The two-cluster ?fish bone? model

Abstract

The resonating group model is reformulated by splitting the microscopic interaction into a dominant part and a residual part. In the equal-width oscillator limit, the dominant part leads to a very simple exchange kernel. In norm kernel eigenstate representation, this kernel has a peculiar, fish bone like symmetry. For the evaluation of the residual interaction, only two-body matrix elements are needed. A physical interpretation of the fish bone symmetry is given in terms of the reflection property of a fermi sphere with a diffuse surface. An optical model is proposed in which the influence of partly Pauliforbidden states on the observables is described by the fish bone symmetry of the interaction. It is speculated that fish bone symmetry might be the key to a better understanding of hadronic interactions.Nuclear Reactions: Scattering theory, nuclear models, optical models, composite particle interaction, symmetry of interactions.

Microscopic optical potentials for composite particle scattering at low energies

“…The overall shape of the potential is qualitatively similar to the results given by [7]. In particular, the peak of the imaginary optical potential is situated below the nuclear radius R 16 O nucl ≈ 2.4 fm of 16 O, which is also the case for the imaginary optical potential of [7]. Osterfeld et al [5] applied the nuclear structure approach to the scattering of neutrons on 40 Ca with a nuclear radius of R In [7] the evaluated imaginary optical potential W is compared to a phenomenological, local one.…”

“…In particular the obtained imaginary potential at the same incident energy shows similar radial characteristics. Especially the dominating peak lies slightly below the nuclear radius of 16 O in agreement with [7].…”

“…(1) to (5) into a numerical code and evaluated as a first example the imaginary part of the optical potential for α-16 O scattering at an incident α-energy of 30 MeV. The structure of the 16 O target nucleus was described by the RPA using the particle-hole amplitudes X J M j 1 j 2 and Y J M j 1 j 2 of Ref. [18], which was based on a configuration space consisting of two subshells above and below the Fermi surface and included also the continuum states in a discretized way.…”

“…Consequently the determination of the scattering wave function requires the solution of the corresponding integrodifferential Schrödinger equation. We have constructed the required numerical tools and calculated the α- 16 O differential cross section. However, the results are not exciting because at this stage, we did not take care of a proper direct potential V DT which accounts for the Pauliprinciple between the incident α-particle and the target nu- cleus.…”

“…This approach was combined in Ref. [8] with the fish-bone model [16] in order to account for the Pauli principle at least in the first order term. For other projectiles the available models are even more phenomenological because of the additional complication of breakup.…”