Speaker: Ami Leviatan (Hebrew University, Jerusalem)

Relativistic pseudospin symmetry in nuclei: doublet structure and supersymmetric partners

The concept of pseudospin symmetry is based on the empirical observation of quasi-degenerate pairs of certain normal-parity shell-model orbitals with non-relativistic quantum numbers (n, l, j = l+1/2) and (n-1, l, j = l+3/2) where n, l, and j are the single-nucleon radial, orbital, and total angular momentum quantum numbers, respectively. The doublet structure, is expressed in terms of a ``pseudo'' orbital angular momentum \tilde{l} = l+1 and ``pseudo'' spin, \tilde {s} = 1/2, coupled to j = \tilde{l} ± \tilde {s}. For example, (2p_{3/2},1f_{5/2}) will have \tilde{l}= 2, etc. This pseudospin symmetry plays a central role in nuclei and only recently has it been shown to originate from a relativistic symmetry of the Dirac Hamiltonian. In the present talk we show that a natural explanation for characteristic features of these doublets (radial and angular momentum quantum numbers, absence of pseudospin partners for intruder levels, supersymmetric-like spectrum) can be obtained by combining the relativistic attributes of pseudospin symmetry with known properties of Dirac bound states.