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[Licence| Download | New Version Template] aetd_v1_0.tar.gz(38 Kbytes)
Manuscript Title: Numerical algorithm for the standard pairing problem based on the Heine-Stieltjes correspondence and the polynomial approach
Authors: Xin Guan, Kristina D. Launey, Mingxia Xie, Lina Bao, Feng Pan, Jerry P. Draayer
Program title: exactPairingHS
Catalogue identifier: AETD_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 185(2014)2714
Programming language: Mathematica.
Computer: Laptop, workstation.
Operating system: Tested with MATHEMATICA version 9.0 on Mac OS X and Windows 7.
RAM: Less than 10MB
Keywords: Exact pairing problem, Heine-Stieltjes polynomial approach, Second-order Fuchsian equation, Richardson-Gaudin theory, Bethe ansatz equations, Newton-Raphson algorithm, Monte Carlo sampling procedure.
PACS: 21.60.Cs, 03.65.Fd, 71.10.Li, 02.60.Cb.
Classification: 17.15.

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.

Running time:
Less than a hundred seconds using a 2.80 GHz processor. The notebook takes approximately 23 minutes to complete.