Quantum Monte Carlo calculations of weak transitions in $A=6–10$ nuclei

Ab initio calculations of the Gamow-Teller (GT) matrix elements in the $\beta$ decays of ${}^6\mathrm{He}$ and ${}^{10}\mathrm{C}$ and electron captures in ${}^7\mathrm{Be}$ 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 ${}^7\mathrm{Be}$, while theory overestimates the ${}^6\mathrm{He}$ and ${}^{10}\mathrm{C}$ data by $\sim 2\%$ and ∼10%, respectively. We show that for these systems correlations in the nuclear wave functions are crucial to explaining the data, while many-body currents increase by ∼2–3% the one-body GT contributions.

Figure 1

Diagrams illustrating the (nonvanishing) contributions to the 2b and 3b axial currents. Nucleons, pions, and external fields are denoted by solid, dashed, and wavy lines, respectively. The circle in (b) represents the vertex implied by the ${\mathcal{L}}_{\pi N}^{\left(2\right)}$ chiral Lagrangian [36], involving the LECs $c_3$ and $c_4$. Only a single time ordering is shown; in particular, all direct- and crossed-box diagrams are accounted for. The power counting of the various contributions is also indicated. See text for further explanations.

Figure 2

Ratios of GFMC to experimental values of the GT RMEs in the ${}^3\mathrm{H}, {}^6\mathrm{He}, {}^7\mathrm{Be}$, and ${}^{10}\mathrm{C}$ weak transitions. Theory predictions correspond to the $\chi \mathrm{EFT}$ axial current in LO (blue circles) and up to N4LO (magenta stars). Green squares indicate “unquenched” shell-model calculations from Ref. [17] based on the LO axial current.