Chapter 1
Nuclear structure far from stability
towards
78
Ni
In the present thesis I shall describe an experiment performed last year with the
PARRNe-ALTO facility in Orsay, whose aim is the study of the exotic neutron-rich
nuclei in the vicinity of
78
Ni. This is part of a series of experiments on the nuclei of
this poorly explored region done in Orsay and in other laboratories as well (Cern,
Oak Ridge).
The
78
Ni nucleus, whose structure is still unknown, has 28 protons and 50
neutrons, and therefore in the framework given by the shell model it is expected
to be one of the few doubly-magic nuclei (see fig. 1.1). Those “special” nuclei
are used as cores for shell-model calculations, dramatically truncating the model
space, thus rendering feasible shell-model calculations in heavy nuclei. The
78
Ni
nucleus is also one of the waiting-points in the astrophysical r-process; to test the
rigidity of its associated gaps is of special interest also for this reason. However,
the study of
78
Ni nucleus is not yet feasible and it requires the next generation
of radioactive beam facilities. One can anyway derive some informations on the
properties of the Z = 28 and N = 50 shell gaps by studying the more accessible
close-by nuclei.
As I shall show in detail in the present thesis, we have studied the -decay
of the neutron rich
84
Ga isotope and of its daughters. The nucleus of interest,
as many others, was produced via a photo-fission reaction induced by an 50 MeV
electron beam of 10 A on a thick UCx target. The gallium atoms were selec-
tively ionized with a newly developed laser ion source. The ions were separated
with the PARRNe mass separator and implanted on a movable mylar tape. Two
germanium detectors in close geometry were used for the detection of -rays and
- coincidence measurement, and a plastic 4 for beta tagging. The final results
of this experiment are the improved level schemes of the neutron-rich
83;84
Ge and
84
As isotopes.
1
The work I was involved primarily is the first step of the data analysis, con-
sisting of the preliminary setting of the coincidences for the creation of the time-
energy matrix, and of the analysis of the time distribution of all the measured
-transitions, in order to attribute each of them to the correct nucleus.
InthischapterIshallbrieflyexplainthephysicalmotivationsoftheexperiment.
In chapters 2 and 3 I shall describe in details the production of neutron-rich nuclei
at ALTO and the method used for the measurement of the -activity. In chapter 4
I shall show the whole data analysis I have performed. Finally, in chapter 5 I
shall show the final results of the experiment, their interpretation with an effective
shell-model interaction and the future perspectives of the study of the nuclei close
to
78
Ni at ALTO.
Figure 1.1: Representation of the nuclide chart, with the indication of the doubly
magic nuclei; among them
78
Ni. The location in the nuclide chart of the very neutron
rich nucleus
84
Ga produced in the present experiment and of its daughters is also given.
2
1.1 The doubly-magic
78
Ni
The very neutron-rich
78
Ni (N=Z’ 1:8) is expected to be a doubly magic nucleus,
since it corresponds to the magic numbers 28 for protons and 50 for neutrons. It
is the most exotic among the doubly-magic nuclei, and it is, to a large extent,
still unknown. In a pioneering experiment, Engelmann et al. [1] were able to
identify three
78
Ni events produced by inflight fission of a uranium beam at the
Gesellschaft für Schwerionenforschung (GSI), demonstrating the existence of this
nuclide. However its excitation modes remain unknown and rely on the extrapo-
lation of the properties of its neighbours.
The region around
78
Ni is interesting in terms of nuclear structure. Firstly
very neutron-rich nuclei play an important role in the astrophysical rapid neutron-
capture process (r process) [2]. The r process is responsible of the origin of about
half of the heavy elements beyond iron in nature, yet its site and exact mecha-
nism are still unknown. The
78
Ni isotope is the only doubly magic nucleus that
represents an important waiting point in the path of the r process, where the
reaction sequence halts to wait for the decay of the nucleus. Secondly, the ex-
perimental information is important to guide the emerging shell-model effective
interactions on the nuclei around
78
Ni. The knowledge of the single particle ener-
gies of
78
Ni is crucial for shell model studies which utilize this nucleus as a core for
shell-model calculations, dramatically truncating the model space, thus rendering
feasible shell-model calculations in heavy nuclei.
Since the
78
Ni nucleus cannot yet be studied directly, it is necessary to deduce
the properties of the Z = 28 and N = 50 shell gaps from the experimental infor-
mation on the less exotic nuclei close to it. In this section I will briefly present
the experimental information available on the single particle states in these nuclei
and how one can extrapolate from them the shell gaps in the
78
Ni nucleus.
