Quantum Monte Carlo calculations of weak transitions in $A\,$=$\,$6--10 nuclei

TL;DR

This paper uses advanced quantum Monte Carlo methods with realistic nuclear interactions to calculate weak transition matrix elements in light nuclei, achieving excellent agreement with some experimental data and providing insights into longstanding discrepancies.

Contribution

It demonstrates that correlations in nuclear wave functions are essential and that many-body currents slightly enhance GT matrix elements, offering a potential resolution to the $g_A$-problem.

Findings

Excellent agreement with experimental electron capture data in $^7$Be.

Overestimation of GT matrix elements in $^6$He and $^{10}$C by 2-10%.

Correlations significantly impact theoretical predictions.

Abstract

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the $\beta$ decays of $^6$He and $^{10}$C and electron captures in $^7$Be are carried out using both variational and Green's function Monte Carlo wave functions obtained from the Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions, and axial many-body currents derived from either meson-exchange phenomenology or chiral effective field theory. The agreement with experimental data is excellent for the electron captures in $^7$Be, while theory overestimates the $^6$He and $^{10}$C data by $\sim 2\%$ and $\sim 10\%$, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explain the data, while many-body currents increase by $\sim 2$--$3\%$ the one-body GT contributions. These findings suggest that the longstanding $g_A$-problem, i.e., the systematic overprediction ($\sim 20 \%$ in $A\le 18$ nuclei) of GT matrix elements in shell-model calculations, may be resolved, at least partially, by correlation effects.