Derivation of an optical potential for statically deformed rare-earth nuclei from a global spherical potential

The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations characterized by nuclear deformations. A proper treatment of such excitations is often essential to the accurate description of experimental nuclear-reaction data and to the prediction of a wide variety of scattering observables. Stimulated by recent work substantiating the near validity of the adiabatic approximation in coupled-channel calculations for scattering on statically deformed nuclei, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on this class of nuclei. To do this, we have deformed the Koning-Delaroche global spherical potential for neutrons, coupling a sufficient number of states of the ground state band to ensure convergence. We present an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions for neutron-induced reactions on statically deformed nuclei in the rare-earth region. We choose isotopes of three rare-earth elements (Gd, Ho, W), which are known to be nearly perfect rotors, to exemplify the results of the proposed method. Predictions from our model for total, elastic and inelastic cross sections, as well as for elastic and inelastic angular distributions, are in reasonable agreement with measured experimental data. These results suggest that the deformed Koning-Delaroche potential provides a useful regional neutron optical potential for the statically deformed rare earth nuclei.

Towards an optical potential for rare-earths through coupled channels

The coupled-channel theory is a natural way of treating nonelastic channels, in particular those arising from collective excitations, defined by nuclear deformations. Proper treatment of such excitations is often essential to the accurate description of reaction experimental data. Previous works have applied different models to specific nuclei with the purpose of determining angular-integrated cross sections. In this work, we present an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions in a consistent manner for neutron-induced reactions on nuclei in the rare-earth region. This specific subset of the nuclide chart was chosen precisely because of a clear static deformation pattern. We analyze the convergence of the coupled-channel calculations regarding the number of states being explicitly coupled. Inspired by the work done by Dietrich emph{et al.}, a model for deforming the spherical Koning-Delaroche optical potential as function of quadrupole and hexadecupole deformations is also proposed. We demonstrate that the obtained results of calculations for total, elastic and inelastic cross sections, as well as elastic and inelastic angular distributions correspond to a remarkably good agreement with experimental data for scattering energies above around a few MeV.

Coupled-channel optical model potential for rare earth nuclei

Inspired by the recent work by Dietrich et al., substantiating validity of the adiabatic assumption in coupled-channel calculations, we explore the possibility of generalizing a global spherical optical model potential (OMP) to make it usable in coupled-channel calculations on statically deformed nuclei. The generalization consists in adding the coupling of the ground state rotational band, deforming the potential by introducing appropriate quadrupole and hexadecupole deformation and correcting the OMP radius to preserve volume integral of the spherical OMP. We choose isotopes of three rare-earth elements (W, Ho, Gd), which are known to be nearly perfect rotors, to perform a consistent test of our conjecture on integrated cross sections as well as on angular distributions for elastic and inelastic neutron scattering. When doing this we employ the well-established Koning-Delaroche global spherical potential and experimentally determined deformations without any adjustments. We observe a dramatically improved agreement with experimental data compared to spherical optical model calculations. The effect of changing the OMP radius to preserve volume integral is moderate but visibly improves agreement at lower incident energies. We find that seven collective states need to be considered for the coupled-channel calculations to converge. Our results for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkable agreement with experimental data. This result confirms that the adiabatic assumption holds and can extend applicability of the global spherical OMP to rotational nuclei in the rare-earth region, essentially without any free parameter. Thus, quite reliable coupled-channel calculations can be performed on such nuclei even when the experimental data, and consequently a specific coupled-channel potential, are not available.

Towards a coupled-channel optical potential for rare-earth nuclei

We present an outline of an extensive study of the effects of collective couplings and nuclear deformations on integrated cross sections as well as on angular distributions in a consistent manner for neutron-induced reactions on nuclei in the rare-earth region. This specific subset of the nuclide chart was chosen precisely because of a clear static deformation pattern. We analyze the convergence of the coupled-channel calculations regarding the number of states being explicitly coupled. A model for deforming the spherical Koning-Delaroche optical potential as function of quadrupole and hexadecupole deformations is also proposed, inspired by previous works. We demonstrate that the obtained results of calculations for total, elastic, inelastic, and capture cross sections, as well as elastic and inelastic angular distributions are in remarkably good agreement with experimental data for scattering energies around a few MeV.

Towards a Microscopic Reaction Description Based on Energy-Density-Functional Structure Models

A microscopic calculation of reaction cross sections for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole excitations in the target and one-nucleon pickup channels. The particle-hole states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm were described in a random-phase framework using a Skyrme functional. Reaction cross sections obtained agree very well with experimental data and predictions of a state-of-the-art fitted optical potential. Couplings between inelastic states were found to be negligible, while the pickup channels contribute significantly. The effect of resonances from higher-order channels was assessed. Elastic angular distributions were also calculated within the same method, achieving good agreement with experimental data. For the first time observed absorptions are completely accounted for by explicit channel coupling, for incident energies between 10 and 70 MeV, with consistent angular distribution results.

Reaction cross-section predictions for nucleon induced reactions

A microscopic calculation of the optical potential for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all the particle-hole (p-h) excitation states in the target and to all relevant pickup channels. These p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and to long-lived compound nucleus resonances. We calculated the reaction cross sections for the nucleon induced reactions on the targets $^{40,48}$Ca, $^{58}$Ni, $^{90}$Zr and $^{144}$Sm using the QRPA description of target excitations, coupling to all inelastic open channels, and coupling to all transfer channels corresponding to the formation of a deuteron. The results of such calculations were compared to predictions of a well-established optical potential and with experimental data, reaching very good agreement. The inclusion of couplings to pickup channels were an important contribution to the absorption. For the first time, calculations of excitations account for all of the observed reaction cross-sections, at least for incident energies above 10 MeV.

Coupled-channels calculations of nonelastic cross sections using a density-functional structure model

A microscopic calculation of the reaction cross-section for nucleon-nucleus scattering has been performed by explicitly coupling the elastic channel to all particle-hole (p-h) excitation states in the target and to all one-nucleon pickup channels. The p-h states may be regarded as doorway states through which the flux flows to more complicated configurations, and subsequently to long-lived compound nucleus resonances. Target excitations for 40,48Ca, 58Ni, 90Zr and 144Sm were described in a QRPA framework using a Skyrme functional. Reaction cross sections calculated in this approach were compared to predictions of a fitted optical potential and to experimental data, reaching very good agreement. Couplings between inelastic states were found to be negligible, while the couplings to pickup channels contribute significantly. For the first time observed reaction cross-sections are completely accounted for by explicit channel coupling, for incident energies between 10 and 40 MeV.