A New Iterative Approach for the Exact Solution of the Standard Pairing Model
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摘要: 建立了一种求解标准对力模型的新迭代方法。该方法基于标准对力模型的多项式方案，为球形和形变系统提供了方便的初始值预测。特别是对于大尺寸系统，该方法将求解k对多项式的系统方程式简化为分步求解1对多项式系统的迭代过程，并通过快速Newton-Raphson以及Monte Carlo采样算法逐步提供初始值预测。通过扩展，本算法还可用于解决Gaudin型量子多体问题，例如考虑超过100条轨道、50对的大尺寸系统，以及超形变核、核裂变的研究中。
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.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.-
Key words:
- standard pairing problem /
- iterative approach /
- super-heavy nuclei /
- nuclear fission
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[1] BOHR A, MOTTELSON B R. Nuclear Structure, Vol. 1:Single-Particle Motion[M]. New York:Benjamin, 1969. [2] BELYAEV S T. Mat Fys Medd Dan Vid Selsk, 1959, 31:11. [3] PING P, SCHUCK P. The Nuclear Many-Body Problem[M]. Berlin:Springer Verleg, 1980. [4] HASEGAWA M, TAZAKI S. Phys Rev C, 1993, 47:188. [5] BARDEEN J, COOPER L N, SCHRIEFFER J R. Phys Rev, 1957, 108:1175. [6] GUAN X, PAN F. Nucl Phys Rev, 2017, 34:121. [7] KERMAN A K, LAWSON R D. Phys Rev, 1961, 124:162. [8] VOLYA A, BROWN B A, ZELEVINSKY V. Phys Lett B, 2001, 509:37. [9] ZELEVINSKY V, VOLYA A. Physics of Atomic Nuclei, 2003, 66:1781. [10] SUN Y. Phys Scr, 2016, 91:043005. [11] SUN Y, WU C L, BHATT K, et al. Nucl Phys A, 2002, 703:130. [12] RICHARDSON R W. Phys Lett, 1963, 3:277; (1963), 5:82; RICHARDSON R W, SHERMAN N. Nucl Phys, 1964, 52, 221; Nucl Phys,(1964), 52:253. [13] GAUDIN M. J Physique, 1976, 37:1087. [14] GUAN X, LAUNEY K D, XIE M X, et al. Phys Rev C, 2012, 86:024313. [15] GUAN X, XU H C, ZHANG Y, et al. Phys Rev C, 2016, 94:024309. [16] QI C, CHEN T. Phys Rev C, 2015, 92:051304(R). [17] GUAN X, LAUNEY K D, XIE M X, et al. Comp Phys Commun, 2014, 185, 2714. [18] FARIBAULT A, EL ARABY O, STRÄTER C, et al. Phys Rev B, 2011, 83, 235124; EL ARABY O, GRITSEV V, FARIBAULT A, Phys Rev B, 2012, 85, 115130. [19] WU Z Y, QI C, WYSS R, et al. Phys Rev C, 2015, 92, 024306. [20] CHANGIZI S A, QI C, WYSS R. Nucl Phys A, 2015, 940, 210. [21] U.S. NATIONAL NUCLEAR DATA CENTER:http://www.nndc.bnl.gov/. -
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