Search for theβ−decay ofCa48

Compressed pellets of ${}_{}{}^{48}{}_{}{}^{}\mathrm{CaCO}_3^{}{}_{}{}^{}$ containing 3.71 g of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ were counted for 206 days in a well-type HPGe detector enclosed in a large NaI(Tl) detector. The cascade γ rays of 983.5, 1037.5, and 1312.1 keV in the ${\beta }^{\mathrm{-}}$ decay of 44-h ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$, which would follow the ${\beta }^{\mathrm{-}}$ decay of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$, were searched for in the HPGe spectrum by requiring coincidences with summed γ rays in the NaI(Tl) detector. A 1900-2560-keV window on the NaI(Tl) included all three photopeak double sums. γγ coincidence efficiencies were determined with a calibrated ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ source produced in the ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$(p,n) reaction at $E_{\mathrm{p}}$=12 MeV. By combining the upper limits on the intensities of the three γ rays, the half-life for ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$ was found to be $T_{1/2}$>6×${10}^{18}$ yr (95% confidence). For the $0^{+}$→$5^{+}$ unique fourth-forbidden ${\beta }^{\mathrm{-}}$ branch of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Ca}$ to the 131-keV first-excited state of ${}_{}{}^{48}{}_{}{}^{}\mathrm{Sc}$, log$f_0$t>24.3. Our experimental half-life limit is a factor of 300 longer than a previous result but is still two orders of magnitude shorter than a recent theoretical estimate.