assuming that the detector physics of a segmented germanium detector is well known, the problem of determining the coordinates of a γ-ray interaction in a large volumes HPGe detector dependence closely on the knowledge of the response of the electronics and on the signal-to-noise ratio. These two aspects have been studied by performing PSA on a data set calculated using the same code used to calculate the reference data set of pulse shapes. On this reference set of shapes different amounts of noise were then added. Each position where then analysed 20 times, each time with different noise added. Also added were linear and differential cross talk. This has been done both for the grid-search method and for the matrix method [238]. The conclusion is that, if it is correctly added to the basis, cross-talk does not have an influence on the result of PSA, and that for very noisy signals the SVD matrix inversion method performs better than grid search. A paper is being prepared on the subject, see section 7.11.

### 5.2.4 Gamma-ray tracking

Gamma rays with energies in the interval of tens of keV to a few MeV, as those emitted when nuclei deexcite, are absorbed in a HPGe detector by a photoelectric event, preceded by one or several Compton scatterings. At the upper edge of the energy range pair production starts to become important whereas at the lower edge direct photoelectric absorption dominates. In figure 5.8 the cross sections for photoelectric, Rayleigh scattering, Compton scattering, and pair production are shown. Although Rayleigh scattering does not produce an energy deposition in the detector, the direction of the photon changes.

The concept of γ-ray tracking array is based on energy-angle relation of Compton scattering,

$$ \Delta E_{\gamma}^{i} = E_{\gamma} \frac{(E_{\gamma}/m_{e}c^{2})(1 - \cos \theta^{i})}{1 + (E_{\gamma}/m_{e}c^{2})(1 - \cos \theta^{i})}, \qquad (5.1) $$

and the extraction of the position of each interaction of the γ ray providing an alternative way of deducing the scattering angle $\theta^i$, namely

$$ \cos \theta^i = \frac{\overrightarrow{r_{i-1}r_i} \cdot \overrightarrow{r_i r_{i+1}}}{|\overrightarrow{r_{i-1}r_i}| |\overrightarrow{r_i r_{i+1}}|} \qquad (5.2) $$

Looking at equation 5.1 one sees that the energy of the photon ($E_γ$) before the scattering is needed. From equation 5.2 one deduces that at least three positions are needed. There are two main families of solutions to these problems, γ-ray Forward Tracking (FT) and γ-ray Backtracking (BT). In the case of BT, tracking is performed by first identifying an interaction point with an energy of more than 100 keV (and if possible less than 250 keV), as this most often corresponds to the final photoelectric absorption. The closest point to this start point is then chosen and the total energy before scattering can be calculated as then sum of the two interaction points. This in turn allows for the calculation of the scattering angle. If this angle coincides (to some specified precision) with the assumed emission point of the γ ray the track is considered as complete. If the angle does not point towards the target a search for
another interaction point in the track is performed. This is repeated until no more
$\gamma$-ray tracks can be constituted. For details see [253, 254].

The Forward Tracking algorithms work by first clustering interaction points to-
gether. Looking from the emission point of the $\gamma$ rays all points within a solid angle
are assumed to belong to one $\gamma$ ray. Cluster with different opening angles are created.
An interaction point can be part of more than one cluster. By assuming that the total
energy of the $\gamma$ ray is the sum of the interaction points in a cluster equations 5.1 and
5.2 can be used to calculate a figure of merit for each possible permutation of the order
of interaction points, starting from the emission point. The clusters are then ordered
according to the best figure of merit. All cluster that have a too bad figure of merit
are rejected. For details of different implementation see [255, 256, 257].

Early in the AGATA project the two tracking philosophies were evaluated [257] and it was concluded that FT is most suitable for an array such as AGATA. The tracking code developed for this work, the Orsay Forward Tracking (OFT) code is also one out of two tracking codes used within the AGATA collaboration.

It is useful to point out that the devil is to be found in the details. How is the
figure of merit calculated for the different implementations of forward $\gamma$-ray tracking?
One can compare angles as given by interaction positions and interaction energies,
one can compare the cosine of the angles, or one can compare energies calculated
from angles (as is presently done in OFT). Without the smearing coming from the
momentum distribution of the electrons and the experimental uncertainties the results
would of course be the same, but as the real data even occasionally gives results that
are nonphysical (e.g. $|\cos\theta| > 1$) and the high non linearity of trigonometric function
the choice seems to matter. Exactly how much is under investigation (as of February
28, 2020).

