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arXiv · 1610.05905

Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case

Feng Pan·Yao-Zhong Zhang·Jerry P. Draayer
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Abstract

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer $J$ cases are discussed. It is clearly shown that double degenerate level energies for half-integer $J$ are symmetric with respect to the $E=0$ axis. It is also shown that the excitation energies of the `yrast' and other `yrare' bands can all be asymptotically given by quadratic functions of $J$, especially when $J$ is large.

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Feng Pan, Yao-Zhong Zhang, Jerry P. Draayer. 2016-12-14. Exact solution of the two-axis countertwisting Hamiltonian for the half-integer $J$ case. https://doi.org/10.1088/1742-5468%2Faa5a28

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