e1e-mail<EMAIL_ADDRESS>
11institutetext: GANIL, CEA/DRF-CNRS/IN2P3, Bd Henri Becquerel, BP 55027,
F-14076 Caen Cedex 5, France 22institutetext: Université de Lyon 1,
CNRS/IN2P3, UMR5822, IP2I, F-69622 Villeurbanne Cedex, France 33institutetext:
IJCLab, Université Paris-Saclay, CNRS/IN2P3, F-91405 Orsay, France
44institutetext: Department of Physics, University of Oslo, PO Box 1048
Blindern, N-0316 Oslo, Norway 55institutetext: IRFU, CEA, Université Paris-
Saclay, 91191, Gif-sur-Yvette, France

# Advancements of $\gamma$-ray spectroscopy of isotopically identified fission
fragments with AGATA and VAMOS++

A. Lemassonaddr1, e1  J. Dudouetaddr2  M. Rejmundaddr1  J. Ljungvalladdr3  A.
Görgenaddr4  W. Kortenaddr5

###### Abstract

$\gamma$-ray spectroscopy of fission fragments is a powerful method for
studies of nuclear structure properties. Recent results on the spectroscopy of
fission fragments, using the combination of the AGATA $\gamma$-ray tracking
array and the VAMOS++ large acceptance magnetic spectrometer at GANIL, are
reported. A comparison of the performance of the large germanium detector
arrays EXOGAM and AGATA illustrates the advances in $\gamma$-ray spectroscopy
of fission fragments. Selected results are highlighted for prompt $\gamma$-ray
spectroscopy studies, measurements of short lifetimes of excited states with
the Recoil Distance Doppler-Shift method, using both AGATA and VAMOS++ and
prompt-delayed $\gamma$-ray spectroscopy studies using AGATA, VAMOS++ and
EXOGAM.

††journal: Eur. Phys. J. A

##  1 Introduction

Nuclear fission is one of the most effective ways of producing and studying
neutron-rich exotic isotopes. Fission fragments cover a wide range of the
nuclear chart and exhibit a variety of phenomena ranging from single-particle
excitations, near shell closures, to collective excitations related to nuclear
vibrations or deformations. The $\gamma$-ray spectroscopy of fission fragments
can be used to probe the evolution of nuclear structure properties as a
function of excitation energy, angular momentum and neutron-proton asymmetry
Hamilton  _et al._ (1995); Ahmad (1995); Navin  _et al._ (2014); Navin (2014);
Leoni  _et al._ (2022).

The prompt $\gamma$-rays emitted by the secondary fission fragments, as they
de-excite to their ground states, provide detailed insight into the structure
of nuclei at large spin and isospin. The prompt $\gamma$-rays are emitted on a
very short time scale (less than few nanoseconds), after scission, although
sometimes isomers can delay the decay process Metag  _et al._ (1980). The
study of prompt $\gamma$ rays faces the challenge of identifying a particular
$\gamma$-ray transition among all $\gamma$ rays emitted by few hundred of
fission fragments produced in a single experiment. The use of known
characteristic $\gamma$ rays, in the fragment of interest or in the
complementary partner fragment, has been proven to be a powerful tool for
characterisation of fission fragments Hamilton  _et al._ (1995); Ahmad (1995).
Experiments making use of high-fold $\gamma$-ray coincidence techniques,
involving the Gammasphere Lee (1997), EUROGAM 2 Urban  _et al._ (1997) and
EUROBALL (Korten, 2003) arrays, to study fission fragments produced in either
spontaneous-fission process or in in-beam heavy-ion induced fission reactions
using stable beams, were used to cover a broad range of topics in nuclear
structure Hamilton  _et al._ (1995). More recently, a similar approach was
used in conjunction with fission induced by cold and fast neutrons Jentschel
_et al._ (2017); Lebois  _et al._ (2020).

Table 1: Summary of the main characteristics of the fission fragment spectroscopy experiments performed with VAMOS++ and AGATA. The beam was 238U at 6.2MeV/A in all the cases.  |  |  | VAMOS | AGATA | References
---|---|---|---|---|---
Exp. | Duration | VAMOS-$\gamma$ | Ang. | B$\rho$ | Tar./Thick. | Deg./Thick. | Dist. | Crystals | Ang. Range |
| [h] | [events] | [deg.] | [Tm] | [$\mu$m] | [$\mu$m] | [cm] |  | [deg.] |
1 | 336 | $4\times 10^{8}$ | 20 | 1.1 |  9Be/1.6, 5 | - | 13.5 | 32 | 90-170 | Kim  _et al._ (2017a); Biswas  _et al._ (2019, 2020); Banik  _et al._ (2020)
2 | 336 | $6\times 10^{8}$ | 28 | 1.1 |  9Be/10 | - | 13.3 | 24 | 90-170 | Dudouet  _et al._ (2017, 2019); Rezynkina  _et al._ (2022)
3 | 248 | $2\times 10^{8}$ | 28 | 1.1 |  9Be/11 | Mg/18.5 | 18.6 | 24 | 120-170 | Delafosse  _et al._ (2018); Delafosse (2019)
4 | 248 | $4\times 10^{8}$ | 19 | 1.11 |  9Be/10 | Mg/16.7 | 23.5 | 35 | 120-170 | Ansari (2019)