<figure><img src="image_21.png" /><figcaption>Figure 5.8: Cross sections of different processes for $\gamma$-ray interactions in Germanium.</figcaption></figure>

5.2.5 Monte Carlo simulations

Early in the AGATA project a Geant4 [258] based Monte Carlo simulation was devel-
oped by Enrico Farnea et al. [233]. This code has then been developed and added to by
a large number of persons. It is extensively used in the planning of experiments and
in the writing of proposals. To a lesser extent the code is also used when analyzing
data to, e.g., determine peak shapes or find normalisation for the extraction of angular
correlations. It has been benched marked against experimental data with good results
[259, 260]. As AGATA moved from Legnaro to GSI, and then to GANIL site specific
functions were added to the code, especially in developing both built in and external
event generators. The code is presently hosted at a svn server at the STFC Daresbury
Laboratory.

Work done by me with and for the AGATA MC simulation package

When AGATA was to move from GSI to GANIL I got involved in the simula-
tions of the expected performance. This included simulations of the expected
efficiency and simulations of Recoil Distance Doppler shift experiments. The
first step in this process was to benchmark the physics of the simulations and
of the event generators I added. To do this I added a "test" geometry consisting
of a sphere. All particles are stopped and the energy deposited locally when
they intersect the sphere. This feature is implemented via the inheritance of
a geant4 G4VProcess class that kills all particles when they enter the volume
named "TestSpherePhys". This allows for simple investigation of quantities
such as attenuation coefficients for γ rays, energy loss for heavy ions in ma-
terials etc. These test allowed the validation of the physics used in the AGATA
simulations and the discovery of a few problems and bugs in the geant4 code
[261, 262].

Having validated the basic physics of the simulations I added an event gen-
erator to include the kinematics of fusion-fission reactions and Coulomb ex-
citations. During this time I also introduced features to include radioactive
sources with a specific source strength and model the experiments with given
beam intensities and beam structures. This work was done to a large extent
for reasons not related to AGATA, but to model an experiment performed at
GANIL in 2012 (see section 9). This work is to be detailed in a future publica-
tion (see section 7.12).

5.2.6 Performance of AGATA as of today (February 28, 2020)

The estimation of the AGATA performance on which the project is based came from
early simulations. As such they represented an "ideal" detection system character-
istics included. The actual performance of AGATA has as a consequence deviated a
bit from the simulations. Quantifying and understanding from where the loss of per-
formance comes is important to improve AGATA. It is not only this "bench marking"
aspect of performance that is important. In many experiments one needs to know the
efficiency of the detection as function of γ-ray energy, count rate, emission angle etc.
The first large work to quantify the performance of AGATA was made during the first
GSI campaign [259]. The efficiency of GSI AGATA was thoroughly measured using
sources of known strengths and using the so-called coincidence method. The driving
force behind was the need to exactly know the efficiency of AGATA in order to elu-
cidate on the isomeric ratio in lead isotopes as a function of how they were produced
[263]. During this work it was found that simulations overestimate the efficiency with
respect to the real AGATA detector, this by about 10%.
Leader of the AGATA performance working group

There is a dedicated working group within the AGATA community to eval-
uate the performance of AGATA. As one of two leaders of this group I have
been leading this work. By combining source data ($^{152}$Eu,$^{60}$Co) with in-beam
data a thorough characterization of AGATA for the early to mid-GANIL cam-
paign has been done. This work is presented in full in the included the paper
presented in section 7.10 but some further details will be given here.

As the size of AGATA has increased, and with it the angular coverage, more
effort has been put into using AGATA for angular correlations and distri-
butions. This has proven a bit of a challenge and is of today (February 28,
2020) not fully resolved. An example of the issues presently found can be
seen in figure 5.9. Here the angular distribution for the γ rays depopu-
lating the 2<sup>1</sup><sub>1</sub> → 0<sup>+</sup> and 3<sup>-</sup><sub>1</sub> → 4<sup>+</sup> in <sup>46</sup>Ti are shown together with fits
of previous measurements [264] for the same reaction <sup>16</sup>O(<sup>36</sup>Ar,α2p)<sup>46</sup>Ti.

<figure><img src="image_22.png" /><figcaption>Figure 5.9: Angular distributions measured using AGATA at GANIL. The non-physical high-frequency structures seen are not understood.</figcaption></figure>

