Unitarity and the optical potential

The optical potential for the elastic scattering of two nuclear fragments with the full inclusion of the Pauli principle is considered. It is shown using unitarity that the optical potential, defined in terms of the Alt, Grassberger and Sandhas off-shell extension of the transition operator, has no singularities across the elastic unitarity cut. Similar results are obtained for general rearrangement scattering.     

Generalized optical theorems for the reconstruction of Green's function of an inhomogeneous elastic medium

This paper investigates the reconstruction of elastic Green's function from the cross-correlation of waves excited by random noise in the context of scattering theory. Using a general operator equation-the resolvent formula-Green's function reconstruction is established when the noise sources satisfy an equipartition condition. In an inhomogeneous medium, the operator formalism leads to generalized forms of optical theorem involving the off-shell T-matrix of elastic waves, which describes scattering in the near-field. The role of temporal absorption in the formulation of the theorem is discussed. Previously established symmetry and reciprocity relations involving the on-shell T-matrix are recovered in the usual far-field and infinitesimal absorption limits. The theory is applied to a point scattering model for elastic waves. The T-matrix of the point scatterer incorporating all recurrent scattering loops is obtained by a regularization procedure. The physical significance of the point scatterer is discussed. In particular this model satisfies the off-shell version of the generalized optical theorem. The link between equipartition and Green's function reconstruction in a scattering medium is discussed.     

Off-shell sensitivity,repulsive correlations and the pion-nucleus optical potential

Repulsive nucleon-nucleon correlations tend to reduce the dependence of pion-nucleus elastic scattering upon the off-shell pion-nucleon dynamics. However, optical potential calculations can in practice be quite sensitive to the particular choice of off-shell model parameters. It is argued that this sensitivity results from the nature of the optical potential as a one-body operator which introduces extra off-shell dependence not found in the physical many-body process itself. Thus, one must be very careful in any attempt to extract correlation or off-shell information, or to predict pion-nucleus phase shifts, by means of an optical potential theory. Results of model calculations are presented for purposes of illustration.     

Improved theoretical pion-nucleus optical potentials

An approach which makes the first order pion-nucleus optical potential theoretically sound is presented. This study should permit higher order improvements to the potential to be more meaningful and the nuclear structure information extracted from pi-nucleus scattering to be more reliable. Based on multiple scattering theory, three optical potentials are constructed and studied in momentum space. These models are the popular Kisslinger potential, the local “Laplacian” potential, and an “improved off-shell potential;” the latter one is derived from absorptive separable pion-nucleon potentials which exactly reproduce on-shell πN scattering. By working in momentum space and explicitly including πN resonances and off-shell effects in the definition of the optical potential, the approach described here is capable of handling any number of pi-nucleon partial waves, is applicable over a very wide energy region, is based on a physical model for off-shell behavior, and is extended easily to include higher order effects. The optical potentials are inserted into two different relativistic wave equations to determine the total cross section and elastic differential cross section for pi-nucleus scattering. It is found that the various models for off-shell πN scattering determine significantly different πC¹² scattering, with the improved off-shell model preferred on theoretical grounds. Also discussed is the importance of properly transforming πN scattering to the pi-nucleus c.m. system, the origin of the shift in the peak position of the π^?C total cross section, and the reason for the increased diffractive nature of the differential cross section at 180 MeV.     

Coupled channel approach to the off-shell transition matrix

We propose a coupled-channel separable potential model with the feature that the off-shell elastic transition matrix can be generated directly from the scattering phase shifts. This should be useful in constructing pion-nucleus optical potentials.     

Multiple scattering, optical potential, and N-body approaches to elastic two-fragment collisions

Two-fragment elastic scattering problems are often studied using multiple scattering theories such as those due to Watson along with Feshbach-type optical potentials. These conventional methods are re-examined, rephased, and generalized using the language and techniques of contemporary N-particle scattering theory. A special realization of the latter theory is developed which is especially useful for relating the older and newer methods. This is facilitated by maintaining the same off-shell continuations of the scattering operators in both approaches. In particular, a set of connected-kernel scattering integral equations is introduced which provides a consistent N-particle framework for the calculation of that definition of the optical potential possessing the Feshbach off-shell continuation. These equations exhibit a multiple-scattering substructure and therefore allow the systematic generalization of some of the usual low-order approximations.     

A survey of pion charge-exchange reactions with nuclei

A survey study of the elastic charge-exchange reactions is presented. The charge-exchange cross sections are evaluated in a coupled-channel framework with optical potentials obtained from the Kisslinger and Laplacian models for the pi-nucleon off-shell scattering amplitude. Considerable differences between these two modles are obtained for pion kinetic energies below the pi-nucleon (3, 3) resonance. The effect of two-nucleon correlations is included by calculating the second-order pi-nucleus optical potential. We find that this effect dominates the charge-exchange reactions at energies of about 100 MeV.     

