VMC Spectroscopic Overlaps

Part I: Pickup Reactions

Part II: Stripping Reactions

Older VMC Spectroscopic Overlaps

GFMC Spectroscopic Overlaps

This web page presents recent spectroscopic overlaps calculated for a variety of nuclei in the range A=3-12. Corresponding one-nucleon densities 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) or the Norfolk Δ-full chiral effective field theory interactions NV2+3-Ia, -Ia*, and -IIb*.

A number of these results have served as input to papers on specific reactions, including:
Mecca, et al., Phys. Lett. B 798, 134989 (2019);
Crespo, et al., Phys. Lett. B 803, 135355 (2020);
Cravo, et al., Phys. Lett. B 859, 139087 (2024).

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.

An excellent overall review of quantum Monte Carlo methods for nuclei can be found at:
Carlson, et al., Rev. Mod. Phys. 87, 1067 (2015)

The Norfolk interactions are described and used in the following papers:
Piarulli, et al., Phys. Rev. C 94, 054007 (2016).
Piarulli, et al., Phys. Rev. Lett. 120, 052503 (2018).
Baroni, et al., Phys. Rev. C 98, 044003 (2018).
Schiavilla, et al., Phys. Rev. C 99, 034005 (2019).

Following are figures and tabulations of the single-nucleon r-space amplitudes A(r) (in fm^-3/2) and the integrated spectroscopic factors with the normalization:

Momentum-space amplitudes are available upon request.

In the following, states are designated by ^AZ(J^π;T) except the T is omitted for states of the lowest isospin available to that nucleus. Second excited states of the same quantum numbers are denoted by ^AZ(J^π₂;T).