It has proven difficult to produce angular distributions that are satisfying and
give fits with low χ². This in contrast to γγ angular correlations that are
rather straight forward (see 7.10). The reason for this is not yet understood
but clustering effects such as those shown in figure 5.10 might be a reason,
although it is not clear why even when normalizing with in-beam data these
clustering effects are still present. In figure 5.11 the difficulty to normalize in-
beam data is shown. The number of counts in each detector for the γ-ray of
interest has been normalized using the γ ray closest in energy from the decay
of ¹⁵²Eu. As can be seen the relative efficiency of each detector is not the same
for in-beam and source measurements. This makes the use of source data for
normalization of the solid angular coverage and efficiencies difficult.
<figure><img src="image_23.png" /><figcaption>Figure 5.10: Density plot of interaction positions in AGATA. Note that for some $\theta$ angles there are an excess of counts.</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Figure 5.11: The difference in angular distribution using tracked data or counts in detectors. Note how the source data, which is isotropic, is correctly normalized using a simulation of isotropic $\gamma$ rays.</figcaption></figure>

### 5.2.7 What should we do to improve AGATA?

If we compare the expected performance of AGATA (or GRETINA) from simulations with experimental results, do we find room for improvement? In general the experimental efficiency is some 10 % lower than simulations suggest (without doing $\gamma$-ray tracking). This might partly be from the active volume of the detectors that differs from the theoretical volume and from charge-carrier cloud effects close to the borders of the Germanium diodes. It is therefore not obvious that any improvements can
be made. It is also found that the measured peak-to-total is lower than is expected from simulations. Experimentally a peak-to-total of 36% is measured whereas "first order simulations" give 49%. If one adds material in the simulations (walls, dipole magnets from VAMOS, dead layers in the HPGe crystal) the simulated peak-to-total comes down to 41%. Tentatively the difference can be attributed to a γ-ray tracking efficiency that is lower in experiments than for simulations. An increase of the tracking efficiency with 10% would give an experimental peak-to-total of 41%. This is a significant improvement and means of achieving it should be investigated. An effort to do this is the OASIS ANR. The short story is that I believe that if it is possible to improve on the performance of γ-ray tracking this is done by improving PSA by better understanding of the detectors (if possible, we know well what is going on) and finding a way of correctly counting the number of interactions in a segment. Also, not only for γ-ray tracking but also for, e.g., understanding the peak shape in γ-ray spectra after Doppler Correction, correct event-by-event error estimations would be of great value.

As list of ideas that I would like to investigate is:

1. To couple the determination of the interaction positions of the γ rays with the γ-ray tracking to create an overall best fit. If the problem of computer power is neglected (one can imagine powerful trigger algorithms...) the first question I ask myself if how to balance the fit of the pulse-shapes to the fit of the γ-ray interaction sequence. Non-absorbed γ rays? Gamma-rays absorbed in one interaction?

2. To propose multiple PSA solutions to γ-ray tracking and let tracking figure out the best. My gut feeling is that this would need good error estimates from PSA (worked on within the OASIS project).

3. Let the γ-ray tracking algorithm move the interaction points in order to optimize the figure of merit of a track. The distance the points can be moved should be determined by the estimated error on the positions. The final interaction position given would be the optimized one (this is not a unique way of thinking [265, 266]).

4. Full scale machine learning, give traces of crystals and energies, ask for γ rays and positions. Or maybe something a bit less dramatic. Ask for number of interaction in segments, number of γ rays etc...

The first three points are rather straight forward to try, but the amount of work needed is rather large. I point out that many features implemented in the AGATAGe-FEM code have been implemented with these kind of developments in mind (it is easily connected to output from the AGATA simulations, can produce output files in the format used by AGATA tools, can work in server-client mode to be used as a "producer" in the AGATA DAQ chain etc.). I estimate each of the three first points to something like up to a year work for me, full time. Each point can be considered a PhD project. The fourth point concerns a subject that has not been investigated within the AGATA community in a long time (work was done by the Munich group and M. Schlarb [241] but mainly on timing). What can be expected is therefore not at all clear for me, nor do I have a clear idea of where to start. However, within the AGATA different projects concerning the use of artificial intelligence have started.
Chapter 6

Measuring picosecond
lifetimes of excited states in
nuclei

The absolute transition strengths between excited states in nuclei is one of a few acces-
sible observables. If the spin, branching ratios, and mixing ratios of the involved states
are known the reduced transition strength can be extracted in a model-independent
way. These reduced transition strengths B(EL/ML) are therefore the preferred quanti-
ties to compare to theoretical calculations as all phase-space factors are removed. The
theory of electromagnetic decays in nuclei is presented in several classic textbooks
such as "Alpha, Beta, and Gamma-ray spectroscopy" [267] and "The electromagnetic
interaction in nuclear spectroscopy" [268] and a repetition here is of no value.

