Reduction of the Lane-Robson “calculable” reaction theory to standard R-matrix form

doi:10.1016/0375-9474(75)90247-X

Nuclear Physics A

Volume 243, Issue 2, 19 May 1975, Pages 260-268

https://doi.org/10.1016/0375-9474(75)90247-X Get rights and content

Abstract

General dynamical equations derived from the Lane-Robson calculable reaction formalism are cast into a form amenable to standard R-matrix treatment, permitting the resonance content of the equations to be made explicit. Formulae are given which enable the collision matrix and the amplitudes of physical eigenfunctions to be calculated directly from the R-matrix with or without the isolation of resonance contributions. The present methodology permits a significant reduction of effort in numerical investigations of the energy dependence inherent in dynamical models of the nucleus. The formalism is illustrated by calculational results obtained from a potential model fitted to ¹⁶O + n scattering data.

References (14)

J. Cugnon et al.
Phys. Rev.
(1974)
R.J. Philpott
Phys. Rev.
(1973)
A.M. Lane et al.
Rev. Mod. Phys.
(1958)
E.P. Wigner et al.
Phys. Rev.
(1947)
A.M. Lane et al.
Phys. Rev.
(1966)
A.M. Lane et al.
Phys. Rev.
(1967)
A.M. Lane et al.
Phys. Rev.
(1969)
A.M. Lane et al.
Phys. Rev.
(1969)
J.L. Adams

There are more references available in the full text version of this article.

Cited by (30)

Dynamics of quantum systems embedded in a continuum
2003, Physics Report
Citation Excerpt :
We may mention that the monopole interaction depends strongly on the isospin and is strongly attractive for T=0, while it is rather weak for T=1. Similar isospin dependence is seen in the SMEC correction Ecorr which is strongly attractive for T=0 monopole interaction [126]. Difference between calculated and experimental one-neutron Sn and two-neutron S2n separation energies is shown in Fig. 26 for the SM (the dashed line) and the SMEC (the solid line).
The relevance of the open quantum system formalism for the description of weakly bound nuclei far from the valley of stability, small droplets of neutral atoms, gas of trapped atoms, open microwave cavities and quantum dots is discussed. We describe nuclear structure and nuclear reaction studies in the shell model embedded in the continuum. This model is an extension of the multiconfigurational shell model including one-particle decay channels. The coupling to multi-particle decay channels, as e.g. in ‘Borromean systems’, is discussed in the alternative formulation of Gamow shell model in the complete Berggren basis. Simple schematical models are used in order to discuss the basic dynamical processes characteristic of open quantum systems. The generic features of these systems in different regimes of multiconfigurational mixing are illustrated by examples of weakly bound atomic nuclei, externally driven atoms and microwave cavities.
The p-shell with one particle in the continuum
2002, Nuclear Physics A
A continuum shell model is now available for p-shell nuclei with exactly the same important properties as a bound-state p-shell model calculation. This means that one can obtain all solutions that correspond to coupling one nucleon to the possible p-shell states of a bound-state calculation. The resulting coupled-channels solutions are antisymmetric and contain no spurious components. This model can be used to describe a very broad range of nuclear phenomena, from capture reactions at astrophysical energies, to knockout reactions at low energies, to nucleon scattering and charge exchange at intermediate energies. Example calculations are shown for the compound systems ⁷Be and ⁷Li. Here it is demonstrated that agreement between theoretical and experimentally determined elastic and inelastic cross sections and analyzing power values can be improved by coupling to all open channels.
Study of nucleon channel reactions for A = 12 and A = 16 systems with the recoil corrected continuum shell model
1980, Nuclear Physics A
Recoil corrected continuum shell model calculations for four-nucleon systems
1979, Nuclear Physics, Section A
Continuum shell model with full correction for target recoil
1977, Nuclear Physics, Section A
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.
Microscopic calculations for the <sup>4</sup>He continuum. (I). General approach
1977, Nuclear Physics, Section A
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.

View all citing articles on Scopus

^☆: Work supported in part by National Science Foundation Grants no. NSF-GP-41834X, NSF-GJ-367 and NSF-GU-2612.

View full text

Reduction of the Lane-Robson “calculable” reaction theory to standard R-matrix form☆

Abstract

Phys. Rev.

Phys. Rev.

Rev. Mod. Phys.

Phys. Rev.

Phys. Rev.

Phys. Rev.

Phys. Rev.

Phys. Rev.