The necessity of knowledge of the characteristic $\gamma$ rays could be
overcome by employing the isotopic identification techniques of fission
fragments using large acceptance magnetic spectrometers such as VAMOS++
Rejmund  _et al._ (2011) and PRISMA Montagnoli  _et al._ (2005). The use of
fission induced by reaction in inverse kinematics in conjunction with these
large acceptance spectrometers resulted in an higher detection efficiency.
This combination has opened new opportunities to study prompt and delayed
$\gamma$ rays emitted by fission fragments Navin  _et al._ (2014); Navin
(2014); Rejmund  _et al._ (2016a, b). The use of the VAMOS++ spectrometer with
the EXOGAM Simpson  _et al._ (2000) large $\gamma$-ray array allowed the first
assignment of prompt $\gamma$ rays in several members of the isotopic chains
of Ag Kim  _et al._ (2017b), Rh Navin  _et al._ (2017), Cd and In Rejmund  _et
al._ (2016a, b). The combination of prompt $\gamma$-ray data-sets obtained in
coincidence with the VAMOS++ magnetic spectrometers with those obtained using
high fold $\gamma$-ray techniques using Gammasphere allowed extended studies
in the isotopic chains of Y Wang  _et al._ (2021), Pr Wang  _et al._ (2015)
and Pm Bhattacharyya  _et al._ (2018), which illustrate the complementarity of
both methods. Furthermore, the experiments with VAMOS++ and EXOGAM using the
Recoil Distance Doppler-Shift Method (RDDS) Dewald  _et al._ (2012) allowed
the measurement of lifetimes of excited states in isotopes of Zr Singh  _et
al._ (2018), Y and Nb Hagen  _et al._ (2017) and Tc and Rh Hagen  _et al._
(2018).

The advent of the new generation of $\gamma$-ray tracking arrays AGATA Akkoyun
(2012) and GRETINA Paschalis  _et al._ (2013) allows an improved determination
of the spatial position of the first interaction point of each $\gamma$-ray in
the detector and an increase of the operating counting rate with larger
$\gamma$-ray multiplicities. Thus the increased effective granularity results
in an improved Doppler correction capability of the energy of the
$\gamma$-rays emitted by nuclei in flight, provided that the velocity vector
$\overrightarrow{\rm{v}}$ of the recoiling fragment is measured on an event-
by-event basis with sufficient precision. To ensure that the final Doppler-
corrected $\gamma$-ray energy resolution only arises from the $\gamma$-ray
tracking capabilities, resolution in the scattering angle of the fragment
better than $1^{\circ}$ and resolution in the interaction point at the target
than 1 mm, are required.

Furthermore, the continuous angular coverage of $\gamma$-ray tracking arrays
provides new opportunities for lifetime measurement in the picosecond range
based on Doppler-Shift method Stahl  _et al._ (2017).

This paper presents recent results on the spectroscopy of fission fragments
using the AGATA $\gamma$-ray tracking array combined with the VAMOS++ large
acceptance spectrometer at GANIL Clément  _et al._ (2017). The presented data
arise from four experiments (whose main characteristics are described in Table
1) that can be summarised as follows:

\- Exp. 1:

Prompt-delayed $\gamma$-ray spectroscopy of 122-131Sb Biswas  _et al._ (2019),
119-121In Biswas  _et al._ (2020), 130-134I Banik  _et al._ (2020) and
experimental methods Kim  _et al._ (2017a),

\- Exp. 2:

Prompt $\gamma$-ray spectroscopy of 96Kr Dudouet  _et al._ (2017) and 81Ga
Dudouet  _et al._ (2019), 83,85,87As Rezynkina  _et al._ (2022),

\- Exp. 3:

Lifetime measurements in 84Ge, 88Kr, 86Se Delafosse  _et al._ (2018);
Delafosse (2019),

\- Exp. 4:

Lifetime measurements in neutron-rich Zr, Mo and Ru Ansari (2019).

Figure 1: VAMOS identification spectra for fission fragments produced in the
238U+9Be reaction at 6.2 MeV/A (a) two-dimensional spectra of energy loss
($\Delta$E) as function of total energy $E$ measured in ionisation chambers of
VAMOS++ (b) two-dimensional spectra of the atomic number $Z$ as a function of
the mass-over-charge ratio ($M/q$) (c) atomic number ($Z$) distribution (d)
atomic mass distribution (A). The data is taken from the Exp. 1, see Table 1.

The performance of VAMOS++ for the isotopic identification of fission
fragments produced in inverse kinematics is presented in Sec. 2. The Doppler
correction of the $\gamma$-ray energy is discussed in Sec. 3. A comparison of
performances for the spectroscopy of fission fragments between EXOGAM and
AGATA is used to illustrate advances in fission fragment spectroscopy. Recent
results for prompt $\gamma$-ray spectroscopy are highlighted in Sec. 4 and for
the measurement of lifetimes of excited states in Sec. 5. Finally, Sec. 6
presents results from prompt-delayed $\gamma$-ray spectroscopy with
combinations of AGATA and EXOGAM with VAMOS++.

##  2 Isotopic Identification of Fission Fragments

The fission fragments were typically produced in fusion and transfer induced
fission by a 238U beam at the energy of $6.2$ MeV/A on a 9Be target of typical
thickness ranging from of $1.6~{}\rm{\mu m}$ to $10~{}\rm{\mu m}$. A typical
beam intensity of $\sim 1~{}\rm{pnA}$ was used. Fission fragments were
isotopically identified in terms of atomic number $Z$, mass number $A$ and
atomic charge $q$, in the VAMOS++ spectrometer, placed at angles between $20$
and $28$ degrees depending on the fragments of interest. One of the two
emitted fragments is detected and isotopically identified in the VAMOS++. The
VAMOS++ focal plane detection system consisted of a multi-wire proportional
counter (MWPC) (stop of the time-of-flight of the ion), two drift chambers
(horizontal and vertical tracking of the fragment trajectory,
$X,\theta,Y,\phi$) and an segmented ionisation chamber (energy loss and energy
of the ion, $\Delta E,E)$. The ionisation chamber was filled with CF4 gas at
pressures between $70-100~{}\rm{mbar}$, depending on the ions of interest. A
dual position sensitive MWPC Vandebrouck  _et al._ (2016) (DPS-MWPC) (start of
the time-of-flight, horizontal and vertical tracking of the fragment
trajectory, $\theta_{target},\phi_{target}$) was placed at the entrance of the
spectrometer. The MWPCs and drift chambers were filled with isobutane gas at a
pressure of $6~{}\rm{mbar}$. The fission fragments were implanted in the gas
inside the ionisation chamber. The atomic number $Z$ of the ions was obtained
based on $\Delta E-E$ correlation technique. The mass number $A$ was obtained
from the reconstructed magnetic rigidity, flight path and the measured time-
of-flight. Details on the identification techniques and performances can be
found in Ref. Rejmund  _et al._ (2011) while details on the acceptance of the
spectrometer for fission reactions are described in Ref. Navin  _et al._
(2014). Typical fission fragment rates in the VAMOS++ focal plane were ranging
between $5$ and $10$kHz and were limited by the pileup in the drift chambers
and ionization chambers.

