Bing-Nan Lu, En-Guang Zhao, Shan-Gui Zhou
Recently we justified rigorously that the pseudospin symmetry (PSS) in single particle resonant states is exactly conserved when the attractive scalar and repulsive vector potentials of the Dirac Hamiltonian have the same magnitude but opposite sign [1, B. N. Lu et al., Phys. Rev. Lett. 109, 072501 (2012)]. In this work we focus on several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances. To this end spherical square well potentials are employed in which the PSS breaking part can be well isolated in the Jost function. By examining the zeros of Jost functions corresponding to small components of the radial Dirac wave functions, general properties of the PSS are analyzed. We show that the conservation and the breaking of the PSS in resonant states and bound states share some similar properties. By examining the Jost function, the occurrence of intruder orbitals is explained and it is possible to trace continuously the PSS partners from the PSS limit to the case with a finite potential depth. The dependence of the PSS in resonances as well as in bound states on the potential depth is investigated systematically. We find a threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners when the depth of the single particle potential varies from zero to a finite value.
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http://arxiv.org/abs/1305.1524
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