Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Open Physics

Method simplifying calculation of coefficients of fractional parentage for translationally invariant shell-model

Saulius Mickevičius, Darius Germanas, R.K. Kalinauskas

Published May 1, 2013• 3 citations
Publisher

Abstract

Abstract A new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator $$P_{N_1 ,N}$$ in a subspace where N 1 and N 2 = N − N 1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators $$P_{N_1 ,N}$$ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.

DOI
10.2478/s11534-013-0215-3

Related papers

Method simplifying calculation of coecients of fractional parentage for translationally invariant

Saulius Mickevi, Darius Germanas, R.K. Kalinauskas

A new procedure for large-scale calculations of the coecients of fractional parentage (CFP) for manyparticle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an ecient method for constructing the eigenvectors of two-particle transposition operator PN1;N in a subspace where N1 and N2 = N N1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators PN1;N eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.

•Jan 1, 2013•0 citations

Elimination the CentreofMass Motion in the Nuclear ShellModel with Isospin 1

A. Deveikis, A. Fedurtsya

oretical classification of manyparticle antisymmetri� cal states allows one to significantly simplify the anti� symmetrization procedure for Aparticle states. The efficiency of the proposed procedure for calculation of coefficients of fractional parentage uprise from the possibility to perform the calculation of translationally invariant CFP's in the ordinary oneparticle basis. The introduced CESO's may be used most effectively for ab initio No Core Nuclear Structure calculations with oscillator intrinsic density matrices within the framework of Reduced Hamiltonian method (2). Abstract—An efficient procedure for largescale calculations of the twoparticle translational invariant coef� ficients of fractional parentage (CESO's) for several jsh ells with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric manyparticle states and efficient algorithms for calcu� lation of the coefficients of fractional parentage for a single jshell and several jshells with isospin. The CESO's may be obtained by diagonalizing the centreofmass Hamiltonian in the basis set of antisymmetric Aparticle oscillator functions with singled out dependenc e on intrinsic coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2. An arbitrary number of oscillator quanta can be involved. The characteristics of the introduced CESO's basis are investi�

•Jan 1, 2011•0 citations

Fractional parentage coefficients and their explicit evaluation

A. Hassitt

Abstract In the independent particle model, the total wave function is expressed as a linear combination of products of single particle wave functions. Fractional parentage coefficients give the part of the expression depending on the symmetry properties of the wave function. An operator is introduced which picks out the antisymmetric part of any n-particle wave function. The operator is given explicit form, and an explicit formula for the fractional parentage coefficients is deduced. The total fractional parentage coefficients can be split into a part depending on the orbital vectors, and a part depending on the spin (and isotopic spin) vectors. The separate parts can have symmetries other than total antisymmetry. Operators are introduced which pick out states of definite symmetry from any state. The operators are given explicit form, and explicit formulae for orbital, or spin, fractional coefficients are deduced. Detailed results are given for the three, four and five particles cases.

Proceedings of the Royal Society of London A Mathematical and Physical Sciences•Apr 5, 1955•12 citations

Coefficients of fractional parentage for the states of an arbitrary number of j=1 bosons

Z. Marić, M. Popović‐Božić

The construction of symmetric states of N particles with angular momentum j=1 is presented. Elliott's result (1958), dealing with the angular momentum content of the symmetric subset of states belonging to the set of states of N particles with angular momentum j=1 is obtained using Racah algebra for the angular momentum coupling. The explicit functional dependence, on the total angular momentum, of the coefficients of fractional parentage (CFP) associated with one, two, three and four removed particles is found for arbitrary values of N. This dependence is expressed through the simple algebraic functions of J and N.

Journal of Physics A Mathematical and General•Sep 1, 1980•1 citation

Mass-ratio parameters expressions for binary clasters of identical fermion systems

R.K. Kalinauskas, Darius Germanas, Saulius Mickevičius

In this contribution, we present the explicit expressions of mass-ratio parameters for binary clasters composed of n(1), and n(2) particles which can be used developing efficient techniques for large-scale calculations of the coefficients of fractional parentage (CFP) for systems consisting of n = n(1) + n(2) identical fermions.

•Jan 1, 2012•0 citations

Calculation of orbital fractional parentage coefficients for five particles in translationally invariant basis

Augustinas Stepšys, Saulius Mickevičius, Darius Germanas +1 more

Computer Physics Communications•Oct 17, 2018•2 citations
Abstract A new procedure for large-scale calculations of the coefficients of fractional parentage (CFP) for many-particle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an efficient method for constructing the eigenvectors of two-particle transposition operator PN1,NP_{N_1 ,N}PN1​,N​ in a subspace where N 1 and N 2 = N − N 1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators PN1,NP_{N_1 ,N}PN1​,N​ eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.
A new procedure for large-scale calculations of the coecients of fractional parentage (CFP) for manyparticle systems is presented. The approach is based on a simple enumeration scheme for antisymmetric N particle states, and we suggest an ecient method for constructing the eigenvectors of two-particle transposition operator PN1;N in a subspace where N1 and N2 = N N1 nucleons basis states are already antisymmetrized. The main result of this paper is that according to permutation operators PN1;N eigenvalues we can distinguish totally asymmetrical N particle states from the other states with lower degree of asymmetry.
oretical classification of manyparticle antisymmetri� cal states allows one to significantly simplify the anti� symmetrization procedure for Aparticle states. The efficiency of the proposed procedure for calculation of coefficients of fractional parentage uprise from the possibility to perform the calculation of translationally invariant CFP's in the ordinary oneparticle basis. The introduced CESO's may be used most effectively for ab initio No Core Nuclear Structure calculations with oscillator intrinsic density matrices within the framework of Reduced Hamiltonian method (2). Abstract—An efficient procedure for largescale calculations of the twoparticle translational invariant coef� ficients of fractional parentage (CESO's) for several jsh ells with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric manyparticle states and efficient algorithms for calcu� lation of the coefficients of fractional parentage for a single jshell and several jshells with isospin. The CESO's may be obtained by diagonalizing the centreofmass Hamiltonian in the basis set of antisymmetric Aparticle oscillator functions with singled out dependenc e on intrinsic coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2. An arbitrary number of oscillator quanta can be involved. The characteristics of the introduced CESO's basis are investi�
Abstract In the independent particle model, the total wave function is expressed as a linear combination of products of single particle wave functions. Fractional parentage coefficients give the part of the expression depending on the symmetry properties of the wave function. An operator is introduced which picks out the antisymmetric part of any n-particle wave function. The operator is given explicit form, and an explicit formula for the fractional parentage coefficients is deduced. The total fractional parentage coefficients can be split into a part depending on the orbital vectors, and a part depending on the spin (and isotopic spin) vectors. The separate parts can have symmetries other than total antisymmetry. Operators are introduced which pick out states of definite symmetry from any state. The operators are given explicit form, and explicit formulae for orbital, or spin, fractional coefficients are deduced. Detailed results are given for the three, four and five particles cases.
The construction of symmetric states of N particles with angular momentum j=1 is presented. Elliott's result (1958), dealing with the angular momentum content of the symmetric subset of states belonging to the set of states of N particles with angular momentum j=1 is obtained using Racah algebra for the angular momentum coupling. The explicit functional dependence, on the total angular momentum, of the coefficients of fractional parentage (CFP) associated with one, two, three and four removed particles is found for arbitrary values of N. This dependence is expressed through the simple algebraic functions of J and N.