Quantum Monte Carlo calculations of magnetic moments and $M1$ transitions in $A⩽7$ nuclei including meson-exchange currents

Green's function Monte Carlo calculations of magnetic moments and $M1$ transitions including two-body meson-exchange current (MEC) contributions are reported for $A⩽7$ nuclei. The realistic Argonne $v_{18}$ two-nucleon and Illinois-2 three-nucleon potentials are used to generate the nuclear wave functions. The two-body meson-exchange operators are constructed to satisfy the continuity equation with the Argonne $v_{18}$ potential. The MEC contributions increase the $A=3,7$ isovector magnetic moments by $16\%$ and the $A=6,7$ $M1$ transition rates by $17–34\%$, bringing them into very good agreement with the experimental data.

Figure 1

Diagrammatic representation of operators included in $j(\Delta )$ due to one-body currents $j^{(1)}(N\to \Delta )$, $j^{(1)}(\Delta \to N)$, and $j^{(1)}(\Delta \to \Delta )$, and transition correlations $U^{N\Delta }$, $U^{\Delta N}$, $U^{\Delta \Delta }$, and corresponding Hermitian conjugates. Wavy, thin, thick, dashed, and dashed with a × lines denote photons, nucleons, Δ isobars, and transition correlations $U^{B{B}^{\text{'}}}$ and ${U^{B{B}^{\text{'}}}}^{†}$, respectively.

Figure 2

Diagrams associated with connected three-body terms, which are neglected in the present work. Wavy, thin, thick, dotted, dashed, and dashed with a × lines denote photons, nucleons, Δ isobars, the two-body current $j^{(2)}(NN\to NN)$, and the transition correlations $U^{B{B}^{\text{'}}}$ and ${U^{B{B}^{\text{'}}}}^{†}$ respectively.

Figure 3

Extrapolated GFMC magnetic moment for the ${}^7\mathrm{Li}$$({\frac{3}{2}}^{-})$ ground state in impulse approximation (green squares) and with MEC (red circles). VMC values (purple lines) and averaged GFMC values (lines with error bars) are also shown.

Figure 4

Extrapolated GFMC $M1$ matrix element for the ${}^6\mathrm{Li}$$(0^{+};1)$ $\to$ ${}^6\mathrm{Li}$$(1^{+};0)$ transition in impulse approximation (green squares) and with MEC (red circles). VMC values (purple lines) and averaged GFMC values (lines with error bars) are also shown.