A multi-channel algebraic scattering theory, to find solutions of coupled-channel scattering problems with interactions determined by collective models, has been structured to ensure that the Pauli principle is not violated. By tracking the results in the zero coupling limit, a correct interpretation of the sub-threshold and resonant spectra of the compound system can be made. As an example, the neutron-12 C system is studied defining properties of 13 C to 10 MeV excitation. Accounting for the Pauli principle in collective coupled-channels models is crucial to the outcome. 25.40.Dn;25.40.Ny;28.20.Cz At energies above 25 MeV, by using optical potentials formed by full folding effective two-nucleon interactions with microscopic (nucleon based) descriptions of the target structure, the importance of treating the Pauli principle has been well established [1]. However, in the domain of low-energy nucleon scattering for which an explicit coupled-channels theory of scattering is essential, the significance of Pauli exclusion effects has not been well defined. Many coupled-channels codes are available, some of which perform phenomenological collective-model calculations searching on parameter values of the chosen function forms to find a best fit to experimental data. But while it has long been known that any such models violate the Pauli principle [2,3], quantification of that violation is lacking.To study the effects of the Pauli principle in a macroscopic (collective model) approach is not a trivial task. In a recent publication [4], the orthogonalizing pseudopotential (OPP) method [5,6] was generalized to treat this problem. That was a small though important part of the full theoretical framework of the multi-channel algebraic scattering (MCAS) theory of scattering [4]. Therein the OPP was used in finding the spectra, bound and resonance properties, of 13 C. However, implications of the role of the Pauli principle in collective model coupledchannel calculations arising from the use of the OPP was not discussed. Such is a purpose of this letter. Another is that the method could be pertinent for any study requiring coupled channel solutions of quantal systems involving fermions. As the example, we study the effects introduced by the Pauli principle in collective, geometrical-type, models for low-energy nucleon-nucleus processes that can be characterized from the spectrum of the compound nucleus. That spectrum includes the states that lie below the nucleon-nucleus threshold and in the continuum as revealed by the narrow and broad resonances that lie upon a smooth but energy dependent background of the elastic scattering cross section. This can be done in a systematic and self-consistent way since the MCAS approach facilitates such a determination of the sub-threshold bound states and resonances of the compound nucleus. This theory, with which one solves the coupled-channel Lippmann-Schwinger (LS) equations for the nucleon-nucleus system considered, is built upon sturmian expansions of an interaction matrix of potent...

A nucleon-nucleus interaction model has been applied to ascertain the underlying character of the negative-parity spectra of four isobars of mass seven, from neutron-to proton-emitter driplines. With one and the same nuclear potential defined by a simple coupled-channel model, a multichannel algebraic scattering approach (MCAS) has been used to determine the bound and resonant spectra of the four nuclides, of which 7 He and 7 B are particle unstable. Incorporation of Pauli blocking in the model enables a description of all known spin-parity states of the mass-7 isobars. We have also obtained spectra of similar quality by using a large space no-core shell model. Additionally, we have studied 7 Li and 7 Be using a dicluster model. We have found a dicluster-model potential that can reproduce the lowest four states of the two nuclei, as well as the relevant low-energy elastic scattering cross sections. But, with this model, the rest of the energy spectra cannot be obtained.

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.

A multi-channel algebraic scattering theory has been used to study the properties of nucleon scattering from 12 C and of the sub-threshold compound nuclear states, accounting for properties in the compound nuclei to ∼ 10 MeV. All compound and quasi-compound resonances observed in total cross-section data are matched, and on seeking solutions of the method at negative energies, all sub-threshold states in 13 C and 13 N are predicted with the correct spin-parities and with reasonable values for their energies. A collective-model prescription has been used to define the initiating nucleon-12 C interactions and via use of orthogonalizing pseudo-potentials, account is made of the Pauli principle. Information is extracted on the underlying structure of each state in the compound systems by investigating the zero-deformation limit of the results.

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