Experimental02+(2.12 MeV) →21+(1.46 MeV)B(E2)Strength and Pairing-Vibration Calculations inAr40

The lifetime of the 2.12-MeV $0_2^{+}$ state in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ has been measured by a $p-\gamma$ delayed-coincidence technique. This state was populated by the ($p,p^{\prime }$) reaction with 5.3-MeV protons bombarding an Ar gas target. A mean lifetime of $\tau =150\mathrm{}\pm 20$ psec was obtained for the $0_2^{+}$ state. This lifetime implies for the $0_2^{+}$ → $2_1^{+}$ transition $B\left(E2\mathrm{}\right)=42.9\mathrm{}\pm 5.7$ ${\mathit{e}}^2$ ${\mathrm{F}}^4$. Pairing-vibration model calculations for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$ were made using experimental information regarding energies and $B\left(E2\mathrm{}\right)\mathrm{}$ strengths for the three lowest levels of both ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$. Three kinds of interaction were considered: first, no interaction; second, a phenomenological quadrupole-quadrupole interaction; and third, the Kuo-Brown bare $G$ matrix elements. None of these calculations can accurately describe both the energy spectrum and the $E2\mathrm{}$ transition strengths in ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$. This result may be an indication of the inadequacy of the pairing-vibration model for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ar}$.