An algebraic solution of the multichannel problem applied to low energy nucleon–nucleus scattering

Abstract

Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated multichannel interactions between the colliding nuclei. Associated with such expanded multichannel interactions are algebraic multichannel scattering matrices. The matrix structure of the inherent Green functions not only facilitates extraction of the sub-threshold (compound nucleus) bound state spin-parity values and energies but also readily gives the energies and widths of resonances in the scattering regime. We exploited also the ability of the sturmian-expansion method to deal with non-local interactions to take into account the strong non-local effects introduced by the Pauli principle. As an example, we have used the collective model (to second order) to define a multichannel potential matrix for low energy neutron-12 C scattering allowing coupling between the 0 + 1 (ground), 2 + 1 (4.4389 MeV), and 0 + 2 (7.64 MeV) states. The algebraic S matrix for this system has been evaluated and the sub-threshold bound states as well as cross sections and polarizations as functions of energy are predicted. The results are reflected in the actual measured data, and are shown to be consistent with expectations as may be based upon a shell model description of the target and of the compound nucleus.

The spectra of exotic light mass nuclei determined with MCAS theory

“…The analytic properties of the S matrix from a separable Schrödinger potential gives the means by which a full algebraic solution of the multichannel scattering problem can be realized. All details of the MCAS theory have been published [1] and so only salient features are repeated herein. Consider a coupledchannel system for each allowed scattering spin-parity J π .…”

“…Elastic scattering observables follow from the on-shell properties (k 1 = k 1 = k) of the scattering matrices. For the elastic scattering of neutrons (spin 1 2 ) from spin zero targets c = c = 1, and S 11 ≡ S J = S (±) are…”

“…[3] for details. of 15 C required that the neutron 0p 1 2 orbit only be Pauli hindered [3]. With the nuclear interaction set, the results from MCAS evaluations of the p+ 14 O system to form the particle unstable 15 F are shown on the right of this figure.…”

“…Consider the mass 13 mirrors, 13 C and 13 N. As in past studies, we fix the matrix of nuclear interaction potentials to be that found for the n+ 12 C system [1] treated as a three state coupled-channel problem, and from which there were reasonable reproductions of known sub-threshold and resonance states (up to 10 MeV excitation). A uniform charge distribution (R c = 2.8 fm) was assumed.…”

“…The MCAS method [1,2] solves coupled channel LippmannSchwinger equations for a chosen two-body system. The theory is built upon sturmian expansions of whatever one chooses to be the interaction matrix of potential functions for the system.…”