Lifetime of the 3.19-MeV (6+) State inCa42

Abstract

The lifetime of the ($6^{+}$) 3.19-MeV state in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ has been measured by obtaining the time distribution of coincidences between positrons forming the state, from the decay of the ($7^{+}$) 615-keV state in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$, and 440-keV-decay $\gamma$ rays. The metastable (61-sec) state in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ was generated by the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^3{}_{}{}^{}\mathrm{He}, p){}_{}{}^{42}{}_{}{}^{}\mathrm{Sc}$ reaction using a 6.10-MeV ${\mathrm{He}}^3$ beam from the University of Iowa Van de Graaff. A 60-sec beam-on-beam-off cycle was employed. Positrons were detected by a 2-in.-diam × 1-in.-high plastic scintillator, and $\gamma$ rays by a 1-in. × 1-in. NaI(Tl) scintillator. Both scintillators were viewed by RCA-8575 photomultipliers whose dynodes were gated to avoid damage during the beam-on time. The value obtained for the mean lifetime was (7.72±0.26) × ${10}^{-9\mathrm{}}$ sec which corresponds to a $B(E2, {6_1}^{+}\to {4_1}^{+})=(6.40\mathrm{}\pm 0.22)e^2$ ${\mathrm{F}}^4$. This value may be compared with the ($2^{+}$) 1.52-MeV to ($0^{+}$) ground-state decay, assuming both represent transitions between ${f_{\frac{7}{2}}}^2$ states. The result indicates that collective admixtures in the $0_1^{+}$ and $2_1^{+}$ wave functions are larger than for the $6_1^{+}$ and $4_1^{+}$ levels. This can be understood quantitatively if one considers the low-lying levels in ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ to be shell-model states mixed with rotational states arising from 4p-2h excitation according to a recent model by Gerace and Green.