Single-Nucleon Momentum Distributions

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).

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 elsewhere on this site. The momentum calculations are based on the method discussed in:
Schiavilla et al., Nucl. Phys. A449, 219 (1986);
with algorithmic improvements given in:
Schiavilla et al., Phys. Rev. Lett. 98, 132501 (2007).

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:

Nστ = 1/(2π)3 ∫ d3k ρστ(k)

where στ denotes spin and isospin degrees of freedom and Nστ 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.
2H(1+)
Figure

Table
3H(1/2+)
Figure 1
Figure 2
Figure 3
Table
Table (dn)
3He(1/2+)
Figure 1
Figure 2
Figure 3
Table
Table (dp)
4He(0+)
Figure 1
Figure 2
Table
Table (tp+dd)
6He(0+)
Figure 1
Figure 2


Table
6Li(1+)
Figure 1
Figure 2
Figure 3
Table
Table (αd)
6Li(3+)
Figure 1
Figure 2
Figure 3
Table
Table (αd)
7Li(3/2-)
Figure 1
Figure 2
Figure 3
Table
Table (αt)
7Li(1/2-)
Figure 1
Figure 2
Figure 3
Table
Table (αt)
7Li(7/2-)
Figure 1
Figure 2
Figure 3
Table
Table (αt)
7Li(5/2-)
Figure 1
Figure 2
Figure 3
Table
Table (αt)
8He(0+)
Figure 1
Figure 2

Table
8Li(2+)
Figure 1
Figure 2

Table
8Be(0+)
Figure 1
Figure 2
Table
Table (αα)
8Be(2+)
Figure 1
Figure 2
Table
Table (αα)
8Be(4+)
Figure 1
Figure 2
Table
Table (αα)
9Li(3/2-)
Figure 1
Figure 2
Table
9Be(3/2-)
Figure 1
Figure 2
Table
10Be(0+)
Figure 1
Figure 2
Table
10B(3+)
Figure 1
Figure 2
Table
11B(3/2-)
PRELIMINARY
Figure

Table
12C(0+)
PRELIMINARY
Figure

Table

Robert B. Wiringa
Last update Mon Feb 10, 2014