1
Project DRIBs
FLNR, JINR, 1999
Physics research programme
with radioactive nuclear beams
Yu.Ts. Oganessian, V.I. Zagrebaev
(submitted to Programme Advisory Committee, April, 1999)
Motivation and Aims
It is well known that the properties of nuclei far from stability differ in many aspects from the
properties of ordinary nuclei. The peculiarities of nuclear forces and many-body systems make
probable the existence of both light and heavy weakly bound nuclei with a diffuse surface layer
(neutron halo, neutron skin). The correlations of the valence neutrons and the strong coupling with
the continuum can significantly distort the shell structure as well as the collective properties of the
weakly bound asymmetric nuclei with N>>Z. Such a big difference should be expected also in the
dynamics of reactions induced by these nuclei. Recently with the advent of acceleration techniques,
it has become possible to produce variable in energy, high-intensity beams of radioactive nuclei in a
wide range of N and Z (light exotic nuclei can be produced in fragmentation reactions or multinucleon transfer reactions, medium and heavy nuclei – as products of fission reactions). The use of
secondary beams of radioactive nuclei considerably widens the possibilities to investigate the
properties of atomic nuclei and nuclear reactions. We suppose that the experiments with radioactive
nuclear beams will be aimed at obtaining new information concerning the following three main
issues of nuclear physics:



investigation of the properties of atomic nuclei far from the stability line, including nuclei at the
proton and neutron drip-lines,
study of the peculiarities of the dynamics of nuclear reactions induced by proton- and neutronrich nuclei,
synthesis and study of the properties of new elements and isotopes.
Although the mentioned above issues are of a rather general character, in the following we
shall consider separately the possible physics research with light radioactive nuclear beams and with
comparatively heavy fission fragments.
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Physics research with light exotic nuclei
The investigation of nuclei far from the stability line has attracted a lot of attention during the last
few years. There is increased attention to the studies of reactions induced by such nuclei at low
energies, since at low energies many more reaction channels can be investigated simultaneously and
in detail (with good momentum and energy resolution). At energies E/A < 40 MeV/A the relative
motion of the “valence” neutrons (their correlations) and their motion in the field of the heavy core to
a large extent determine the reaction dynamics, whose detailed study can give more information than
the ordinary particle momentum distributions, measured in fragmentation reactions at high energies.
Moreover, the low-energy reactions of few-nucleon transfer open up new possibilities to investigate
the cluster structure and to obtain the spectroscopic characteristics of short-lived nuclei, as it has
been done formerly for stable nuclei. Of big interest are all reaction channels: elastic scattering,
fusion, transfer reactions and fragmentation reactions. These are closely correlated and give new
information both on the structure of weakly bound nuclei and on the nuclear dynamics in which they
participate. It should be noted that the cosmological reactions of nucleosynthesis, in which nuclei far
from stability play an important role, also take place at very low (sub-barrier) energies. It seems to us
that the range of energies from 4 to 30 MeV/A, in which the main experiments planned in FLNR will
be performed, is most interesting. This field of research has still not been investigated in detail and
has not found its place in the scientific programmes of many big projects.
1. Elastic scattering
10
d/d , mb/sr
10
10
10
10
10
4
8
Fig.1. Potential elastic scattering of
8 He and 4He at different beam energies
(E/A, MeV).
He + 4 He  8 He + 4 He
2
0
-2
-4
-6
0
20
20
40
40
60
80
100
120
140
160
180
cm ,deg
The elastic scattering of light exotic nuclei gives information on the nucleus-nucleus interaction of
systems far from stability, which are characterized by large isospin and strong coupling to the
continuum, namely with the break-up channel of the weakly bound nucleus. The parameters of this
interaction are of interest not only by themselves, but are also necessary for the analysis and
understanding of the dynamics of more complicated reactions (fusion, break-up, few-nucleon transfer
reactions). Of considerable interest is the study of elastic scattering on both light and heavy targets,
leading to the Coulomb dissociation of the weakly bound systems. The theoretical study of elastic
scattering of light radioactive nuclei reveal the significant lowering of the depth of the real part of the
optical potential compared to the mean (global) quantities, derived for stable nuclei: V0(6,8He, 11Li,
8
B,...) = V0(global) - V(E). Besides, the radial dependence of this potential should contain a longrange component due to the strong coupling to the break-up channel. The imaginary part of the
optical potential should be significantly larger (and extended) than the mean global values, thus
3
reflecting the larger value of the total reaction cross section for weakly bound nuclei. The derivation
of these parameters is possible only from the analysis of the experimental cross sections of elastic
scattering, measured in a wide range of angles and energies. At present, such kind of experiments
have been carried out only at energies higher than 40 MeV/A and in a very narrow angular range at
small angles, which does not permit to unambiguously deduce the optical potential parameters even
in such systems like 6,8He+p or 11Li+p. We would like to note that in the energy range 15 MeV/A
the elastic scattering of light nuclei has a strong interference structure (Fig.1), making it possible to
derive with high accuracy the OMP parameters in the fitting process. Another interesting feature of
low-energy elastic scattering of light weakly-bound nuclei is the possible existence of resonances of
quasi-molecular type, which have been predicted theoretically, e.g. for the scattering 6He + 4He 
10
Be*  6He + 4He, where in the intermediate state a system may arise consisting of two -particles,
bound by means of two valence neutrons.