For lifetimes in the picosecond range, say a bit less than 1 ps to some hundred picoseconds, methods based on the Doppler shift of γ rays emitted in-flight by the ions were developed as soon as acceleration of heavy ions was available, see e.g. chapter VII.H by Fossan and Warburton in "Nuclear spectroscopy and reactions Part C" [269]. Traditionally two different methods have been used, the Doppler Shift Attenuation Method (DSAM) where the peak shape coming from the slowing down inside foil is analysed and the Recoil Distance Doppler Shift (RDDS). My work has focused on the RDDS by the use of a Plunger. In figure 6.1 a sketch of an experiment using a Plunger is shown. High-Purity Germanium detectors, placed at angles where the Doppler Shift is considerable, surround the target. Downstream the target a stopper or degrader foil is placed. This foil changes the velocity of the recoiling ion and hence the Doppler shift of the detected γ rays. The emission of γ rays at different velocities give rise to two components from the same γ-ray transition. By using the plunger device to carefully control the distance between the target and the stopper/degrader foil the relative intensity between these two components is changed. As the recoil velocity is known (can always be deduced from the Doppler Shift) this corresponds to tracing out the fraction of decays before the stopper/degrader as a function of time. Recent developments and considerations are given in Dewald et al. [80].

Example of spectra from a few experiments using different version of the Orsay
Universal Plunger System (see separate box for details) are shown in figure 6.2. The
spectra are taken from three different experiments performed with the OUPS. The
leftmost column shows data from the commissioning experiment of the OUPS, where
<figure><img src="image_25.png" /><figcaption>Figure 6.1: A sketch over a Plunger setup. The beam of heavy ions impinge on the target from the left and the excited reaction product recoils out of the target to the right. Gamma rays are emitted from the excited state either before or after the second foil. The second foil can be either a stopper or degrader foil.</figcaption></figure>
excited states in <sup>74</sup>Kr where produced in the reaction <sup>45</sup>Sc(<sup>35</sup>Cl,2p2n)<sup>76</sup>Kr with a beam energy of 126 MeV. This was an experiment where there was sufficient statistics to gate on the in-flight component of the feeding 6<sup>+</sup><sub>1</sub> → 4<sup>+</sup><sub>1</sub> transition. The lifetime of about 4 ps for the 4<sup>+</sup><sub>1</sub> state is long compared to the stopping time of the <sup>76</sup>Kr ion in the gold stopper foil used in the experiment. Peak intensities are relatively easily extracted from these spectra by fitting Gaussian functions to the peaks. Further more, the gating from above on the in-flight component of the feeding transition removes systematical errors from unknown feeding. This is an example of where the use of Differential Decay Curve Method [270] can provide lifetimes that are both accurate and free from systematical uncertainty. Also errors from the deorientation effect seen in nuclei recoiling in vacuum are canceled [271] (note that this is only valid for a "stopper foil" in which the recoiling ions are stopped and the hyperfine interaction is "frozen").

In the middle column of figure 6.2 data from an experiment, performed with the
γ-ray spectrometer AGATA at GANIL, is shown. A <sup>238</sup>U beam impinged on a 1.86
mg/cm<sup>2</sup> thick <sup>9</sup>Be foil, creating fission fragments. These fission fragments were iden-
tified in the VAMOS spectrometer. VAMOS also provides the velocity vector for an
event-by-event Doppler Correction. A 4.5 mg/cm<sup>2</sup> thick <sup>nat</sup>Mg foil was used as a
degrader foil. The γ-ray spectra shown are γ-ray singles. As compared to the γγ
coincidence measurement shown in the left-most column this data poses more chal-
lenges. First of all there is the problem of dealing with long-lived unobserved feeding
that introduces systematic errors towards longer lifetimes. The best remedy against
such bias is to have a rather large number of distances to work with, allowing the
identification of a distance dependence on the resulting lifetime, a clear indication of
problem with feeding transitions (see discussion in Dewald et al. [270]). Secondly,
the influence of the deorientation from recoil-in-vacuum can not be assumed of no
importance. A third complication arises from the non-Gaussian components in the
peak shapes, arising from the distributions in velocity due to the large acceptance
of VAMOS, and the relatively long transit time in the degrader as compared to the
shorter lifetimes that are measured (down to some picosecond). For this type of exper-
iments the velocity distribution is also large, and care has to be taken when extracting
the lifetimes [272]. As lifetimes measurements, using first the AGATA demonstrator
at Legnaro and later on different sub-arrays of AGATA at GANIL have been corner
stones in the explored physics, the question concerning systematical biases are not
without interest.

