${}^{34}\mathrm{P}({}^7\mathrm{Li},{}^7\mathrm{Be}+\gamma )$ Reaction at $100A\mathrm{MeV}$ in Inverse Kinematics

We report on the first successful extraction of a ${\beta }^{+}$ Gamow-Teller strength distribution from a radioactive isotope in an intermediate-energy charge-exchange experiment in inverse kinematics. The (${}^7\mathrm{Li},{}^7\mathrm{Be}+\gamma (429\mathrm{keV})$) reaction at $100A\mathrm{MeV}$ was used to measure Gamow-Teller transition strengths from ${}^{34}\mathrm{P}$ to states in ${}^{34}\mathrm{Si}$. The results show that little mixing occurs between $sd$ and $pf$ shell configurations for the low-lying $0^{+}$ and $2^{+}$ states even though ${}^{34}\mathrm{Si}$ neighbors the island of inversion and low-lying $2\hslash \omega$ intruder states exist. Shell-model calculations in the $sdpf$ model space are consistent with these findings.

Figure 1

(a) Doppler-reconstructed $\gamma$ spectrum gated on all ${}^{34}\mathrm{Si}$ events in the S800 spectrograph. The spectrum is fitted with responses for previously reported transitions (blue), plus a 2.00 MeV line (see text). The complete fit is also shown (red). (b) $\gamma$-spectrum in the laboratory frame gated on ${}^{34}\mathrm{Si}$ events. The peak due to ${}^7\mathrm{Be}_1\to {}^7\mathrm{Be}_0$ transitions is indicated, as well as the gates used in the further analysis. (c) ${}^{34}\mathrm{Si}$ energy spectrum measured in the spectrograph gated on the 429 keV $\gamma$-gate (I) and the sideband gate (II). Events gated on the ${}^{34}\mathrm{P}^{14+}$ charge-state are also shown. $S_n({}^{34}\mathrm{Si})$ indicates the threshold for decay by neutron emission for ${}^{34}\mathrm{Si}$ ($E({}^{34}\mathrm{Si})\approx 3395\mathrm{MeV}$). The ${}^{34}\mathrm{Si}$ energy spectrum is compared with MC simulations (see text).

Figure 2

(a) Dispersive angular distribution for transitions to states of various multipolarity in ${}^{34}\mathrm{Si}$ based on DWBA calculation and taking into account experimental conditions in a MC simulation. (b) Comparison between the measured angular distribution for the transition to the ${}^{34}\mathrm{Si}(0^{+})$ ground state and the predicted distribution (scaled to produce best fit). (c) Comparison between the measured angular distribution for the transition to the 5.33-MeV state in ${}^{34}\mathrm{Si}$ and the prediction (scaled to produce the best fit) for a $\Delta L=0$ transition to a $2^{+}$ state. (d) Comparison between measured and shell-model $B(\mathrm{GT})$ distributions in ${}^{34}\mathrm{Si}$. For energies above the threshold for neutron emission, no data are available.