2. Near-barrier fusion
It is well known that the coupling of channels in the fusion process of atomic nuclei is of such
importance as is the shape of the potential barrier. And, while the role of rotation and deformation of
the nuclear surface is in general known, the role of the neutron degrees of freedom is practically not
studied. This role should be especially noticeable in the case of fusion of weakly bound neutron-rich
nuclei. In addition to the expected decrease of the height of the potential barrier due to the increased
radii of such nuclei, there are several non-trivial mechanisms by means of which the motion of the
“valence” neutrons influence the dynamics of the fusion process of light nuclei and the value of the
fusion cross section in the near-barrier energy region.
(1) The break-up of the weakly bound projectile in the stage of approaching the target-nucleus may
cause the decrease of the fusion cross section compared to the value for the stable isotopes of the
same element.
(2) The transfer of the valence neutrons from the weakly bound projectile to the target-nucleus leads
to gain in energy and, therefore, to the increase of fusion cross section in the near-barrier region.
(3) The polarization of the neutron-rich nucleus in the Coulomb field of the target-nucleus may lead
to intermediate states of quasi-molecular type, in which the valence neutrons are located between
the projectile-core and the target-nucleus, thus causing lowering in the total potential energy,
which in turn causes increase in the fusion cross section. For instance, 6He+A  4He-2n-A 
Bcomp.
(4) The cluster structure of such nuclei like 6He = 4He + 2n makes the relative motion of the core and
the di-neutron play an important role. This motion, added to the translational motion of the whole
nucleus may lead to a noticeable increase of the incomplete fusion reaction cross section in the
sub-barrier energy region. No doubt, this mechanism holds also for other nuclei with a distinct
cluster structure.
For this reason, the study of the dynamics of near-barrier fusion of light weakly bound nuclei is of
great interest.
3. Reactions of few-nucleon transfer
In order to study the unusual structure of weakly-bound radioactive nuclei, such as 6He, 8He, 10He,
8
B etc. (neutron halo, neutron skin, multi-neutron correlations, proton halo, clusterization), it seems
reasonable to use reactions of few-nucleon transfer instead of fragmentation reactions, as it had been
done up till now. The cross section for transfer reactions falls rapidly with increasing projectile
energy and is difficult to measure at energies above 50 MeV/A due to the low intensities of the
secondary beams of radioactive nuclei. The production of such beams of high enough intensity with
energies 25 MeV/A will allow to measure the differential cross section of transfer reactions
4
(including multi-nucleon transfer reactions) in a wide angular range. The analysis of transfer
reactions using adequate theoretical models will shed light on the cluster structure of the studied
nuclei and on spectroscopy of their different configurations, for example,
?
?
6 He = 4 He + 2 n
6 He = 3 H + 3 H
8 B = 4 He + 3 He + p
8 B = 7 Be + p
?
?
8 He = 4 He + 2 n + 2 n
8 He = 4 He + 4 n
8 He = 6 He + 2 n
.
8 Li = 4 He + 3 H + n
8 Li = 4 He + d + 2 n
and others.
Another opportunity, given by transfer reactions, concerns the investigation of the properties
and spectroscopy of excited states of weakly bound exotic nuclei. The observation, for instance, of
the p1/2-state of 7He (whose ground state is 3/2) would allow to draw a conclusion about the
magnitude of the spin-orbit interaction in neutron-rich nuclei. This state may be populated in
reactions, such as 8He + 1H  7He*(p1/2) + 2H or 6He + 2H  7He*(p1/2) + p using beams with
energy resolution better than 1 MeV. There are also indications about the unusual properties of some
excited states of light exotic nuclei, if we consider their unusual decay modes (A.Korsheninnikov).
This means that exotic nuclei may have excited states that are not less exotic, and the study of these
states is of definite interest.
Multi-neutron transfer reactions can be used for the investigation of the properties of neutronrich actinide nuclei in reactions where heavy radioactive targets are used, e.g.,
8
He + 250Cm  4He + 254Cm,
8
He + 252Cf  4He + 256Cf.
The cross sections of such reactions at energies about 5 MeV/A are to be of the order of several tens
of microbarn and, in this way, they could possibly be used for the studies of the spectroscopic as well
as the decay properties of the produced heavy nuclides. The 4n-transfer process from the 8He nucleus
could be used also when studying the properties of lighter neutron-rich nuclei, for example 68Ni,
whose ground state is still unknown.
4. Low-energy fragmentation
Light weakly bound nuclei can break-up into several fragments even at relatively low beam energy.