3H(1/2+)-> AV18+UX 2H(1+)+n Figure 2H(1+)+n Table	3H(1/2+)-> NV2+3-Ia 2H(1+)+n Figure 2H(1+)+n Table	3He(1/2+)-> AV18+UX 2H(1+)+p Figure 2H(1+)+p Table	3He(1/2+)-> NV2+3-Ia 2H(1+)+p Figure 2H(1+)+p Table
	4He(0+)-> AV18+UX 3H(1/2+)+p Figure 3H(1/2+)+p Table 3He(1/2+)+n Figure 3He(1/2+)+n Table	4He(0+)-> NV2+3-Ia 3H(1/2+)+p Figure 3H(1/2+)+p Table 3He(1/2+)+n Figure 3He(1/2+)+n Table	4He(0+)-> NV2+3-Ia* 3H(1/2+)+p Figure 3H(1/2+)+p Table 3He(1/2+)+n Figure 3He(1/2+)+n Table	4He(0+)-> NV2+3-IIb* 3H(1/2+)+p Figure 3H(1/2+)+p Table 3He(1/2+)+n Figure 3He(1/2+)+n Table
	6He(0+)-> AV18+UX 5H+p Summary 5H(1/2+)+p Figure 5H(1/2+)+p Table 5H(5/2+)+p Figure 5H(5/2+)+p Table 5H(3/2+)+p Figure 5H(3/2+)+p Table 5He+n Summary 5He(3/2-)+n Figure 5He(3/2-)+n Table 5He(1/2-)+n Figure 5He(1/2-)+n Table	6Li(1+)-> AV18+UX 5He+p Summary 5He(3/2-)+p Figure 5He(3/2-)+p Table 5He(1/2-)+p Figure 5He(1/2-)+p Table
	7He(3/2-) -> AV18+UX 6He(0+)+n Figure 6He(0+)+n Table 6He(2+)+n Figure 6He(2+)+n Table	7Li(3/2-;3/2) -> AV18+UX 6He(0+)+p Figure 6He(0+)+p Table 6Li(0+;1)+n Figure 6Li(0+;1)+n Table	7Be(3/2-;3/2) -> AV18+UX 6Li(0+;1)+p Figure 6Li(0+;1)+p Table 6Be(0+)+n Figure 6Be(0+)+n Table	7B(3/2-) -> AV18+UX 6Be(0+)+p Figure 6Be(0+)+p Table 6Be(2+)+p Figure 6Be(2+)+p Table
		7Li(3/2-) -> AV18+UX 6He+p Summary 6He(0+)+p Figure 6He(0+)+p Table 6He(2+)+p Figure 6He(2+)+p Table 6Li+n Summary 6Li(1+)+n Figure 6Li(1+)+n Table 6Li(3+)+n Figure 6Li(3+)+n Table 6Li(0+;1)+n Figure 6Li(0+;1)+n Table	7Li(3/2-) -> NV2+3-Ia 6He+p Summary 6He(0+)+p Figure 6He(0+)+p Table 6He(2+)+p Figure 6He(2+)+p Table 6Li+n Summary 6Li(1+)+n Figure 6Li(1+)+n Table 6Li(3+)+n Figure 6Li(3+)+n Table 6Li(0+;1)+n Figure 6Li(0+;1)+n Table	7Li(3/2-) -> NV2+3-Ia* 6He+p Summary 6He(0+)+p Figure 6He(0+)+p Table 6He(2+)+p Figure 6He(2+)+p Table 6Li+n Summary 6Li(1+)+n Figure 6Li(1+)+n Table 6Li(3+)+n Figure 6Li(3+)+n Table 6Li(0+;1)+n Figure 6Li(0+;1)+n Table	7Li(3/2-) -> NV2+3-IIb* 6He+p Summary 6He(0+)+p Figure 6He(0+)+p Table 6He(2+)+p Figure 6He(2+)+p Table 6Li+n Summary 6Li(1+)+n Figure 6Li(1+)+n Table 6Li(3+)+n Figure 6Li(3+)+n Table 6Li(0+;1)+n Figure 6Li(0+;1)+n Table	7Be(3/2-) -> AV18+UX 6Be+n Summary 6Be(0+)+n Figure 6Be(0+)+n Table 6Be(2+)+n Figure 6Be(2+)+n Table 6Li+p Summary 6Li(1+)+p Figure 6Li(1+)+p Table 6Li(3+)+p Figure 6Li(3+)+p Table 6Li(0+;1)+p Figure 6Li(0+;1)+p Table	7Be(3/2-) -> NV2+3-Ia 6Be+n Summary 6Be(0+)+n Figure 6Be(0+)+n Table 6Be(2+)+n Figure 6Be(2+)+n Table 6Li+p Summary 6Li(1+)+p Figure 6Li(1+)+p Table 6Li(3+)+p Figure 6Li(3+)+p Table 6Li(0+;1)+p Figure 6Li(0+;1)+p Table
