Testing the importance of collective correlations in neutrinoless ββ decay

We investigate the extent to which theories of collective motion can capture the physics that determines the nuclear matrix elements governing neutrinoless double-β decay. To that end we calculate the matrix elements for a series of isotopes in the full pf shell, omitting no spin-orbit partners. With the inclusion of isoscalar pairing, a separable collective Hamiltonian that is derived from the shell model effective interaction reproduces the full shell-model matrix elements with good accuracy. A version of the generator coordinate method that includes the isoscalar pairing amplitude as a coordinate also reproduces the shell model results well, an encouraging result for theories of collective motion, which can include more single-particle orbitals than the shell model. We briefly examine heavier nuclei relevant for experimental double-β decay searches, in which shell-model calculations with all spin-orbit partners are not feasible; our estimates suggest that isoscalar pairing also plays a significant role in these nuclei, though one we are less able to quantify precisely.This work was supported in part by an International Research Fellowship from the Japan Society for the Progress of Science (JSPS), and JSPS KAKENHI Grant No. 26·04323, by the Deutsche Forschungsgemeinschaft through Contract No. SFB 634, by the Helmholtz Association through the Helmholtz Alliance Program, Contract No. HA216/EMMI “Extremes of Density and Temperature: Cosmic Matter in the Laboratory”, by the European Research Council under Grant No. 307986 STRONGINT, by the U.S. Department of Energy through Contract No. DE-FG02-97ER41019, and by the Spanish MINECO under Programa Ramón y Cajal 11420 and FIS-2014-53434-