In Fig. 1 the typical identification spectra obtained for fission fragments
using VAMOS++ are shown. The two-dimensional correlations are shown in panel
(a) energy loss versus total energy ($\Delta E$ vs. $E$) and (b) atomic charge
versus mass-over-charge ($q$ vs. $M/q$). The corresponding one-dimensional
spectra are shown in panel (c) atomic number ($Z$) and (d) atomic mass ($A$).
The data is taken from the Exp. 1, see Table 1.

The velocity vector $\overrightarrow{\rm{v}}$ of the fragment was measured
using the DPS-MWPC detector as described in Ref. Vandebrouck  _et al._ (2016).
Figure 2(a) shows the correlation between the angle of the fragment in the
laboratory system ($\theta_{L}$) detected in VAMOS++ and its velocity $\rm{v}$
for fission fragments with the atomic number $Z=40$, $50$ and $60$. The data
is taken from the Exp. 1, see Table 1. The typical portion of the kinematics
of fission fragments measured can be seen in the figure. The much stronger
kinematic focusing of the heavier fragments with respect to the lighter ones
can be seen. Figure 2(b) shows the correlation of the angle $\alpha$, between
the $\gamma$-ray emission vector $\overrightarrow{\rm{v_{\gamma}}}$ versus the
velocity vector $\overrightarrow{\rm{v}}$ of the detected fragment (see also
Sec. 3), and the velocity $\rm{v}$. In Fig. 2 one can observe the angular
opening of VAMOS++ (panel (a)) and AGATA (panel (b)). Also, from the range of
the velocity $\rm{v}$ of $2.9-4$ cm/ns and the mean flight path in VAMOS
$D=760$ cm, one can infer the typical time-of-flight from the target to the
focal plane of $190-260$ ns.

##  3 Doppler Correction of $\gamma$ ray energy

The prompt $\gamma$ rays ($\gamma_{P}$), emitted near the target position were
detected by the AGATA Akkoyun (2012) $\gamma$-ray tracking array and acquired
in coincidence with fragment detected in VAMOS. The array was placed at a
distances from the target ranging from $13.5$ cm to $23.5$ cm depending on the
configuration used, see Ref. Akkoyun (2012); Clément  _et al._ (2017) for
details of the different configurations. The detection efficiency of the AGATA
array in the different configurations is discussed in Refs. Clément  _et al._
(2017); Ljungvall  _et al._ (2020); Kim  _et al._ (2017a). Typical counting
rates in the AGATA detectors was $\sim 20$ kHz per crystal. The AGATA array
holding structure and the VAMOS++ spectrometer were supported on a common
platform which could rotate around a vertical axis perpendicular to the beam
axis at the target position. The AGATA detectors typically covered angles from
$\sim 100^{\circ}$ to $\sim 170^{\circ}$, relative to the axis of the VAMOS++
spectrometer. The $\gamma$-ray emission vector
$\overrightarrow{\rm{v_{\gamma}}}$ was determined using the first three-
dimensional interaction point of the $\gamma$-ray in the AGATA array, obtained
from pulse shape analysis and tracking procedures Akkoyun (2012). A typical
position resolution of $\sim 5$ mm (FWHM) Recchia (2008); Recchia  _et al._
(2009); Söderström  _et al._ (2011); Ljungvall  _et al._ (2020) has been
reported for $\gamma$-ray energies around $1.3$ MeV. The measured velocity
vector of the detected fragment $\overrightarrow{\rm{v}}$ and $\gamma$-ray
emission vector $\overrightarrow{\rm{v_{\gamma}}}$ were used to derive the
Doppler-corrected $\gamma$-ray energy on an event-by-event basis. The Doppler
correction was obtained using the following relationship

$E_{RF}=E_{LAB}\cdot(1-\beta\cdot cos(\alpha))\cdot\gamma$

where: $E_{RF}$ and $E_{LAB}$ are respectively the energies of the $\gamma$
ray in the rest frame of the nucleus and in the laboratory system,
$\beta=v/c$, $\gamma=\frac{1}{\sqrt{1-\beta^{2}}}$ and $\alpha$ is the angle
between vector $\overrightarrow{\rm{v}}$ and
$\overrightarrow{\rm{v_{\gamma}}}$. It should be noted that $\gamma$ rays
emitted by the complementary fragment will have an incorrect doppler
correction applied, resulting in Doppler broadened and shifted peaks that
contribute to the background of the spectra. It was demonstrated in Refs.
Navin  _et al._ (2014); Navin (2014) that Doppler correction for the binary
partner can be achieved using two-body kinematics derived from the velocity
vector of the measured fragment.

Figure 2: (a) The laboratory angle $\theta_{L}$ versus the velocity $\rm{v}$
of fission fragments with the atomic number $Z=40$, $50$ and $60$. (b) The
angle $\alpha$, between the $\gamma$-ray emission vector
$\overrightarrow{\rm{v_{\gamma}}}$ and the velocity vector
$\overrightarrow{\rm{v}}$ (see also Sec. 3), versus the velocity $\rm{v}$ of
fission fragments for the same dataset as pannel (a). The data is taken from
the Exp. 1, see Table 1.  Figure 3:  Prompt Doppler-corrected $\gamma$-ray
spectra measured in coincidence with isotopically identified 98Zr in VAMOS++:
(a) with $\gamma$ rays measured with the EXOGAM array (b) with $\gamma$ rays
measured with AGATA $\gamma$-ray tracking array. The two $\gamma$-ray spectra
are normalised to the same total number of counts. The insets highlight part
of the corresponding $\gamma$-ray spectra in the $650$ keV to $710$ keV range.

