Interpretation of the Perey-Buck nonlocality in terms of the relativistic optical model formalism

Journal Article · Mon Apr 01 04:00:00 EST 1985 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.31.1173· OSTI ID:6024033

Rawitscher, G H

Under certain conditions the solution of a nonlocal, nonrelativistic Schroedinger equation is the same as the upper component of a relativistic four-spinor which obeys a local Dirac equation. This result is obtained by combining the observation recently made by Fiedeldey and Sofianos, that a nonlocal Schroedinger equation can be transformed into a local one if a gradient term (or velocity term) is added, together with the well-known fact that the upper component of the solution of a Dirac equation also obeys a second-order equation which has a gradient term. For the case of a nonlocality of the Perey-Buck--type, the gradient term is nearly equal to the Darwin term, and hence the conditions for the validity of the relativistic-nonrelativistic equivalence are nearly valid. A numerical example is presented for the case of 21.7 MeV neutrons scattering elastically from /sup 40/Ca, for which a local relativistic optical potential has been recently obtained. The gradient term is given in terms of derivatives of the Wronskian of two independent solutions of the nonlocal equation, and numerical values for the latter are compared with the corresponding relativistic quantity. The differences are not larger than 25%. Results for the nonlocality due to exchange are also shown, and are found to be very similar to the Perey-Buck nonlocality. An implication of these results is that the relativistic optical potential may be less nonlocal than the nonrelativistic one.

• Research Organization: Physics Department, University of Connecticut, Storrs, Connecticut 06268
• OSTI ID: 6024033
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 31:4; ISSN PRVCA
• Country of Publication: United States
• Language: English

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BARYON REACTIONS
CALCIUM 40 TARGET
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELASTIC SCATTERING
ENERGY DEPENDENCE
EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
HADRON REACTIONS
MATHEMATICAL MODELS
NEUTRON REACTIONS
NONLOCAL POTENTIAL
NUCLEAR MODELS
NUCLEAR REACTIONS
NUCLEON REACTIONS
OPTICAL MODELS
PARTIAL DIFFERENTIAL EQUATIONS
PEREY-BUCK MODEL
POTENTIALS
RELATIVITY THEORY
RENORMALIZATION
SCATTERING
SCHROEDINGER EQUATION
TARGETS
WAVE EQUATIONS
WAVE FUNCTIONS