# Nucleon scattering on actinides using a dispersive optical model with extended couplings

## TL;DR

This paper extends the Tamura coupling model to include additional low-lying rotational bands in actinides, employing a dispersive optical model with multi-band couplings to accurately fit experimental scattering data and improve predictions of nuclear reactions.

## Contribution

The study introduces an extended multi-band coupling scheme in the dispersive optical model for actinides, enhancing the accuracy of scattering data fits and nuclear reaction predictions.

## Key findings

- Reproduces total cross-section differences within experimental uncertainty.
- Multi-band coupling significantly affects scattering predictions, especially in even-even nuclei.
- Coupling of ground-state rotational levels suffices for odd-A nuclei when saturated.

## Abstract

Tamura coupling model has been extended to consider the coupling of additional low-lying rotational bands to the ground state band. Rotational bands are built on vibrational bandheads (even-even targets) or single particle bandheads (odd-$A$ targets) including both axial and non-axial deformations. These additional excitations are introduced as a perturbation to the underlying axially-symmetric rigid rotor structure of the ground state rotational band. Coupling matrix elements of the generalized optical model are derived for extended multi-band transitions in even-even and odd-$A$ nuclei. Isospin symmetric formulation of the optical model is employed. A coupled-channels optical model potential (OMP) containing a dispersive contribution is used to fit simultaneously all available optical experimental databases including neutron strength functions for nucleon scattering on $^{232}$Th, $^{233,235,238}$U and $^{239}$Pu nuclei and quasi-elastic ($p$,$n$) scattering data on $^{232}$Th and $^{238}$U. Lane consistent OMP is derived for all actinides if corresponding multi-band coupling schemes are defined. Calculations using the derived OMP potential reproduce measured total cross-section differences between several actinide pairs within experimental uncertainty for incident neutron energies from 50 keV up to 150MeV. Multi-band coupling is stronger in even-even targets due to the collective nature of the coupling; the impact of extended coupling on predicted compound-nucleus formation cross section reaches 5% below 3 MeV of incident neutron energy. Coupling of ground-state rotational band levels in odd-$A$ nuclei is sufficient for a good description of the compound-nucleus formation cross sections as long as the coupling is saturated (a minimum of 7 coupled levels are typically needed).