The third and final column of figure 6.2 shows the 2<sup>+</sup> transition from <sup>112</sup>Xe, pro-
duced in the fusion-evaporation experiment performed with AGATA for γ-ray detec-
tion, NEDA [273] for neutrons and DIAMANT [274] for charged particles. The OUPS
Mk III was used as the plunger. The spectra are background subtracted and gated on
2 protons, 2 neutrons, and the in-flight component of the 4<sup>+</sup><sub>1</sub> → 2<sup>+</sup><sub>1</sub> transition. The
reaction used was <sup>58</sup>Ni(<sup>58</sup>Ni,2p2n)<sup>112</sup>Xe. The main challenge here is the statistics.
In this experiment a degrader was used, although no detection of the recoiling ions
was done. This to allow the measurement of lifetimes short compared the stopping
time of the <sup>112</sup>Xe ion recoil in a stopper foil and to optimize the peak width for γ
rays, emitted both before and after the degrader foil. As a degrader was used, there
is a theoretical risk for influence from reorientation effects. Once a preliminary life-
time, with corresponding statistical errors, has been determined possible biases from
vacuum reorientation should be investigated.
<figure><img src="image_26.png" /><figcaption>Figure 6.2: Spectra from experiments using Oups Mk I,Mk II, or Mk III. Each column have spectra from two different distances showing the variation in intensity for the peak emitted before or after the change in velocity induced by the stopper/degrader foil. For details see text.</figcaption></figure>
the Orsay Universal Plunger System (OUPS)

The development of the Orsay Universal Plunger System started in 2009-2010 with the explicit goal of creating a Plunger that easily could be adapted to different installations, mainly in France. At the time Spiral2 with the possibility of post-accelerated beams was still a perspective.

A Plunger device to be used for RDDS measurements, and for g-factor measurements using the recoil-in-vacuum method, should fulfill a set of requirements:

* the possibility to vary the distances between target and stopper foil from some micrometers to some tens of millimeters with a sub-micrometer precision,

* small absorption of γ rays emitted from the deexciting nuclei,

* a mechanism to stretch target and stopper foils,

* and an active feedback to compensate for changes in target-stopper foil distance induced by the target-beam interaction.

For the OUPS a choice was made to try to meet these requirements using commercially available piezo step-motors. These motors have linear movement with a range of up to 20 mm and a smallest step-size in the order of 20 nm. Mark I of OUPS was built upon the Physics Instruments PI N-661 linear motor. Its core is shown in figure 6.3. By the means of pre-threaded holes a stopper-foil support is mounted on the moving upper half of the piezo motor. The PI N-661 itself is mounted on an aluminum support plate, to which the target-holder support is also attached. This structure is supposed to remain the same independently of the type of experiment performed. Due to the relative thickness of the PI linear motor assembly the amount of material in the downward direction is quite large, but this is of lesser importance since the Doppler shift of emitted γ rays usually is too small for RDDS measurement at angles close to 90 degrees.
<figure><img src="image_27.png" /><figcaption>Figure 6.3: (color online) Main components of the Orsay plunger.</figcaption></figure>

<figure><img src="image_28.png" /><figcaption>Figure 6.4: Photo showing the Mark I OUPS.</figcaption></figure>

Electronics used for Mk I was a classic setup with a high-precision pulse
generator, a spectroscopic amplifier and acquisition and a motor control
using a National Instrument Data Acquisition Card. It is described in detail in
Ljungvall et al. [166] (included as a publication, see 7.3). The Mk I has been
used at the ALTO facility for several campaigns [100, 275].

When OUPS was adapted for use at GANIL together with AGATA and
the VAMOS spectrometer, the used linear motor N-661 was no longer
in production with Physik Instrumente. It was replaced with the LPS-
24 stage from Physik Instrumente. Furthermore, the target and degrader
holders were modified to be compatible with the design of the Compact
Cologne Plunger (see section 5.5 in Dewald et al. [80]). In figure 6.5 a
drawing of OUPS Mark II is shown inside the VAMOS reaction chamber.

<figure><img src="image_29.png" /><figcaption>Figure 6.5: Bird eyes view of the Oups Mk II inside the VAMOS reaction chamber. The beam comes from up right, and VAMOS is positioned at the bottom of the picture.</figcaption></figure>

The main difference in design between Oups Mk I and Mk II is that for Mk
II emphasis has been put on the possibility to have a beam that impinged
on the target with an angle. This because, when used with VAMOS, the ex-
cited ions are typically produced using fusion-fission of multi nucleon trans-
fer reactions which requires VAMOS to be positioned with an angle rela-
tive to the beam axis, typically between 20° and 45°. Furthermore, VA-
MOS has a large acceptance angle (≈ ±7°). As the time of flight between
the target and the degrader foil has to be known with high precision for
RDDS measurements it is necessary to keep the foils orthogonal to the VA-
MOS axis rather, than to the beam axis. This requirement largely deter-
mines the design of a plunger device to be used in this setup. In figure 6.6
AGATA, VAMOS, and the target chamber containing the Oups Mk II is shown.
<figure><img src="image_30.png" /><figcaption>Figure 6.6: Photo of AGATA, VAMOS, and the target chamber</figcaption></figure>

For the campaign using Oups Mk II. at GANIL the electronics used was also simplified, relying on the National Instruments PCIE-6361 X Series DAQ - a PCI express card mounted in the control PC, both to generate the periodic test signal and to measure the output from the plunger. When needed the output was amplified and filtered using a spectroscopic amplifier. In some experiments the amplifier was replaced with a simple low-pass filter, made out of high-precision components for thermal stability.