Contrary to the situation at high energies, low-energy fragmentation is determined mainly by two
factors – the separation energy Qgg = B(A) - B(ai) and the spectroscopic amplitude S of the given
configuration (ai) in the initial nucleus A. Therefore, by measuring the yield of different
configurations in the process of low-energy break-up of the studied nucleus as a function of Qgg (see
the schematic plot, Fig.2), we could draw definite conclusions about the spectroscopic weight of
these configurations. If the yield of any configuration were lower than the average dependence, this
would mean that the given configuration is very improbable in the initial nucleus and vice versa.
Of special interest is the study of correlations between different fragments, formed in the
process of break-up of light exotic nuclei. Such correlations (for instance, in the reaction 8B + 1H 
4
He + 3He + p + p) shed light on the relative motion of the given fragments inside the projectile, i.e.
on the many-body wave function of its ground state. Besides, in correlation experiments one can
observe and distinguish break-up processes, which take place via intermediate excited states of
exotic nuclei, the investigation of which is of interest by itself. For instance, the fragmentation of the
nucleus 8He into 6He and two neutrons can take place in two ways – direct: 8He + A  6He + n +
(nA), and sequential: 8He + A  7He + (nA)  6He + n + (nA), with the formation of an
intermediate state of 7He (in its ground or excited state), decaying subsequently into 6He + n. The
5
correlation between the 6He nuclei and the neutron should indicate which process dominates and also
give additional information on the structure of the 7He nucleus. If the intermediate nucleus 7He
decays with the formation of the excited 6He(2+) and a neutron, the observed in the exit channel particles (6He(2+)  4He + 2n) should have a narrow momentum distribution, reflecting their
properties in the 6He nucleus, but not in the initial 8He nucleus. In spite of the many-particle states
formed in the fragmentation process of light exotic nuclei, a detailed analysis of such processes can
give information on the unique structure of these nuclei, as well as on the dynamics of the processes
A+B
a i + B
100
Yield
S(a3+ a4) << 1
10
a3+a4
a1+a2
1
-Q
Fig.2. Yield of different configurations
(different fragment combinations) in lowenergy fragmentation process of a light
loosely bound nucleus (schematic plot).
themselves.
5. Tritium target
The use of a tritium target will give additional unique opportunities to investigate light radioactive
nuclei. First of all, this concerns the production of extremely neutron-rich systems in two-neutron
transfer reactions, whose cross sections amount to several millibarn and, therefore, can be measured
at beam intensities of the order of 105 pps. In reactions like 8He+3H10He+p or 6He+3H8He+p one
could observe not only the ground and excited states of the final neutron-rich nuclei, but also study
the structure of these states by measuring and analyzing the angular distributions of the emitted
protons.
The tritium target could also be used for studying multi-neutron states in the reactions 6He +
3
H  2n + 7Li, 8He + 3H  4n + 7Li and 8He + 3H  6n + 5Li(+p). The advantage of such
reactions lies not in the small reaction Q-values, but rather in the configurations of the initial nuclei,
where multi-neutron states are, in some sense, ready and it is necessary just to “softly” separate them
without imparting significant momentum to the system. In the excitation energy spectrum of 7Li
there is only one particle stable state (lying below the threshold for decay into 4He + 3H), which
should be taken into account in the analysis of the results. In the last reaction (with the formation of
6
n), the energy of 5Li can be easily derived using the energies of the detected -particles and protons.
It is worthwhile noting that it is interesting to search not only for the ground states of multi-neutron
systems, but also for their “isomeric” states with L > 0, which could happen to live even longer.
The tritium target is very convenient for performing spectroscopic studies of light exotic
nuclei, such as 5H in the reaction 6He + 3H  4He + 5H. Taking into account the existence of haloanalog states in A=6 nuclei, viz. 6He(0+), 6Li*(3.56,0+), 6Be(0+), and having indications of the
existence of the halo-analog state of 8He in 8Li* (probably a 1+-state at an excitation energy in the
region of 9 MeV, which follows from the properties of -decay of 8He), we could determine this
level directly in the reaction 6Li + 3H  8Li*(1+) + p.
For this reason, the region of low energies from 4 to 30 MeV/A is practically not well studied
as far as reactions induced by light radioactive nuclei are concerned. It is also unique, since in this
region we could study the structure of exotic nuclei using processes, which are not accessible at
higher energies. We should as well add that the structure of many light nuclei (not only those
6
mentioned above as examples) is of great interest and has to be studied in order to understand better
the nature of few-body nuclear systems.
