[en] By way of evaluating a new procedure for energy-dependent inversion we have compared the energy dependence of the local potential phase equivalent to the Perey-Buck non-local potential with the energy dependence of local potentials derived from RGM and phenomenology. (author)

No abstract available

[en] The Perey-Buck approximation is studied, and corrections to it are discussed, for the physically interesting case in which both the wavelength and the range of the non-locality are small compared to the distances over which the wavelength and the interactions change appreciably. In one dimension the Perey-Buck formula is the leading term of an expansion in the spirit of WKB. Further terms in the expansion are defined and terms up to second order given explicitly. This expansion is equivalent to that of Perey and Saxon, but it displays the orders of magnitude of the terms more clearly. For three-dimensional problems with central symmetry the angular integration can be performed in the non-local form, and the approximation of sect. 2 applied to the radial equation. The approximation is tested numerically on two simple models resembling the n-α and n-⁴⁰Ca interactions. In the latter case there is no significant difference between our approximation and that of Perey and Buck, both being satisfactory; in the former case agreement is achieved only by taking into account the second-order corrections. (orig.)

[en] Some connections among nonlocal, almost local and local descriptions of scattering processes are investigated. An extension of the Perey-Saxon expansion for the Frahn-Lemmer model gives formally an equivalent potential whose nonlocality is restricted to the nuclear surface. Hence, a local phase-equivalent potential and a corresponding almost local Perey effect are found to the second order of the surface terms. Under general conditions on the nonlocal optical potential an almost local equivalent potential of the Kisslinger's form is obtained. This is parity-conserving and reproduces exactly the nonlocal wave functions. Some general properties (like breakdown of causality and of spherical symmetry) are investigated from a qualitative point of view. (orig.)

[en] We show that good approximations to the exact equivalent local potential (ELP) and damping factor of a nonlocal Perey-Buck potential can be calculated in the partial wave WKB approximation of Horiuchi. The exact ELP and damping factor are obtained by means of a method previously given by one of us. We also confirm that an approximate ELP proposed by Bauhoff et al. is of comparable accuracy as the Horiuchi approximation. These l-dependent ELP's exhibit reduced attraction in the interior and provide a test for higher order WKB approximations. We subsequently obtain an equivalent velocity dependent potential (EVDP) which is even exactly wave function equivalent to the original nonlocal potential. This almost local potential, unlike the trivial equivalent local potential, is smooth and well-behaved and is therefore particularly useful in nuclear reactions where the off-shell behaviour of the potential is important. (orig.)

[en] Based on the Perey–Buck nonlocal optical model potential, F. Perey and B. Buck, Nucl. Phys. 32 (1962) 353, we obtain a new set of nonlocal optical model potential (NLOMP) parameters for proton and neutron scattering off nuclei. The experimental angular distributions of nucleon scattering off nuclei ranging from "2"7Al to "2"0"8Pb with incident energies around 10 MeV to 30 MeV are adopted in the fitting procedures. This NLOMP is energy independent. The chi-squares χ"2 obtained in the fittings are comparable to those from the KD03 phenomenological local optical model potentials (OMP) A. Koning and J. Delaroche, Nucl. Phys. A 713 (2003) 231. Good agreement is found in comparisons between optical model calculations using this NLOMP and KD03 in their reproduction to the experimental angular distributions of elastic scattering cross-sections and analyzing powers. (author)

[en] We give a prescription how to construct the maximally local equivalent potentials to be used in the coupled channel equation when the coupled channel equation with the non-local potentials is given. In constructing equivalent potentials we make use of the WKB treatment of the coupled channel equation which is given in the first paper of the present series. The diagonal equivalent local potentials by our method are near the corresponding diabatic equivalent local potentials. When the original non-local coupling potentials are not symmetric we are forced to introduce into the equivalent coupling potentials the term depending linearly on the momentum. The coupling equivalent potential contains in it as the multiplicative factor the product of the diabatic Perey factors of the channels which the coupling potential connects. (author)

[en] Wave functions of the coupled channel system with the equivalent potentials are compared with the wave functions generated by the original non-local potentials. The equivalent potentials to be used in the coupled channel equation are constructed by using the WKB prescription proposed in a previous paper of this series. Under a condition which is usually satisfied, the Perey factors of the coupled channel system are found to be given by the diabatic Perey factors. Although the probability densities and the velocities due to the equivalent potentials are different from the corresponding densities and velocities due to the original non-local potentials, the probability flux by the equivalent potentials is found to have the same value in each channel as the probability flux by the original non-local potentials. (author)

[en] Various equivalent local potentials and their Perey factors are discussed. The Wronskian and inversion-type equivalent local potentials for the energy dependent nonlocal interaction induced by the coupling of the elastic to the nonelastic channels are investigated numerically. Their Perey factors are found to be closer to unity than those associated with exchange-type nonlocal potentials

[en] A separable projectile-nucleon interaction is used in the single-folding model to generate a nonlocal projectile-nucleus potential. The latter is found to be of the Perey-Buck type, provided only s-waves are considered for the projectile-nucleon interaction. The Perey-Buck potential is also used as an input in the nonlocal folding model, in which case the angular-momentum algebra is greatly simplified. Gaussian form factors are used both for potentials and densities