A third version of the Oups, Mk III, was developed to be used together with AGATA for γ detection, NEDA [273] for neutrons and DIAMANT [274] for charged particles. For Mk III the target holders and frames used for Mk II were reused. However, as the DIAMANT detector requires space in the target chamber, the holding structure of the motor and target and stopper assemblies had to be modified. This while trying to minimize the shadowing of both AGATA and DIAMANT. The final design is shown in figure 6.7, where the plunger rests on the ring used to adjust its position inside the chamber (mostly not visible). Also shown are the DIAMANT charged particle detector and some of the box-like ending of the target chamber, collecting different vacuum feedthroughs needed to bring the signals for the Oups Mk III and the DIAMANT detector out from the target chamber.
<figure><img src="image_31.png" /><figcaption>Figure 6.7: CAD drawing of Oups Mk III inside the AGATA target chamber used during the AGATA+NEDA+DIAMANT campaign.</figcaption></figure>

## Experiments performed with an Orsay Universal Plunger

This is a complete list of experiments performed with the Oups family. "No publication" means that no publication is expected, "No publication as of February 28, 2020" means that at least one publication is expected.

### 1. Commissioning

* Spokesperson J. Ljungvall

* At the ALTO using ORGAM 2011

* $^{45}$Sc($^{35}$Cl, 2p2n)$^{76}$Kr

* 1.1mg/cm$^2$ $^{45}$Sc target, 5mg/cm$^2$ Au stopper

* Published [166]

### 2. Probing the boundary of shape coexistence south of Z=82: Lifetime measurements of excited states in $^{170}$Os using the RDDS method

* Spokesperson J. Ljungvall

* At the ALTO using ORGAM 2012

* $^{142}$Nd($^{32}$S, 4n)$^{170}$Os

* Ta backing, Au stopper
* Published [167]

3. Search for X(5) symmetry in the ¹⁶⁸W nucleus

• Spokesperson K. Gladnishki

• At the ALTO using ORGAM 2012

• ¹⁴¹Pr(³¹P, 4nγ)¹⁶⁸W

• ¹⁴¹Pr on 2mg/cm² Ta foil, Au stopper

• No publication

4. Development of the Time Dependent Recoil In Vacuum technique for "radioactive-beam geometry"

• Spokespersons G. Georgiev and A. Stuchberry

• At the ALTO using ORGAM 2012

• ²⁴Mg(⁹³Nb,γ)²⁴Mg

• ⁹³Nb 2.4 mg/cm², Au "reset foil", Coulex

• Published [100]

5. Lifetime measurements using RDDS method after incomplete fusion

• Spokesperson A. Goasduff, J. Ljungvall

• At the ALTO using ORGAM 2013

• ⁷⁰Zn(⁷Li,αxpyn)

• LiSO₄ 1mg/cm² on 1µm Ni

• No publications, see 10.

6. Octupole collectivity in ¹⁵⁶Gd: lifetime measurements of the first 4⁻ and 6⁻ states in ¹⁵⁶Gd

• Spokesperson Loïc Sengelé

• At the ALTO using ORGAM 2013

• ¹²C(¹⁵⁰Nd, α 2n)¹⁵⁶Gd

• Discussed in thesis by L. Sengelé [276].

7. Lifetime measurement of ¹⁰⁰Ru: A possible candidate for the E(5) Critical Point symmetry

• Spokesperson T. Konstantinopoulos

• At the ALTO using MINORCA 2014

• ¹⁴C(⁸⁸Sr, 2n)¹⁰⁰Ru

• SrF₂ 0.6 mg/cm² on 1mg/cm² Au, Au stopper

• Published [275]

8. Lifetime measurements in ¹¹³Te: Determining Optimal effective charges approaching the N=Z=50 doubly-magic shell closure.
* Spokesperson D. Cullen

