Quantum Monte Carlo calculations of electromagnetic transitions in ${}^8\mathrm{Be}$ with meson-exchange currents derived from chiral effective field theory

We report quantum Monte Carlo calculations of electromagnetic transitions in ${}^8\mathrm{Be}$. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon potentials are used to generate the ground state and nine excited states, with energies that are in excellent agreement with experiment. A dozen $M1$ and eight $E2$ transition matrix elements between these states are then evaluated. The $E2$ matrix elements are computed only in impulse approximation, with those transitions from broad resonant states requiring special treatment. The $M1$ matrix elements include two-body meson-exchange currents derived from chiral effective field theory, which typically contribute 20%–30% of the total expectation value. Many of the transitions are between isospin-mixed states; the calculations are performed for isospin-pure states and then combined with empirical mixing coefficients to compare to experiment. Alternate mixings are also explored. In general, we find that transitions between states that have the same dominant spatial symmetry are in reasonable agreement with experiments, but transitions between different spatial symmetries are often underpredicted.

Figure 1

Experimental spectrum of ${}^8\mathrm{Be}$: horizontal lines denote energy levels, with blue for $T=0$ states, magenta for mixed $T=0+1$ states, and violet for $T=2$; black dash-dotted lines indicate thresholds for breakup as indicated and shaded areas denote the large widths of the ${}^8\mathrm{Be}$ rotational states. Vertical lines with arrows indicate the electromagnetic transitions studied: short-dashed (blue) for $E2$, long-dashed (red) for $M1$, and dash-dotted (magenta) for combined $E2$ and $M1$ transitions.

Figure 2

GFMC propagation in imaginary time $\tau$ of the energy expectation values of the first three states in the ${}^8\mathrm{Be}$ spectrum. Lower black circles represent GFMC propagation points for the ground state; middle (blue) circles, the $(2^{+};0)$ rotational state at $\sim$3-MeV excitation; and upper (red) circles, the $(4^{+};0)$ state at $\sim$11-MeV excitation. Solid lines represent a linear fit to the GFMC points in the indicated time interval and dashed lines show a one-standard-deviation Monte Carlo statistical error for the fit.

Figure 3

GFMC propagation in imaginary time $\tau$ of the point proton radius expectation values of the first three states in the ${}^8\mathrm{Be}$ spectrum; notation is the same as for Fig. 2.

Figure 4

GFMC propagation in imaginary time $\tau$ of the reduced $E2$ matrix elements among the first three states in the ${}^8\mathrm{Be}$ spectrum; upper (red) circles represent the $(4^{+};0)\to (2^{+};0)$ transition; lower (blue) circles, the $(2^{+};0)\to (0^{+};0)$ transition; and open stars, the extrapolated values.

Figure 5

One-body (IA) $M1$ transition density (in ${\mu }_N$ per ${\mathrm{fm}}^3)$ for selected M1 transitions (see text for explanation).

Figure 6

Two-body (IA) $M1$ transition density (in ${\mu }_N$ per ${\mathrm{fm}}^3)$ for selected M1 transitions (see text for explanation).