##  4 Prompt-$\gamma$-ray spectroscopy

###  4.1 AGATA versus EXOGAM

To illustrate the performances obtained with AGATA for the prompt-$\gamma$-ray
spectroscopy of fission fragments, the Fig. 3 shows Doppler-corrected
$\gamma$-ray spectra in coincidence with isotopically identified 98Zr in
VAMOS++. Figure 3(a) shows the prompt $\gamma$ rays measured with the EXOGAM
array Simpson  _et al._ (2000) consisting of $11$ Compton-suppressed segmented
clover HPGe detectors ($15$ cm away from the target), in coincidence with the
isotopically identified fragments. The $\overrightarrow{\rm{v}}$ of the
fragment along with the position of the center of the electrical segment of
the clover detector that had registered the highest energy deposit were used
to obtain the $\gamma$-ray energy in the rest frame of the emitting fragment
Bhattacharyya  _et al._ (2008). Figure 3(b) shows the prompt $\gamma$ rays
measured with the AGATA array in coincidence with the isotopically identified
fragments. The data is taken from Exp. 1, see Table 1.

The comparison of the spectra clearly illustrates the improved $\gamma$-ray
energy resolution arising from the position resolution of the first
interaction point derived in AGATA. The $1222.9$ keV $\gamma$ ray,
$2^{+}\rightarrow 0^{+}$ transition in 98Zr, can be used to evaluate the
obtained energy resolution of Doppler-corrected spectra. Considering all
clovers from EXOGAM (including $90^{\circ}$ and $135^{\circ}$ rings), a
resolution of $15$ keV was obtained. Considering only backward angles in
EXOGAM, a resolution of $7$ keV was measured. This is to be compared with a
resolution of $5$ keV obtained with AGATA for angular coverage ranging from
$100^{\circ}$ to $170^{\circ}$. The improved resolving power can be further
seen in the insets of Fig. 3, where within an expanded region of the
$\gamma$-ray spectra several weak transitions, unresolved using the EXOGAM
array, could be resolved using the AGATA array.

###  4.2 $\gamma$-ray spectroscopy of 96Kr

The sudden appearance of the onset of the collectivity at $N=60$ has been one
of the early successes of the $\gamma$-ray spectroscopy of fission fragments.
After decades of studies establishing the sudden transition towards the
deformation at $N=60$ in Zr ($Z=40$) and Sr ($Z=38$), the detailed description
of this island of deformation still challenges theoretical models. In Ref.
Dudouet  _et al._ (2017), the prompt $\gamma$-ray spectroscopy of the neutron-
rich 96Kr ($Z=38$ and $N=60$) has contributed to delineate the limits of this
island of deformation. The nucleus of interest, 96Kr, was produced in
transfer- and fusion-induced fission processes, using the 238U beam impinging
on a 9Be target. This experiment is referred to as Exp. 2, see Table 1. The
prompt Doppler-corrected $\gamma$-ray spectrum measured in coincidence with
96Kr isotopically identified in VAMOS++ is shown in Fig 4(a). Three
$\gamma$-ray transitions at the energies of $554(1)$ keV, $621(2)$ keV, and
$515(2)$ keV can be seen in the spectrum. The $554$ keV transition confirms
the excitation energy of the first $2^{+}$ state of Ref. Albers  _et al._
(2012). The $621$ keV transition was observed in coincidence with the $554$
keV transition as can be seen in the inset in Fig.4(a). It was interpreted as
the transition depopulating the first $4^{+}$ excited state at the energy of
$1175(3)$ keV. Because of the limited statistics, it was not possible to
obtain a significant coincidence analysis for the $515$ keV transition which
was not placed in the level scheme. The presence of low-lying $2^{+}_{2}$
excited states in the Kr isotopic chain suggests the possible assignment of
the $515$ keV $\gamma$ ray to the $2^{+}_{2}\rightarrow 2^{+}_{1}$ transition.

Figure 4:  The data is obtained from the Exp. 2, see Table 1. (a) Doppler-
corrected $\gamma$-ray spectra measured in AGATA in coincidence with 96Kr
detected and identified isotopically in VAMOS++ Dudouet  _et al._ (2017).
(Inset) $\gamma$-ray spectrum measured in coincidence with the $554$ keV
transition. (b) The $R_{4/2}$ ratio against the atomic number $Z$ for
$N=58–62$ isotonic chains. Horizontal dashed lines represent a schematic
classification between spherical vibrational and rotor nuclei from Ref. Casten
(1990). The $R_{4/2}$ point for 98Kr at $N=62$ obtained from Ref. Flavigny
_et al._ (2017) has been added to the figure. The figure is adapted from Ref.
Dudouet  _et al._ (2017) CC BY 4.0. © 2017, J. Dudouet et al., published by
American Physical Society.

Recently, the spectroscopy of 96Kr from knock-out and inelastic reactions was
reported Gerst  _et al._ (2022). A $888~{}(16)$ keV state, decaying by
$887^{+24}_{-23}$ keV and $334~{}(16)$ keV $\gamma$-ray transitions, was
tentatively assigned to the $2^{+}_{2}$ state based on coincidence arguments.
These $\gamma$-ray transitions were not observed in Ref. Dudouet  _et al._
(2017) due to the available statistics. The $515~{}(2)$ keV transition was
also observed and reported in coincidence with the $2^{+}->0^{+}$ transition,
but it was not placed either in the level scheme. The nature of the state
depopulated by the $515$ keV transition remains an open question to be
addressed.