Physics research with accelerated fission fragments
The study of medium and heavy nuclei far from the valley of stability (mainly neutron-rich) is as
interesting as the study of light exotic nuclei. Even the general properties (masses, radii,
deformations, fission barriers, decay modes and lifetimes) are known only for a limited number of
nuclei, located far enough from the neutron drip-line. The high value of the isotopic spin, the strong
coupling of the weakly bound neutrons with the continuum and the strengthening of nucleon-nucleon
correlations can bring forth significant changes in the shell and collective properties of strongly
asymmetric nuclei: inversion in the filling of nuclear shells, change or vanishing of shell gaps,
neutron exfoliation of nuclear matter and appearance of a neutron layer, change of the surface
properties of nuclei and of fission barriers, etc. The study of these nuclei is of interest also due to the
fact that through these nuclei passes the line of the nucleosynthesis r-process – the multiple capture
of neutrons, competing with -decay and coming to an end in the region of heavy nuclei because of
the competition with fission. In order to investigate this process it is necessary to know the singleparticle, -decay and fission properties of neutron-rich nuclei, close to the line of neutron stability.
Of special interest are the nuclei in the region of closed neutron shells (“waiting points” in the rprocess), in particular, the nuclei with N~50 и N~82. The unusual properties of the collective nuclear
dynamics must manifest themselves in the interaction of such nuclei: in complete fusion reactions, in
multi-nucleon transfer reactions and in inelastic processes of excitation of collective degrees of
freedom.
1. Investigation of the properties of medium and heavy nuclei far from the
stability line
The neutron-rich nuclei with masses 80<A<108 and 126<A<150 can be produced in relatively big
quantities in the photofission of 238U. The only problem is their separation, storing and acceleration.
Other neutron-rich nuclei (including, possibly, the superheavies) can, in principle, be produced either
in complete fusion reactions of accelerated fission fragments and stable targets or in multi-neutron
transfer reactions in the process of isospin equilibration (see below).
Spectroscopy of single particle and hole states (Е*, lnjn, Slj)
The study of the detailed properties of a nucleus starts with determination of its spectroscopic
characteristics: energies, spin and parity of its ground and excited states. In the case of neutron-rich
nuclei such investigations are very important, since in this sphere our knowledge about the nucleonnuclear interaction are quite limited and the theoretical predictions are not really reliable. The
closeness of the continuum strengthens the nucleon-nucleon correlations, the shell gaps may be
strongly distorted, and the surface diffusion may increase, while the deformation may decrease. The
spin-orbit splitting may decrease and become considerably different for protons and neutrons. As a
beginning, the following basic properties of the shell structure of unstable nuclei and the nucleonnuclear interaction should be clarified:





the order of filling nuclear shells and their possible inversion,
the size and position of the shell gaps in neutron-rich nuclei including deformed ones,
the isospin part of the nucleon-nuclear interaction,
the change of the magnitude of the spin-orbit interaction,
the derivation of the effective nucleon-nucleon interaction in neutron-rich nuclei,
7

spectroscopy of low-lying single particle states.
The solution of most of these problems can be achieved with the help of the well-studied
processes of few-nucleon transfer, such as (d,p), (p,d), (t,p) etc., in inverse kinematics, when the
studied nucleus is used as a projectile. The energy spectra of the secondary light particles in the exit
channel determine the energy spectra in the studied radioactive nucleus, the light particle angular
distributions – the spins of the states, and the comparison of the absolute values of the experimental
and theoretical cross sections – the spectroscopic amplitude of the investigated state. The study of
deeply sub-barrier reactions of one-neutron transfer is also of interest as, in this case, one could
directly “measure” the magnitude of the wave function of the single particle state outside the
nucleus, which by itself determines the capture cross section for thermal neutrons (kT ~ 50 – 250
keV) in the r-process. It is also clear that special attention should be paid to the study of nuclei close
to the doubly magic 78Ni and 132Sn.
Study of the collective degrees of freedom in neutron-rich nuclei
The high value of the isospin and the lowering of the neutron binding energy may considerably
change the collective properties of neutron-rich nuclei. First of all, this concerns the properties of the
surface rich in neutrons, which may be more diffuse, less rigid and easily deformable. The properties
of the giant dipole resonance may also be changed in the weakly-bound neutron-rich nuclei. Of
interest is its splitting in deformed nuclei, as well as the search for its “soft” component. Finally, the
dependence of the fission barrier on the neutron number for heavy nuclei may happen to be quite
unexpected, since its height is determined simultaneously by the properties of the surface and the
shell properties of the nucleus, which, in their turn, may be strongly changed in the neutron-rich
nuclei. The following experimental investigations of the collective degrees of freedom can be
performed using beams of accelerated neutron-rich nuclei:





excitation of quadrupole and octupole vibrations of the surface and measurement of its rigidity
for nuclei with large N/Z values,
investigation of the shape-transitional region and of the region of large deformations (N~60,
Fig.3, and Z~70, N~100), the possibility of shape coexistence,
population of high-spin states and study of their properties,
excitation and decay of the giant isovector dipole resonance,
search for the “soft” mode of the dipole oscillations of weakly-bound valence neutrons in
neutron-rich nuclei,
determination of fission barriers for cold and hot neutron-rich nuclei.
E2+, keV
2000
2d
A
40 ZrN
A
38 SrN
5
_
2
Fig.3. Energies of the first 2 + excited
states in the Sr and Zr isotops.
