Kabatayeva R.S.*,
Rubtsova Î.À.**, Kukulin V.I.**, Zhusupov Ì.À.*
*al-Farabi Kazakh
National University, Almaty, Kazakhstan;
**D.V.Skobeltsyn Scientific Research Institute for Nuclear Physics
of M.V.Lomonosov Moscow State University, Moscow, Russia
Elastic scattering of a-particles
on 6Li nucleus in the three particle model
There is a consideration of a-particles scattering from weakly bound cluster nucleus 
in the framework of three cluster 
model in the present work. Continuum 
states are projected on the finite basis of stationary wave
packets what allows to lead the total problem of three bodies to a problem of bound channels. There are represented the calculations
results of 
-scattering differential cross
sections in the framework of three particle model and comparison with other
authors.
The problem about
low energy scattering of 
-particles on the weakly bound 
isotopes has a great fundamental and applied importance. From the fundamental
side the scattering in 
system is interesting, first of all, owing to anomalous low
binding energy of 
by 
channel (
= 1.47 MeV), i.e. proximity to
disintegration threshold. This means the relative easiness of 
excitation into the states of 
continuum in the process of interaction with incident 
-particle. In turn, such an
excitation of 
continuum leads to the great contribution of intermediate three
cluster 
states in the scattering process at small energies. And the three cluster configurations are
virtually the excited states of 
nucleus. That is why it is possible to predict the strong
transitions (for example, radiation) of 
continuum states into the ground state of 
.
From the other
side such a process of a particle and weakly bound nucleus interaction is
typical for interaction of non stable (radioactive) nuclei as 
and etc. with stable targets. That is why we can think that it is
better to understand the features of such interactions of the stable particle
with non stable (weakly bound) nucleus by investigation of interaction with
well investigated cluster nucleus such as 
which has an anomalous low binding energy.
From the applied
side, the nuclear reactions of nucleons and 
-particles with 
nucleus are important for the better understanding of elements
evolution in the Big Bang and at super nova outburst. This is closely connected
to the old problem of abundance of 
isotopes in the Universe, observed in the “iron” stars, in
comparison with the predictions of the standard astrophysical models. It is clear that for sure estimations of 
isotopes abundance it is necessary to know as possible exact the
probability of its synthesis and its disintegration in different nuclear reactions.
And the channel 
is one of the main channels.
In this work we
have investigated the role of the intermediate states of 
-continuum of target nucleus 
in the process of 
-particles interaction with 
nucleus. The simple general physical considerations show that
these 
states are to give the most contribution into the cross sections
of elastic and inelastic 
scattering, and also into the cross sections of 
radiation capture.
Since the total
solution of scattering in 
system is too tedious and time-consuming because of the big
coulomb effects, we carried out the packet reduction [1] of the problem. The
packet reduction means in our case that we projected the states of the three
particle continuum on the discrete basis of wave packets and instead of the
solution of the total three particles Schrodinger equation moved to a problem
for the coupled channel.
There are
represented the calculated differential cross sections in the figure.
Fig. The differential
cross sections of the elastic 
-scattering: dashed curve – with the
coupling potential accounting only the ground state of 
, dotted – with the folding
potential, the solid curve – with the potential, accounting all channels of
excitation of 
in 
continuum, the chain line – with the inverse potential [2].
In the work [2]
the differential cross sections of 
scattering were found for model of potential, obtained from the
solution of the inverse scattering problem on the base of the empirical scattering
data. In work [3] the wave functions of the nucleus 
in 
model were found with the help of variation method, then these
functions were used for a construction of the folding potential, responding to 
-scattering on the nucleus 
, considered as a whole particle,
i.e. without accounting its internal excitations into the 
continuum.
We considered the
role of the states of the intermediate 
continuum with 
in the elastic scattering of 
-particles on the weakly bound nuclei
. For calculations in the framework
of the 
model there were used the method of the stationary wave packets and
packet reduction of the three particles scattering equations in the three cluster
system 
. We found, that the account of the
states of the intermediate continuum noticeably smoothed the sharp oscillations
of the scattering differential cross sections, typical for the folding model
potential and made the cross sections closer to the empirical cross sections of
scattering, obtained on the base of the potential of inverse problem, i.e. one
can say that the account of the intermediate continuum substantially approaches
the solution of the three particles model problem to the exact solution of
scattering problem (extracted directly from the experimental data).
References
1. V.I. Kukulin, V.N. Pomerantsev, Î.À. Rubtsova. Theoret.Math.Phys. 150, 473 (2007).
2. R.S. Mackintosh, S.G. Cooper, V.I. Kukulin, Nucl. Phys. A 645.
399(1999).
3. S.B. Dubovichenko, Phys.Atom.Nucl. 73, 1573(2010).