Breakdown of shell closure in helium-10
The studies of exotic nuclei at the edges of nuclear
stability make the one of the most important trends in
the modern nuclear physics. Unusual forms of nuclear
dynamics are often arising here. One of the most
prominent phenomena met here is the shell
breakdown – the deviation from the expected shell
10
population in the exotic nuclei. On one hand He is a
“double-magic” nucleus. On the other hand it has
enormous neutron excess, neutron number N to
proton number Z ratio equal 4, bringing it to the edge
10
of nuclear matter asymmetry. Thus, the He nucleus is
an important system for the development of our
understanding of nuclei located far from the  stability
valley and even beyond the neutron and proton
driplines. Here we present new insights into the basic
properties of this nucleus illuminating its shell
structure and indicating strong deviation from the
simple shell population picture.
Shell structure in nuclei. Periodic Table of Elements
for more than hundred years provides basis for
understanding the major chemical laws. The existence
of the Periodic Table is connected with systematics of
quantum-mechanical atomic shells. Nuclide chart “N
vs. Z ” can be considered as analog of the Periodic
Table in the “realm of nuclei”, see Fig. 1.
Nuclear shell model is destined to treat systems
consisting of particles with semi-integer spin. Its
essential idea is that the particles are moving in bound
orbitals in response to the remainder of the system.
Each orbital has well designated energy, angular
momentum, and parity. The electrons, as well as
Figure 1. Chart of the nuclides presented in coordinate plane Z vs. N. Displayed in the lower part are nuclei with Z = 1  83.
Black squares show stable nuclei form the stability valley. The areas of nuclei with life-times ranging from more than one year
to milliseconds are shown in gray with intensity varying from the darkest to light paints. The horizontal and vertical dashed
lines denote the proton and neutron magic numbers. The dash-dotted and long-dashed lines show the expected proton and
neutron driplines. Being produced in some nuclear process, nuclei situated far on the left (right) side of the proton (neutron)
dripline emit protons (neutrons) instantly. In the close proximity to these critical zones there are many fragile nuclei
observable in the so-called resonance states, signifying the nuclear states characterized by very short life-times:  s is
the period which allows nucleon to traverse nucleus 10 – 1000 times. The upper left drawing presents a close-up of the region
of atomic numbers Z = 1 – 12. Halo nuclei are marked with shaded crosses. Exotic resonance state nuclei – true 2p or true 2n
emitters – are singled out by green color.
nucleons, having spin 1/2 can form such systems. In
the Bohr model of atom no two electrons occupy the
same state, i.e. have identical sets of quantum
numbers. This principle attributed to Pauli results in a
finite number of electrons occupying a given energy
level, and thus, leads to the concept of closed (filled)
shells.
Basic data (binding energies, nucleon separation
energies, spin/parity systematic of excited states, etc.)
indicate that closed shells occur in nuclei at proton and
neutron numbers Z(N) = 2, 8, 20, 28, 50, 82, and N =
126 (see in the nuclide chart in Fig. 1). The shell model
treats each nucleon, interacting in the nucleus with
the A1 remaining nucleons, as one moving in a
spherical potential well. In accord with Pauli principle,
the vast deficit of free positions in the nuclear orbitals
below the Fermi level causes long free nucleon paths.
To explain the known specific magic numbers of
protons and neutrons Mayer (1949) and Axel, Jensen,
and Suess (1949) proposed a model of independent
nucleons confined by a surface corrected, isotropic
harmonic oscillator plus a strong attractive spin-orbit
term. This primordial shell model, with a Wood-Saxon
potential used instead of harmonic oscillator,
describes quite well closed-shell nuclear structures
and single-particle and hole states built on them.
Moving away from the stability valley, with Z
numbers different from N, brings to a situation of
“asymmetric nuclear matter”. Sooner or later with the
increased asymmetry the strong (nuclear) interaction
becomes not able to keep the nucleons together. So,
the neutron/proton “driplines” appear (see Fig. 1).
Beyond the driplines the nuclear systems show up as
short-living resonance states with lifetimes (widths) of
about  s (around MeV). Nuclei don’t become so
broad immediately at the driplines. The discovery of
true two-proton (2p) radioactivity of proton dripline
nuclei is an important result obtained recently. The
search for nuclei on the neutron dripline showing 2n
radioactivity is now in waiting list.