_
2d 3
2
7
1g _
2
1
3s _
2
1500
Large deformations

1000
500
40
44
48
52
56
60
Neutron number
?
64
68
8
General properties of nuclei far from stability



mass, charge and matter radii
lifetimes, peculiarities of -decay and of -delayed decays
neutron skin and its diffuseness
In spite of the big progress in the production of new nuclei far from stability, in many cases we still
do not know their most general properties. For instance, in the region Z75 we know neither the
masses, nor the decay modes of nuclei situated only a few neutrons away from the line of stability.
The charge radii are also measured in a rather narrow region: for Kr isotopes, for example, only up to
A=90, while for Sn isotopes – up to A=125. At the same time, these characteristics, in particular the
comparison of charge and matter radii, are of crucial importance when making conclusion about the
structure of nuclei. For extremely neutron-rich nuclei some theoretical models predict splitting of
nuclear matter and the appearance of a surface neutron layer, which increase when approaching the
neutron drip-line, Fig.4. A similar phenomenon in light nuclei – the neutron halo – has already been
observed and is being intensively investigated. The direct experimental confirmation of its existence
in medium and heavy nuclei involves the comparison of the charge radius of a nucleus (measured,
e.g., using laser spectroscopic methods) with its matter radius, which can be derived from reaction
cross sections and angular distributions of elastic scattering on well known nuclei.
Fig.4. Estimated difference in neutron
and proton root-mean-square radii of the
Sn isotopes (H.Lenske).
5.8
100-140
5.6
Sn rms-Radii
½
< r2 >p,n , fm
5.4
5.2
5.0
Neutrons
4.8
4.6
4.4
Protons
4.2
100
105
110
115
120
125
130
135
140
Mass Number
2. Isospin dependence of nuclear reactions and nuclear forces
The investigation of the dynamics of reactions induced by neutron-rich nuclei is as interesting as the
investigation of their properties. This is explained by the following two reasons. First of all, the
unusual properties of these nuclei and the additional (isospin) degree of freedom undoubtedly should
manifest themselves in the dynamics of the reactions and, possibly, will give rise to new phenomena.
Second, the big choice of radioactive nuclei (with lifetimes Т1/2 > 1s) used as projectiles can
considerably widen our opportunities in the investigation of all kinds of nuclear reactions induced by
heavy ions - from elastic scattering to complete fusion.
Elastic scattering, OM potentials and their isovector part
The investigation of elastic scattering of radioactive nuclei on protons, as well as on heavy targets, is
very important, because it makes it possible to estimate the matter radii of these nuclei and the
diffuseness of their surface, and also to derive other parameters of the nucleon-nucleus and nucleusnucleus interaction. Of special interest is the isovector part of the nucleon-nucleus interaction, which
9
is proportional to the isospin asymmetry (N-Z)/A. The magnitude of this interaction is badly known,
because in experiments with stable nuclei it does not exceed 4% of the total potential for nuclei with
40<A<208, and, moreover, the choice of projectile-target combinations is rather limited. The use of a
wide range of accelerated radioactive isotopes, e.g. of Kr or Sn, will give a possibility to determine
with higher confidence the magnitude of the isovector part of the nucleon-nucleus interaction. The
spin-orbit interaction, which is used in the analysis of nucleon-nucleus elastic scattering, usually is
chosen independently of isospin. However, there are theoretical grounds to assume its significant
weakening in neutron-rich systems. Taking into account its noticeable role in any shell-model
calculations, it seems very important to derive it with higher precision for the case of proton elastic
scattering on neutron-rich nuclei.
The estimation of the OM potential parameters for radioactive nuclei are necessary also
because they are needed in any theoretical analysis of other nuclear reactions induced by such nuclei,
for instance, in spectroscopic experiments (mentioned above).
Few-nucleon transfer reactions and quasi-elastic scattering
The process of few-nucleon transfer in reactions with light targets (1-3Н, 3Не, etc.) can be used to
study the spectroscopic properties of radioactive nuclei, for example, 132Sn(d,p)133Sn(En,lnjn).
However, a definite interest exists also in transfer reactions when heavy targets are involved. First of
all, this concerns the study of two-neutron transfer by the so-called “super-fluid” nuclei, for which a
significant strengthening of this process is observed (W.von Oertzen). In the case of neutron-rich
nuclei, when the two-neutron separation energy becomes extremely small compared to the value for
the stable target-nucleus (positive reaction Q-values), the cross sections for two-neutron transfer
should amount to several tens of millibarn for energies above the barrier. Therefore, such reactions
can be efficiently used in the studies of neutron-neutron correlations in these nuclei.
In the process of few-nucleon transfer, when two heavy nuclei are involved, according to the
kinematical conditions (-matching) it is possible to populate weakly-collective high-spin states,
lying above the yrast line. Such states are rather poorly studied when neutron-rich nuclei are
concerned, in spite of the fact that it is in this region that high-spin isomerism (Yb-Os) and
hyperdeformation (N=42-46, 58-66, 80-88) should be mostly wide-spread.
