Predictions for cross sections of light proton-rich isotopes in $^{40}$Ca + $^{9}$Be reaction

TL;DR

This paper predicts cross sections for light proton-rich isotopes produced in a $^{40}$Ca + $^{9}$Be reaction using empirical and theoretical models, suggesting a new magic number at Z=14 based on the results.

Contribution

It introduces a combined approach using empirical formulas, binding energy models, and statistical models to predict cross sections of proton-rich isotopes in projectile fragmentation.

Findings

Predicted cross sections for Tz=-3 isotopes are around 10^-10 mb.

Z=14 is proposed as a new magic number in light proton-rich nuclei.

Predictions suggest experimental feasibility for studying these isotopes.

Abstract

The cross sections for the $Z=$ 10 -- 19 with isotopes $T_{z}=-3/2$ to $-5$ in the 140$A$ MeV $^{40}$Ca + $^{9}$Be projectile fragmentation reaction have been predicted. An empirical formula based on the correlation between the cross section and average binding energy of isotope has been adopted to predict the cross section. The binding energies in the AME16, WS4, and the theoretical prediction by the spherical relativistic continuum Hartree$-$Bogoliubov theory have been used. Meanwhile, the {\sc fracs} parametrization and the modified statistical abrasion-ablation model are also used to predict the cross sections for the proton-rich isotopes. The predicted cross sections for the $T_{z}=-$3 isotopes are close to $10^{-10}$ mb, which hopefully can be studied in experiment. In addition, based on the predicted cross sections, the $Z=$ 14 is suggested to be a new magic number in the light proton-rich nuclei with $T_{z} \leq-$3/2, of which the phenomenon is much more evident than it is from the average binding energy per nucleon.