10
The He puzzle. Helium-10 is the second lightest
double-magic nucleus. The expectation for existence
10
of a bound He has been discussed long ago as it
could imply long-reaching consequences involving the
20
bound He as well. When the nuclear instability of
10
He was fixed it become important to find out how
much unbound it is. This could have an impact on
theory judgment about the nuclear matter properties,
nuclear equation of state and astrophysical
Figure 2. Cryogenic tritium target. Left panel: refrigerator
head unit capable to cool down to 26 K the target cell hidden
in the thermal screen cooled to 77 K (liquid nitrogen
temperature). The target cell is a double-chamber unit where
the 6 mm thick internal chamber is filled with tritium gas to a
1 bar pressure and high vacuum is provided by a titanium
getter in the small volume between the two chambers. Thus,
are excluded any leaks of tritium caused by its diffusion
through the extremely thin 10 micron stainless steel entrance
and exit windows transparent for particles of interest. Right
panel: all operations with tritium target system are
performed by the authorized staff in protective suits.
nucleosynthesis paths. The last but not least point is
10
interest to the study of correlations of the He decay
10
fragments (8He+n+n). The instability of the two He
subsystems causes its “true”, i.e. instantaneous, threebody decay in 8He+n+n. In quantum mechanics this
class of decays remains not completely understood.
10
The He case is one where the ascertainment of
details of such decay will be an important step for this
exciting subject.
10
10
Production of He. The He nucleus is complicated
for experimental study. Promising ways to investigate
this nucleus are offered by radioactive nuclear beams
available nowadays in several laboratories in the
10
world. In the present work He was reached by
addition of two neutrons to the heaviest particle8
stable Helium isotope He (Z = 2, N = 6). The heaviest
3
particle-stable Hydrogen isotope H (Z = 1, N = 2) was
8
used to transfer the two neutrons to He, i.e. to realize
8
3
10
the He + H → p + He reaction. Uniqueness and of
this nuclear reaction consists in the fact that both the
target and projectile are β radioactive nuclei. Because
it is a nontrivial task to realize such a nuclear reaction
10
the attainment of He in this way was delayed for a
long time.
In this experiment, 172-MeV short-living (T1/2 = 119
8
ms) He nuclei were produced in fragmentation
Counts/500 keV
Experimental spectrum
40
30
2+
20
10
0
-2
2
6
4
8
10
E T (MeV)
-0.5
-1
_
0
cos 8Не
Counts (arb. un.)
1
0+
-0.5
-1
0
cos 8Не
0.5
-0.5
1
dW
0
|A0 P00 + A1 P10 + A2 P2 |2
dcos8He
0
cos 8Не
Probability (%)
-1
0.5
0.5
1
Spectrum
decomposition
1
80
60
40
20
0
-2
|A0|2
|A1|2
2
|A2|
0
2
4
6
8
10
E T (MeV)
10
10
Figure 3. The He spectrum and correlations. Upper left panel: The He energy spectrum derived from the measured
10
energies and pathways of recoil protons emitted in the 8He + 3H  10He + p reaction. The total He energy ET is given with
8
8
10
reference to the He+n+n decay threshold. Three middle panels show the angular distributions of He in the He rest frame
for energy ranges indicated by shading. Polar angle 8He is taken with respect to axis Z parallel to the vector of momentum
10
10
transferred to He in the reaction. In this frame, states with J = {0+,,2+} in He can be related, under certain assumptions,
to pure Legendre polynomial distributions {P0, P1, P2}. Green curves show the fits by coherent sums of these polynomials
(see the provided equation). Gray curves give the contributions of the isolated Legendre polynomials showing the importance
of the state interference forming the observed correlation patterns. The relative contributions of different components to the
10
fit are given in the lower right panel indicating the J = {0+,,2+} level ordering in He.
11
reaction of an B nuclear beam obtained from the
U400M cyclotron in Dubna (Russia). The in-flight
separator ACCULINNA provided isolation and shaping
8
of a beam with intensity of 10000 He nuclei hitting a
unique cryogenic tritium target (Fig. 2). Work with
radioactive tritium requires strict adherence to the
regulations and radiation safety standards. A set of
environmentally safe equipment was developed,
which made it possible to fill the target cell with
tritium gas, evacuate and recover tritium, perform
radiation monitoring in technological lines and in work
rooms. These demands are worth of fulfillment as
tritium gives essential advantages which were used in
full in this experiment. Nowadays equipment for work
with tritium gas is available only in very few military
labs. This part of our work can be seen as a nice
example of conversion of military technology for
application in fundamental science.
10
Basic properties established for He. Remarkable
feature of the 8He + 3H → p + 10He reaction is that it is
goes with maximum probability when the recoil
10
protons are emitted back with the He partners flying
forward and decaying almost immediately in two
8
neutrons and He. By detecting the coincident protons
8
and He nuclei one can determine the energy
10
spectrum of He nuclei and extract significant
information about the angular and energy correlations
10
of the He decay products. In the obtained spectrum
10
shown in Fig. 3 the ground state of He is seen as a
broad resonance with maximum at ET = 2.1  0.2
MeV.
