#### Title

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

#### Document Type

Article

#### Publication Date

2-6-2017

#### 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.

#### Publication Source (Journal or Book title)

Journal of Statistical Mechanics: Theory and Experiment

#### Recommended Citation

Pan, F., Zhang, Y., & Draayer, J.
(2017). Exact solution of the two-axis countertwisting hamiltonian for the half-integer J case.* Journal of Statistical Mechanics: Theory and Experiment**, 2017* (2)
https://doi.org/10.1088/1742-5468/aa5a28