R. M. Thaler

Scattering from correlated systems

Abstract A difficulty usually encountered in formulating the problem of scattering of identical particles from correlated systems is that the customary choice of an unperturbed Hamiltonian as the target Hamiltonian plus the kinetic energy of the projectile is not symmetric under particle exchange. This choice of unperturbed Hamiltonian leads to wavefunctions which, if they are antisymmetrized, are not orthonormal. In this paper an orthonormal, antisymmetrized set of basis states is constructed. These states are then used to construct a symmetric unperturbed Hamiltonian, so that a formal scattering equation with appropriate boundary conditions can be written. An expression for a T matrix describing nucleon-nucleus scattering can then be obtained. The formalism leads to a two-potential form for the T matrix, the first term of which describes the effect of the orthogonality of the scattering state and the negative energy states.

Propagator modifications in elastic nucleon-nucleus scattering within the spectator expansion.

The theory of the elastic scattering of a nucleon from a nucleus is presented in the form of a spectator expansion of the optical potential. Particular attention is paid to the treatment of the free projectile-nucleus propagator when the coupling of the struck target nucleon to the residual target must be taken into consideration. First order calculations within this framework are shown for neutron total cross sections and for proton scattering for a number of target nuclides at a variety of energies. The calculated values of these observables are in very good agreement with measurement.

Application of multiple scattering theory to lower-energy elastic nucleon-nucleus scattering

The optical model potentials for nucleon-nucleus elastic scattering at 65 meV are calculated for [sup 12]C, [sup 16]O, [sup 28]Si, [sup 40]Ca, [sup 56]Fe, [sup 90]Zr, and [sup 208]Pb in first-order multiple scattering theory, following the prescription of the spectator expansion, where the only inputs are the free nucleon-nucleon (NN) potentials, the nuclear densities, and the nuclear mean field as derived from microscopic nuclear structure calculations. These potentials are used to predict differential cross sections, analyzing powers, and spin rotation functions for neutron and proton scattering at 65 MeV projectile energy and compared with available experimental data. The theoretical curves are in very good agreement with the data. The modification of the propagator due to the coupling of the struck nucleon to the residual nucleus is seen to be significant at this energy and invariably improves the congruence of theoretical prediction and measurement.

Theory of the scattering of pions from nuclei

Abstract A nonrelativistic quantum field theoretic formulation of pion-nucleus scattering is presented. A nonrelativistic boson-complex-target Low equation is developed, in which the coupling between the incident boson and target constituent particles is completely general. This development is then particularized to the case where the bosons are pions and the target is a nucleus of A nucleons. Special detailed attention is paid to the case where the pion-nucleon coupling is linear. The pion-nucleus Low equation is decomposed into a finite series of A terms, referred to as a spectator expansion, of which the first term involves one active particle and ( A -1) spectators and the higher terms involve an increasingly larger number of active target particles. Within the framework of the nonrelativistic pion-nucleus Low equation, a formal definition of the pion-nucleus optical potential is also given.

The multiple scattering and N-body approaches to nuclear reactions

Abstract The relationship between conventional multiple scattering approaches and the recently developed N -body approaches to nuclear reactions is considered with a view towards elastic scattering applications. Connectivity expansions in the N -body approach and multiple scattering expansions in the Watson approach are developed by a common technique so that a comparison of the physical content of each can be made. In the N -body case this leads to a new derivation of the equations of Bencze, Redish, and Sloan in both particle-labelled and partition-labelled form and this yields new insight into the minimal dimensionality of these equations and into the role of channel coupling schemes within this formulation. The relative simplicity and generality with which these results are obtained is designed to be easily understood by those unfamiliar with N -body formalisms. The two approaches are contrasted first for the three-particle problem and subsequently for the many-body problem. We argue that a strict adherence to the connected-kernel property which is advantageous for the three-particle problem may not be so advantageous for the many-body elastic scattering problem. Undesirable physical characteristics of the connectivity expansion for elastic scattering are identified and their rectification is discussed. The off-shell transformation associated with the N -body approach is examined critically. The origin of the multiplicity of N -body coupling schemes is elucidated. It is shown that a modified concept of connectivity, called inclusive connectivity, can be introduced to guide expansions which can be truncated in a physically meaningful way. The inclusive connectivity expansion is seen to be identical to the spectator expansion for an elementary projectile but differs in the case of a composite projectile. Extant elastic scattering optical potential formulations based on the two concepts of connectivity are compared and contrasted. We show that connected kernel integral equations of the few-body type are required for computation of the individual low-order terms of the inclusive connectivity expansion of the optical potential.

Total cross sections for neutron scattering

Measurements of neutron total cross sections are both extensive and extremely accurate. Although they place a strong constraint on theoretically constructed models, there are relatively few comparisons of predictions with experiment. The total cross sections for neutron scattering from [sup 16]O and [sup 40]Ca are calculated as a function of energy from 50 to 700 MeV laboratory energy with a microscopic first-order optical potential derived within the framework of the Watson expansion. Although these results are aleady in qualitative agreement with the data, the inclusion of medium corrections to the propagator is essential to correctly predict the energy dependence given by the experiment. In the region between 100 and 200 MeV, where off-shell [ital t][rho] calculations for both [sup 16]O and [sup 40]Ca overpredict the experiment, the modification due to the nuclear medium reduces the calculated values. Above 300 MeV these corrections are very small and depending on the employed nuclear mean field tend to compensate for the underprediction of the off-shell [ital t][rho] results.