VMC Wigner functions

This web page presents tables and figures of Wigner distributions W_NS(k,r) where NS denotes proton/neuton spin-up/down for a variety of nuclei in the range A=2-12. Some results are also given for W_NS(k_z,r_T) where the momentum k_z is in the z-direction, and r_T is in the transverse direction, i.e., r_T = √(r_x²+r_y²).

This is supplemental material for the paper
Tomography of Atomic Nuclei, N. Rocco, et al., arXiv:TBD

Results are shown for two Hamiltonians: Argonne v18 two-nucleon plus Urbana X three-nucleon (AV18+UX) interaction and the Norfolk chiral EFT NV2+3-Ia interaction.

Original density and momentum distribution results for AV18+UX were reported in:
Wiringa, et al., Phys. Rev. C 89, 024305 (2014).

Density and momentum distribution results with Norfolk chiral EFT interactions are reported in:
Piarulli, et al., Phys. Rev C 107, 014314 (2023).

These VMC wave functions are the starting trial functions for a number of 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 normalization of W_NS(k,r) is chosen such that

²H

³He

⁴He

⁶He

⁶Li

⁷Li

⁸He

⁹Be

¹⁰B

¹¹B

¹²C

Robert B. Wiringa
Last update June 2, 2026