Neutron-proton pairing and double-beta decay in the interacting boson model
Background: The interacting boson model (IBM) has been used extensively to calculate the matrix elements governing neutrinoless double-beta decay. Studies within other models indicate that a good description of neutron-proton pairing is essential for accurate calculations of those matrix elements. The usual interacting boson model is based only on like-particle pairs, however, and the extent to which it captures neutron-proton pairing is not clear. Purpose: To determine whether neutron-proton pairing should be explicitly included as neutron-proton bosons in IBM calculations of neutrinoless double-beta decay matrix elements. Method: An isospin-invariant version of the nucleon-pair shell model is applied to carry out shell-model calculations in a large space and in a collective subspace, and to define effective operators in the latter. A democratic mapping is then used to define corresponding boson operators for the IBM, with and without an isoscalar neutron-proton pair boson. Results: IBM calculations with and without the isoscalar boson are carried out for nuclei near the beginning of the $pf$ shell, with a realistic shell-model Hamiltonian and neutrinoless double-beta-decay operator as the starting point. Energy spectra and double-beta matrix elements are compared to those obtained in the underlying shell model. Conclusions: The isoscalar boson does not improve energy spectra but does improve double-beta matrix elements. To be useful at the level of precision we need, the mapping procedure must be further developed to better determine the dependence of the boson Hamiltonian and decay operator on particle number and isospin. But the benefits provided by the isoscalar boson suggest that through an appropriate combination of mappings and fitting, it would make IBM matrix elements more accurate for the heavier nuclei used in experiments.