1.1.1 Evolution of the Z = 28 and N = 50 shell gaps
From the evolution of the proton effective single-particle energy in Cu isotopes it
was shown that the 1f
5=2
orbital goes down and crosses the 2p
3=2
orbital at N = 44
- 46 [3] when approaching the more neutron-rich region. It was interpreted as an
indication of the reduction of the Z = 28 shell gap due to the tensor part of the
nucleon-nucleon interaction [4, 5].
The magic number 50 originates from the spin-orbit part of the nuclear inter-
action which lowers the energy of 1g
9=2
orbit from theN = 4 major shell and
locates it close to the orbits fromN = 3 major shell. Its partner, the 1g
7=2
orbit,
is pushed to the upper edge of the gap, above/below the 2d
5=2
orbit (see fig. 1.2).
The
78
28
Ni
50
isotope is a doubly-magic nucleus due to the spin-orbit interaction
term as
20
6
C
14
,
42
14
Si
28
and
132
50
Sn
82
. The magic numbers 14 and 28 do not belong to a
3
Figure1.2: Singleparticleslevelsaroundtheshellclosuresexpectedforthe
78
Ninucleus
(i.e. Z = 28 and N = 50).
Figure 1.3: (Left:) Experimental E(2
+
) and (right:) the ratios of 4
+
/2
+
energies
for Z = 30 - 38 and N = 46 - 54 [6, 7].
major harmonic oscillator closure but result from the additional spin-orbit interac-
tion. In
42
Si, the measurements of the low-lying level energies of the neighbouring
nuclei indicates the collapse of the N = 28 shell closure and an oblate deformation
for the ground state [8]. Such a deformed configuration can be also expected for
the ground state or a low-lying state of
78
Ni [9].
The evolution of the size of the N = 50 shell gap between Z = 28 and Z = 38
depends on proton-neutron interactions between the proton f
5=2
,p
3=2
orbitals and
the neutron g
9=2
and d
5=2
orbitals [10]. The 2
+
state in the N = 50 isotonic chain
is expected to be formed by proton excitations within the proton fp shell. The
experimental energies of the 2
+
states and the ratios of the energies of 4
+
to 2
+
states for Z = 30 - 38 (N = 46 - 54) are plotted in Figure 1.3. The high energies
of the 2
+
states and the low E(2
+
)=E(4
+
) ratio at N = 50 clearly point to the
persistence of the N = 50 gap.
4
Figure 1.4: Evolution of the N = 50 shell gap from the difference in the two-neutron
binding energies between N = 50 , 52 isotones [6, 7].
Another important observable, used to comprehend the structural evolution
and to see the emergence of magic numbers is the two-nucleon separation energy.
The gap derived from the difference of two-neutron binding energies of the nuclei
of the N = 50 isotonic chain (BE
2n
(N = 52) - BE
2n
(N = 50)) plotted in Figure 1.4
presents a staggering as a function of Z and a change of slope at Z = 32. Two-
neutron separation energies provide evidence for the reduction of the N = 50 shell
gap energy towards germanium (Z = 32). This reduction was not expected from
the systematics of the 2
+
energies or the B(E2) values. As a consequence one can
observe an increase of the shell gap at gallium (Z = 31) which was interpreted
by Hakala at. al. [11] as an indication of the persistent rigidity of the shell
gap towards nickel (Z = 28). The reduction of the spherical gap at Z = 32 was
described by Bender at. al. [12] in terms of beyond mean-field dynamic collective
quadrupole correlations, and has been confirmed with the empirical evaluation
one or two-neutron separation energies of ground or isomeric state by Porquet et.
al. [9]. This minimum, explained by means of theorerical calculations [13, 14]
as originating from the extra nuclear correlations (the quadrupole deformations)
points at the importance of the collectivity at Z = 32. By studying this region of
interest one aims to understand the evolution of collectivity and draw conclusions
on the magicity of
78
Ni.
5
1.1.2 EvolutionofcollectivityinZ=32germaniumisotopes
The intriguing features of the low-lying states in the even-even neutron-rich ger-
manium isotopes have been discussed in a number of experimental and theoretical
papers. The Ge isotopes around A = 72 - 80 are well known to exhibit the shape
coexistence phenomenon characterized by prolate-oblate and spherical-deformed
competition. The maximum of deformation is reached at N = 42 and then de-
creases while increasing number of neutrons. The
76;78
Ge isotopes were also found
to show the characteristics of an asymmetric rotor with ’ 30
[15].