	8He(0+)-> AV18+UX 7He+n Summary 7He(3/2-)+n Figure 7He(3/2-)+n Table 7He(1/2-)+n Figure 7He(1/2-)+n Table	8Li(2+)-> AV18+UX 7He+p Summary 7He(3/2-)+p Figure 7He(3/2-)+p Table 7He(5/2-)+p Figure 7He(5/2-)+p Table	8Li(2+)-> NV2+3-Ia 7He+p Summary 7He(3/2-)+p Figure 7He(3/2-)+p Table 7He(5/2-)+p Figure 7He(5/2-)+p Table	8Li(2+)-> NV2+3-Ia* 7He+p Summary 7He(3/2-)+p Figure 7He(3/2-)+p Table 7He(5/2-)+p Figure 7He(5/2-)+p Table	8Li(2+)-> NV2+3-IIb* 7He+p Summary 7He(3/2-)+p Figure 7He(3/2-)+p Table 7He(5/2-)+p Figure 7He(5/2-)+p Table
		8Li(2+)-> AV18+UX 7Li+n Summary 7Li(3/2-)+n Figure 7Li(3/2-)+n Table 7Li(1/2-)+n Figure 7Li(1/2-)+n Table 7Li(7/2-)+n Figure 7Li(7/2-)+n Table 7Li(5/2-)+n Figure 7Li(5/2-)+n Table 7Li(5/2-2)+n Figure 7Li(5/2-2)+n Table 7Li(7/2-2)+n Figure 7Li(7/2-2)+n Table	8Li(2+)-> NV2+3-Ia 7Li+n Summary 7Li(3/2-)+n Figure 7Li(3/2-)+n Table 7Li(1/2-)+n Figure 7Li(1/2-)+n Table 7Li(7/2-)+n Figure 7Li(7/2-)+n Table 7Li(5/2-)+n Figure 7Li(5/2-)+n Table 7Li(5/2-2)+n Figure 7Li(5/2-2)+n Table 7Li(7/2-2)+n Figure 7Li(7/2-2)+n Table	8Li(2+)-> NV2+3-Ia* 7Li+n Summary 7Li(3/2-)+n Figure 7Li(3/2-)+n Table 7Li(1/2-)+n Figure 7Li(1/2-)+n Table 7Li(7/2-)+n Figure 7Li(7/2-)+n Table 7Li(5/2-)+n Figure 7Li(5/2-)+n Table 7Li(5/2-2)+n Figure 7Li(5/2-2)+n Table 7Li(7/2-2)+n Figure 7Li(7/2-2)+n Table	8Li(2+)-> NV2+3-IIb* 7Li+n Summary 7Li(3/2-)+n Figure 7Li(3/2-)+n Table 7Li(1/2-)+n Figure 7Li(1/2-)+n Table 7Li(7/2-)+n Figure 7Li(7/2-)+n Table 7Li(5/2-)+n Figure 7Li(5/2-)+n Table 7Li(5/2-2)+n Figure 7Li(5/2-2)+n Table 7Li(7/2-2)+n Figure 7Li(7/2-2)+n Table	8B(2+)-> AV18+UX 7Be+p Summary 7Be(3/2-)+p Figure 7Be(3/2-)+p Table 7Be(1/2-)+p Figure 7Be(1/2-)+p Table 7Be(7/2-)+p Figure 7Be(7/2-)+p Table 7Be(5/2-)+p Figure 7Be(5/2-)+p Table 7Be(5/2-2)+p Figure 7Be(5/2-2)+p Table 7Be(7/2-2)+p Figure 7Be(7/2-2)+p Table	8B(2+)-> NV2+3-Ia 7Be+p Summary 7Be(3/2-)+p Figure 7Be(3/2-)+p Table 7Be(1/2-)+p Figure 7Be(1/2-)+p Table 7Be(7/2-)+p Figure 7Be(7/2-)+p Table 7Be(5/2-)+p Figure 7Be(5/2-)+p Table 7Be(5/2-2)+p Figure 7Be(5/2-2)+p Table 7Be(7/2-2)+p Figure 7Be(7/2-2)+p Table
		9Li(3/2-) -> AV18+UX 8He+p Summary 8He(0+)+p Figure 8He(0+)+p Table 8He(2+)+p Figure 8He(2+)+p Table 8Li+n Summary 8Li(2+)+n Figure 8Li(2+)+n Table 8Li(1+)+n Figure 8Li(1+)+n Table 8Li(3+)+n Figure 8Li(3+)+n Table	9Li(3/2-) -> NV2+3-Ia 8He+p Summary 8He(0+)+p Figure 8He(0+)+p Table 8He(2+)+p Figure 8He(2+)+p Table 8Li+n Summary 8Li(2+)+n Figure 8Li(2+)+n Table 8Li(1+)+n Figure 8Li(1+)+n Table 8Li(3+)+n Figure 8Li(3+)+n Table	9Li(3/2-) -> NV2+3-Ia* 8He+p Summary 8He(0+)+p Figure 8He(0+)+p Table 8He(2+)+p Figure 8He(2+)+p Table 8Li+n Summary 8Li(2+)+n Figure 8Li(2+)+n Table 8Li(1+)+n Figure 8Li(1+)+n Table 8Li(3+)+n Figure 8Li(3+)+n Table	9Li(3/2-) -> NV2+3-IIb* 8He+p Summary 8He(0+)+p Figure 8He(0+)+p Table 8He(2+)+p Figure 8He(2+)+p