M. Razavy

Scattering by non-local potentials

Abstract The kernels of a class of non-local potentials are related to the Green functions of the second order differential equations. For these potentials, the integro-differential wave equation may be transformed into a set of coupled ordinary differential equations, which can be solved by a factorization method. A solvable example of the non-separable kernel is given and the variation of the exact wave function with the non-locality of the interaction is studied. The effective mass approximation of Frahn and Lemmer for the optical potential is derived and the connection between the wave function in this approximation and the wave function for the equivalent local potential is discussed.

THE EFFECT OF THE NON-STATIC FORCES IN NUCLEAR MATTER

Abstract The relation between two different forms of the non-static potentials arising from the relativistic corrections and the recoil effects in the nucleon-nucleon interaction is investigated. It is shown that by a suitable choice of the static parts, these two different forms are equivalent and will produce the same phase shift for two-nucleon scattering. However, in the many-body problem, in general they give different results for the amplitude of the reaction matrix. Modified Born approximation has been used to evaluate the change in the single particle potential energy in nuclear matter caused by the addition of the quadratic spin-orbit potentials of Breit and Hamada-Johnson. This change which is about 6 MeV for the Breit potential at the density corresponding to the Fermi momentum k F = 1.5 fm −1 is important both for the determination of the binding energy and the equilibrium density of nuclear matter.

DISPERSION RELATION APPROACH TO THE NUCLEAR STRUCTURE CALCULATION.

Abstract Partial wave dispersion relations are used as dynamical equations describing nucleon-nucleon scattering. For each state, from the empirical values of the phase shifts for different relative energies of the two nucleons, the first term of the Born series is obtained. In this connection, approximate methods of solving the inverse of a dispersion relation are discussed, and the results are compared with those obtained from the Schrodinger equation. Off-diagonal elements of the Born term for energy non-conserving processes are found by extrapolating the diagonal elements. The matrix obtained in this way enables one to calculate the reaction matrix and also the harmonic oscillator matrix elements directly from the phase shifts. Numerical results for both types of calculation are presented and compared with recent works of Elliott and collaborators.

The dependence of the photodisintegration cross section on the off-shell T-matrix

Abstract Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T -matrix, it cannot be used to discriminate between alternative off-shell T -matrices. We have constructed classes of different off-shell T -matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.

Summation of partial waves for large-angle scattering

Abstract For large-angle elastic scattering different methods of summing partial wave amplitudes are investigated for their accuracy and simplicity of computation. It is found that among the approximations considered, the method of expanding the T -matrix in terms of the weighted orthogonal polynomials proposed by Brysk is the most accurate way of calculating the scattering amplitude in the backward direction. If the two-particle interaction is assumed to be a Yukawa potential, then the l th partial sum of the T -matrix with the weighted polynomials can be expressed as the l th partial sum with the Legendre polynomials and a correction term which depends on the phase shift for the l th partial wave.

LONG-RANGE PART OF THE TWO-NUCLEON INTERACTION AND THE PROPERTIES OF NUCLEAR MATTER.

Abstract The separation method is applied to the calculation of the re-arrangement energy, the symmetry energy and the compressibility of the nuclear matter. The cut-off distance and its derivatives with respect to the density are determined from the values of the binding energy and the equilibrium density of the many-nucleon system. The re-arrangement energy and the compressibility for the Brueckner-Gammel-Thaler potential are found to be 11.7 and 239 MeV, respectively. For the same potential, using the free-particle reaction matrix in the singlet-even and the triplet-odd states, the value obtained for the symmetry energy is about 22 MeV.

Model for scattering from the bound state of a two-body system

An exactly solvable model for scattering of a particle from the bound state of a two-body system is studied. In this model the motion of all particles is confined to one dimension. It is also assumed that the interaction between the projectile and the target is nonlocal and separable, but the potential between the target particles is local. Depending on the form of the latter potential two cases are considered: (1) the target is the ground state of a system whose eigenvalues are discrete and eigenfunctions localized, and (2) the target has only one bound state. In both cases the problem can be solved with overlapping as well as nonoverlapping potentials. This model is used to test the accuracy of the fixed scatterer approximation. It turns out that in this approximation the two cases yield similar results. (AIP)

RELATION BETWEEN PHASE SHIFT, THE BINDING ENERGY, AND THE RANGE OF THE FORCE.

Abstract Using energy-dependent boundary conditions for interactions of finite range, a relation between the phase shift, the range and the binding energy is obtained. This relation is compared with Chadans single-channel sum rules and it is shown that for few simple cases where sum rules can be calculated analytically the two methods give identical results. Similar relations are derived for multichannel scattering and for potentials with a tail. As an application, the deuteron binding energy is obtained from the triplet neutron-proton phase shifts and the range of the twonucleon interaction.