The pseudospin symmetry has been introduced in nuclear structure
physics many years ago [105,106], in order to account
for ``unexpected'' degeneracies in single-particle spectra. It has
been attributed to an accidental cancelation between the spin-orbit
field
and the
term in the Nilsson
potential [107], the latter reflecting the fact that the
nuclear single-particle field has a flat bottom due to the saturation
of nuclear forces. Later, many similar degeneracies were also
observed among rotational bands, see, e.g., the pair of bands in
187Os studied in Ref. [108] and references cited
therein.
Recently, a very elegant and natural explanation was suggested [109,110,111], which is based on simple relativistic arguments and properties of the RMF Dirac equation for nucleons. Indeed, when the Dirac Hamiltonian is solved with the vector and scalar potentials, VV and VS, respectively,
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In finite nuclei, condition VV+VS=const is, of course, violated
because the potentials have finite range, and hence, they must depend
on the distance from the center of the nucleus. However, it turns out
that in realistic situations the lower Dirac components of the
pseudospin partners are still fairly close to one another, and their
single-particle energies are almost degenerate. This is illustrated
in Fig. 8 [112], where the upper (left panel) and
lower (right panel) components of two bound states, 2s1/2 and
1d3/2, in 208Pb are plotted. These two states are the
pseudospin partners corresponding to
=1,
i.e., to the 1
and 1
orbitals, and
their lower Dirac components are very similar indeed.
Nevertheless, the utility of the idea of the pseudospin symmetry crucially depends on the symmetry breaking schemes in real nuclei, and this aspect of the proposed relativistic explanation requires further study, see the analyses presented in Refs. [113,114] and references cited therein. In particular, an explanation of the fact that the pseudospin symmetry does not hold in light nuclei is still lacking (relativity arguments should hold irrespective of the number of particles). Similarly, it would be very interesting to see if the pseudospin symmetry still holds in neutron rich nuclei, where changes in the surface diffuseness may act against it [76].