Calculation of the 6He + p elastic scattering cross sections within the folding approach and the high-energy approximation for the optical potential

Data on cross sections for the ⁶He + p elastic scattering at energies of tens of MeV/nucleon are analyzed by calculating the microscopic optical potential (OP) (its real and imaginary parts). The effect produced on the cross section by the dependence of the nucleon-nucleon potential on the nuclear matter density, the role of the spin-orbit interaction, and the role of nonlinearity and renormalization of the microscopic OP are studied. A comparison with the experimental data allows sensitivity of cross sections to these effects to be tested.     

Calculations of 6He + p elastic-scattering cross-sections using folding approach and high-energy approximation for the optical potential

Calculations of microscopic optical potentials (OPs) (their real and imaginary parts) are performed to analyze the ⁶ He + p elastic-scattering data at a few tens of MeV/nucleon (MeV/N). The OPs and the cross-sections are calculated using three model densities of ⁶He . Effects of the regularization of the NN forces and their dependence on nuclear density are investigated. Also, the role of the spin-orbit terms and of the non-linearity in the calculations of the OPs, as well as effects of their renormalization are studied. The sensitivity of the cross-sections to the nuclear densities was tested and one of them that gives a better agreement with the data was chosen.     

A generalized leading-term approximation of high-energy scattering amplitudes in Yang-Mills theory

In this paper, the high-energy vector meson-vector meson elastic scattering amplitudes of a Yang-Mills theory of an SU(2) model are calculated in a generalized leading-term approximation (s→∞ with t fixed). The resulting amplitude, through the 10th order, coincides with the expansion of an eikonal formula. The present method is generalizable to other non-Abelian gauge theories.     

Magnus expansion and eikonal approximation in potential scattering

An expansion procedure due to Magnus is applied to the case of potential scattering. This technique, which is superior to the usual Born-Dyson expansion in that it preserves unitarity at each state, leads in first approximation to an expression for the scattering amplitude which contains as special cases the eikonal approximation and also the second Born approximation. In particular the first Magnus approximation provides a basis for the ad hoc addition of the real part of the second Born contribution to the eikonal scattering amplitude as was considered by Byron et al.     

Reconstruction of the scattering potential from the high-energy differential cross section

A simple equation is derived for use in reconstructing the scattering potential from the angular distribution of scattered particles at a given energy. This equation is useful in the classical approximation of small angles and in the semiclassical quantum-mechanical treatment. Experimental data and this equation are used to reconstruct the interaction potentials for the scattering of helium, neon, and argon ions by atoms from the same group in various combinations, at 25, 50, and 100 keV. The simplicity of the equation allows potentials to be found at distances larger than were found previously by Everhart and Lane and with a smaller error in the approximate numerical calculations.Translated from Izvestiya VUZ. Fizika, No. 8, pp. 118–123, August, 1970.The authors thank O. M. Tsoi for assistance in the numerical calculations.     

Closure approximation to the absorptive potential in heavy ion scattering

We propose a simple model which is based on the Feshbach's theory of the optical potential. The use of closure relation in both nuclei implies that we implicitly include all possible channels, in particular inelastic scattering and one-nucleon transfer processes. The local absorptive potential is calculated at large distances and its energy dependence is studied. The results are compared with other theoretical works and with phenomenological potentials.     

Shallow folding potential for O + C elastic scattering

The ¹⁶O + ¹²C elastic scattering data have been well described, for the first time, with a shallow folded potential obtained from a single folding method. The constituent parameters of the potential, excepting one, for its real part are generated from the nucleon–¹⁶O and α–¹⁶O potentials, and the cluster structure of ¹²C. Only the repulsive part of the α–¹⁶O potential needs some adjustment to fit the data, reflecting the need to include the Pauli exclusion effects among the unclustered nucleons.     

The imaginary part of the nucleon-nucleus optical potential in semiclassical approximation

We calculate in a novel Thomas-Fermi theory for multiparticle-multihole states the contributions of the correlation and polarization graphs to the imaginary part of the nucleon-nucleus optical potential $\text{W(ω,}\text{R}\text{,}\text{P}\text{)}$ depending on energy, radius and momentum. The present theory generalizes the older Fermi-gas and local-density approximations to this problem in the sense that we can assess precisely the validity of our approach. We show that it yields results which coincide with the average part of a corresponding quantal calculation. We use a gaussian finite-range effective interaction derived from the Gogny force and phenomenological mean-field potentials of the Woods-Saxon or harmonic-oscillator type. With these ingredients and no further adjustable parameters our results for the depth and volume integrals are in good agreement with the average trend of the elastic scattering data. Further, the resulting momentum dependence of W is strong, especially for small P. The influence of the Pauli principle is studied in detail.     

