Fusion Reactions Between Neutron-rich Nuclei

Fusion reactions between neutron-rich nuclei have been proposed as a potentially important heat source in the outer-crust of an accreting neutron star, possibly triggering an X-ray superburst.  The underpinning element of this hypothesis is that the fusion of neutron-rich nuclei is enhanced relative to their beta-stable counterparts. Such an enhancement could arise from the increased polarizability of the neutron-rich nucleus due to the decreased average binding of the outermost neutrons and the existence of low-energy collective modes.  This increased polarizability, the prelude to neutron transfer, is schematically illustrated in Fig. 1. Examining the evolution of the fusion cross-section with increasing neutron number for an isotopic chain provides the best means to address this question.

The experiment was conducted at the ReA3 facility where beams of ³⁹K and ⁴⁷K at near-barrier energies were incident on a ²⁸Si target. Fusion products were identified by measuring their energy and time-of-flight using a simple yet highly efficient experimental setup. Use of a highly efficient setup is mandated by the low intensity associated with radioactive beams. Presented in Fig. 2 is the dependence on incident energy of the fusion cross-section for ⁴⁷K + ²⁸Si as compared to ³⁹K + ²⁸Si. The relative fusion cross-section s(⁴⁷K)/s(³⁹K) clearly increases with decreasing incident energy. This increase in the relative cross section with decreasing energy reflects both the larger size of the neutron-rich nucleus, specifically the increased extent of its neutron density distribution, and the dynamics associated with the additional neutrons. [J. Vadas et al., Phys. Rev. C 97 031601 (R) (2018)]

 

Fig. 1: Schematic illustrating the fusion of ³⁹K and ⁴⁷K nuclei with ²⁸Si nuclei. The influence of polarization on the fusion barrier is indicated.

 

 

 

Fig. 2: Dependence of the relative cross-section for fusion of ⁴⁷K and ³⁹K with ²⁸Si nuclei on incident energy. With decreasing incident energy the relative cross-section increases rapidly. Polarization is included in the CCFULL and CCFULL+ n-Trans calculations. The role of mutual excitation of the two nuclei and neutron transfer is evident.