Exact evaluation of the nuclear form factor for new kinds of majoron emission in neutrinoless double beta decay

We have developed a formalism, based on the Fourier-Bessel expansion, that facilitates the evaluation of matrix elements involving nucleon recoil operators, such as appear in several exotic forms of neutrinoless double beta decay (ββ0ν). The method is illustrated by applying it to the “charged” majoron model, which is one of the few that can hope to produce an observable effect. From our numerical computations within the QRPA performed for 76Ge, 82Se, 100Mo, 128Te and 150Nd nuclei, we test the validity of approximations made in earlier work to simplify the new matrix elements, showing that they are accurate to within 15%. Our new method is also suitable for computing other previously unevaluated ββ0ν nuclear matrix elements.