10
The definitely established energy of the He ground
state with spin-parity J = 0+ is an important result. Its
reliability follows from auspicious features of the twoneutron transfer reactions making it a trusty tool for
the study of nuclei with large neutron excess. The
10
shape and energy position of the He ground state
verify that, just as it is in other nuclei with the magic
number of eight neutrons, the six neutrons, available
10
4
in He above the He core, take up their positions to
complete the 0p shell. This is in accord with the
9
recently obtained energy of the He ground-state
resonance lying at 2 MeV above the 9He  8He + n
decay threshold. Coupling the S = 1/2 spin of the odd
(unpaired) neutron with the p-shell orbital momentum
9
l = 1 gives a spin-parity of the He ground-state
10
resonance J = 1/2+. The two J = 1/2+ neutrons in He
are paired resulting in the ground-state spin-parity J
= 0+. A quite “normal” pairing energy of about 1.9
MeV comes out for the two last (i.e. valence) neutrons
10
of He.
10
+
isotone is provided in Fig. 4. The 2 state demonstrates
abrupt variations with shell completion. It can be seen
for the  state that the energy gap between the 0p
10
and 1s orbitals is reduced in He by 2 – 3 times as
compared to the other members of the isotone
12
belonging to stability valley. Pattern of the Be energy
levels shown in Fig. 4 demonstrates that the melting of
the N = 8 shell gap was observed in this nucleus also.
However, the established breakdown of the shell
10
closure in the He nucleus is quite unexpected: no
restoration of the expected shell behavior due to its
double-magic nature occurs in this nuclide.
10
Conclusion. Binding energy of the He nucleus is
10
established now. Moreover, He is the system with
the largest nuclear matter asymmetry N/Z, for which
the excitation spectrum is defined. This spectrum
shows anomalous level ordering providing evidence
10
for the shell structure breakdown in He, which is
much unexpected for the double-magic nucleus. The
importance of this case is that nuclei with just few
nucleons should become “reference” systems for the
expansion of our knowledge further into the yet
unexploited regions of nuclear driplines. Recently the
first results also promoting this research line have
been obtained about the heavier ground state true 2n
13
16
emitters Li at GSI (Darmstadt, Germany) and Be,
26
O at NSCL (Michigan State University).
Excitation energy E * (MeV)
Correlations and level ordering in He. Already the
10
ground state of He is quite broad and it can be
expected that the excited states are even broader.
Indeed, it can be seen in Fig. 3 that the excitation
10
spectrum of He is quite featureless consisting
presumably of broad overlapping structures. However,
expressed correlations patterns can be formed in
transfer reactions in certain
shell population scheme
frame which may allow
1s-0d
disentangling contributions of
0p1/2
states with different J. It
0p
actually appears to be
0p3/2
10
possible in the case of He,
0s
see Fig. 3 for details.
np
np
np
np
np
Important finding emerging

from the correlation data
1
2+
obtained in this work is that
2+
+
10
2
6
the first excitation in He is a
1
1
 state with very low
excitation energy E* ~ 2.8
4
N = 8 isotone
1
MeV. In a simple picture of

state
2
1
2+
2+
is formed by particle-hole
0+ ground state
excitation 0p → 1s and its
0
18
16
14
12
10
energy is directly related to
Ne
O
C
Be
He
the gap between shells.
+
Figure 4. Evolution of excitation energy for the first 2 and 1 states for N = 8 isotone.
The systematics of lowest Shell population is schematically shown on top of the panel. Shaded rectangles indicate
+
 and 2 excitations for N = 8 the uncertainty of the 10He level positions due to their width.
For background information see EXOTIC NUCLEI;
CLOSED SHELL; MAGIC NUMBERS; NUCLEAR
REACTIONS; NUCLEAR STRUCTURE; RADIOACTIVE
BEAMS
Gurgen M. Ter-Akopian
Sergey I. Sidorchuk
Leonid V. Grigorenko
10
Bibliography. S.I. Sidorchuk et al., He low-lying
states structure uncovered by correlations, Phys. Rev.
Lett. 108, 202502 (2012); M.S. Golovkov et al., New
9
insights into the low-energy He spectrum, Phys. Rev.
C76 021605 (2007); B. Jonson, Light dripline nuclei,
Physics Reports 389, 1 (2004); M. Thoennessen, Rep.
Prog. Phys. 67, 1187 (2004); M. Pfützner, M. Karny,
L.V. Grigorenko, and K. Riisager, Radioactive decays at
limits of nuclear stability, Rev. Mod. Phys. 84, 567
(2012).