Transition Densities for Neutrinoless Double Beta Decay

This web page presents two-nucleon transition densities calculated for a variety of nuclei in the range A=6-12. These are from variational Monte Carlo calculations (VMC) using (unless otherwise noted) 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);
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)

Results for some of the new Norfolk NV2+3 potentials based on chiral effective field theory with intermediate Δ states are now being added:
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).

Some of the results below have been used in a series of (ever-improving) benchmark studies of neutrinoless double beta decay:
Pastore, et al., Phys. Rev. C 97, 014606 (2018).
Wang, et al., Phys. Lett. B 798, 134974 (2019).
Cirigliano, et al., Phys. Rev. C 100, 055504 (2019).
Weiss, et al., Phys. Rev. C 106, 065501 (2022).

6He(0+;1)->6Be(0+;1) AV18 Figure Table	6He(0+;1)->6Be(0+;1) AV18+UX Figure Table	6He(0+;1)->6Be(0+;1) NV2+3-Ia* Figure Table	6He(0+;1)->6Be(0+;1) NV2+3-IIb* Figure Table
8He(0+;2)->8Be(0+;0) AV18 Figure Table	8He(0+;2)->8Be(0+;0) AV18+UX Figure Table	8He(0+;2)->8Be(0+;0) NV2+3-Ia* Figure Table	8He(0+;2)->8Be(0+;0) NV2+3-IIb* Figure Table
	10He(0+;3)->10Be(0+;1) AV18+UX Figure Table
	10Be(0+;1)->10C(0+;1) AV18+UX Figure Table	10Be(0+;1)->10C(0+;1) NV2+3-Ia* Figure Table	10Be(0+;1)->10C(0+;1) NV2+3-IIb* Figure Table
	12Be(0+;2)->12C(0+;0) AV18+UX Figure Table 2 Table 5	12Be(0+;2)->12C(0+;0) NV2+3-Ia* Figure Table 2 Table 5	12Be(0+;2)->12C(0+;0) NV2+3-IIb* Figure Table 2 Table 5

Robert B. Wiringa
Last update April 26, 2023