# Applicability of the Wong formula for fusion cross sections from light to heavy systems

## TL;DR

This paper evaluates the Wong formula's effectiveness in estimating fusion cross sections across light to heavy nuclear systems, highlighting its limitations for lighter systems and the energy dependence of its accuracy.

## Contribution

It systematically compares approximate Wong formula results with exact calculations across a wide range of nuclear masses, revealing its limitations and energy dependence.

## Key findings

- Wong formula approximates well for heavy systems
- Large deviations occur for light systems
- Critical energy increases with target mass

## Abstract

We discuss the applicability of the Wong formula for fusion cross sections in a single-channel problem. To this end, we carry out a systematic study and compare the approximate fusion cross sections with the exact results in a wide mass region of reaction systems. We show that the deviation of the approximate results from the exact cross sections is large for light systems, even though the Wong formula provides a reasonable approximation for heavy systems. We also discuss the energy dependence of the deviation, and show that for a given projectile nucleus the critical energy, at which the deviation exceeds 5\% of the exact cross sections, increases as a function of the mass number of the target nucleus.