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

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.