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 serveral exotic forms of neutrinoless double beta decay ($\beta\beta_{0\nu}$). 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 $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$ and $^{150}Nd$ 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 $\beta\beta_{0\nu}$ nuclear matrix elements.