Numerical renormalization using dimensional regularization: A simple test case in the Lippmann-Schwinger equation

Journal Article · Sat Apr 01 04:00:00 EST 2000 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PhysRevC.61.044002· OSTI ID:20215882

Phillips, D R ^[1]; Afnan, I R ^[2]; Henry-Edwards, A G ^[2]

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1. Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
2. Department of Physics, The Flinders University of South Australia, G.P.O. Box 2100, Adelaide 5001, (Australia)

Dimensional regularization is applied to the Lippmann-Schwinger equation for a separable potential which gives rise to logarithmic singularities in the Born series. For this potential a subtraction at a fixed energy can be used to renormalize the amplitude and produce a finite solution to the integral equation for all energies. This can be done either algebraically or numerically. In the latter case dimensional regularization can be implemented by solving the integral equation in a lower number of dimensions, fixing the potential strength, and computing the phase shifts, while taking the limit as the number of dimensions approaches three. We demonstrate that these steps can be carried out in a numerically stable way, and show that the results thereby obtained agree with those found when the renormalization is performed algebraically to four significant figures. (c) 2000 The American Physical Society.

• OSTI ID: 20215882
• Journal Information: Physical Review. C, Nuclear Physics, Journal Name: Physical Review. C, Nuclear Physics Journal Issue: 4 Vol. 61; ISSN 0556-2813; ISSN PRVCAN
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BORN APPROXIMATION
INTEGRAL EQUATIONS
LIPPMANN-SCHWINGER EQUATION
NUMERICAL ANALYSIS
RENORMALIZATION
SCATTERING
THEORETICAL DATA