The process of Coulomb excitation will make it possible to study collective degrees of
freedom, first of all rotation of deformed nuclei and vibration properties of the surface. The cross
sections of such processes are big enough and, therefore, even low-intensity radioactive nuclear
beams (~104 pps) can be used in such experiments. The gamma-spectroscopy of excited states will
allow determining not only the energy levels (which are of separate interest by themselves), but also
their spin and lifetimes, which is important for deriving the magnitude and character of deformation
of neutron-rich nuclei. As mentioned above, in nuclei with weakly-bound valence neutrons, in
principle, collective oscillations of these neutrons relatively to the charged core is possible – the socalled “soft” dipole mode, which can also be excited by the Coulomb field of the heavy targetnucleus. The real existence of such oscillations is possible, obviously, only for nuclei close to the
neutron drip-line with neutron separation energies amounting to 1-2 MeV.
Deep-inelastic collisions and reactions of multi-neutron transfer




mechanism of proton and neutron transfer, equilibration of isospin
isospin dependence of driving potentials
synthesis of neutron-rich nuclei with Z>70
decay of “hot” neutron-rich nuclei
10
Obviously, the isospin degree of freedom plays a very important role in the interactions of nuclei
with a large (N-Z) asymmetry. The dynamics of binary low-energy processes of heavy-ion
interaction to a large extent are directed by nucleon-exchange processes, which lead to transfer of
mass, energy, and angular momentum. The nucleon transfer should be most noticeable in the
interaction of nuclei with different N/Z ratios. The overfall of the energy in the driving potentials of
such systems can be of the order of 20 MeV – Fig.5. This means that the forces, corresponding to the
isospin degree of freedom, should be very large and, therefore, they should determine the evolution
of the system at the Coulomb barrier or at the saddle point, where all other forces are more or less
equilibrated.
Driving potential of the
92
36 Kr 56 +
92
42 Mo 50 system
V(Z=36,N), MeV
V(Z,N=56), MeV
190
44
42
180
40
Z PLF
Kr
Kr
38
170
Kr
36
34
160
32
48
50
52
54
56
N PLF
58
60
50
52
54
N PLF
56
34
36
38
40
42
Z PLF
Fig.5. Potential energy in the 92Kr + 92Mo system at the top of the Coulomb barrier depending on
neutron and proton transfer. Experimental masses and nuclear proximity interaction were used in the
calculation.
The mechanism of nucleon transfer at the relaxation of the isospin is not well studied,
because in reactions with stable nuclei it is not possible to choose combinations (similar to the ones
shown in Fig.5), in which the isospin degree of freedom could play an important role. In principle, it
is possible that two completely different nucleon transfer mechanisms exist: non-correlated transfer
of independent particles (equilibration of the chemical potential of the two gases) and coherent
transfer due to the damped oscillations of the system relative to the equilibration point in the isospin
space. These mechanisms could be experimentally distinguished because of the different excitation
energy dependence of the width of the charge distribution of the final nuclei (H.Nifenecker). The
mechanism of nucleon transfer should also strongly depend on the shell structure of the interacting
nuclei. The presence of a filled proton (or neutron, as in 132Sn) shell in the nucleus with a large value
of the isospin will hinder the transfer of protons (or, correspondingly, neutrons). For nuclei, where
the shells are not filled, the isospin relaxation should proceed on account of the opposite flow of
neutrons and protons. In the excitation of the giant dipole resonance, the transfer of protons and
neutrons should be anti-correlated, i.e. it should proceed in different directions. The wide choice of
neutron-rich fission fragments, used as projectiles in binary reactions of multi-neutron transfer at
energies 5-10 MeV/A makes it possible to successfully solve these problems.
Multi-nucleon transfer reactions could be also used for the synthesis and study of the
properties of neutron-rich nuclei with Z>70, which cannot be produced by fission. In this region we
know nuclei, which are only a few nucleons away from the line of stability, i.e. here we are farthest
from the neutron drip-line. In the same region is the shell with N=126, for which only three nuclids
11
with Z<82 are known and only two of them has been studied (207Tl and 206Hg). The isotopes of Hg,
Au, Pt, Ir with neutron numbers equal or close to 126 could be produced in transfer processes
involving as much as 2-3 protons and neutrons, if reactions with extremely heavy neutron-rich
projectiles, such as 150Ce, are used. In a similar way, one could get neutron-rich nuclei with Z<30, for
instance, the heavy isotopes of Ni.
In deep-inelastic interactions of heavy ions, almost total transfer of the kinetic energy of
relative motion into internal energy of the final nuclei can be achieved. The investigation of the
decay mechanism of the produced excited nuclei is of significant interest. The competition of the
channels with neutron, charged particle and gamma-ray emission, as well as fission, should strongly
depend on the isospin, which determines the separation energy of the different particles and the
height of the fission barrier. The study and comparison of the decay properties of the proton- and
neutron-rich nuclei can shed additional light on the mechanism of deexcitation of highly excited
nuclear systems.