To understand, quantify, and characterise the evolution of the nuclear
structure along isotopic chains, a systematic study of the energy ratio
$R_{4/2}=E(4^{+})/E(2^{+})$ is often used Casten (1990). The newly measured
energy of the $4^{+}$ state results in the energy ratio of $R_{4/2}=2.12(1)$.
In Fig.4(b) the $R_{4/2}$ ratio is shown as a function of atomic number $Z$
for isotonic chains with $N=58$, $60$ and $62$. It is seen that at the $N=58$
the nuclei between Kr and Pd exhibit very little collectivity and are situated
between the transitional and spherical vibrator regime. For $N=60$ and $62$,
the collectivity increases with decreasing $Z$, reaching the maximum in Sr. In
96Kr one observes an abrupt decrease of the collectivity. The $R_{4/2}$
obtained for 98Kr Flavigny  _et al._ (2017) follows the same behaviour. This
new measurement highlights an abrupt transition of the degree of collectivity
as a function of the proton number at $Z=36$. A possible reason for this
abrupt transition could be related to the insufficiently large amplitude of
the proton excitation in the g9/2, d5/2, and s1/2 orbitals to generate strong
quadrupole correlations or coexistence of competing different shapes.

This measurement established the Kr isotopic chain as the low-$Z$ boundary of
the island of deformation for $N=60$ isotones. The comparison with available
theoretical predictions using different beyond mean-field approaches shows
that these models fail to reproduce the abrupt transitions at $N=60$ and
$Z=36$ and that the precise description of the region remains challenging. See
Ref. Dudouet  _et al._ (2017) for further details.

###  4.3 $\gamma$-ray spectroscopy of 81Ga

Figure 5: (a) Tracked Doppler-corrected $\gamma$-ray spectrum measured in
coincidence with the isotopically identified 81Ga. Known transitions are
labelled by their energy, while newly reported transitions are marked with an
additional star symbol. The inset shows the $\gamma-\gamma$ coincidence gated
on the $813.6$ keV transition in 81Ga. (b) Experimental and theoretical level
schemes of 81Ga. The experimental levels marked with red (blue) correspond to
dominant contribution from $0p-h$ ($1p-h$) excitations of the 78Ni core. The
data is obtained from the Exp. 2, see Table 1. The figure is adapted with
permission from Ref. Dudouet  _et al._ (2019), © 2019, by American Physical
Society.

It is agreed that 78Ni ($Z=28$, $A=50$) manifests a doubly magic character.
However, in Ref. Nowacki  _et al._ (2016) the sudden emergence of collective
states and their coexistence with the spherical states are predicted. These
spherical states arise mainly from one particle-hole excitations across the
magic shell gaps ($Z=28$ and $N=50$). Collective states arise from multi
particle-hole excitations, giving rise to a deformed collective band,
providing a striking example of shape coexistence. The excited states of
$N=50$ isotones provide complementary insight into the coupling of single
particle-hole configurations with valence protons where the particle-hole
configuration are intimately related to the properties of the $N=50$ shell
gap.

The high-spin states of the neutron-rich 81Ga, with three valence protons
outside a 78Ni core, were measured for the first time Dudouet  _et al._
(2019). This experiment is referred to as the Exp. 2, see Table 1. The tracked
Doppler-corrected $\gamma$-ray spectrum obtained in coincidence with 81Ga is
shown in Fig. 5(a). The inset shows the $\gamma$-$\gamma$ coincidence spectrum
gated on the $813.6$ keV transition. The derived level scheme is shown in Fig.
5(b). The newly observed high-spin states in 81Ga are interpreted using the
results of state of the art Large Scale Shell Model (LSSM) calculations
Nowacki  _et al._ (2016) using the PFSDG-U interaction, see Fig. 5(b). The
lower excitation energy levels are understood as resulting from the recoupling
of three valence protons to the closed doubly magic core, while the highest
excitation energy levels correspond to excitations of the magic $N=50$ neutron
core.

These results support the doubly magic character of 78Ni and the persistence
of the $N=50$ shell closure, but also highlight the presence of strong proton-
neutron correlations associated with the promotion of neutrons across the
magic $N=50$ shell gap, only few nucleons away from 78Ni. See Ref. Dudouet
_et al._ (2019) for further details.

##  5 Lifetime measurement using RDDS method

###  5.1 RDDS method

Figure 6: Two dimensional spectra of the angle $\alpha$ (the angle between
vector $\overrightarrow{\rm{v_{d}}}$ and $\overrightarrow{\rm{v_{\gamma}}}$)
as a function of the $\gamma$-ray energy for a target-to-degrader distance of
470 $\mu$m in coincidence with 98Zr identified in VAMOS++, (a) detected in the
laboratory frame (b) Doppler-corrected using the fragment velocity after the
degrader $\overrightarrow{\rm{v_{d}}}$. The unshifted (U) and Doppler-shifted
(S) components are marked. The data is taken from the Exp. 4, see Table 1.
Figure 7: Comparison of Doppler-corrected $\gamma$-ray spectra using
$\overrightarrow{\rm{v_{d}}}$, measured in coincidence with isotopically
identified 98Zr in VAMOS++ obtained with AGATA (a) and (b) and EXOGAM (c) and
(d). The target-to-degrader distances are given. Panels (a) and (c) show
Doppler-shifted and unshifted components for the $1222.9$ keV transition de-
exciting the $2^{+}$ state. Panels (b) and (d) show Doppler-shifted and
unshifted components of the $620.5$ keV and $647.6$ keV transitions de-
exciting the $4^{+}$ and $6^{+}$ states. The data from the AGATA array is
taken from the Exp. 4, see Table 1 and adapted from Ref. Ansari (2019). The
pannel (c) and (d) for the EXOGAM array are adapted with permission from Ref.
Singh  _et al._ (2018), © 2018, by American Physical Society.

