Inclusive breakup of Borromean nuclei

TL;DR

This paper derives a comprehensive formula for inclusive breakup cross sections of Borromean nuclei, incorporating a novel three-body absorption term, advancing understanding of three-fragment nuclear reactions.

Contribution

It introduces a four-body generalization of the Austern formula including a new three-body absorption component for Borromean nuclei.

Findings

Derived the inclusive breakup cross section formula for three-fragment nuclei.

Identified the role of three-body absorption in nuclear reactions.

Provided methods to calculate the three-body absorption contribution.

Abstract

We derive the inclusive breakup cross section of a three-fragment projectile nuclei, $a = b +x_1 + x_2$, in the spectator model. The resulting four-body cross section for observing $b$, is composed of the elastic breakup cross section which contains information about the correlation between the two participant fragments, and the inclusive non-elastic breakup cross section. This latter cross section is found to be a non-trivial four-body generalization of the Austern formula \cite{Austern1987}, which is proportional to a matrix element of the form, $\langle\hat{\rho}_{{x_1},{x_2}}\left|\left[W_{{x_1}} + W_{{x_2}} + W_{3B}\right]\right|\hat{\rho}_{{x_1}, {x_2}}\rangle$. The new feature here is the three-body absorption, represented by the imaginary potential, $W_{3B}$. We analyze this type of absorption and supply ideas of how to calculate its contribution.