R.J. Philpott

Continuum shell model with full correction for target recoil

Abstract The nuclear continuum shell model is reformulated in such a manner that target recoil is taken fully into account. The reformulation is achieved by employing dynamical R -matrix discretization based on intrinsic harmonic oscillator expansion functions. The desired intrinsic matrix elements are computed directly from corresponding shell-model matrix elements. The importance of the recoil corrections for light nuclei is illustrated by detailed calculations for nucleon scattering from closed shell nuclei. When recoil corrections are included, these calculations reproduce corresponding resonating group results. Since the inherent power and convenience of the shell-model ansatz is retained, it will be feasible to carry out more general calculations, including more elaborate target configurations and inelastic channels. A variety of forms for the nuclear interaction may be employed.

Consistent folding model description of nucleon elastic, inelastic, and charge-exchange scattering from 6,7Li at 25–50 MeV

Abstract The results of a consistent theoretical microscopic single scattering model study of nucleon elastic, inelastic, and charge-exchange scattering from 6,7 Li at E p(n) = 25–50 MeV are reported. A realistic effective nucleon-nucleon interaction, adopted from the work of Mahaux and collaborators and Bertsch and coworkers, has been employed in the model calculations. The density distributions needed to describe the structure of the mass 6 and 7 systems in the calculations are the same as those used in recent proton-nucleus scattering studies of these targets at E p = 200 MeV. The present, parameter-free model calculations provide an excellent description of the available low-energy nucleon-nucleus scattering data on 6,7 Li.

On the practical application of the generalized R-matrix method to problems in nuclear physics

Abstract The role of the generalized R-matrix method as a calculational tool applicable to a large class of problems in nuclear physics is examined. The rapid convergence observed when the channel radii are held constant can be further improved if the channel radii are allowed to vary. A criterion is proposed which governs the selection of an optimal set of channel radii. The absolute convergence of the method obtained when the criterion is employed is demonstrated by explicit calculations performed for (i) a Woods-Saxon potential model of 16O + n scattering, (ii) a coupled channels model of 12C + n scattering, and (iii) a microscopic model of 14C + n scattering. The methods introduced here provide the means for a systematic treatment of the convergence of the method, enabling optimal accuracy to be obtained from any given set of basis functions. In addition, a fair indication of the accuracy of the final result is obtained.

Microscopic calculations for the 4He continuum: (I). General approach☆

Abstract A new model for the 4He nucleus in which structure and reaction aspects are treated on an equal footing is introduced. The model is constructed within the framework of the dynamical R-matrix methodology. The internal states are expanded on a basis of properly symmetrized translationally invariant harmonic oscillator eigenstates including all states up to 4 h ω of oscillator excitation. All three two-body break-up channels, namely d+d, t+p, and 3He+n are explicitly included. The two-body interaction is based on the Sussex matrix elements. In this paper, the formulation of the model is described, including the choice of two-body interaction, and results are given for the spectrum of resonances obtained within the model and for d+d elastic scattering and the 2H(d, p)3H reaction near threshold. The initial results are very encouraging, but also suggest that some further adjustments to the model are necessary.

Spin dependence in the nucleus-nucleus optical potential☆

Abstract The general multipole decomposition of a complete nucleon-nucleon interaction containing central, tensor, and spin-orbit components is presented in a form suitable for double-folding calculations of arbitrary nucleus-nucleus elastic scattering and transition potentials. This multipole decomposition is used to derive a general expression for the optical potential for the elastic scattering of two complex nuclei with arbitrary spin. The relationships between the terms in the nucleus-nucleus potential, the components of the nucleon-nucleon interaction, and various aspects of nuclear structure are discussed. These results are applied to obtain an estimate of the cross section and vector and tensor analyzing powers for the elastic scattering of 7 Li + 58 Ni at E 7 Li = 20.3 MeV which has recently been investigated experimentally. A realistic nucleon-nucleon interaction is employed in the calculations and a coupled-equations formalism is used to obtain the scattering observables. A reasonable description of the available experimental data is obtained.

Elastic scattering of spin−32 particles☆

Abstract The elastic scattering of spin − 3 2 particles is discussed with particular emphasis on the theoretical interpretation of analyzing power measurements. The observables are analyzed in terms of Hooton-Johnson scattering amplitudes, which provide the most direct link to the tensorial structure of the underlying interaction. Data from 58Ni(7Li, 7Li)58Ni are analyzed and compared with the results of optical model calculations. Explicit formulae are presented whose purpose is to facilitate such optical model calculations.

Radiative capture to 4He

Abstract Particle capture calculations to 4 He have been performed within the framework of the continuum shell model with full correction for target recoil and with non-central forces. Differential cross section and polarization results are presented for both neutron and proton capture. The calculations include E1, E2 and M2 contributions. The calculated ratio of total cross sections, σ(γ, p)/σ(γ, n) is close to one above E p = 4 MeV. Possible corrections to this ratio are discussed. The calculated E2 strength is very broad and structureless. The maximum E2 strength is near 63 A − 1 3 MeV excitation. Of this E2 strength virtually all is 1 D 2 .

Study of nucleon channel reactions for A = 12 and A = 16 systems with the recoil corrected continuum shell model☆

Abstract The continuum shell-model with full correction for target recoil and including non-central forces is applied to the A = 12 and A = 16 systems. A modification of the g -matrix interaction of Bertsch et al . is employed. A comprehensive study of particle channels has been made in the 1p–1h approximation. Calculated level diagrams and cross sections compare favorably with experiment.

Recoil corrected continuum shell model calculations for four-nucleon systems

Abstract The continuum shell model with full correction for target recoil is extended to 1p-1h configurations. The procedure is discussed in a framework which allows generalization to more complicated configurations. An application is made to nucleon reaction channels in 4 He using the g -matrix interaction of Bertsch et al . Excellent agreement with the data is obtained.

Single-particle model of capture to continuum states

Abstract A formalism is developed for treating the single-particle description of continuum to continuum electromagnetic transitions. Convenient formulae are given for the measured observables and for the single-particle matrix elements of the transition operators. Target recoil is taken explicitly into account. The long-wavelength approximation is not made. Convergence is demonstrated both for the radial integrals and with respect to partial waves and transition multipoles. The model is compared with available experimental data. Many of the observed features are reproduced.