AnalogE2transitions in theA=30nuclei; lifetime and branching ratio measurements of levels inP30

The $\gamma$-ray decays of the first two $J^{\pi }=2^{+}$, $T=1\mathrm{}$ states in ${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$ ($T_z=0\mathrm{}$) at $E_x=2.938\mathrm{} \mathrm{and} 4.183$ MeV have been studied through the ${}_{}{}^{29}{}_{}{}^{}\mathrm{Si}$($p$,$\gamma$)${}_{}{}^{30}{}_{}{}^{}\mathrm{P}$ reaction. One new branch from the 2.938 MeV state and three new branches from the 4.183 MeV state were found. The recently reported isoscalar $E2\mathrm{}$ transition 4.183($2^{+}$,1) →0.677($0^{+}$,1) MeV was confirmed and the relative intensity of (1.3±0.3)% was determined. Employing the Doppler-shift attenuation (DSA) method, the lifetime ${\tau }_m=(90\mathrm{}\pm 11)$ fs was determined for the 2.938 MeV state and in the present, exceptionally advantageous conditions the lifetime (3.1±0.9) fs for the 4.183 MeV state was determined for the first time. In the analysis, the Monte-Carlo method was employed. The $E2\mathrm{}$ branches 2.938($2^{+}$,1)→0.677($0^{+}$,1) and 4.183($2^{+}$,1)→0.677($0^{+}$,1) MeV are compared with the analog transitions in ${}_{}{}^{30}{}_{}{}^{}\mathrm{Si}$ ($T_z=+1\mathrm{}$) and ${}_{}{}^{30}{}_{}{}^{}\mathrm{S}$ ($T_z=-1\mathrm{}$) as well as with shell-model calculations.