Scaling laws for near barrier Coulomb and Nuclear Breakup

TL;DR

This paper derives and confirms scaling laws for nuclear and Coulomb breakup cross sections of $^6$Li in nuclear collisions, providing useful insights for experimental planning with exotic nuclei.

Contribution

It introduces new scaling laws for nuclear and Coulomb breakup cross sections based on CDCC calculations, extending understanding to near barrier energies.

Findings

Nuclear breakup cross section scales linearly with $A_T^{1/3}$.

Coulomb breakup cross section scales linearly with atomic number Z.

Results are consistent with previous high-energy findings.

Abstract

We investigate the nuclear and the Coulomb contributions to the breakup cross sections of $^6$Li in collisions with targets in different mass ranges. Comparing cross sections for different targets at collision energies corresponding to the same $E/V_{\mathrm{\scriptscriptstyle B}}$, we obtain interesting scaling laws. First, we derive an approximate linear expression for the nuclear breakup cross section as a function of $A_{\mathrm{% \scriptscriptstyle T}}^{1/3}$. We then confirm the validity of this expression performing CDCC calculations. Scaling laws for the Coulomb breakup cross section are also investigated. In this case, our CDCC calculations indicate that this cross section has a linear dependence on the atomic number of the target. This behavior is explained by qualitative arguments. Our findings, which are consistent with previously obtained results for higher energies, are important when planning for experiments involving exotic weakly bound nuclei.