This web page presents two-nucleon densities calculated for a variety of nuclei in the range A=2-10 with some preliminary results for A=11,12. Corresponding single-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 AV1
4+UVII

Lonardoni, *et al.*, arXiv:1705.04337 for A=16,40 with AV18+UIX.

The results are generated as distributions for proton-proton, neutron-proton and neutron-neutron (where different). The densities are for the same wave functions used in generating the two-nucleon momentum distributions given here.

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

NZ = ∫ d

N(N-1)/2 = ∫ d

Where pp and nn densities are the same, as in T=0 nuclei, we give only one set.

^{2}H(1+)Figure Table |
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^{3}H(1/2+)Figure Table |
^{3}He(1/2+)Figure Table |
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^{4}He(0+)Figure Table |
^{4}He(0+)AV18 Figure Table |
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^{5}H(1/2+)Figure Table |
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^{6}He(0+)Figure Table |
^{6}Li(1+)Figure Table |
^{6}Be(0+)Figure Table |
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^{7}Li(3/2-)Figure Table |
^{7}Be(3/2-)Figure Table |
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^{8}He(0+)Figure Table |
^{8}Li(2+)Figure Table |
^{8}Be(0+)Figure Table |
^{8}B(2+)Figure Table |
^{8}C(0+)Figure Table |
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^{9}Li(3/2-)Figure Table |
^{9}Be(3/2-)Figure Table |
^{9}C(3/2-)Figure Table |
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^{10}Be(0+)updated Figure Table |
^{10}B(3+)updated Figure Table |
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^{11}Li(3/2-)Figure Table |
^{11}B(3/2-)updated 02-Aug-18 Figure Table |
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^{12}Be(0+)updated 18-Aug-18 Figure Table |
^{12}C(0+)updated 02-Jun-18 Figure Table |
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^{16}O(0+)CVMC AV18+UIX Figure Table |
^{16}O(0+)CVMC AV18 Figure Table |
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^{40}Ca(0+)CVMC AV18+UIX Figure Table |
^{40}Ca(0+)CVMC AV18 Figure Table |

*Robert B. Wiringa
Last update Aug 20, 2018
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