Neutrino-less double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>decay of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ca</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>48</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>studied by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>CaF</mml:mi><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>(Eu) scintillators

We searched for the neutrino-less double-$\ensuremath{\beta}$ decay($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) 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 ${Q}_{\ensuremath{\beta}\ensuremath{\beta}}$ value region for the data of 3394 kg \ifmmode\cdot\else\textperiodcentered\fi{} day. It gives a lower limit (90% confidence level) of ${T}_{1/2}^{0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}}&gt;2.7\ifmmode\times\else\texttimes\fi{}{10}^{22}$ year for the half-life of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ of $^{48}\mathrm{Ca}$. Combined with our previous data for 1553 kg \ifmmode\cdot\else\textperiodcentered\fi{} day [I. Ogawa et al., Nucl. Phys. A730, 215 (2004)], we obtained a more stringent limit of ${T}_{1/2}^{0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}}&gt;5.8\ifmmode\times\else\texttimes\fi{}{10}^{22}$ year.