* At the ALTO using MINORCA 2014

* $^{63}$Cu($^{54}$Fe, 3pn)$^{113}$Te

* $^{54}$Fe 1mg/cm$^2$, 12mg/cm$^2$ Au stopper

* No publication as of February 28, 2020

9. Time dependent recoil in vacuum for Na-like $^{56}$Fe ions

* Spokesperson Andrew Stuchbery

* At the ALTO using MINORCA 2014

* $^{56}$Fe(,γ)$^{56}$Fe (coulex)

* $^{12}$C 230 µg/cm$^2$ on natNi backing (0.5 µm), reset foils thin Ni

* No publication as of February 28, 2020

10. Lifetime and g-factor measurements in the vicinity of $^{68}$Ni using the AGATA, Oups and VAMOS

* Spokespersons J. Ljungvall and Andreas Görgen

* At GANIL using AGATA and VAMOS 2015

* $^{238}$U($^{64}$Ni, $^{62}$Fe)

* $^{64}$Ni 1.25mg/cm$^2$, 3.3 mg/cm$^2$ natMg degrader

* Published [86]

11. Neutron monopole drifts near the N=50 closed shell towards $^{78}$Ni

* Spokesperson David Verney

* At GANIL using AGATA and VAMOS 2015

* $^{238}$U(°Be,)Fission

* 10 um °Be, 5 mg/cm$^2$ Mg

* Published [111]

12. Shape evolution in neutron-rich fission fragments in the mass A~100 region

* Spokespersons Wolfram Korten and Andreas Görgen

* At GANIL using AGATA and VAMOS 2017

* $^{238}$U(°Be,)Fission

* 1.85 mg/cm$^2$ °Be target, 4.5 mg/cm$^2$ Mg degrader

* No publication as of February 28, 2020

13. Shell evolution of neutron-deficient Xe isotopes: Octupole and Quadrupole Correlations above $^{100}$Sn

* Spokespersons Emanuel Clément, J.J Valiente-Dobón, A. Gadea

* At GANIL using AGATA+NEDA+DIAMANT 2018

* $^{58}$Ni($^{58}$Ni, 2p2n)$^{112}$Xe

* 1 mg/cm$^2$ $^{58}$Ni target, 5 mg/cm$^2$ Au degrader

* No publication as of February 28, 2020
## 6.1 Lifetime measurements using Recoil Distance Doppler Shift with AGATA at Legnaro and GANIL

Once the decision of starting the AGATA demonstrator phase at INFN Legnaro with AGATA coupled to the PRISMA spectrometer [277] had been taken it stood clear that the AGATA+PRISMA would be a very interesting setup for RDDS measurements of moderately neutron-rich nuclei. The concentration of solid angle, and hence efficiency, at angles close to 180° as compared to the entrance axis of PRISMA assured this. For this campaign the Cologne group developed a Compact Plunger [80] that was, and is, used extensively. There was also an emphasis on lifetime measurements the first part of the AGATA at GANIL campaign, this time with Oups Mk II and the Cologne Compact Plunger sharing the burden. Several publications have come out of these campaigns (e.g. [86, 90, 278, 279, 280, 281, 282, 283]). These experiments have been characterized by the rather low production rates and total efficiencies of the detection system (AGATA+spectrometer) limiting the total number of distances that has been measured in each experiment. Another consequence of the limited statistics is that all data have been analyzed in γ singles. This opens up for potential issues with unobserved feeding giving apparent longer lifetimes of the excited nuclear state of interest. The canonical way of checking that unobserved feeding is negligible or correctly modeled is to assure that the deduced lifetime is independent of the target-degrader distance (e.g. see discussion in Dewald et al. [270]). This has not been possible for these experiments as the number of distances within the sensitive region have been small. To compensate, by using the spectrometers, the excitation energy in the system has been limited to control the feeding. For the most exotic nuclei this is not possible as the loss in statistics then prohibits a measurement. Ways of dealing with the low statistics have been developed, aiming at a complete solution of the Bateman equations allowing summing the distances used during a measurement [279, 281]. This type of analysing techniques requires a good knowledge of the absolute distances, which is more difficult that just knowing the relative distances (which is what is calibrated using the plungers). Another complication is that the compact geometry given of AGATA gives difficulties when recoil-in-vacuum effects are to be estimated. Only angles close to 180° are covered by AGATA making measurements of angular distributions (or rather correlations as the outgoing ion is detected) of the γ rays all but impossible. It is therefore not a surprise that some of the lifetimes measured during these campaigns are in contradiction with earlier B(E2) measurements performed with low-energy Coulomb excitation (e.g. $B(E2:4_1^+ \rightarrow 2_1^+)$ in $^{74}$Zn, compare Van de Walle et al. [284] and Louchart et al. [90]). I here take the stand that the Coulomb excitation, despite the underlying assumption of a zero quadrupole moment of the $4_1^+$ state, is a more reliable measurement. A depth discussion of the challenges, faced when doing plunger measurements, can be found in the review by Dewald et al. [80].

