This web page presents singlenucleon densities calculated for a variety of nuclei in the range A=210 with some preliminary results for A=11,12. These are from variational Monte Carlo calculations (VMC) using the Argonne v18 twonucleon and Urbana X threenucleon potentials (AV18+UX). (Urbana X is intermediate between the Urbana IX and Illinois7 models; it has the form of UIX supplemented with a twopion Swave piece, while the strengths of its terms are taken from the IL7 model. It does NOT have the threepionring 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 spindown, neutron spinup, proton spindown, and proton spinup, for the M=J state. The densities are for the same wave functions used in generating the singlenucleon 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:
where στ denotes spin and isospin degrees of freedom and N_{στ} is the total number (out of A) nucleons with the given spinisospin projection. Where proton and neutron momentum distributions are the same, as in T=0 nuclei, we give only one set, and similarly, if spinup and spindown projections are the same, as in 0+ states, we give totals only.
^{2}H(1+) Figure 1 Figure 2 Table 

^{3}H(1/2+) Figure 1 Figure 2 Table 
^{3}He(1/2+) Figure 1 Figure 2 Table 

^{4}He(0+) Figure 1 Figure 2 Table 

^{6}He(0+) Figure 1 Figure 2 Table 
^{6}Li(1+) Figure 1 Figure 2 Table 
^{6}Be(0+) Figure 1 Figure 2 Table 

^{7}Li(3/2) Figure 1 Figure 2 Table 

^{8}He(0+) Figure 1 Figure 2 Table 
^{8}Li(2+) Figure 1 Figure 2 Table 
^{8}Be(0+) Figure 1 Figure 2 Table 
^{8}B(2+) Figure 1 Figure 2 Table 
^{8}C(0+) Figure 1 Figure 2 Table 

^{9}Li(3/2) Figure 1 Figure 2 Table 
^{9}Be(3/2) Figure 1 Figure 2 Table 
^{9}C(3/2) Figure 1 Figure 2 Table 

^{10}Be(0+) Figure 1 Figure 2 Table 
^{10}B(3+) Figure 1 Figure 2 Table 
^{10}C(0+) Figure 1 Figure 2 Table 

^{11}B(3/2) PRELIMINARY Figure 1 Figure 2 Table 

^{12}C(0+) PRELIMINARY Figure 1 Figure 2 Table 
Robert B. Wiringa
Last update Wed Sep 29, 2014