The Recoil Distance Doppler-Shift method is a well established technique for
the determination of picosecond lifetimes of excited nuclear states.
Traditionally, a nucleus produced in a nuclear reaction in a thin target
leaves the target with a velocity $\rm{v_{t}}$ and is stopped after flying
trough a well-defined distance in a stopper foil. The excited state in the
nucleus can de-excite by an emission of a $\gamma$ ray either in-flight or at
rest in the stopper foil. One can observe, the intensity of either Doppler-
shifted (S) or unshifted (U) components of the $\gamma$-ray transition,
respectively. The lifetime of the corresponding state can be measured using
the so called decay curve or flight curve based on the intensities of the
Doppler-shifted and unshifted components. An alternative procedure called the
Differential Decay Curve Method (DDCM) is also used. See further details in
Ref. Dewald  _et al._ (2012).

For the experiments, where the recoiling nuclei of interest are to be
detected, as it is the case when using VAMOS++ spectrometer, the stopper foil
can be replaced by a degrader foil. One can observe either the $\gamma$ rays
emitted after the target at the recoil velocity $\rm{v_{t}}$ or after the
degrader foil at $\rm{v_{d}}$. Typically, the Doppler correction uses the
velocity of the nucleus measured after the degrader $\rm{v_{d}}$, therefore
the $\gamma$ rays emitted after the degrader are seen as unshifted and those
emitted before the degrader as Doppler-shifted.

In Fig. 6(a), the $\gamma$-ray energy measured in the laboratory frame is
shown as function of the angle $\alpha$, between the vectors
$\overrightarrow{\rm{v_{d}}}$ and $\overrightarrow{\rm{v_{\gamma}}}$, in
coincidence with isotopically identified 98Zr in VAMOS++ for the target-to-
degrader distance of $470$ $\mu$m in the Exp. 4, see Table 1. In Fig. 6(b) the
same events are shown, but a Doppler correction on an event-by-event basis was
applied using the measured velocity vector after the degrader
$\overrightarrow{\rm{v_{d}}}$. The well-defined in energy, unshifted (U)
component can be seen in the figure. The Doppler-shifted (S) component becomes
dependent on $\alpha$ and appears at a lower energy because the $\gamma$ ray
was emitted at a larger velocity, $\rm{v_{t}}>\rm{v_{d}}$, and the AGATA array
was placed at backward angles, $\alpha>90^{\circ}$.

The use of the AGATA array for lifetime measurements using the RDDS method has
several important assets namely (i) a very good energy resolution for Doppler-
corrected $\gamma$-ray transitions, (ii) a good coverage for the very backward
solid angle where the Doppler effect is largest (iii) the availability of a
continuous measurement of the angle $\alpha$, see Fig. 6.

###  5.2 AGATA versus EXOGAM

Doppler-corrected $\gamma$-ray spectra of several transitions in 98Zr,
isotopically identified in VAMOS++, are shown in Fig. 7. Panels (a) and (b)
show spectra obtained with AGATA Ansari (2019) from Exp. 4, see Table 1.
Panels (c) and (d) show corresponding spectra with comparable target-to-
degrader distances obtained with EXOGAM Singh  _et al._ (2018). Panels (a) and
(c) show the components of the $1223$ keV transition de-exciting the $2^{+}$
state ($\tau=3.8\pm 0.8$ ps) and panels (b) and (d) the $620$ keV and $647$
keV transitions de-exciting the $4^{+}$ ($\tau=7.5\pm 1.5$ ps) and $6^{+}$
($\tau=2.6\pm 0.9$ ps) states. The evolution of the intensity of the Doppler-
shifted (S) component relative to the unshifted (U) component, for the
transitions de-exciting the states with different lifetimes, is evident as a
function of the target-to-degrader distance. The improved energy separation
between the two components, due to the improved first interaction position of
the $\gamma$ ray and thus its energy resolution can be also seen in the
figure. This results in an improved the precision of the lifetime analysis and
extracted reduced transition strength.

###  5.3 Lifetime measurement of excited states in 84Ge

Figure 8:  $B(E2,2^{+}\rightarrow 0^{+})$ systematic of the light $N=52$ even-
even isotones from $Z=38$ down to $Z=30$. ”Exp. Lif.”: experimental values
from lifetimes measurements (from Ref. Delafosse  _et al._ (2018), except Sr
Basu (2020); ”Exp. Coul.”: experimental values from Coulomb excitation
measurements Elman  _et al._ (2017); “DD-PC1”: beyond mean- field calculations
using the relativistic functional DD-PC1 (Ref. Delafosse  _et al._ (2018));
“SM,Ni78-I” shell-model calculations from Sieja  _et al._ (2013); “(g9/2)
P-SU(3)”: pseudo-SU(3) limit Sieja  _et al._ (2013) (or including one $N=50$
core-breaking g9/2 pair promotion, as illustrated by the inset). The data is
obtained from the Exp. 3, see Table 1. (The figures are adapted from Ref.
Delafosse  _et al._ (2018) CC BY 4.0. © 2018, C. Delafosse et al., published
by American Physical Society).

The recent intense experimental and theoretical efforts on the investigation
of the nuclear structure in the vicinity of doubly magic 78Ni ($Z=28$,
$N=50$), have triggered experimental measurements of lifetimes of excited
states.

In Ref. Delafosse  _et al._ (2018), lifetime measurements of excited states of
the light $N=52$ isotones 88Kr ($Z=36)$, 86Se ($Z=34$), and 84Ge ($Z=32$)
using the RDDS method with VAMOS++ and AGATA were reported. The reduced
electric quadrupole transition probabilities $B(E2,2^{+}\rightarrow\,0^{+})$
and $B(E2,4^{+}\rightarrow\,2^{+})$ were obtained for the first time for the
hard-to-reach 84Ge. The nuclei of interest were produced in transfer- and
fusion-induced fission processes, using the 238U beam impinging on a 9Be
target followed by a Mg degrader. This experiment is referred to as the Exp.
3, see Table 1.

