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 $\ensuremath{\gamma}$ 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 \ifmmode\times\else\texttimes\fi{} 1-in.-high plastic scintillator, and $\ensuremath{\gamma}$ rays by a 1-in. \ifmmode\times\else\texttimes\fi{} 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\ifmmode\pm\else\textpm\fi{}0.26) \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}9}$ sec which corresponds to a $B(E2, {{6}_{1}}^{+}\ensuremath{\rightarrow}{{4}_{1}}^{+})=(6.40\ifmmode\pm\else\textpm\fi{}0.22){e}^{2}$ ${\mathrm{F}}^{4}$. 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.