Single-Nucleon Densities

Now including Cluster VMC (CVMC) for 16O and 40Ca !!

Two-Nucleon Densities

This web page presents single-nucleon densities calculated for a variety of nuclei in the range A=2-10 with some preliminary results for A=11,12. Corresponding two-nucleon densities can be found here. These are from variational Monte Carlo calculations (VMC) using (unless otherwise noted) the Argonne v18 two-nucleon and Urbana X three-nucleon potentials (AV18+UX). (Urbana X is intermediate between the Urbana IX and Illinois-7 models; it has the form of UIX supplemented with a two-pion S-wave piece, while the strengths of its terms are taken from the IL7 model. It does NOT have the three-pion-ring term of IL7.)

These VMC wave functions are the starting trial functions for a number of recent Green's function Monte Carlo (GFMC) calculations:
Brida, et al., Phys. Rev. C 84, 024319 (2011);
McCutchan, et al., Phys. Rev. C 86, 024315 (2012);
Pastore, et al., Phys. Rev. C 87, 035503 (2013);
Pastore, et al., Phys. Rev. C 90, 024321 (2014).

More details of the wave function construction can be found in
Wiringa, Phys. Rev. C 43, 1585 (1991) for A=3,4;
Pudliner, et al., Phys. Rev. C 56, 1720 (1997) for A=6,7;
Wiringa, et al., Phys. Rev. C 62, 014001 (2000) for A=8;
Pieper, et al., Phys. Rev. C 70, 044310 (2002) for A=9,10.

The largest nuclei are evaluated using the cluster VMC (CVMC) method.

The CVMC method is described in
Pieper, et al., Phys. Rev. C 46, 1741 (1992) for A=16 with AV14+UVII
Lonardoni, et al., arXiv:1705.04337 for A=16,40 with AV18+UIX.

The results are generated as distributions for neutron spin-down, neutron spin-up, proton spin-down, and proton spin-up, for the M=J state. The densities are for the same wave functions used in generating the single-nucleon momentum distributions given here

Following are figures and files that tabulate the proton and neutron densities to give an overall view of their shapes. The normalization is chosen such that:

ANS = ∫ d3r ρNS(r)

where NS denotes proton or neutron, spin up or down, and ANS is the total number (out of A) nucleons with the given nucleon-spin projection. Where proton and neutron density distributions are the same, as in T=0 nuclei, we give only one set, and similarly, if spin-up and spin-down projections are the same, as in 0+ states, we give totals only.

2H(1+)
Figure 1
Figure 2
Table
3H(1/2+)
Figure 1
Figure 2
Table
3He(1/2+)
Figure 1
Figure 2
Table
4He(0+)

Figure 1
Figure 2
Table
4He(0+)
AV18
Figure 1
Figure 2
Table
5H(1/2+)
Figure 1
Figure 2
Table
6He(0+)
Figure 1
Figure 2
Table
6Li*(0+)
Figure 1
Figure 2
Table
6Be(0+)
Figure 1
Figure 2
Table
6Li(1+)
Figure 1
Figure 2
Table
7He(3/2-)
Figure 1
Figure 2
Table
7Li*(3/2-)
Figure 1
Figure 2
Table
7Be*(3/2-)
Figure 1
Figure 2
Table
7B(3/2-)
Figure 1
Figure 2
Table
7Li(3/2-)
Figure 1
Figure 2
Table
7Be(3/2-)
Figure 1
Figure 2
Table
8He(0+)

Figure 1
Figure 2
Table
8Li(2+)

Figure 1
Figure 2
Table
8Be(0+)

Figure 1
Figure 2
Table
8Be(0+)
AV18+UIX
Figure 1
Figure 2
Table
8B(2+)

Figure 1
Figure 2
Table
8C(0+)

Figure 1
Figure 2
Table
9Li(3/2-)
Figure 1
Figure 2
Table
9Be(3/2-)
Figure 1
Figure 2
Table
9C(3/2-)
Figure 1
Figure 2
Table
10Be(0+)
Figure 1
Figure 2
Table
10B(3+)
Figure 1
Figure 2
Table
10C(0+)
Figure 1
Figure 2
Table
11Li(3/2-)
Figure 1
Figure 2
Table
11B(3/2-)
Figure 1
Figure 2
Table
12Be(0+)
Figure 1
Figure 2
Table
12C(0+)

Figure 1
Figure 2
Table
12C(0+)
AV18+UIX
Figure 1
Figure 2
Table
16O(0+)
CVMC
AV18+UIX
Figure 1
Figure 2
Table
16O(0+)
CVMC
AV18
Figure 1
Figure 2
Table
40Ca(0+)
CVMC
AV18+UIX
Figure 1
Figure 2
Table
40Ca(0+)
CVMC
AV18
Figure 1
Figure 2
Table

Robert B. Wiringa
Last update May 16, 2017