Double-β-decay matrix elements

The validity of the commonly assumed closure approximation has been tested by explicit calculations of the 0ν ββ-decay matrix elements of ${}_{}{}^{76}{}_{}{}^{}\to _{}^{76}{}_{}{}^{}$Se performed in the context of the quasiparticle random-phase approximation with a realistic model space. The closure approximation seems to work well for those matrix elements not very suppressed. Our results indicate that unlike the 2ν decay, the 0ν ββ-decay matrix elements are not greatly suppressed, but are comparable to those of shell model calculations. They are dominated by multipoles other than $0^{+}$ and $1^{+}$.