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-beta 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-beta 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.