Speaker
Description
Coefficients of fractional parentage (CFPs) are fundamental ingredients of the nuclear shell model, providing a recursive construction of antisymmetric many-body wave functions and an efficient evaluation of one- and two-body matrix elements. Their calculation in the isospin formalism is considerably more difficult than for identical particles because antisymmetry must simultaneously be satisfied with respect to orbital, spin, and isospin degrees of freedom. Consequently, complete CFP sets with isospin have been available only for limited model spaces. We present a unified computational framework for the calculation of CFPs with isospin together with its extensions to generalized and intrinsic CFPs [1-5]. The method combines a simple enumeration scheme for antisymmetric many-particle states with an efficient construction of the eigenvectors of the antisymmetrization operator, an idempotent matrix whose unit-eigenvalue eigenvectors are precisely the required CFPs. This eliminates repeated diagonalization of large matrices, provides excellent numerical stability, and is naturally suited for parallel implementation [1,2]. The developed algorithms enable large-scale calculations of one-particle and two-particle CFPs for single j-shells with isospin [3]. The methodology has been further extended to generalized CFPs for multishell configurations [4] and to intrinsic two-particle CFPs (CESOs), which combine antisymmetry with translational invariance by eliminating spurious center-of-mass motion [5]. The algorithms avoid costly matrix diagonalizations, are numericaly stable, and provide an effective computational foundation for contemporary large-scale nuclear-structure calculations.
References
[1] A. Deveikis, R. K. Kalinauskas, and B. R. Barrett, Calculation of coefficients of fractional parentage for large-basis harmonic-oscillator shell model, Ann. Phys. 296 (2), 287-298 (2002).
[2] A. Deveikis, Orthogonalization procedure for antisymmetrization of J-shell states, in: Parallel scientific computing and optimization advances and applications, Vol. 27, ed. R. Čiegis et.al. (Springer, New York, 2009) pp. 213-221.
[3] A. Deveikis, A program for generating one-particle and two-particle coefficients of fractional parentage for the single j-orbit with isospin, Comput. Phys. Commun. 173 (3), 186-192 (2005).
[4] A. Deveikis, A. Juodagalvis, A computer program for two-particle generalized coefficients of fractional parentage, Comput. Phys. Commun. 179, (8), 607-613 (2008).
[5] A. Deveikis, A computer program for two-particle intrinsic coefficients of fractional parentage, Comput. Phys. Commun. 183 (6), 1397-1401 (2012).