Two-Nucleon Momentum Distributions

This web page presents two-nucleon momentum distributions calculated for various light nuclei in the range A=3-12 as discussed in Wiringa, Schiavilla, Pieper, and Carlson: Phys. Rev. C 89, 024305 (2014) (or arXiv:1309.3794). Corresponding single-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.

Some of the results are distributions for relative pair momenta q = (k1-k2)/2 projected into total pair spin S=0 or 1 and isospin T=0 or 1. Other results are generated as a function of both q and total pair momentum Q = (k1+k2) projected into pp, np, and nn pairs.. 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).

ST Pair momentum distributions as functions of q

Following are files for various nuclei tabulating and illustrating the ST-projected pair momentum distributions ρST(q) as a function of the relative momentum q = (k1-k2)/2 between pairs. The normalization of these distributions is given by

NST = 1/(2π)3 ∫ d3q ρST(q)

where NST is the total number of pairs with total spin S=0 or 1 and T=0 or 1.

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

NN Pair momentum distributions as functions of q

Alternatively, we can project NN pair momentum distributions ρNN(q), i.e., as pp, pn, and nn pairs, again as function of the relative momentum q = (k1-k2)/2 between pairs.
4He(0+)
Figure
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6He(0+)
Figure
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6Li(1+)
Figure
Table
8He(0+)
Figure
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8Be(0+)
Figure
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10B(3+)
Figure
Table
12C(0+)
PRELIMINARY
Figure
Table

NN Pair momentum distributions as functions of Q

NN pair momentum distributions can also be computed as a function of of the total center-of-mass pair momentum Q = (k1+k2).
3He(1/2+)
Figure
Table
4He(0+)
Figure
Table
6He(0+)
Figure
Table
6Li(1+)
Figure
Table
8He(0+)
Figure
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8Be(0+)
Figure
Table
12C(0+)
PRELIMINARY
Figure
Table

Pair momentum distribution functions of both q and Q

3He(1/2+)

Following are files for 3He with tabulations of the pn and pp momentum distributions along with figures to give an overall view of the distributions. Each file is for a given total Q = (k1+k2) and contains a tabulaton of ρpN(q,Q) as a function of relative q = (k1-k2)/2 The normalization is chosen such that:

ρpN(Q) = 1/(2π)3 ∫ d3q ρpN(q,Q)

and the integrals up to 5 fm-1 in q are given at the top of the file. The total normalization is:

NpN = 1/(2π)3 ∫ d3Q ρpN(Q)

where NpN is the total number of pN pairs in the nucleus.

Q = 0.00 fm-1
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Q = 0.25 fm-1
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Q = 0.50 fm-1
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Q = 0.75 fm-1
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Q = 1.00 fm-1
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Q = 1.25 fm-1
Figure
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4He(0+)

Following are files for 4He with tabulations of the pn and pp momentum distributions along with figures to give an overall view of the distributions. Normalizations as given above.

Q = 0.00 fm-1
Figure
Table
Q = 0.25 fm-1
Figure
Table
Q = 0.50 fm-1
Figure
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Q = 0.75 fm-1
Figure
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Q = 1.00 fm-1
Figure
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Q = 1.25 fm-1
Figure
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Q = 1.50 fm-1
Figure
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Q = 1.75 fm-1
Figure
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Q = 2.00 fm-1
Figure
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Q = 0.05 fm-1
Figure
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Q = 0.30 fm-1
Figure
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Q = 0.55 fm-1
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Q = 0.10 fm-1
Figure
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Q = 0.35 fm-1
Figure
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Q = 0.60 fm-1
Figure
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Q = 0.15 fm-1
Figure
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Q = 0.40 fm-1
Figure
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Q = 0.65 fm-1
Figure
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Q = 0.20 fm-1
Figure
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Q = 0.45 fm-1
Figure
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Q = 0.70 fm-1
Figure
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6Li(1+)

Following are files for 6Li with tabulations of the pn and pp momentum distributions along with figures to give an overall view of the distributions. Normalizations as given above.

Q = 0.00 fm-1
Figure
Table

7Li(3/2-)

Following are files for 7Li with tabulations of the pn and pp momentum distributions along with figures to give an overall view of the distributions. Normalizations as given above.

Q = 0.00 fm-1
Figure
Table

8Be(0+)

Following are files for 8Be with tabulations of the pn and pp momentum distributions along with figures to give an overall view of the distributions. Normalizations as given above.

Q = 0.00 fm-1
Figure
Table

10B(3+)

Following are files for 10B with tabulations of the pn and pp momentum distributions along with figures to give an overall view of the distributions. Normalizations as given above.

Q = 0.00 fm-1
Figure
Table

Robert B. Wiringa
Last update Mon Feb 10, 2014