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

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dc.creatorPhillips, D. R.
dc.creatorAfnan, I. R.
dc.creatorHenry-Edwards, A. G.
dc.date1999-10-25
dc.date2000-01-12
dc.date.accessioned2026-07-07T13:05:15Z
dc.date.available2026-07-07T13:05:15Z
dc.descriptionDimensional 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.
dc.description22 pages, LaTeX, 5 figures, uses epsfig.sty; minor changes to text to clarify certain points. Version accepted for publication in Phys. Rev. C
dc.identifierhttps://arxiv.org/abs/nucl-th/9910063
dc.identifierhttp://arxiv.org/abs/nucl-th/9910063
dc.identifierPhys.Rev.C61:044002,2000
dc.identifierdoi:10.1103/PhysRevC.61.044002
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227432
dc.subjectNuclear Theory
dc.titleNumerical renormalization using dimensional regularization: a simple test case in the Lippmann-Schwinger equation
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