A multi-channel algebraic scattering (MCAS) method has been used to solve coupled sets of Lippmann-Schwinger equations for $alpha$+nucleus systems to find spectra of the compound systems. Low energy spectra for ${}^{12}$C, ${}^{16}$O, and ${}^{20}$Ne
are found with the systems considered as the coupling of an $alpha$ particle with low-excitation states of the core nuclei, ${}^8$Be, ${}^{12}$C, and ${}^{16}$O, respectively. Collective models have been used to define the matrices of interacting potentials. Quadrupole (and octupole when relevant) deformation is allowed and taken to second order. The calculations also require a small monopole interaction to provide an extra energy gap commensurate with an effect of strong pairing forces. The results compare reasonably well with known spectra given the simple collective model prescriptions taken for the coupled-channel interactions. Improvement of those interaction specifics in the approach will give spectra and wave functions suitable for use in analyses of cross sections for $alpha$ scattering and capture by light-mass nuclei; reactions of great importance in nuclear astrophysics.
One theoretical method for studying nuclear scattering and resonances is via the multi-channel algebraic scattering (MCAS) formalism. Studies to date with this method have used a simple collective-rotor prescription to model target states with which
a nucleon couples. While generally these target states all belong to the same rotational band, for certain systems it is necessary to include coupling to states outside of that main band. Here, we extend MCAS to allow coupling of different strengths between such states and the rotor band. This is an essential consideration in studying the example examined herein, the scattering of neutrons from 22Ne.
Predictions of cross sections and analyzing powers using g-folding optical potentials for the scattering of 71A MeV 6,8He ions from (polarized) hydrogen are compared with data. A g-folding model in which exchange amplitudes are evaluated explicitly w
as used with wave functions of 6,8He specified from a no-core shell model that used a complete (0+2+4)hw basis. The analyzing powers reveal some sensitivities to the details of the wave functions, especially in the case of halo nuclei.
A survey of known threshold excitations of mirror systems suggests a means to estimate masses of nuclear systems that are uncertain or not known, as does a trend in the relative energies of isobaric ground states. Using both studies and known mirror-
pair energy differences, we estimate the mass of the nucleus 17-Na and its energy relative to the p+16-Ne threshold. This model-free estimate of the latter is larger than that suggested by recent structure models.
The physics of radioactive ion beams implies the description of weakly-bound nuclear systems. One key aspect concerns the coupling to low-lying collective-type excited states, which for these systems might not be stable levels, but particle emitting
resonances. In this work we describe how the scattering cross section and compound spectra change when the colliding fragments have such collective excitations featuring particle emission. We explore this question in the framework of a multi-channel algebraic scattering method of determining nucleon-nucleus cross sections at low energies. For a range of light-mass, particle-unstable nuclear targets, scattering cross sections as well as the spectra of the compound nuclei formed have been determined from calculations that do and do not consider particle emission widths for nuclear states. Assuming a resonance character for target states markedly varies evaluated cross sections from those obtained assuming the target spectrum to have entirely discrete states.
Using a Multi-Channel Algebraic Scattering (MCAS) approach we have analyzed the spectra of two hyper-nuclear systems, Lambda9Be and Lambda13C. We have studied the splitting of the two odd-parity excited levels (1/2- and 3/2-) at 11 MeV excitation in
Lambda13C, originated by the weak Lambda-nucleus spin-orbit force. We have also considered the splittings of the 3/2+ and 5/2+ levels in both Lambda9Be and Lambda13C, finding how they originate from couplings to the collective 2+ states of the core nuclei. In both hyper-nuclei, we suggest that there could be additional low-lying resonant states in the Lambda-nucleus continua. From the MCAS approach one can extract also the full coupled-channel scattering wave-function to be used in the calculation of various transition matrix elements. As a first application, we have considered the EM-transition matrix elements for the capture reaction Alpha + 3He -> 7Be + Gamma .
A Multi-Channel Algebraic Scattering (MCAS) approach has been used to analyze the spectra of two hyper-nuclear systems, Lambda-9Be and Lambda-13C. The splitting of the two odd-parity excited levels (1/2^- and 3/2^-) at 11 MeV excitation in Lambda-13C
is driven mainly by the weak Lambda-nucleus spin-orbit force, but the splittings of the 3/2^+ and 5/2^+ levels in both Lambda-9Be and Lambda-13C have a different origin. These cases appear to be dominated by coupling to the collective 2+ states of the core nuclei. Using simple phenomenological potentials as input to the MCAS method, the observed splitting and level ordering in Lambda-9Be is reproduced with the addition of a weak spin-spin interaction acting between the hyperon and the spin of the excited target. With no such spin-spin interaction, the level ordering in Lambda-9Be is inverted with respect to that currently observed. In both hyper-nuclei, our calculations suggest that there are additional low-lying resonant states in the Lambda-nucleus continua.
Diverse means are used to investigate the spectra of the radioactive, exotic ions, 17,19C. First, estimates have been made using a shell model for the systems. Information from those shell model studies were then used in evaluating cross sections of
the scattering of 70A MeV 17,19C ions from hydrogen. Complementing those studies, a multichannel algebraic scattering (MCAS) theory for n+16,18C coupled-channel problems has been used to identify structures of the compound systems. The results show that the shell model structure assumed for these ions is reasonable with little need of effective charges. The conditions that two excited states exist within a few hundred keV of the ground state places some restriction upon the structure models. Other positive parity states are expected in the low-lying spectra of the two nuclei.
How does the scattering cross section change when the colliding bound-state fragments are allowed particle-emitting resonances? This question is explored in the framework of a multi-channel algebraic scattering method of determining nucleon-nucleus c
ross sections at low energies. Two cases are examined, the first being a gedanken investigation in which n + carbon-12 scattering is studied with the target states assigned artificial widths. The second is a study of neutron scattering from beryllium-8; a nucleus that is particle unstable. Resonance character of the target states markedly varies evaluated cross sections from those obtained assuming stability in the target spectrum.
Cross-section and analyzing power data from 197 MeV $(p,p)$ scattering and longitudinal and transverse form factors for electron scattering to low lying states in $^{10}$B have been analyzed as tests of the structure of the nuclear states when they a
re described using a no-core $(0+2)hbaromega$ shell model. While the results obtained from the shell model clearly show the need of other elements, three-body forces in particular, to explain the observed spectrum, the reasonable level of agreement obtained in the analyses of the scattering data suggest that the wavefunctions from our shell model using only a two-body potential are credible. Any changes to the wavefunctions with the introduction of three-body forces in the shell model Hamiltonian should therefore be relatively minor.