Because of low statistics, the RDDS-analysis variant developed in Ref.
Litzinger  _et al._ (2015) had to be applied, which consists in summing the
statistics obtained over all distances and determining the lifetime, see Ref.
Delafosse  _et al._ (2018) for further details.

The obtained $B(E2)$ values are placed in the systematics of light $N=52$
isotones in Fig. 8, where a comparison with several calculations is also
provided.

Shell-model results from Ref. Sieja  _et al._ (2013) (open circles), assuming
an inert 78Ni core, are in excellent agreement with the experimental values
(closed circles) obtained for 88Kr and 86Se. Interestingly enough, both shell-
model and experimental values exhaust the limit for pure pseudo-SU(3) symmetry
(down triangles) for these two isotones. This clearly means that the
quadrupole coherence offered by this subspace is maximally expressed in these
two nuclei. In contrast, both shell-model and pseudo-SU(3) values barely reach
the lower tip of the experimental error bar for 84Ge. The more in-depth
analysis of the experimental data in Ref. Delafosse  _et al._ (2018) suggests,
for the first time, a shape transition from $Z=34$ (soft triaxial) to $Z=32$
(prolate deformed), a result all the more unexpected as the shell model
predicts a ”fifth island of inversion” only for much lighter ($Z<28$) systems
Nowacki  _et al._ (2016).

##  6 Prompt-delayed $\gamma$-ray spectroscopy

###  6.1 Experimental method

Figure 9:  (a) The partial level scheme of 132Te (below $4.3$ MeV). The
transitions above (below) isomeric states are indicated in blue (red). (b)
132Te Doppler-corrected prompt $\gamma$ ray ($\gamma_{P}$) spectrum with the
condition that a delayed $\gamma$ ray with energy $E_{\gamma_{D}}=151$ keV was
detected. (c) 132Te delayed $\gamma$ ray ($\gamma_{D}$) spectrum in
coincidence with the prompt $E_{\gamma_{P}}=1040$ keV $\gamma$ ray. The data
is taken from the Exp. 1, see Table 1. The figures reproduced with permission
from Ref. Kim  _et al._ (2017a), © 2017, published by Springer.  Figure 10:
The level schemes of 125–128Sb. The newly observed $\gamma$-ray transitions
above and below the isomer are indicated in red and blue, respectively. The
width of the arrows represent the intensity of the transitions. The isomeric
states are indicated by a thick line. Previously known half-lives that were
remeasured in Ref. Biswas  _et al._ (2019) have been underlined by a red line,
whereas the newly measured half-lives have been marked with a red box. The
half-lives not measured in Ref. Biswas  _et al._ (2019) are also shown. The
data is taken from the Exp. 1, see Table 1. The figure is adapted from Ref.
Biswas  _et al._ (2019) CC BY 4.0. © 2017, S. Biswas et al., published by
American Physical Society.

A new experimental setup to measure prompt-delayed $\gamma$-ray coincidences
from isotopically identified fission fragments, over a wide time range, $100$
ns - $200$ $\mu$s, is presented in Ref. Kim  _et al._ (2017a). The fission
fragments are isotopically identified, on an event-by-event basis, using the
VAMOS++ large acceptance spectrometer. The prompt $\gamma$ rays ($\gamma_{P}$)
emitted near the target were detected using the AGATA $\gamma$-ray tracking
array . The fission fragments reaching the focal plane after a typical time-
of-flight of $\sim 200$ ns, were stopped in the ionisation chamber. Delayed
$\gamma$ rays ($\gamma_{D}$) were detected using seven EXOGAM HPGe Clover
detectors Simpson  _et al._ (2000) arranged in a wall-like configuration at
the focal plane of the VAMOS++ spectrometer. A $2$ mm thick aluminium window
between the ionisation chamber and the Clover detectors was used to minimise
the attenuation of the emitted $\gamma$ rays. A $3$ mm thick lead shielding
was placed after and in-between the Clover detectors to minimise the events
arising from the room-background and Compton scattering between the Clover
detectors. The details of the experimental setup and analysis methods are
discussed in Ref. Kim  _et al._ (2017a).

The results obtained using this experimental set-up will be illustrated based
on the case of well studied 132Te Wolf (1976); Fogelberg  _et al._ (1986);
Astier  _et al._ (2012); McDonald (1973); Hughes  _et al._ (2005); Roberts
_et al._ (2013); Genevey  _et al._ (2001); Biswas  _et al._ (2016). Figure
9(a) shows the partial level scheme of 132Te (below $4.3$ MeV). Several
different isomeric states have been reported for this nucleus, in particular,
the $7^{-}$ excited state at $1925$ keV with the half-life of $t_{1/2}=28.1$
$\mu$s McDonald (1973). In earlier works the prompt transitions $1040$ keV and
$292$ keV have been observed and placed tentatively in the level scheme as
feeding the $7^{-}$ state Hughes  _et al._ (2005); Biswas  _et al._ (2016).
However, the prompt-delayed correlation between the $\gamma$ rays populating
and depopulating the $7^{-}$ state could not be observed. In Fig. 9(b) the
Doppler corrected prompt $\gamma$ ray ($\gamma_{P}$) spectrum observed in
coincidence with delayed $E_{\gamma_{D}}=151$ keV $\gamma$-ray, which
depopulates the $7^{-}$ isomeric state, is shown. The prompt $\gamma$ rays
$292$ keV, $624$ keV, $900$ keV and $1040$ keV, are seen in the spectrum.
Figure 9(c) shows the delayed $\gamma$-ray spectrum in coincidence with the
prompt $E_{\gamma_{P}}$ at $1040$ keV. The delayed $\gamma$ rays $103$ keV,
$151$ keV, $697$ keV and $974$ keV, are seen in the spectrum. This measurement
confirms experimentally proposed the level scheme, and illustrates the
capabilities of the VAMOS-AGATA-EXOGAM setup to properly correlate prompt and
delayed $\gamma$ rays across a long-lived isomer. Further details are
discussed in Ref. Kim  _et al._ (2017a).

