Recent progresses on the pseudospin symmetry in single particle resonant states

Bing-Nan Lu,En-Guang Zhao,Shan-Gui Zhou

doi:10.1088/1742-6596/533/1/012021

Bing-Nan Lu, En-Guang Zhao + Show 1 more

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https://doi.org/10.1088/1742-6596/533/1/012021

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The pseudospin symmetry (PSS) is a relativistic dynamical symmetry directly connected with the small component of the nucleon Dirac wave function. Much effort has been made to study this symmetry in bound states. Recently, a rigorous justification of the PSS in single particle resonant states was achieved by examining the asymptotic behaviors of the radial Dirac wave functions: The PSS in single particle resonant states in nuclei is conserved exactly when the attractive scalar and repulsive vector potentials have the same magnitude but opposite sign. Several issues related to the exact conservation and breaking mechanism of the PSS in single particle resonances were investigated by employing spherical square well potentials in which the PSS breaking part can be well isolated in the Jost function. A threshold effect in the energy splitting and an anomaly in the width splitting of pseudospin partners were found when the depth of the square well potential varies from zero to a finite value.

Highlights

In 1969, the pseudospin symmetry (PSS) was found in atomic nuclei: Doublets of single particle levels with quantum numbers and in the same major shell are nearly degenerate [1, 2]
It was revealed that the PSS in nuclei is a relativistic symmetry which is exactly conserved when the scalar potential S(r) and the vector potential V (r) have the same size but opposite sign, i.e., Σ(r) ≡ S(r) + V (r) = 0 [8], or, more generally, when dΣ(r)/dr = 0 [9, 10]
The PSS is usually viewed as a dynamical symmetry [11, 12] because, in either limit, Σ(r) = 0 or dΣ(r)/dr = 0, there are no bound states in realistic nuclei, in realistic nuclei the PSS is always broken

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Introduction

1. Introduction In 1969, the pseudospin symmetry (PSS) was found in atomic nuclei: Doublets of single particle levels with quantum numbers (nr, l, j = l + 1/2) and (nr − 1, l + 2, j = l + 3/2) in the same major shell are nearly degenerate [1, 2]. We gave a rigorous justification of the PSS in single particle resonant states and investigated several open problems related to the exact conservation and breaking mechanism of the PSS in single particle resonances [36, 37, 15].

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