Fusion of neutron-rich nuclei and nuclei with closed shells
The dynamics of near-barrier fusion of heavy nuclei with the formation of a fissioning compound
nucleus is not studied well. This is explained by the following. First of all, in fusion reactions of
heavy nuclei an important role play at the same time several degrees of freedom, as well as the shell
structure of the nuclei themselves, which makes this process very complicated. Second, the
production cross sections of heavy fissionable nuclei rapidly fall with increasing the charge and mass
of the fusing nuclei, which, in turn, hinders the performance of detailed experimental measurements
of such reactions. Finally, the choice of possible combinations of stable or long-lived projectiles and
targets is quite limited and does not allow to systematically study the investigated processes in a
wide range of N and Z. The use of accelerated fission fragments will considerably widen our
opportunities in the investigation of the mechanism of nuclear fusion, a process as interesting as
important for nuclear physics.
First of all, it is necessary to clarify the role of the isospin degree of freedom in the nearbarrier fusion and in the decay of compound nuclei. The strong dependence of the total potential
energy of nuclei on N and Z (driving potential, Fig.5) should lead to intense nucleon transfer. On the
other hand, the polarization of nuclei and the increase of the number of neutrons in the region
between the nuclei (neck formation) should drastically decrease their Coulomb repulsion, thus
leading to the appearance of additional potential pockets. Finally, as mentioned earlier, the valence
neutrons can strongly change the properties of the nuclear surface, its “deformability”, which, in
turn, will change the position and height of the saddle point in the “distance-deformation” space. All
this means, that the role of the neutron degrees of freedom is very important and, if we do not clarify
it, we may not understand the dynamics of near-barrier fusion.
A second important point about near-barrier fusion of heavy nuclei concerns its dependence
on the shell structure of the nuclei. This dependence is also not well studied, because in experiments
with stable nuclei we have quite a limited choice of combinations. The use of accelerated fission
fragments gives almost unlimited opportunities in the selection of the wanted combination of nuclei.
Of special interest is the use as projectiles of the heavy isotopes of tin. Their fusion with the magic
nucleus 90Zr(Z=40,N=50) leads to the formation of Th isotopes, the fission probability of which is
not so large and, therefore the evaporation residue cross sections can be measured with high
accuracy. A noticeable feature of such an experiment is that in the fusion of tin isotopes with А=126132 with the nucleus 90Zr at an energy, corresponding to the interaction Coulomb barrier, the final Th
nuclei are formed with practically equal excitation energy, see Fig.6. This means that the uncertainty,
connected with the survival probability of the final nucleus, determined by the number of evaporated
neutrons, in the given case is negligible and we could directly study the role of neutrons in the
entrance channel and, most important, the role of the doubly magic shell in the nucleus
12
132
Sn(Z=50,N=82). We can assume that the role of closed shells in the fusing nuclei does not imply
only a gain in the excitation energy of the compound nucleus, but also influences the dynamics of the
process due to the change in the surface properties of these nuclei and the high threshold for exciting
their internal degrees of freedom. It is worth noting, that in the entrance channel in one of the
combinations we also obtain a nucleus with a closed shell - 216Th, the role of which is of interest in
connection with the shells N=162 and N=184 to which one comes in experiments on the synthesis of
superheavy nuclei.
50
90
A
Zr + 50 Sn
40 50
N

90+A
90 Th
250
B
46
VC
42
Q gg
V C , Q gg , MeV
38
216
90Th 126
34
B
E *min , MeV
200
Fig.6. Lowest excitation energy E*min of
the compound Th nuclei produced in the
90 Zr + A Sn fusion reactions at center-ofmass energies corresponding to the
Coulomb barrier in the entrance channel
(Bass parametrization).
E *min
100
30
132
50Sn 82
26
120
124
128
132
136
50
Sn mass number
The complexity of the dynamics of the fusion process of heavy nuclei is caused by that this
process depends on many factors and proceeds in a multi-dimensional space of parameters describing
the di-nuclear system – distance between the nuclei, their deformation and orientation, the number of
transferred protons and neutrons, etc. When the nuclei touch and their kinetic energy becomes very
small, the further evolution of the system is governed basically by the multi-dimensional potential
energy of their interaction. In order to understand the dynamics of fusion, it is necessary to find the
most important quantities (variables), to select the correct parameterization and to determine the
shape of multi-dimensional potential surface on which the process takes place. The complex
landscape of this surface (multi-dimensional barriers, saddle points, valleys and potential pockets)
makes the fusion process not trivial. The use of different combinations of the interacting nuclei will
allow reaching different points of this surface and investigating its formerly inaccessible regions.