The lack of statistics and limited number of distances measured removes, in my opinion, some of the intrinsic benefits of the Plunger technique. This is also true for the use at high energy facilities such as RIKEN and NSCL/FRIB. Other techniques, than the RDDS, to measure lifetimes or transition strengths offer under these condition good alternatives. Centroid shifts, resulting from the varying emission point for a nuclear state with a finite lifetime, as well as Coulomb excitation (limited to low spin states in case of relativistic Coulomb excitation) offer interesting alternatives at radioactive beam facilities. For recent examples of the use of "alternative" techniques
to measure lifetimes see the following references [285, 286, 287, 288].

The question of choice of method to measure a lifetime (or if there is the alternative, directly measure the B(E/ML) of a state) is therefore raised. My answer would be that the Plunger technique has added value when the statistics allows for a time-dependent measurement as this allows for easier detection of and correction for unobserved feeding. This translates into the need to measure at least lifetimes within the "sensitive" region that are independent. This translates into four distances in the sensitive region, which is very difficult when studying exotic nuclei.

## 6.2 Future developments for Recoil Distance Lifetime measurements and the Oups family in particular

I observe a trend of performing ever more demanding experiments, always at the limit of feasibility, with an increasing reliance on simulation and modelling of the experiment to extract the lifetimes. The time-dependant aspect of RDDS is also less pronounced as the number of measured distances are reduced to achieve a significant statistics for the γ-ray peaks in the spectra. It is suggested that at facilities such as FRIB or RIKEN the use plungers with two degrader foils can help with the statistics problem [289] but the need to model and simulate the experiments remain. I feel this removes an important aspect of the RDDS technique as compared to when used together with the Differential Decay Curve Method [270] method as the "time-dependence" is crucial to discover unobserved feeding and other systematical errors. Despite these reservation one is left with little choice for exotic nuclei. The development of these tools is therefore natural, and some of these methods, such as the simulation of the γ-ray peak shapes was developed and used during the analysis of the first AGATA+VAMOS experiment, published by Klintefjord et al. [86], see figure 6.8. The adaptation of already existing frameworks for this or some more original work is foreseen for the Oups family.

It is my opinion that it would be nice to construct a system that allows for reproducible foil tensions and foil alignments for a plunger. This is not so much related to performance in terms of what is the closest distance between the two foils that can be used during an experiment, or max beam current. This is mainly limited by the target and degrader foil quality and material. The main motivations are instead the predictability of the performance, and hence the experiment and the possibility to have the system in an inert atmosphere allowing the use of targets which are sensitive to oxidation. To measuring foil tensions, and in the prolongation of that have automated systems that stretches the foil to a preset tension, is a non-trivial task on foils with a thickness of mg/cm². What I have in mind is the development of an opto-acoustic system where piezo-elements are exciting the proper modes of the foils and optical elements are detecting and imaging these modes. Standing wave patterns, combined with mathematical modeling of the target, frames, etc allows for the determination of the ratio tension/mass per area of a target. A second measurement is needed to determine the thickness of the target. An idea would be to apply a small pressure difference and measure the deflection of the target foil. It would be presumptuous of me to think that the thin foils we use for our experiments have reproducible mechanical characteristics. Therefore one of the goals of such a setup would be to make statistics on when and how target foils would fail from stretching. This would allow reasonable predictions for experiments. In an ideal world this system would be mounted on the
<figure><img src="image_32.png" /><figcaption>Figure 6.8: Realistic simulation of the first AGATA@GANIL experiment. In these simulations the populations and lifetime of levels have been adapted to reproduce experimental spectra as a function of distance between the target and the degrader foil. The purpose of the simulations was to determine the peak shape of the "slow" component.</figcaption></figure>

plunger itself, also providing protective atmosphere to the foils. While dreaming it is
also transparent to γ rays and can be remotely controlled in order to open valves for
the beam to enter and exit the plunger.

Of great importance for plunger experiments is the target production. With the
arrival of reasonably high-intensity radioactive beams, targets that will allow inverse
kinematics transfer reactions are very desirable. More precisely targets containing
ions such as deuterium, lithium, or oxygen. This is a part of the development that I
have yet to involve myself in but I do believe it is important for the pertinence of the
Plunger technology for the feature.

Finally, for the Oups family, there remains some control software developments
to be made. There are some minor details that should be added such as the possibility
to use a joystick for controlling the distance between the two foils which would make
the setup phase of the plunger easier.
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