Numerical algorithm for the standard pairing problem based on the Heine-Stieltjes correspondence and the polynomial approach. Nature of problem: The program calculates exact pairing energies based on the Heine-Stieltjes polynomial approach. Existing conventional exact-pairing approaches require solving systems of highly nonlinear equations, which are difficult and often impossible to solve beyond the simplest of the quantum-mechanical many-particle systems. In this study, the Heine-Stieltjes polynomial approach is employed to provide solutions for more than one or two pairs of particles residing in many energy levels. Solution method: The new Heine-Stieltjes polynomial approach transforms the pairing problem to one that involves the handling of only two matrix equations. This, combined with an efficient numerical algorithm implemented by the fast Newton-Raphson method with a Monte Carlo sampling procedure for the initial guesses, makes exact pairing solutions feasible even when more energy levels or heavy nuclei (many pairs) are considered.
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References in zbMATH (referenced in 4 articles )
Showing results 1 to 4 of 4.
- Pan, Feng; Zhou, Dan; He, Yingwen; Yang, Siyu; Zhang, Yunfeng; Draayer, J. P.: Exact solution of spherical mean-field plus special orbit-dependent non-separable pairing model with multi non-degenerate (j)-orbits (2019)
- Pan, Feng; Zhang, Yao-Zhong; Draayer, Jerry P.: Exact solution of the two-axis countertwisting Hamiltonian for the half-integer (J) case (2017)
- Lukyanenko, Inna; Isaac, Phillip S.; Links, Jon: An integrable case of the (p+\mathrmip) pairing Hamiltonian interacting with its environment (2016)
- Guan, Xin; Launey, Kristina D.; Xie, Mingxia; Bao, Lina; Pan, Feng; Draayer, Jerry P.: Numerical algorithm for the standard pairing problem based on the Heine-Stieltjes correspondence and the polynomial approach (2014)