Microscopic Nuclear Structure and Reaction Calculations in the FMD Approach

TL;DR

This paper applies the Fermionic Molecular Dynamics (FMD) approach to low-energy nuclear reactions, successfully reproducing experimental data for the $^3$He($ ext{α}$,$ ext{γ}$)$^7$Be radiative capture, demonstrating FMD's effectiveness in nuclear reaction modeling.

Contribution

First application of FMD to low-energy nuclear reactions, accurately modeling the $^3$He($ ext{α}$,$ ext{γ}$)$^7$Be process and matching experimental data.

Findings

FMD reproduces the energy of bound states in $^7$Be.

Charge radius of $^7$Be ground state agrees with experiments.

Calculated S factor matches experimental measurements.

Abstract

We present here a first application of the Fermionic Molecular Dynamics (FMD) approach to low-energy nuclear reactions, namely the $^3$He($\alpha$,$\gamma$)$^7$Be radiative capture reaction. We divide the Hilbert space into an external region where the system is described as $^3$He and $^4$He clusters interacting only via the Coulomb interaction and an internal region where the nuclear interaction will polarize the clusters. Polarized configurations are obtained by a variation after parity and angular momentum projection procedure with respect to the parameters of all single particle states. A constraint on the radius of the intrinsic many-body state is employed to obtain polarized clusters at desired distances. The boundary conditions for bound and scattering states are implemented using the Bloch operator. The FMD calculations reproduce the correct energy for the centroid of the $3/2^-$ and $1/2^-$ bound states in $^7$Be. The charge radius of the ground state is in good agreement with recent experimental results. The FMD calculations also describe well the experimental phase shift data in the $1/2^+$, $3/2^+$ and $5/2^+$ channels that are important for the capture reaction at low energies. Using the bound and scattering many-body wave functions we calculate the radiative capture cross section. The calculated $S$ factor agrees very well, both in absolute normalization and energy dependence, with the recent experimental data from the Weizmann, LUNA, Seattle and ERNA experiments.