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Neutrinoless double-beta decay nuclear transition matrix elements aregenerated by an effective two-body transition operator and it consists ofGamow-Teller like and Fermi like (also tensor) operators. Spectral distributionmethod for the corresponding transition strengths (squares of the transitionmatrix elements) involves convolution of the transition strength densitygenerated by the non-interacting particle part of the Hamiltonian with aspreading function generated by the two-body part of the Hamiltonian. Extendingthe binary correlation theory for spinless embedded $k$-body ensembles toensembles with proton-neutron degrees of freedom, we establish that thespreading function is a bivariate Gaussian for transition operators$\co(k_\co)$ that change $k_\co$ number of neutrons to $k_\co$ number ofprotons. Towards this end, we have derived the formulas for the fourth-ordercumulants of the spreading function and calculated their values for some heavynuclei; they are found to vary from $\sim -0.4$ to -0.1. Also for nuclei from$^{76}$Ge to $^{238}$U, the bivariate correlation coefficient is found to varyfrom $\sim 0.6 - 0.8$ and these values can be used as a starting point forcalculating nuclear transition matrix elements using the spectral distributionmethod.

Spectral distribution method for neutrinoless double-beta decay nuclear transition matrix elements: Binary correlation results