The very neutron-rich germanium isotopes (A = 80 - 82) were populated via
-decay respectively from
80
Ga and
82
Ga [16–19]. The high energy of the 2
+
state (1348 keV) of
82
32
Ge
50
and the low B(E2) value at the N = 50 indicate the
persistence of the magic number 50 for the germanium isotopes. When passing
the neutron number 50, the first attempt to study the
84
Ge isotope was made at
ISOLDE-CERN by Koster et al. [20] and at IPN Orsay by Lebois et al. [21].
The two observed -rays (624- and 1046-keV) were attributed to the de-excitation
of the 2
+
1
and 4
+
1
states. Because of the high energy ratio (E(4
+
1
)/E(2
+
1
) = 2.67)
a sudden increase of collectivity in
84
Ge with two neutrons above N = 50 was
proposed by Lebois. The location of the 4
+
1
state was not confirmed by Winger [19]
who proposed the 4
+
1
state at 1389 keV; the location of this level is still unknown
and more information is needed on the excitation levels of this very neutron-rich
isotope. It is therefore important to study how the nuclear collectivity evolves in
this neutron-rich region while crossing the magic number N = 50 and to test the
rigidity of this magic number.
When following the systematics of the germanium isotopes in the N = 40 - 50
region one could expect to see a collective behavior in
84
Ge. The nature of the
collectivity can be probed by measuring the excitation energies of the first 2
+
, 4
+
and 0
+
excited states. In the experiment performed in the framework of this thesis
we aimed to populate the excited states in
84
Ge via -decay of
84
Ga in order to
study the evolution of the collectivity of the neutron-rich nuclei beyond N = 50.
1.1.3 Single-particle energies in the N = 51 isotonic chain
Within the systematics of the low-lying positive parity states in the N = 51 iso-
tonic chain one can see that the spin of the ground-state of the N = 51 odd-even
isotones from
81
Zn up to
101
Sn is well established to be 5=2
+
, originating from the
occupation by the valence neutron of the d
5=2
orbital [10, 22]. In the low-lying
spectra of odd-even N = 51 isotones two types of states can be identified: those
corresponding to the coupling of the d
5=2
neutron to the first 2
+
excitation of the
semi-magic N = 50 core and the single particle states due to the external neutron.
An attempt to locate the neutron single-particle centroids by using a direct (d,p)
6
reaction with radioactive beams of
84
Se and
82
Ge has been made [23]. The d
5=2
nature of the ground state and of the 3s
1=2
nature of the first excited state in
both
85
Se and
83
Ge were confirmed, but the results remained inconclusive for other
low-lying states due to the limited statistics.
Since this region is experimentally hard to reach, our knowledge on the low-
lying states in the N = 51 isotonic chain is poor. Up to now, the
83
Ge nucleus
is the most exotic N = 51 isotone studied in terms of excitation energies but
only a few transitions were assigned to its level scheme. The low-lying excited
states of
83
Ge were populated in (d,p) reaction with a
82
Ge beam at Oak Ridge
National Laboratory (ORNL) [23, 24], and with the -decay of
83
Ga performed
at IPN Orsay [25, 26] and at HRIBF [19] ( -decay of
83
Ga, -n decay of
84
Ga).
We have studied -n decay of
84
Ga in order to populate the yet unknown excited
states of
83
Ge. The knowledge on the low-lying excited state in
83
Ge is extremely
valuable in order to perform a correct tuning of the monopole part of the residual
interactions used in shell model calculations to help us to understand the nuclear
structure beyond N = 50.
1.1.4 The N = 51 odd - odd nucleus
84
As
From the -decay study of
80 86
As isotopes the ground state spin assignment (3
)
was proposed by Katz et. al. [27]. The first transitions in the odd-odd nucleus
84
As were identified first by Omtvedt et. al. [28] who studied the -decay of the
84 85
Ge isotopes. The level scheme was later updated by Winger et. al. [29] and
Lebois et. al. [26]. The latest updated level scheme of
84
As was presented in the
thesis of Tastet [17]. He confirmed the already known -transitions at 42.7 keV,
100 keV, 242 keV, 386 keV and 608 keV [26, 28, 29], added two -lines, one at
346.5 keV the other at 794 keV, both in coincidence with 242 keV, and made a
spin assignement of low-lying levels. The
84
As is the most exotic odd-odd N = 51
isotone where a few excitation levels and -transitions are identified. This nucleus
is very interesting to study since it can give information on the proton-neutron
interaction of the two valence particles. We have populated in our experiment the
excitation levels of
84
As in the subsequent -decay of
84
Ge (originating from the
decay of
84
Ga).
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