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:

where στ denotes spin and isospin degrees of freedom and
N_{στ} 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.

^{2}H(1+)Figure 1 Figure 2 Table |
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^{3}H(1/2+)Figure 1 Figure 2 Table |
^{3}He(1/2+)Figure 1 Figure 2 Table |
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^{4}He(0+)Figure 1 Figure 2 Table |
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^{6}He(0+)Figure 1 Figure 2 Table |
^{6}Li(1+)Figure 1 Figure 2 Table |
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^{7}Li(3/2-)Figure 1 Figure 2 Table |
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^{8}He(0+)Figure 1 Figure 2 Table |
^{8}Li(2+)Figure 1 Figure 2 Table |
^{8}Be(0+)Figure 1 Figure 2 Table |
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^{9}Li(3/2-)Figure 1 Figure 2 Table |
^{9}Be(3/2-)Figure 1 Figure 2 Table |
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^{10}Be(0+)Figure 1 Figure 2 Table |
^{10}B(3+)Figure 1 Figure 2 Table |
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^{11}B(3/2-)PRELIMINARY Figure 1 Figure 2 Table |
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^{12}C(0+)PRELIMINARY Figure 1 Figure 2 Table |

*Robert B. Wiringa
Last update Wed May 4, 2013
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