It is an interesting and important aspect of some of the group-theory-based
formalisms that they allow for a simultaneous, correct from the many
body formulation point of view, description of fermions and bosons.
In the simplest interpretation, the former are just the unpaired nucleons
while the latter correspond to the coupled pairs of nucleons. A starting point
of the formalism consists in employing a unitary supersymmetry U(n/m).
Using such a formalism it has been shown
that the nuclei corresponding to the second half
of the s-d shell are well described while those from the first half are not,
important differences being predicted also by the shell model calculations.
We would like to extend this type of studies and better approach the coupling
mechanisms, in particular between the odd proton and the odd neutron.
We should like to emphasize that the proton-neutron coupling, also
in heavier rotating nuclei is an important current problem of the high-spin
physics. Our study would bring an interesting possibility of confronting
the results of various formalisms and conclude about a possible changing
in the proton-neutron coupling schemes in function of nuclear mass, isospin
and spin.
The supersymmetry concepts are also directly applicable
in another physical context: that of the pseudo-spin symmetry and pseudo-spin
transformation, both introduced originally many years ago and revisited recently
in the context of nuclear superdeformation. We would like to examine a
pseudo-spin transformation on the level
of the Dirac equation together with the relations between the group of
Lorentz/Poincaré and the group Osp(1/2). This research would allow to
understand a deeper physical role of the pseudo-spin symmetry in both
relativistic and non-relativistic formulations of the nuclear interaction
problem.