Direct Reduction to Talmi Integrals Without Use of Transformation Brackets

R. H. Richardson; J. Shapiro; F. B. Malik

doi:10.1103/PhysRevC.3.84

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Direct Reduction to Talmi Integrals Without Use of Transformation Brackets

R. H. Richardson^* and J. Shapiro

F. B. Malik^†

Department of Physics, Fordham University, Bronx, New York 10458

Department of Physics, Indiana University, Bloomington, Indiana 47401

^*Present address: Department of Physics, Manhattan College, Bronx, New York.
^†Work supported in part by a National Science Foundation grant.

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Phys. Rev. C 3, 84 – Published 1 January, 1971

DOI: https://doi.org/10.1103/PhysRevC.3.84

Abstract

The two-body shell-model matrix elements for central and tensor forces can be expanded as linear combinations of Talmi integrals. A closed form, which does not involve vector-coupling coefficients or transformation brackets, is obtained for the coefficients appearing in this expansion. For the case that all the oscillator constants are the same, the result is simple enough to allow tabulation. A table of these coefficients for matrix elements involving the shell-model states $0 s$ , $0 p$ , and $0 d$ is included. The main advantage of this method over the Talmi-Brody-Moshinsky method is discussed.

References (7)

I. Talmi, Helv. Phys. Acta 25, 185 (1952)
M. Moshinsky, Nucl. Phys. 13, 104 (1959)
T. A. Brody and M. Moshinsky, Tables of Transformation Brackets for Nuclear Shell-Model Calculations (Dirección General de Publicaciones, Universidad Nacional de Mexico, Ciudad Universitaria, Mexico, D. F., 1960)
A. Gal, Ann. Phys. (N.Y.) 49, 341 (1968)
R. H. Richardson, Ph. D. thesis, Fordham University, 1969 (unpublished)
R. H. Richardson and J. Shapiro, Bull. Am. Phys. Soc. 14, 626 (1969)
K. W. Ford and E. J. Konopinski, Nucl. Phys. 9, 218 (1958)

[c1] I. Talmi, Helv. Phys. Acta 25, 185 (1952)

[c2] M. Moshinsky, Nucl. Phys. 13, 104 (1959)

[c3] T. A. Brody and M. Moshinsky, Tables of Transformation Brackets for Nuclear Shell-Model Calculations (Dirección General de Publicaciones, Universidad Nacional de Mexico, Ciudad Universitaria, Mexico, D. F., 1960)

[c4] A. Gal, Ann. Phys. (N.Y.) 49, 341 (1968)

[c5] R. H. Richardson, Ph. D. thesis, Fordham University, 1969 (unpublished)

[c6] R. H. Richardson and J. Shapiro, Bull. Am. Phys. Soc. 14, 626 (1969)

[c7] K. W. Ford and E. J. Konopinski, Nucl. Phys. 9, 218 (1958)

Physical Review C

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Direct Reduction to Talmi Integrals Without Use of Transformation Brackets

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References (7)

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