A One-Particle Generalized Coefficients of Fractional Parentage Calculation Method for Atomic Nucleus Harmonic Oscillator Shell Model

Algirdas Deveikis

Abstract


A method for the calculation of the one-particle generalized coefficients of fractional parentage for several j-orbits with isospin and an arbitrary number of oscillator quanta (generalized CFPs or GCFPs) is presented. The approach is based on a simple enumeration scheme for antisymmetric many-particle states, an efficient algorithm for calculation of the CFPs for a single j-orbit with isospin, and a general procedure for computation of the angular momentum (isospin) recoupling coefficients describing the transformation between different momentum coupling schemes. The method provides fast calculation of GCFPs for a given particle number and produces results possessing small numerical uncertainties. The introduced GCFPs may be used for calculation of expectation values of one-particle nuclear shell-model operators within the isospin formalism.

https://doi.org/10.15181/csat.v7i0.1763


References


Aktulga, Metin; Yang, Chao; Ng, Esmond; Maris, Pieter; Vary, James (2011). „Large-scale parallel null space calculation for nuclear configuration interaction“. In: Proceedings of the 2011 International Conference on High Performance Computing and Simulation: 176–185.

Allison, Donald (1969). „Fractional parentage coefficients for equivalent p shell and equivalent d shell electrons“. Computer Physics Communications, 1, 1: 15–20.

Allison, Donald; McNulty, John. (1974). „Fractional parentage coefficients for equivalent f shell electrons“. Computer Physics Communications, 8, 3: 246–256.

Bacher, Robert; Gousmit, Samuel (1934). „Atomic energy relations. I“. Physical Review, 46, 11: 948–969.

Barrett, Bruce; Navrátil, Petr; Vary, James (2013). „Ab initio no core shell model“. Progress in Particle and Nuclear Physics, 69: 131–181.

Chivers, Alfred (1973). „A new version of the program to compute the fractional parentage coefficients for equivalent d shell electrons“. Computer Physics Communications, 6, 2: 88–88.

de-Shalit, Amos; Talmi, Igal (1963). Nuclear Shell Theory. New York: Academic Press.

Deveikis, Algirdas; Kamuntavičius, Gintautas (1995). „Coefficients of fraction parentage for nuclear shell model“. Lithuanian Physics Journal, 35, 1: 14–19.

Deveikis, Algirdas; Kamuntavičius, Gintautas (1996). „Intrinsic density matrices of the nuclear shell model“. Lithuanian Physics Journal, 36, 2: 83–95.

Deveikis, Algirdas; Kalinauskas, Ramutis; Barrett, Bruce (2002). „Calculation of coefficients of fractional parentage for large-basis harmonic-oscillator shell model“. Annals of Physics, 296: 287–298.

Deveikis, Algirdas (2005). „A program for generating one-particle and two-particle coefficients of fractional parentage for the single j-orbit with isospin“. Computer Physics Communications, 173, 3: 186–192.

Dikmen, Erdal; Lisetskiy, Alexander; Barrett, Bruce; Maris, Pieter; Shirokov, Andrey; Vary, James (2015). „Ab initio effective interactions for sd-shell valence nucleons“. Physical Review C, 91: 034312.

Draayer, Jerry; Dytrych, Tomas; Sviratcheva, Kristina; Bahri, Chairul (2008). „Symplectic ab initio no-core shell model“. Mexicana De F'isica S, 54 (3): 36–41.

Dytrych, Tomas; Maris, Pieter; Launey, Kristina; Draayer, Jerry; Vary, James; Langr, Daniel; Saule, Erik; Caprio, Mark; Ҫatalyürek, Ümit; Sosonkina, Masha (2016). „Efficacy of the SU(3) scheme for ab initio large-scale calculations beyond the lightest nuclei“. Computer Physics Communications, 207: 202–210.

Edmonds, Alan; Flowers, Brian (1952). „Studies in jj–coupling. II. Fractional parentage coefficients and the central force energy matrix for equivalent particles“. Proceedings Royal Society London, A 214: 515-530.

Fano, Ugo (1965). „Interaction between configurations with several open shells“. Physical Review, 140: A67–A75.

Fritzsche, Stephan (2009). „Maple procedures for the coupling of angular momenta. An up-date of the RACAH module“. Computer Physics Communications, 180, 10: 2021–2023.

Gaigalas, Gediminas; Fritzsche, Stephan; Fricke, Burkhard (2001). „Maple procedures for the coupling of angular momenta. III. Standard quantities for evaluating many-particle matrix elements“. Computer Physics Communications, 135, 2: 219–237.

Gaigalas, Gediminas; Fritzsche, Stephan; Gaidamauskas, Erikas; Kiršanskas, Gediminas; Žalandauskas, Tomas (2006). „JAHN-A program for representing atomic and nuclear states within an isospin basis“. Computer Physics Communications, 175, 1: 52–66.

Grant, Ian (1972). „CFPJJ-Fractional parentage coefficients for equivalent electrons in jj-coupling“. Computer Physics Communications, 4, 3: 377–381.

Kagawa, Takashi (1992). „A program to calculate fractional parentage coefficients for jj-coupling states with equivalent particles“. Computer Physics Communications, 72, 2-3: 165-174.

Levinsonas, Josifas (1957). „Coefficients of fractional parentage of configuration with few shells“. Works of Lithuanian SSR Academy of Sciences, 4, 4: 17–31.

Maris, Pieter; Aktulga, Metin; Caprio, Mark; Ҫatalyürek, Ümit; Eg, Edmont; Oryspayev, Dossay; Potter, Hugh; Saule, Erik; Sosonkina, Masha; Vary, James; Yang, Chao; Zhou, Zheng (2012). „Large-scale ab initio configuration interaction calculations for light nuclei“. Journal of Physics: Conference Series, 403, 1: 012019.

Navrátil, Petr; Vary, James; Barrett, Bruce (2000). „Large-basis ab initio no-core shell model and its application to 12C“. Physical Review C, 62: 054311.

Racah, Giulio (1943). „Theory of complex spectra. III“. Physical Review, 63, 9 and 10: 367-382.

Redmond, Peter (1954). „An explicit formula for the calculation of fractional parentage coefficients“. Proceedings Royal Society London, A 222: 84–93.

Shin, Ik; Kim, Youngman; Maris, Pieter; Vary, James; Forssén, Christian; Rotureau, Jimmy; Michel, Nicolas (2017). „Ab initio no-core solutions for 6Li“. Journal of Physics G: Nuclear and Particle Physics, 44, 7: 075103.

Skouras, Leonidas; Kossionides Stathis (1986). „Generalized fractional parentage coefficients for shell-model calculations“. Computer Physics Communications, 39, 2: 197–212.

Wang, Jia-jun; Han, Qi-zhi; Liu, Yu-xin (1995). „A new Fortran program for CFPs of an identical fermion system“. Computer Physics Communications, 85, 1: 99–109.

Wang, XiaoBao; Dong, GuoXiang; Li, QingFeng; Shen, CaiWan; Yu, ShaoYing (2016). „An investigation of ab initio shell-model interactions derived by no-core shell model“. Science China Physics, Mechanics & Astronomy, 59, 9: 692011.


Full Text: PDF

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

eISSN: 2029-9966

Creative Commons License