# An Empirical Scaling formula for fragments production in projectile fragmentation reactions

## TL;DR

This paper introduces an empirical scaling formula for predicting fragment production in projectile fragmentation reactions, demonstrating improved accuracy over existing models and enabling better yield predictions.

## Contribution

The paper proposes a new empirical scaling formula that accounts for system size and asymmetry, improving fragment yield predictions in projectile fragmentation reactions.

## Key findings

- The empirical formula better reproduces measured fragment yields than existing models.
- It successfully predicts fragment production in $^{68}$Ni/$^{69}$Cu/$^{72}$Zn + $^9$Be reactions.
- The formula accounts for system size and asymmetry effects.

## Abstract

A scaling phenomenon in the cross section for fragments has been found in the projectile fragmentation reaction, and an empirical scaling formula is proposed by considering the dependence of cross section on the size and asymmetry of the reaction system and the fragment itself. Furthermore, the empirical scaling formula is used to predict the production of fragment in the $^{68}$Ni/$^{69}$Cu/$^{72}$Zn + $^9$Be reactions around 90$A$ MeV. Compared to the results calculated by the statistical abrasion ablation model and the {\sc epax3} parameterizations, the empirical scaling formula can better reproduce the measured fragments. The empirical scaling formula can be used to predict the yield for fragment in projectile fragmentation reaction.