Gamma Decay of the 3.90-MeV (2+) Level inCa40

The lifetime and $\gamma$-ray branching of the 3.90-MeV ($2^{+}$) state of ${\mathrm{Ca}}^{40}$ have been measured using the reactions ${\mathrm{Ca}}^{40}(p,p^{\prime }){\mathrm{Ca}}^{{40}^{*}}$ at a bombarding energy of 7.32 MeV and ${\mathrm{K}}^{39}(p,\gamma ){\mathrm{Ca}}^{40}$ at the $E_p=1.344\mathrm{}$-MeV resonance. Consistent values for the lifetime were obtained from the Doppler shifts of the 3.90-MeV $\gamma$ rays in both reactions and from the 0° line shape in the ${\mathrm{K}}^{39}(p,\gamma ){\mathrm{Ca}}^{40}$ reaction. A value of $\tau =50\mathrm{}\pm 5$ fsec is adopted for the mean lifetime of the 3.90-MeV state. The 3.90→3.35-MeV branching ratio was measured by observing the 0.555-MeV cascade $\gamma$ rays in quadruple coincidence with the two annihilation $\gamma$ rays and the inelastic protons in the ${\mathrm{Ca}}^{40}(p,p^{\prime }){\mathrm{Ca}}^{{40}^{*}}$ reaction, or in triple coincidence with annihilation $\gamma$ rays in the ${\mathrm{K}}^{39}(p,\gamma ){\mathrm{Ca}}^{40}$ reaction. Results are in agreement and the adopted branch is (7.95 ± 0.8) × ${10}^{-4\mathrm{}}$. By combining the lifetime and branching results, the 0.555-MeV $E2\mathrm{}$ transition rate corresponds to a $B(E2\mathrm{}$; 3.90 ($2^{+}$) → 3.35 ($0^{+}$)) of 250 ± 35 $e^2$ ${\mathrm{fm}}^4$. This result is in excellent agreement with recent theoretical estimates of the transition strength. The mean lifetime of the 5.28-MeV ($4^{+}$) state of ${\mathrm{Ca}}^{40}$ was measured to be 310 ± 60 fsec. The corresponding $B(E2\mathrm{}$; 5.28 ($4^{+}$) → 3.90 ($2^{+}$1)) of 535 ± 110 $e^2$ ${\mathrm{fm}}^4$ is in reasonable agreement with expectations based on a strong-deformation rotational model of the states.