Table 8Li+n Summary 8Li(2+)+n Figure 8Li(2+)+n Table 8Li(1+)+n Figure 8Li(1+)+n Table 8Li(3+)+n Figure 8Li(3+)+n Table	9C(3/2-) -> AV18+UX 8C+n Summary 8C(0+)+n Figure 8C(0+)+n Table 8C(2+)+n Figure 8C(2+)+n Table 8B+p Summary 8B(2+)+p Figure 8B(2+)+p Table 8B(1+)+p Figure 8B(1+)+p Table 8B(3+)+p Figure 8B(3+)+p Table 8B*(0+;2)+p Figure 8B*(0+;2)+p Table	9C(3/2-) -> NV2+3-Ia 8C+n Summary 8C(0+)+n Figure 8C(0+)+n Table 8C(2+)+n Figure 8C(2+)+n Table 8B+p Summary 8B(2+)+p Figure 8B(2+)+p Table 8B(1+)+p Figure 8B(1+)+p Table 8B(3+)+p Figure 8B(3+)+p Table 8B*(0+;2)+p Figure 8B*(0+;2)+p Table
			9Be(3/2-) -> AV18+UX 8Li+p Summary 8Li(2+)+p Figure 8Li(2+)+p Table 8Li(1+)+p Figure 8Li(1+)+p Table 8Li(3+)+p Figure 8Li(3+)+p Table 8Be+n Summary 8Be(0+)+n Figure 8Be(0+)+n Table 8Be(2+)+n Figure 8Be(2+)+n Table 8Be(2+2)+n Figure 8Be(2+2)+n Table	9Be(3/2-) -> NV2+3-Ia 8Li+p Summary 8Li(2+)+p Figure 8Li(2+)+p Table 8Li(1+)+p Figure 8Li(1+)+p Table 8Li(3+)+p Figure 8Li(3+)+p Table 8Be+n Summary 8Be(0+)+n Figure 8Be(0+)+n Table 8Be(2+)+n Figure 8Be(2+)+n Table 8Be(2+2)+n Figure 8Be(2+2)+n Table	9Be(3/2-) -> NV2+3-Ia* 8Li+p Summary 8Li(2+)+p Figure 8Li(2+)+p Table 8Li(1+)+p Figure 8Li(1+)+p Table 8Li(3+)+p Figure 8Li(3+)+p Table 8Be+n Summary 8Be(0+)+n Figure 8Be(0+)+n Table 8Be(2+)+n Figure 8Be(2+)+n Table 8Be(2+2)+n Figure 8Be(2+2)+n Table	9Be(3/2-) -> NV2+3-IIb* 8Li+p Summary 8Li(2+)+p Figure 8Li(2+)+p Table 8Li(1+)+p Figure 8Li(1+)+p Table 8Li(3+)+p Figure 8Li(3+)+p Table 8Be+n Summary 8Be(0+)+n Figure 8Be(0+)+n Table 8Be(2+)+n Figure 8Be(2+)+n Table 8Be(2+2)+n Figure 8Be(2+2)+n Table
			10Be(0+) -> AV18+UX 9Li+p Summary 9Li(3/2-)+p Figure 9Li(3/2-)+p Table 9Li(1/2-)+p Figure 9Li(1/2-)+p Table 9Be+n Summary 9Be(3/2-)+n Figure 9Be(3/2-)+n Table 9Be(1/2-)+n Figure 9Be(1/2-)+n Table	10Be(0+) -> NV2+3-Ia 9Li+p Summary 9Li(3/2-)+p Figure 9Li(3/2-)+p Table 9Li(1/2-)+p Figure 9Li(1/2-)+p Table 9Be+n Summary 9Be(3/2-)+n Figure 9Be(3/2-)+n Table 9Be(1/2-)+n Figure 9Be(1/2-)+n Table	10Be(0+) -> NV2+3-Ia* 9Li+p Summary 9Li(3/2-)+p Figure 9Li(3/2-)+p Table 9Li(1/2-)+p Figure 9Li(1/2-)+p Table 9Be+n Summary 9Be(3/2-)+n Figure 9Be(3/2-)+n Table 9Be(1/2-)+n Figure 9Be(1/2-)+n Table	10Be(0+) -> NV2+3-IIb* 9Li+p Summary 9Li(3/2-)+p Figure 9Li(3/2-)+p Table 9Li(1/2-)+p Figure 9Li(1/2-)+p Table 9Be+n Summary 9Be(3/2-)+n Figure 9Be(3/2-)+n Table 9Be(1/2-)+n Figure 9Be(1/2-)+n Table	10C(0+) -> AV18+UX 9C+n Summary 9C(3/2-)+n Figure 9C(3/2-)+n Table 9C(1/2-)+n Figure 9C(1/2-)+n Table	10C(0+) -> NV2+3-Ia 9C+n Summary 9C(3/2-)+n Figure 9C(3/2-)+n Table 9C(1/2-)+n Figure 9C(1/2-)+n Table
