# Study of corrections to the eikonal approximation

## TL;DR

This paper enhances the eikonal approximation for nuclear reaction modeling by introducing corrections that extend its validity to lower energies and larger angles, improving accuracy for radioactive-ion beam experiments.

## Contribution

It proposes two novel corrections to the eikonal approximation, allowing better modeling of nuclear reactions at lower energies and wider angles.

## Key findings

- Corrections improve the accuracy of the eikonal model at lower energies.
- Enhanced model better accounts for projectile deflection.
- Results validated against partial-wave expansion calculations.

## Abstract

For the last decades, multiple international facilities have developed Radioactive-Ion Beams (RIB) to measure reaction processes including exotic nuclei. These measurements coupled with an accurate theoretical model of the reaction enable us to infer information about the structure of these nuclei. The partial-wave expansion provides a precise description of two-body collisions but has a large computational cost. To cope with this issue, the eikonal approximation is a powerful tool as it reduces the computational time and still describes the quantum effects observed in reaction observables. However, its range of validity is restricted to high energy and to forward scattering angles. In this work, we analyse the extension of the eikonal approximation to lower energies and larger angles through the implementation of two corrections. These aim to improve the treatment of the nuclear and Coulomb interactions within the eikonal model. The first correction is based on an expansion of the $T$-matrix while the second relies on a semi-classical approach. They permit to better account for the deflection of the projectile by the target, which is neglected in the standard eikonal model. The gain in accuracy of each correction is evaluated through the analyses of angular cross sections computed with the standard eikonal model, its corrections and the partial-wave expansion. These analyses have been performed for tightly bound projectiles ($^{10}\mathrm{Be}$) from intermediate energies (67 MeV/nucleon) down to energies of interest of future RIB facilities such as HIE-ISOLDE and ReA12 at MSU (10 MeV/nucleon).