Quantum Monte Carlo calculations of spectroscopic overlaps in $A⩽7$ nuclei

We present Green’s function Monte Carlo calculations of spectroscopic overlaps for $A⩽7$ nuclei. The realistic Argonne $v_{18}$ two-nucleon and Illinois-7 three-nucleon interactions are used to generate the nuclear states. The overlap matrix elements are extrapolated from mixed estimates between variational Monte Carlo and Green’s function Monte Carlo wave functions. The overlap functions are used to obtain spectroscopic factors and asymptotic normalization coefficients, and they can serve as an input for reaction calculations.

Figure 1

Imaginary time evolution of SFs in the $s_{1/2}$ channel of the $\langle$${}^3$H$|$${}^4$He$\rangle$ overlap obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. Only statistical errors are shown. Horizontal lines are SFs for VMC and time-averaged mixed and GFMC overlaps, as described in the text.

Figure 2

Linear (a) and logarithmic (b) plots of VMC and time-averaged mixed and GFMC $s_{1/2}$$\langle$${}^3$H$|$${}^4$He$\rangle$ overlaps obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. Only statistical errors are shown. Also shown in (b) are a WS fit to the GFMC overlap and the asymptotic Whittaker function corresponding to the experimental separation energy. Superimposed in the linear plot is the sampling probability (arbitrary scale).

Figure 3

Imaginary time evolution of SFs in the $p_{3/2}$ channel of the $\langle$${}^6$He$\left(0^{+}\right)$$|$${}^7$Li$(3/2^{-})$$\rangle$ overlap obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. The GFMC wave functions originated from type I VMC wave functions. Only statistical errors are shown. Horizontal lines are SFs for VMC and time-averaged mixed and GFMC overlaps, as described in the text.

Figure 4

Linear (a) and logarithmic (b) plots of VMC and time-averaged mixed and GFMC $p_{3/2}$$\langle$${}^6$He$\left(0^{+}\right)$$|$${}^7$Li$(3/2^{-})$$\rangle$ overlaps obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. The GFMC wave functions originated from type I VMC wave functions. Only statistical errors are shown. Also shown are a WS fit to the GFMC overlap and the asymptotic Whittaker function corresponding to the experimental separation energy in the logarithmic plot.

Figure 5

The ratio $C\left(r\right)$ of VMC, GFMC, and fitted GFMC overlaps to asymptotic Whittaker functions. The WS fits and the Whittaker functions assume experimental core-valence separation energies. (a) $\langle$${}^3$H$|$${}^4$He$\rangle$ overlaps from Fig. 2; (b) $\langle$${}^6$He$\left(0^{+}\right)$$|$${}^7$Li$(3/2^{-})$$\rangle$ overlaps from Fig. 4.

Figure 6

Comparison of the $s_{1/2}$ and the $d_{3/2}$$\langle$${}^2$H$|$${}^3$H$\rangle$ (a), and the $s_{1/2}$ $\langle$${}^3$H$|$${}^4$He$\rangle$ (b) overlaps obtained for the $\mathrm{AV}18+\mathrm{UIX}$ potential within VMC, GFMC, and HH. Only statistical errors are shown on Monte Carlo overlaps.

Figure 7

VMC and GFMC $s_{1/2}$ and $d_{3/2}$$\langle$${}^2$H$|$${}^3$H$\rangle$ (a) and $s_{1/2}$$\langle$${}^3$H$|$${}^4$He$\rangle$ (b) overlaps obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. Only statistical errors are shown. Also shown are WS fits of GFMC overlaps.

Figure 8

VMC and GFMC $p_{1/2}$ (a) and $p_{3/2}$ (b) $\langle$${}^6$Li$\left(1^{+}\right)$$|$${}^7$Li$(3/2^{-})$$\rangle$ overlaps obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. Only statistical errors are shown. Also shown are WS fits of GFMC overlaps. Superimposed as dashed lines are the “density” functions ${(R\times r)}^2$.

Figure 9

VMC and GFMC $p_{3/2}$$\langle$${}^6$He$\left(0^{+}\right)$$|$${}^7$He$(3/2^{-})$$\rangle$ overlaps obtained for the $\mathrm{AV}18+\mathrm{IL}7$ potential. Only statistical errors are shown. Also shown is the irregular Coulomb function $G\left(r\right)/r$ for the experimental separation energy representing the scattering asymptotics at ${90}^{\circ }$ phase shift.