Matrix elements of shell model Hamiltonians in multiple angular momentum coupling schemes

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Abstract
Coefficients of fractional parentage (CFP’s) in an L-S (or J-T) coupling scheme have recently been computed by using a new algorithm extending two procedures introduced many years ago: a factorization procedure introduced by Jahn and a combination of numerical and analytic methods introduced by Bayman and Lande. As a consequence of the factorization, coefficients of fractional parentage between states of arbitrary permutational symmetry must be computed within each angular momentum subspace separately. The new algorithm is extended here to calculate Hamiltonian matrix elements in the second quantized formalism. The matrix elements of the creation and annihilation operators, within each individual subspace, between states of arbitrary symmetry, are defined to be proportional to the corresponding coefficients of fractional parentage. The matrix elements for the one- and two-body operators in the Hamiltonian are constructed by combining the matrix elements in the individual subspaces using a new sum-over-path-overlaps technique. This procedure is extremely efficient for quark shell model calculations, where the quarks carry multiple quantum numbers of angular momentum, or more general, type (L, S, color, and flavor).