The ${}^9$Be photodisintegration cross section within Cluster Effective Field Theory

TL;DR

This paper calculates the low-energy photodisintegration cross section of ${}^9$Be using a cluster effective field theory approach, incorporating two- and three-body interactions and many-body current effects.

Contribution

It introduces a novel low-energy calculation of ${}^9$Be photodisintegration within a cluster EFT framework, including a detailed treatment of many-body currents.

Findings

Calculated ${}^9$Be photodisintegration cross section at low energies.

Demonstrated the impact of many-body currents on the transition matrix elements.

Provided a consistent EFT-based description of ${}^9$Be's three-body binding and reactions.

Abstract

A low-energy calculation of ${}^9$Be photodisintegration cross section is presented within an $\alpha\alpha n$ cluster approach. The $\alpha n$ and $\alpha\alpha$ contact interactions are derived from cluster effective field theory. The two-body potentials defined in momentum space are regularized by a Gaussian cutoff. The associated low-energy constants are found by comparing the calculated low-energy T-matrix with its effective range expansion. A three-body state-dependent potential is also introduced in the model. First, the ${}^9$Be three-body binding energy is studied within the non-symmetrized hyperspherical harmonics method. Then, the low-energy cross section is calculated via the Lorentz integral transform method, focussing on the dominant electric dipole transitions. A twofold evaluation of the nuclear current matrix element is presented, employing both the electric dipole transition operator (Siegert theorem) and the one-body convection current operator. This approach is adopted to allow for a discussion of the effect of the many-body currents.