Numerical quasiparticle representation of the nucleon-nucleon T matrix

Journal Article · Mon Jul 01 04:00:00 EDT 1991 · Physical Review, C (Nuclear Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevC.44.60· OSTI ID:5726710

Rawitscher, G H; Canton, L ^[1]

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1. Physics Department, University of Connecticut, Storrs, Connecticut 06268 (US)

In this paper we develop a practical hybrid'' numerical representation of the nucleon-nucleon {ital T} matrix. Part of the expression contains nonseparable terms which are easily calculated, and the rest consists of a separable representation of small rank in terms of Weinberg states. The method rests on the observation that when a set of positive-energy Weinberg states is used to obtain a separable representation of the potential {ital V} then the residue {Delta}{ital V}, due to the basis-set truncation, has very special properties: (1) The contribution {Delta}{ital T} to the {ital T} matrix due to {Delta}{ital V} is identical to the undistorted {ital T} matrix for {Delta}{ital V} alone, {ital T}{sub {Delta}}, i.e., the usual Moeller distortion factors in the two-potential formula are unity in this case. (2) A perturbative-iterative treatment of {ital T}{sub {Delta}} in powers of {Delta}{ital V} is found to be equivalent to the finite-rank representation of operators of the type {ital T}, {ital T}{minus}{ital V}, {ital T}{minus}{ital V}{minus}{ital VG}{sub 0}{ital V}, and so on. This equivalence has both practical and theoretical implications. On the one hand, it provides a reliable method for calculating the {ital T} matrix and for analyzing the corresponding accuracy properties. On the other hand, a connection is established between each order of the quasiparticle method and the different variational principles which underlie the finite-rank representation of operators such as {ital T}, {ital T}{minus}{ital V}, {ital T}{minus}{ital V}{minus}{ital VG}{sub 0}{ital V}, etc. Numerical examples are provided for two different nucleon-nucleon singlet potentials (Reid soft core and Malfliet-Tjon).

• OSTI ID: 5726710
• Journal Information: Physical Review, C (Nuclear Physics); (USA), Journal Name: Physical Review, C (Nuclear Physics); (USA) Vol. 44:1; ISSN 0556-2813; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653001* -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
FUNCTIONS
GREEN FUNCTION
MATRICES
NUCLEON-NUCLEON POTENTIAL
NUMERICAL SOLUTION
POTENTIALS
QUASI PARTICLES
REID POTENTIAL
S MATRIX