				10B(3+) -> AV18+UX 9Be+p Summary 9Be(3/2-)+p Figure 9Be(3/2-)+p Table 9Be(5/2-)+p Figure 9Be(5/2-)+p Table	10B(3+) -> NV2+3-Ia 9Be+p Summary 9Be(3/2-)+p Figure 9Be(3/2-)+p Table 9Be(5/2-)+p Figure 9Be(5/2-)+p Table	10B(3+) -> NV2+3-Ia* 9Be+p Summary 9Be(3/2-)+p Figure 9Be(3/2-)+p Table 9Be(5/2-)+p Figure 9Be(5/2-)+p Table	10B(3+) -> NV2+3-IIb* 9Be+p Summary 9Be(3/2-)+p Figure 9Be(3/2-)+p Table 9Be(5/2-)+p Figure 9Be(5/2-)+p Table
				11B(3/2-) -> AV18+UX 10Be+p Summary 10Be(0+)+p Figure 10Be(0+)+p Table 10Be(2+)+p Figure 10Be(2+)+p Table 10Be(2+2)+p Figure 10Be(2+2)+p Table 10B+n Summary 10B(3+)+n Figure 10B(3+)+n Table 10B(1+)+n Figure 10B(1+)+n Table 10B*(0+;1)+n Figure 10B*(0+;1)+n Table 10B(1+2)+n Figure 10B(1+2)+n Table	11B(3/2-) -> NV2+3-Ia 10Be+p Summary 10Be(0+)+p Figure 10Be(0+)+p Table 10Be(2+)+p Figure 10Be(2+)+p Table 10Be(2+2)+p Figure 10Be(2+2)+p Table 10B+n Summary 10B(3+)+n Figure 10B(3+)+n Table 10B(1+)+n Figure 10B(1+)+n Table 10B*(0+;1)+n Figure 10B*(0+;1)+n Table 10B(1+2)+n Figure 10B(1+2)+n Table	11C(3/2-) -> AV18+UX 10C+n Summary 10C(0+)+n Figure 10C(0+)+n Table 10C(2+)+n Figure 10C(2+)+n Table 10C(2+2)+n Figure 10C(2+2)+n Table 10B+p Summary 10B(3+)+p Figure 10B(3+)+p Table 10B(1+)+p Figure 10B(1+)+p Table 10B*(0+;1)+p Figure 10B*(0+;1)+p Table 10B(1+2)+p Figure 10B(1+2)+p Table	11C(3/2-) -> NV2+3-Ia 10C+n Summary 10C(0+)+n Figure 10C(0+)+n Table 10C(2+)+n Figure 10C(2+)+n Table 10C(2+2)+n Figure 10C(2+2)+n Table 10B+p Summary 10B(3+)+p Figure 10B(3+)+p Table 10B(1+)+p Figure 10B(1+)+p Table 10B*(0+;1)+p Figure 10B*(0+;1)+p Table 10B(1+2)+p Figure 10B(1+2)+p Table
			12Be(0+) -> AV18+UX 11Be+n Summary 11Be(1/2-)+n Figure 11Be(1/2-)+n Table 11Be(3/2-)+n Figure 11Be(3/2-)+n Table 11Be(3/2-2)+n Figure 11Be(3/2-2)+n Table	12B(1+) -> AV18+UX 11Be+p Summary 11Be(1/2-)+p Figure 11Be(1/2-)+p Table 11Be(3/2-)+p Figure 11Be(3/2-)+p Table 11Be(5/2-)+p Figure 11Be(5/2-)+p Table 11B+n Summary 11B(3/2-)+n Figure 11B(3/2-)+n Table 11B(1/2-)+n Figure 11B(1/2-)+n Table 11B(3/2-2)+n Figure 11B(3/2-2)+n Table	12C(0+) -> AV18+UX 11B+p Summary 11B(3/2-)+p Figure 11B(3/2-)+p Table 11B(1/2-)+p Figure 11B(1/2-)+p Table 11B(3/2-2)+p Figure 11B(3/2-2)+p Table 11C+n Summary 11C(3/2-)+n Figure 11C(3/2-)+n Table 11C(1/2-)+n Figure 11C(1/2-)+n Table 11C(3/2-2)+n Figure 11C(3/2-2)+n Table	12C(0+) -> NV2+3-Ia 11B+p Summary 11B(3/2-)+p Figure 11B(3/2-)+p Table 11B(1/2-)+p Figure 11B(1/2-)+p Table 11B(3/2-)2+p Figure 11B(3/2-2)+p Table	12C(0+) -> NV2+3-Ia* 11B+p Summary 11B(3/2-)+p Figure 11B(3/2-)+p Table 11B(1/2-)+p Figure 11B(1/2-)+p Table 11B(3/2-)2+p Figure 11B(3/2-2)+p Table	12C(0+) -> NV2+3-IIb* 11B+p Summary 11B(3/2-)+p Figure 11B(3/2-)+p Table 11B(1/2-)+p Figure 11B(1/2-)+p Table 11B(3/2-)2+p Figure 11B(3/2-2)+p Table

Robert B. Wiringa
Last update December 23, 2024