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We present the results of a National Science Foundation Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a roadmap for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The roadmap includes specific projects in theoretical and computational physics as well as the use of Bayesian methods to quantify both intra- and inter-model uncertainties. The goal of this ambitious program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play.

Self-conjugate nuclei in the A≈70–80 region have attracted a great deal of attention due to phenomena such as shape coexistence and increasing collectivity along the N=Z line. We investigate the structure of nuclei in this region through lifetime measurements using the GRETINA array. The first implementation of the Differential Recoil Distance Doppler Shift technique with fast radioactive beams is demonstrated and verified through a measurement of the well-known B(E2;21+→01+) transition strength in 74Kr. The method is then applied to determine the B(E2;21+→01+) transition strength in 74Rb, the heaviest odd–odd N=Z nucleus for which this quantity has been determined. This result and extended systematics along N=Z suggest the dominance of the isoscalar part of the quadrupole transition strengths in self-conjugate nuclei, as well as the possible presence of shape coexistence in 74Rb.

Self-conjugate nuclei in the A≈70–80 region have attracted a great deal of attention due to phenomena such as shape coexistence and increasing collectivity along the N=Z line. We investigate the structure of nuclei in this region through lifetime measurements using the GRETINA array. The first implementation of the Differential Recoil Distance Doppler Shift technique with fast radioactive beams is demonstrated and verified through a measurement of the well-known B(E2;21+→01+) transition strength in 74Kr. The method is then applied to determine the B(E2;21+→01+) transition strength in 74Rb, the heaviest odd–odd N=Z nucleus for which this quantity has been determined. This result and extended systematics along N=Z suggest the dominance of the isoscalar part of the quadrupole transition strengths in self-conjugate nuclei, as well as the possible presence of shape coexistence in 74Rb.

The calcium isotopes have emerged as an important testing ground for new microscopically derived shell-model interactions, and a great deal of focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with $1f_{7/2}$ neutron hole states in $^{47, 49}$Ca following one-neutron knockout reactions from $^{48,50}$Ca. The observed reduction of strength populating the lowest 7/2$^{-}_{1}$ state in $^{49}$Ca, as compared to $^{47}$Ca, is consistent with the description given by shell-model calculations based on two- and three-nucleon forces in the neutron $pf$ model space, implying a fragmentation of the $l$=3 strength to higher-lying states. The experimental result is inconsistent with both the GXPF1 interaction routinely used in this region of the nuclear chart and with microscopic calculations in an extended model space including the $\nu1g_{9/2}$ orbital.

The quadrupole transition rate for the 41+→21+ transition of Ni58 was determined from an application of the recoil distance method with the Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA). The present result of the B(E2;41+→21+) was found to be 50-6+11e2fm4, which is about three times smaller than the literature value, indicating substantially less collectivity than previously believed. Shell model calculations performed with the GXPF1A effective interaction agree with the present data and the validity of the standard effective charges in understanding collectivity in the nickel isotopes is discussed.

The calcium isotopes have emerged as an important testing ground for new microscopically derived shell-model interactions, and a great deal of focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with $1f_{7/2}$ neutron hole states in $^{47, 49}$Ca following one-neutron knockout reactions from $^{48,50}$Ca. The observed reduction of strength populating the lowest 7/2$^{-}_{1}$ state in $^{49}$Ca, as compared to $^{47}$Ca, is consistent with the description given by shell-model calculations based on two- and three-nucleon forces in the neutron $pf$ model space, implying a fragmentation of the $l$=3 strength to higher-lying states. The experimental result is inconsistent with both the GXPF1 interaction routinely used in this region of the nuclear chart and with microscopic calculations in an extended model space including the $\nu1g_{9/2}$ orbital.

The quadrupole transition rate for the 41+→21+ transition of Ni58 was determined from an application of the recoil distance method with the Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA). The present result of the B(E2;41+→21+) was found to be 50-6+11e2fm4, which is about three times smaller than the literature value, indicating substantially less collectivity than previously believed. Shell model calculations performed with the GXPF1A effective interaction agree with the present data and the validity of the standard effective charges in understanding collectivity in the nickel isotopes is discussed.

The calcium isotopes have emerged as an important testing ground for new microscopically derived shell-model interactions, and a great deal of focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with $1f_{7/2}$ neutron hole states in $^{47, 49}$Ca following one-neutron knockout reactions from $^{48,50}$Ca. The observed reduction of strength populating the lowest 7/2$^{-}_{1}$ state in $^{49}$Ca, as compared to $^{47}$Ca, is consistent with the description given by shell-model calculations based on two- and three-nucleon forces in the neutron $pf$ model space, implying a fragmentation of the $l$=3 strength to higher-lying states. The experimental result is inconsistent with both the GXPF1 interaction routinely used in this region of the nuclear chart and with microscopic calculations in an extended model space including the $\nu1g_{9/2}$ orbital.