Quantum Monte Carlo calculations of electroweak transition matrix elements in $A=6,7$ nuclei

Green's function Monte Carlo (GFMC) calculations of magnetic dipole, electric quadrupole, Fermi, and Gamow-Teller transition matrix elements are reported for $A=6,7$ nuclei. The matrix elements are extrapolated from mixed estimates that bracket the relevant electroweak operator between variational Monte Carlo (VMC) and GFMC propagated wave functions. Because they are off-diagonal terms, two mixed estimates are required for each transition, with a VMC initial (final) state paired with a GFMC final (initial) state. The realistic Argonne $v_{18}$ two-nucleon and Illinois-2 three-nucleon interactions are used to generate the nuclear states. In most cases we find good agreement with experimental data.

Figure 1

$E2$ transitions for ${}^6\mathrm{Li}$$(3^{+};0)$ and ${}^6\mathrm{Li}$$(2^{+};0)$ to ${}^6\mathrm{Li}$$(1^{+};0)$ ground state.

Figure 2

GFMC E(τ) for different states of ${}^6\mathrm{Li}$.

Figure 3

$M1$ transition for ${}^6\mathrm{Li}$$(0^{+};1)$ to ${}^6\mathrm{Li}$$(1^{+};0)$.

Figure 4

$E2$ transition for ${}^7\mathrm{Li}$$({\frac{7}{2}}^{-})$ to ${}^7\mathrm{Li}$$({\frac{3}{2}}^{-})$.

Figure 5

Gamow-Teller transitions for ${}^7\mathrm{Be}$$({\frac{3}{2}}^{-})$ to ${}^7\mathrm{Li}$$({\frac{3}{2}}^{-})$ and ${}^7\mathrm{Be}$$({\frac{3}{2}}^{-})$ to ${}^7\mathrm{Li}$$({\frac{1}{2}}^{-})$.