Pick-up and inelastic scattering contributions to the proton optical potential

The contributions from couplings with the available inelastic (p, p′) and pick-up (p, d) channels to the elastic scattering of 30 MeV protons from ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb were studied. The equivalent non-local potentials were constructed and attempts were made to find local equivalents to them. These potentials are dependent upon angular momentum. Inelastic scattering produces an attractive contribution to the real potential but pick-up results in a much larger repulsive term. The main features of the observed scattering from ²⁰⁸Pb can be reproduced by coupling to 24 channels provided a supplementary absorptive term is included. The explicit couplings by themselves can produce 90 % of the observed absorption cross section but only about one-half of the empirical absorptive potential strength.     

On the separable expansion method in an optical potential scattering

Potential separable expansion method (PSE) in harmonic oscillator basis is applied to the two-body scattering problem with a complex optical potential. The introduction of smoothing Lanczos-factors considerably improves the convergence. The efficiency of the PSE method is demonstrated on model example.     

Pion-nuclear optical potential.s Wave scattering

Difficulties in the theoretical interpretation of thes wave phenomenological parameters of the pion-nuclear optical potential are considered. One-nucleon and two-nucleon parameters of such a potential for slow pion scattering are calculated. Uncertainties in the separation of the dispersive part of the potential into one- and two-nucleon contributions are discussed. It is shown that taking into account off-shell behaviour of the πN amplitude in the calculation of the two-nucleon parameters is important.     

Thermodynamical approach in high-energy scattering

A non-conventional thermodynamical approach earlier for high-energy collisions is considered in more detail. The approach provides a physical interpretation not only of the shape of the hadron form factor but also of the increase in its radius with energy . A precise analysis of experimental data on elastic scattering for is performed with the formulae derived. Predictions in the multi TeV range and comparison of results with recent data of the E 710 Collaboration for 1.8 TeV are made. Agreement occurs when the experimental t-distribution is scaled up by 11%.     

Doorway state approach to optical potential scattering

We extend and apply the doorway state approach in the context of optical potential scattering. This entalls construction of doorway basis states for resolving the transition operator. We focus on analytic solutions to comparatively simple problems in optical potential scattering. Both low and high energy limits are considered, and absorptive interactions are treated; both on- and off-shell partial wave amplitudes are constructed. Further, the full scattering amplitude in the high energy limit is calculated directly in the doorway expansion. With our analytic results, it is possible to identify the physical parameters controlling convergence of the doorway expansion. The same parameters apply over the entire range of cases studied. These parameters are related simply to the target geometry and to the interaction strength. For interactions appropriate to hadron-nucleus scattering, convergence of both on- and off-shell amplitudes is very rapid.     

The optical potential for the elastic heavy ion scattering

For the elastic scattering of heavy ions a microscopic model is developed which uses shell model wave functions which are localised at a certain distance both in coordinate and momentum space. The antisymmetrization is treated exactly. Using oscillator functions and the Brink-Boeker force the energy dependent real part of the optical potential for O₁₆- O₁₆ scattering is numerically determined. The results are compared with the analysis of experiments.     

Electrical resistance of binary alloys with short-range order (the weak scattering approximation in the coherent potential approximation)

A simple version of the coherent-potential approximation is proposed for taking into account the short-range order in the first coordination sphere in a binary alloy. The residual electrical resistance is calculated in the limit of weak scattering. It is shown that the correlation contribution to the resistance depends very much on the position of the Fermi energy in the band, and that a nonmonotonic variation in the resistance is possible when short-range order develops in the alloy. The results are used for a qualitative interpretation of the different nature of the dependence of the resistance of alloys on the degree of short-range order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 45–49, March, 1980.     

Target excitations and the optical potential for protons scattering from nuclei

We calculate the contributions to the optical potential for 30 MeV protons due to inelastic excitations of the target nucleus. The scattering due to this non-local potential is calculated exactly and some of the results subjected to conventional optical model analysis. When only one excited state is included, a resonant dependence on the excitation energy is observed. Even with ten excited states, the position of a single one can strongly influence the scattering. It is possible to account for about $\text{3}\text{4}$ of the observed absorption in ⁴⁰Ca and ²⁰⁸Pb, but only by postulating unobserved states which exhaust the remainder of the experimental sum rules at somewhat unreasonably low energies. It was not possible to find simple local potentials which gave the same scattering because of the strong L-dependence of the absorption. The constructed potentials concentrate the absorption at too small radii. It is suggested that rearrangement (pick-up) processes contribute a substantial amount of absorption at larger radii, while compound formation will give rise to a volume term in the imaginary potential.