It is known that a similar potential energy, depending on deformation parameters and mass
asymmetry, determines the fission process of heavy nuclei. It is almost obvious that these two
surfaces somewhere cross each other or transform one into the other, and the process of quasi-fission,
in which the di-nuclear system on the way to formation of the compound nucleus goes into the
fission channel, directly confirms this. The determination of the connection between these two
surfaces, i.e. the connection between the fusion and fission processes, is one of the key issues of
nuclear physics. Since in low-energy nuclear fission mainly neutron-rich fragments are formed, in
experiments with stable projectiles and targets it is not possible to reproduce “the process inverse to
fission”. The use of accelerated fission fragments, however, allows doing this quite naturally, fusing,
for instance, nuclei such as
13
132Sn
+
82Ge +

150Nd 
100Mo
232U(E*
min~
232U(E*
min~
24 MeV)
30 MeV).
The final nucleus 232U is practically in the valley of stability, its excitation energy is not high and
after the evaporation of 2 or 3 neutrons the evaporation residue can be identified with high precision.
Obviously, there exist other interesting combinations for the study of cold fusion, “inverse to the
fission process”, with the formation of other long-lived transuranium elements, situated in the valley
of stability, whose fission characteristics are either known or can be relatively easily studied. For
example, 94Kr + 150Nd  244Cm, 94Kr + 160Gd  254Fm, etc. The investigation of such reactions will
let us define common trends in the dynamics of fusion and fission, and also the reasons that make
these two processes quite different from each other.
3. Synthesis of new heavy isotopes and elements close to the -stability line
If the production cross section of the heavy evaporation residues is really strongly dependent on the
isospin and shell structure of the fusing nuclei, then beams of accelerated neutron-rich fission
fragments, in spite of their relatively low intensity, could be used for the synthesis of new
transfermium elements and isotopes. The strong dependence (with a trend to rise) of the production
cross section of the evaporation residue on the projectile neutron number is already experimentally
known for some combinations. For example, in the 62,64Ni + 208Pb reaction the production cross
section of element 110 rises by a factor of 4.5 when the projectile neutron number is increased by 2
units (G.Munzenberg). Such enhancement may be due both to the increase of the fusion cross section
of the neutron-rich nuclei on account of the change of their surface properties (see above) and to the
increase of the “survival” probability of the compound nucleus in the process of its cooling on
account of the systematic increase with N of the ratio Гn/Гf, defining the competition between the
fission and neutron evaporation channels. The influence of the shell structure is of no less importance
to the process of formation of superheavy nuclei. Here, as we know, an important role play both the
shells of the fusing nuclei and the transition to closed shells in the compound nuclei. In the latter
case, this can be connected to the increase in the fission barriers of the final nuclei, which leads to an
increase of the “survival” probability.
One of the most interesting tasks is to synthesize and study the properties of nuclei with the
closed neutron shell N=162 in the region 100Z110. The study of nuclei close to this shell – their
half-lives T1/2(A), neutron separation energies Sn(A), properties of the surface E(2+), fission barriers,
etc. – will let us make more definite conclusions about the nuclei of the next shell, N=184. In
connection with the synthesis of new elements it is interesting to measure the yields of heavy
evaporation residues in fusion reactions as a function of the neutron number of the projectile and the
target. In this region of nuclei, we could use, for example, the neutron-rich isotopes of Kr in the
reactions
82-94Kr + 176Yb  258-270Sg
152-164.
This would allow us to determine the magnitude of the change of the fusion cross section and the
yield of evaporation residues of superheavy systems for a significant change of the neutron numbers
in the entrance channel and for the approach to the closed shell of the compound nucleus (in the
given case, N=162). The use of reactions induced by 94Kr on targets of 186W or 192Os will make it
possible to produce the heavy isotopes 280110 and 286112 in the transition region to the “island of
stability”.
The relatively low expected intensities of the accelerated neutron-rich fission fragments (<
10
10 pps) do not let us hope to achieve a quick and easy production of superheavy elements with
Z>114. In connection with this, the detailed study of the fusion dynamics of heavy nuclei, of which
14
we mentioned earlier, seems to be a necessary step towards the synthesis of new elements. The deep
understanding of this dynamics and the possible observation of new phenomena in the fusion-fission
process would let us approach with greater confidence to selection of optimal reactions. In particular,
of considerable interest is the comparison of “warm”, “cold” and “super-cold” reactions of synthesis
of one and the same element in symmetric and asymmetric combinations 48Ca+244Pu, 84Ge+208Pb,
94
Kr+198Pt, 132Sn+160Gd, 142Xe+150Nd  292114.
4. Atomic and chemical properties of new elements
There are theoretical predictions concerning the big role of relativistic effects, caused by the
strong Coulomb field of the nucleus, on the formation of the properties of valence electron shells in
superheavy elements. It is important to deduce to what extend the chemical properties of atoms will
be changed. The present-day methods allow determining the basic chemical properties of elements,
produced in single atoms and living about 10 s or more. Up till now the chemical properties of
elements with Z> 106 have not been derived experimentally and can be only extrapolated from the
periodic table. The production of neutron-rich isotopes of these elements with lifetime long enough
to allow their chemical identification (see the preceding paragraph) seems to be one of the key issues
of atomic physics.