We searched for the neutrino-less double-$\beta$ decay($0\nu \beta \beta$) of ${}^{48}\mathrm{Ca}$ by using ${\mathrm{CaF}}_2$(Eu) scintillators. Analysis of their pulse shapes was effective to reduce backgrounds. No events are observed in the $Q_{\beta \beta }$ value region for the data of 3394 kg · day. It gives a lower limit (90% confidence level) of $T_{1/2}^{0\nu \beta \beta }>2.7\times {10}^{22}$ year for the half-life of $0\nu \beta \beta$ of ${}^{48}\mathrm{Ca}$. Combined with our previous data for 1553 kg · day [I. Ogawa et al., Nucl. Phys. A730, 215 (2004)], we obtained a more stringent limit of $T_{1/2}^{0\nu \beta \beta }>5.8\times {10}^{22}$ year.

• Received 2 September 2008

DOI:https://doi.org/10.1103/PhysRevC.78.058501