###  6.2 Prompt-delayed $\gamma$-ray spectroscopy of neutron-rich isotopes of
Sb

The $Z=50$ shell closure, near $N=82$, is unique in the sense that it is the
only shell closure with the spin-orbit partner high-spin orbitals, $\pi$g9/2
and $\pi$g7/2, enclosing the magic gap. The interaction of the proton
hole/particle in the above-mentioned orbitals with neutrons in the high-spin
$\nu$h11/2 orbital is an important prerequisite to the understanding of the
nuclear structure near $N=82$ and establishing the features of the $\nu\pi$
interaction.

Figure 11:  Plot of the energy differences between states with neutron
seniority $\upsilon_{\nu}=n$ and $\upsilon_{\nu}=n+2(n=0,\ldots,4)$, for
odd-$A$ and even-$A$ 119-130Sn and 121–131Sb nuclei. Figure reproduced from
Biswas  _et al._ (2019) CC BY 4.0. © 2017, S. Biswas et al., published by
American Physical Society

Prompt-delayed $\gamma$ ray of high-spin states in neutron-rich 122-131Sb
($Z=51$) Biswas  _et al._ (2019), 130-134I ($Z=53$) Banik  _et al._ (2020) and
119,121In ($Z=49$) Biswas  _et al._ (2020), using the unique experimental
setup combining AGATA, VAMOS++ and EXOGAM were reported. This experiment is
referred to as the Exp. 1, see Table 1. In this section we will restrict
ourselves to the isotopes of Sb Biswas  _et al._ (2019).

Figure 10 shows the level schemes of 125–128Sb. The newly observed
$\gamma$-ray transitions above and below the isomer are indicated in red and
blue, respectively. Previously known half-lives have been remeasured and are
underlined by a red line, whereas the newly measured half-lives are marked
with a red box. The wealth of the new experimental data obtained in Ref.
Biswas  _et al._ (2019) can be clearly seen from the figure.

The experimental data was compared with theoretical results obtained from
LSSM. A consistent agreement with the excitation energies and the $B(E2)$
transition probabilities in neutron-rich Sn and Sb isotopes was obtained. The
isomeric configurations in Sn and Sb were found to be relatively pure. The
LSSM calculations revealed that the presence of a single valence proton,
mainly in the $\pi$g7/2 orbital in Sb isotopes, leads to significant mixing,
due to the $\nu\pi$ interaction, of (i) the neutron seniorities
($\upsilon_{\nu}$)111$\upsilon_{\nu}$ stands for neutron seniority, which
refers to the number of unpaired neutrons and (ii) the neutron angular
momentum ($I_{\nu}$). The above features have a weak impact on the excitation
energies, but have an important impact on the nuclear wave function of the
excited states and thus on the corresponding $B(E2)$ transition probabilities.
In addition, a striking feature of the constancy of the energy differences,
where the increase in the number of broken neutron pairs is involved, was
observed. A plot of such energy differences in 119–130Sn and 122–131Sb
isotopes is shown in Fig. 11. This figure shows that the average energy for
the breaking of the first and second pair of neutrons is $\sim 1.1$ MeV, and
that this energy is constant (with a deviation of $\sim 100$ keV) for a wide
range of mass numbers, irrespective of the excitation energy and mixing of
neutron seniorities ($\upsilon_{\nu}$) in the case of Sn and Sb. In addition,
it follows the behavior of even-$A$ Sn isotopes for $E(2^{+}\rightarrow
0^{+})$. Further details are discussed in Ref. Biswas  _et al._ (2019).

##  7 Summary and Conclusions

Among a large variety of experiments performed at GANIL using the AGATA
$\gamma$-ray array, four have focussed on the nuclear structure studies of
isotopically identified fission fragments employing the VAMOS++ magnetic
spectrometer in coincidence.

The combination of the AGATA $\gamma$-ray array with the VAMOS++ spectrometer
forms a unique, highly performant experimental setup combining efficiency with
counting rate capabilities, as well as selectivity with excellent Doppler
correction of $\gamma$-ray energy and precise isotopic identification. The
performed experiments have been very fruitful and numerous pertinent results
have been obtained including the $\gamma$-ray spectroscopy of 96Kr Dudouet
_et al._ (2017), 81Ga Dudouet  _et al._ (2019), 83,85,87As Rezynkina  _et al._
(2022), lifetime measurements of excited states using the RDDS method in 84Ge,
88Kr, 86Se Delafosse  _et al._ (2018); Delafosse (2019), neutron-rich Zr, Mo
and Ru Ansari (2019) and prompt-delayed $\gamma$-ray spectroscopy, using the
EXOGAM array for delayed $\gamma$ rays, of 122-131Sb Biswas  _et al._ (2019),
119-121In Biswas  _et al._ (2020) and 130-134I Banik  _et al._ (2020).

In the future, fission fragments spectroscopy program will be pursued at LNL
using combination of AGATA and the PRISMA Montagnoli  _et al._ (2005)
spectrometer. The ongoing development of 238U beams at energies around the
Coulomb barrier will extend measurements using inverse kinematics reactions in
addition to presently available 208Pb beams. Further, the increased number of
available AGATA crystals will allow to cover 2$\pi$ solid angle at the nominal
detector distance, effectively doubling the solid angle coverage compared to
the experiments presented in this work. This will improve the $\gamma-\gamma$
coincidence efficiency, allowing to expand investigations of exotic neutron-
rich nuclei by fission-fragment spectroscopy.

## Acknowledgments

The authors thank the AGATA collaboration, the e661, e680, e669 and e706 GANIL
experimental collaborations and the technical teams at Grand Accélérateur
National d’Ions Lourds for their support during the experiments. A.G. has
received funding from the Norwegian Research Council, project 325714.

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