# Single-Nucleon Momentum Distributions

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

This web page presents single-nucleon momentum distributions calculated for
a variety of nuclei in the range A=2-12 as discussed in
Wiringa, Schiavilla, Pieper, and Carlson:
Phys. Rev. C 89, 024305 (2014) (or
arXiv:1309.3794).
Corresponding two-nucleon momentum distributions can be found
here.
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);

Datar, *et al.*, Phys. Rev. Lett. **111**, 062502 (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 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 single-nucleon densities corresponding to
these wave functions are given here

### Spin-polarized nucleon momentum distributions as functions of k

Following are files that tabulate the proton and neutron momentum distributions
along with figures to give an overall view of the distributions.
The normalization is chosen such that:

A_{NS} =
1/(2π)^{3} ∫ d^{3}k ρ_{NS}(k)
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 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.
The kinetic energy from these distributions is also given.

--- NEW! ---

We now include (in many cases) the number of nucleons with momenta
k ≥ 2 fm^{-1} and their contribution to the kinetic energy.
This is the momentum where there is a significant change of
slope and is an approximate definition of the Fermi surface in these
finite nuclei.

--- NEW! ---

*Robert B. Wiringa*

Last update December 21, 2016