Neutron Transfer Reactions for Deformed Nuclei Using Sturmian Basis States

Abstract

We study the spin-parity distribution P(J${}^{\pi }$,E) of ${}^{156}$Gd excited states above the neutron separation energy $S_n=8.536$ MeV \cite{156Gd_list_of_levels} that are expected to be populated via the 1-step neutron pickup reaction ${}^{157}$Gd(${}^3$He,${}^4$He)${}^{156}$Gd. In analogy with the rotor plus particle model \cite{Bohr&Mottelson-II}, we view excited states in ${}^{156}$Gd as rotational excitations built on intrinsic states consisting of a neutron hole in the ${}^{157}$Gd core, that is, a neutron removal from a deformed Woods-Saxon type single-particle state \cite{Woods-Saxon:1954} in ${}^{157}$Gd. The particle-core interaction usually dominated by a Coriolis coupling are accounted via first order perturbation theory \cite{VGGueorguiev:07062002}. The reaction cross section to each excited state in ${}^{156}$Gd is calculated as coherent contribution using a standard reaction code \cite{CHUCK} based on spherical basis states. The spectroscopic factor associated with each state is the expansion coefficient of the deformed neutron state in a spherical Sturmian basis along with the spherical form factors \cite{VGGueorguiev:07062002}. The total cross section, as a function of the excitation energy, is generated using Lorentzian smearing distribution function. Our calculations show that, within the assumptions and computational modeling, the reaction ${}^3$He+${}^{157}$Gd $\to$ ${}^4$He+${}^{156}$Gd${}^{\star }$ has a smooth formation probability P(J${}^{\pi }$,E) within the energy range relevant to the desired reaction ${}^{155}$Gd+n $\to$ ${}^{156}$Gd${}^{\star }$. The formation probability P(J${}^{\pi }$,E) resembles a Gaussian distribution with centroids and widths that differ for positive and negative parity states.

Comments: 9 pages, 2 figures, Contribution to the International Workshop "Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects" (SDANCA-17), 5-7 October 2017, Sofia, Bulgaria, http://ntl.inrne.bas.bg/events/sdanca17/, Contributions Published in Bulgarian Journal of Physics, ISSN 1310-0157, http://www.bjp-bg.com/papers.php?year=2017&vol=44&issue=4