Properties of trapped neutrons interacting with realistic nuclear Hamiltonians

We calculate properties of neutron drops in external potentials using both quantum Monte Carlo and no-core full configuration techniques. The properties of the external wells are varied to examine different density profiles. We compare neutron drop results given by a selection of nuclear Hamiltonians, including realistic two-body interactions as well as several three-body forces. We compute a range of properties for the neutron drops: ground-state energies, spin-orbit splittings, excitation energies, radial densities and rms radii. We compare the equations of state for neutron matter for several of these Hamiltonians. Our results can be used as benchmarks to test other many-body techniques and to constrain properties of energy-density functionals.

Figure 1

Contours of VMC energies for 12 neutrons in a 10-MeV HO well with $\mathrm{AV}{8}^{\prime }+\mathrm{UIX}$ versus the 0$d$ and 1$s$ coefficients in the BCS wave function. The dots show the cases that were computed using GFMC.

Figure 2

Ground-state energy for 10 neutrons in a HO well of (a) 10 MeV and (b) 20 MeV for a series of finite basis space calculations with JISP16. Note that our results in the 20-MeV well converge much more rapidly than in the 10-MeV well. The symbols represent extrapolated results as discussed in the text and the error bars signify our uncertainty estimate at that basis space $\hslash \omega$; the yellow band represents our final result including numerical error estimates.

Figure 3

The rms radius [left, (a) and (b)] and internal energy [right, (c) and (d)] for 10 neutrons in a HO well of 10 MeV [top, (a) and (c)] and 20 MeV [bottom, (b) and (d)] for a series of finite basis space calculations with JISP16. Note that our results in the 20-MeV well converge much more rapidly than in the 10-MeV well. The yellow band represents our best estimate (including an error estimate) for the infinite basis space result.

Figure 4

Energy of the lowest neutron drop states confined in a HO well with (a) $\hslash \Omega =10$ MeV and (b) $\hslash \Omega =20$ MeV as a function of the number of neutrons. Results for AV8${}^{\prime }$ (plus TNI) were obtained using AFDMC, with MC statistical error bars as well as a band indicating the 1$\%$ systematic uncertainty discussed in Sec. 3d; results for JISP16 are obtained from NCFC with error bars reflecting the total numerical uncertainty, and strict upper bounds obtained with NCSM in finite basis spaces. Note the pronounced dips at the expected HO magic numbers $N=2$, 8, and 20.

Figure 5

Single-energy differences in a (a) 10-MeV and (b) 20-MeV HO well. Results of different Hamiltonians are compared. AFDMC and GFMC error bars are statistical only; NCFC error bars reflect the total numerical uncertainty. Horizontal line segments indicate energy differences expected from pure HO energies.

Figure 6

Double energy differences $\Delta \left(N\right)={(-1)}^{N+1}\{E\left(N\right)-\frac{1}{2}\left[E(N-1)+E(N+1)\right]\}$ in a (a) 10-MeV and (b) 20-MeV HO well. Results of different Hamiltonians are compared. AFDMC and GFMC error bars are statistical only; the NCFC error bars are omitted for the 10-MeV HO well, because they would cover the entire vertical range for 12 neutrons and above, though a significant part of the NCFC numerical error is systematic, and cancels between neighboring neutron drops. For completeness, we did include the total numerical uncertainty for the NCFC results in panel (b).

Figure 7

Spin-orbit splitting in (a) the $p$ shell and level splittings in (b) the $sd$ shell and as a function of external field strength. Results of different Hamiltonians are compared. (Inset) Blowup of the $s_{\frac{1}{2}}$ and $d_{\frac{5}{2}}$ levels for the 5- and 10-MeV HO wells.

Figure 8

Internal energy for up to 14 neutrons in a HO trap with $\mathrm{AV}{8}^{\prime }+\mathrm{UIX}$ and with JISP16. For details, see Table .

Figure 9

Radii for the lowest $J$ states up to 14 neutrons in a HO trap with $\mathrm{AV}{8}^{\prime }+\mathrm{UIX}$ and with JISP16. For details see Table .

Figure 10

Radial density distributions for (a) 8 neutrons and (b) 14 neutrons in different HO traps with JISP16 and with $\mathrm{AV}{8}^{\prime }+\mathrm{UIX}$.

Figure 11

Equation of state of neutron matter as a function of the density for different Hamiltonians.