# Single-Nucleon Densities

### Now including Cluster VMC (CVMC) for ^{16}O and ^{40}Ca !!

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:

A_{NS} =
∫ d^{3}r ρ_{NS}(r)
where NS denotes proton or neutron, spin up or down, and
A_{NS} 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.

*Robert B. Wiringa*

Last update May 16, 2017