Analytic Sturmian functions and convergence of separable expansions

Journal Article · Sat Aug 01 04:00:00 EDT 1987 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.36.475· OSTI ID:6212037

Hartt, K; Yidana, P V.A.

A method for solving integral equations is developed and applied to the homogeneous Lippmann-Schwinger equation in momentum space. It has been used with Yukawa-type potentials, V(r) = ..sigma.., and yields solutions that are analytic expressions rational in the variable k/sup 2/. More specifically, the principal-value form of the homogeneous Lippmann-Schwinger equation is solved by making an analytic series expansion of the integral, which is then summed using Pade approximants. An application to the Malfliet-Tjon potential V in s wave is given. In a finite subspace of rational functions with fixed denominators, the solutions, referred to as Sturmian functions, are obtained corresponding to the energy -0.35 MeV, which is the physical bound state energy for this potential. With these analytic eigenfunctions as form factors and with the associated eigenvalues, a separable expansion, namely, the unitary pole expansion, is constructed for the local potential. The unitary pole expansion is then used for analytic k-matrix calculations. At intermediate energies through E/sub c.m./ = 666 MeV, and at ultrahigh momenta, as the rank of the unitary pole expansion approaches 13, analytic wave functions (or, equivalently, half-shell k matrices) and phase shifts are found that are in good agreement with exact results.

• Research Organization: Physics Department, University of Rhode Island, Kingston, Rhode Isl 02881
• OSTI ID: 6212037
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 36:2; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANALYTICAL SOLUTION
BANACH SPACE
BOUND STATE
EIGENVALUES
EQUATIONS
FUNCTIONS
GAMOW-TELLER RULES
HILBERT SPACE
INTEGRAL EQUATIONS
K MATRIX
LIPPMANN-SCHWINGER EQUATION
MATHEMATICAL SPACE
MATRICES
NUCLEAR POTENTIAL
NUCLEON-NUCLEON POTENTIAL
PADE APPROXIMATION
PARTIAL WAVES
PHASE SHIFT
POTENTIALS
S MATRIX
S WAVES
SPACE
UNITARY POLE APPROXIMATION
WAVE FUNCTIONS
YUKAWA POTENTIAL