Off-shell extension of the π-nucleon transition matrix and separable π-nucleon potentials

The off-shell extension of the P-wave π-nucleon transition matrix given by the Chew-Low model is compared with the one obtained from a separable potential. It is shown that the two off-shell extensions are rather different; π-deuteron scattering results are compared for the two cases.     

The Δ-nucleus spin-orbit interaction in π-nucleus scattering

The role of the Δ-nucleus spin-orbit interaction in π-nucleus scattering is studied within the isobar-hole formalism. Due to the peripheral nature of the π-nucleus interaction, elastic scattering is very sensitive to the presence of such an L-S term. We report results for pion scattering on light nuclei in the resonance region. The systematics of the phenomenological Δ-nucleus optical potential are discussed.     

Off-shell extension function from a generalised phase-function method

It is shown that the Combined-variable-phase-off-shell scattering theory or the generalised phase-function method provides efficient algorithms to calculate the off-shell extension function which plays a role in the theories of three-particle scattering. In order to assert this we have chosen to work with a model potential for theα-α interaction. The functions which occur in the context of our approach exhibit certain interesting features with regard to effect of the potential in producing on-and off-shell quantities like the phase shift and quasi-phase. Interpolating off-shell extension function is seen to exhibit a discontinuity where the phase function goes through a zero.     

Generalization and applications of the Sasakawa theory

The Sasakawa theory of scattering is phrased in the form of a Fredhohn reduction technique for integral equations possessing a fixed-point singularity in their kernels. This permits the generalization of this theory to a large variety of scattering integral equations. Some specific applications include the two-particle off-shell and multichannel scattering problems. In the first instance a rank-three approximation to the fully off-shell transition matrix is derived which is exact on and half-off shell, satisfies off-shell unitarity, and which possesses no unphysical singularities. In the second problem it is shown how the method leads to the generation of a unitary approximation to the multichannel amplitudes.     

Model dependence of the impulse approximation

We investigate the model dependence of the impulse approximation for proton-nucleus elastic scattering stemming from off-shell and non-local effects. A perturbative treatment allows a direct comparison between off-shell and relativistic effects. Off-shell effects are found to be significantly smaller and unable to account in a natural way for the needed repulsive central potential in the nuclear interior region at proton energies between 300 and 800 MeV.     

Separable energy-dependent approximation to local potentials

An extension of the single-pole separable approximation of a two-body t-matrix in which the effects of several poles are included is made. The simple form for the t-matrix derived from a single separable potential is retained. However, the separable potential is constructed using an energy-dependent superposition of the states corresponding to the various poles. The energy dependence is chosen so as to obtain the correct residue of both the on-shell and off-shell t-matrices at each of these poles, while preserving unitarity. The formalism is specialized to the case of s-wave scattering from an attractive square well. Comparison to the exact s-wave cross section gives good results.     

动量空间中能质子-12C弹性散射截面和自旋量的研究

在KMT理论框架下，应用微观的动量空间一级光学势，包括了库仑修正，自旋关联，NN振幅反对称，离壳效应，核子反冲和结合能转换，Lorentz不变的角变换.在整个中能区域系统地计算了质子-¹²C弹性散射微分截面和自旋观测量，并与实验数据及Glauber理论框架下或已有的其他理论计算结果做了比较，其结果显示，在200—1000MeV，该理论与实验结论符合程度较好.     

Kinematically correct optical potentials

The Watson multiple scattering formalism for the optical potential describing elastic nucleon-nucleus scattering is developed while paying careful attention to the kinematics. No approximations are made in handling the recoil of the target nucleus so that internal and external energies can be uniquely separated. The resultant formalism allows a careful examination of the impulse, form-factor, and closure approximations without the confusion of the admixture of recoil energies; it also allows an explicit display of the nuclear correlations due to target recoil. With the many necessary (but incompletely understood) approximations explicity displayed, it appears that their confluence makes it unlikely that meaningful information about dynamical correlations in light nuclei can be obtained from elastic double-scattering experiments.     

Ambiguity on the imaginary potentials in the Dirac formalism for the elastic and the inelastic scattering of nucleons

The Dirac formalism for the elastic scattering of nucleons has been extended to a coupled channel formalism taking into account collective excited states. Calculations for the scattering of 500 MeV protons on ⁴⁰Ca shows large second-order effects on the elastic scattering. The imaginary scalar potential and the imaginary vector potential can be varied widely without giving so large effects on the elastic scattering. This large ambiguity is not limited to this case.