Single-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. These are from variational Monte Carlo calculations (VMC) using 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).

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 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 elsewhere on this site.

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:

Nστ = ∫ d3r ρστ(r)

where στ denotes spin and isospin degrees of freedom and Nστ is the total number (out of A) nucleons with the given spin-isospin projection. Where proton and neutron momentum 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
6He(0+)
Figure 1
Figure 2
Table
6Li(1+)
Figure 1
Figure 2
Table
6Be(0+)
Figure 1
Figure 2
Table
7Li(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
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
10Be(0+)
Figure 1
Figure 2
Table
10B(3+)
Figure 1
Figure 2
Table
11B(3/2-)
PRELIMINARY
Figure 1
Figure 2
Table
12C(0+)
PRELIMINARY
Figure 1
Figure 2
Table

Robert B. Wiringa
Last update Wed May 4, 2013