Determining ground-state wave functions in light, stable and exotic nuclei

The nuclear shell model, analogous to the atomic electron shell model, is perhaps the most important and general model for calculating a wide range of nuclear properties. A stringent test that has been developed over many years is to compare the measured probability for the transfer of a single neutron in a direct reaction to the probability predicted using the shell model wave functions of the nuclei. This ratio is called the spectroscopic factor and provides a simple measure of how well the shell model can describe a given nuclear state. Recently, scientists at the National Superconducting Cyclotron Lab (NSCL) on the campus of Michigan State University produced a consistent and systematic set of spectroscopic factors from a wide range of data on single neutron transfer reactions. With the exception of very small spectroscopic factors and reactions leading to a few states near 40Ca (outside the theoretical shell model space) the agreement between the measurements and the predictions from the most recent, large basis-set, shell model calculations was found to be approximately 30%. Thus, this analysis indicates that modern shell model calculations can provide good descriptions of ground state nuclear wave functions.

 

A photograph of the sixteen identical detectors that make up the HiRA array used to measure charged particles emitted from energetic nuclear collisions. The energy and angular distributions of the particles can be used to deduce the ground-state wave functions of extremely exotic nuclei such as proton-rich 34Ar and neutron-rich 46Ar.

 

Given the good agreement with existing data for transfer reactions, the NSCL group very recently measured the cross sections for neutron transfer reactions with the very exotic proton rich nucleus 34Ar and with the very neutron rich 46Ar nucleus. The light reaction products were observed with the High Resolution Array (HiRA, constructed with an MRI grant) in coincidence with the heavy products detected in a large magnetic spectrometer. The new data obtained for these exotic nuclei was found to be consistent with the shell model predictions. However, the results of other recent measurements with a different reaction mechanism in which single neutrons are cleanly knocked out from a nucleus gave different results. The apparent disagreement between the knockout and transfer reactions indicates that the theoretical descriptions of both reaction mechanism themselves should be reexamined.