Half-life of the $I^{\pi }=4^{-}$ intruder state in ${}^{34}$P: $M2$ transition strengths approaching the island of inversion

The half-life of the 2305-keV, $I^{\pi }=4^{(-)}$ intruder state in ${}^{34}$P has been measured as $t_{1/2}=2.0\left(1\right)$ ns using $\gamma$-ray coincidence, fast-timing techniques with the Bucharest HPGe and LaBr${}_3$:Ce detector array. Excited states in ${}^{34}$P were populated using the ${}^{18}$O${(}^{18}\text{O},pn$${)}^{34}$P fusion-evaporation reaction at a beam energy of 36 MeV. Reduced transition probabilities have been calculated for different values of the $M2/E3$ mixing ratio, ${\delta }_{E3/M2}$, and compared with shell-model estimates. For small values of the mixing ratio, the $B\left(M2\right)$ value was found to be consistent with similar transitions associated with the occupation of neutron $f_{7/2}$ configurations in this mass region.

Figure 1

Partial level scheme for ${}^{34}$P relevant to this work, adapted from Refs. [6, 8].

Figure 2

Coincidence $\gamma$-ray spectra created from $\gamma$-$\gamma$ matrices in this work. The top panels show spectra from the HPGe detectors when gating on transitions detected in the HPGe detectors. The bottom panels show the equivalent spectra from the LaBr${}_3$:Ce detectors when gating on transitions detected in the LaBr${}_3$:Ce detectors. Panels (a) and (c) show $\gamma$-ray spectra in coincidence with the 429-keV transition in ${}^{34}$P. Panels (b) and (d) show spectra in coincidence with the 1048-keV transition in ${}^{34}$P.

Figure 3

Time spectra for ${}^{34}$P from the LaBr${}_3$:Ce $E_{\gamma 1}$-$E_{\gamma 2}$-$\Delta T$ cube, showing the time difference between (a) 429- and 1048-keV $\gamma$ rays, (b) 1048- and 429-keV $\gamma$ rays, (c) 429- and 1876-keV $\gamma$ rays, and (d) 1876- and 429-keV $\gamma$ rays. The solid lines in panels (a) and (b) are Gaussian-exponential convolution fits to the spectra.

Figure 4

$B\left(M2\right)$ (left) and $B\left(E3\right)$ (right) values for the $4^{-}\to 2^{+}$ transition in ${}^{34}$P as a function of the mixing ratio, ${\delta }_{E3/M2}$, calculated with $t_{1/2}=2.0\left(1\right)$ ns. The curving dashed lines represent the limits defined by the error in the half-life measurement. The shaded regions (A) represent the limits of $-1.03\le {\delta }_{E3/M2}\le -0.27$ from Ref. [6] and the vertical dash-dotted lines (B) are the measurement of ${\delta }_{E3/M2}=0.0\left(1\right)$ from Ref. [10]. The horizontal dashed lines are the theoretical shell-model (SM) estimates of $B\left(M2\right)$ and $B\left(E3\right)$ from this work.

Figure 5

(a) Systematics of experimental $B\left(M2\right)$ values and (b) experimental mixing ratios, $\left|\delta \right|$, for $N=19$ isotones. Values for ${}^{34}$P are shown at mixing ratios of ${\delta }_{E3/M2}=0.0\left(1\right)$ [10] and the upper and lower limits of ${\delta }_{E3/M2}=-0.27$ and ${\delta }_{E3/M2}=-1.03$ from Ref. [6].