A New Iterative Approach for the Exact Solution of the Standard Pairing Model

GUAN Xin; AI Xin

doi:10.11804/NuclPhysRev.35.04.518

A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.

A New Iterative Approach for the Exact Solution of the Standard Pairing Model

Department of Physics, Liaoning Normal University, Dalian 116029, Liaoning, China

Funds: Natural Science Foundation of China (11675071)

Received Date: 2018-09-18

Rev Recd Date: 2018-10-05

Publish Date: 2020-05-03

Key words:

Abstract: A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.

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Reference (21)

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A New Iterative Approach for the Exact Solution of the Standard Pairing Model

doi: 10.11804/NuclPhysRev.35.04.518

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