The isovector giant dipole resonance (GDR) of an $\alpha$ cluster in ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$, and its analogs in ${}^{6,7}\mathrm{Be}$ and ${}^{6,7}\mathrm{He}$ were searched for by using the ${}^{6,7}\mathrm{Li}\left(p,p^{\prime }\right)$, ${}^{6,7}\mathrm{Li}\left({}^3\mathrm{He},t\right)$, and ${}^{6,7}\mathrm{Li}\left({}^7\mathrm{Li},{}^7\mathrm{Be}\right)$ reactions at the incident energies of 300, 450, and $455\text{MeV}$, respectively. New dipole resonances were found at $E_x=27.0\pm 1.5\text{MeV}$ in ${}^6\mathrm{Li}$ and at $E_x=29.0\pm 1.5\text{MeV}$ in ${}^7\mathrm{Li}$, both with widths (full width at half maximum) of $12\pm 2\text{MeV}$. In ${}^6\mathrm{He}$, ${}^6\mathrm{Be}$, ${}^7\mathrm{He}$, and ${}^7\mathrm{Be}$, the dipole resonances with a width of $12\pm 2\text{MeV}$ were observed at $E_x=24.0\pm 1.5,23.5\pm 1.5,18.0\pm 1.5$, and $28.0\pm 1.5\text{MeV}$, respectively. The resonance shapes were reproduced well with the GDR shape observed in the ${}^4\mathrm{He}\left(\gamma ,n\right)$ reactions. The averaged value for the ratios of the resonance cross section in $A=6$ to that in $A=7$ for each element was $1.2\pm 0.3$. The averaged value for the ratios of the resonance cross section to the GDR cross section in the respective target nuclei was $0.44\pm 0.08$, which was consistent with the ratios of the GDR cross section in ${}^4\mathrm{He}$ to that in ${}^{6,7}\mathrm{Li}$ reported in the photonuclear reactions. The excitation energies for the dipole resonances in $A=6$ and 7 nuclei relative to the separation energies of an $\alpha$ particle in ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$, respectively, agreed well with the excitation energy for the GDR in ${}^4\mathrm{He}\left(\sim 26\text{MeV}\right)$. We conclude that the resonances observed in ${}^{6,7}\mathrm{Li}$ are consistent with the GDR of the $\alpha$ cluster and the resonances in ${}^{6,7}\mathrm{He}$ and ${}^{6,7}\mathrm{Be}$ are consistent with the analogs of the GDR in the $\alpha$ cluster. The $Q$ value for the excitation of the GDR of the $\alpha$ cluster in $A=7$ nuclei is deeper by $1.6\pm 0.3\text{MeV}$ on the average than that in $A=6$.

• Received 25 December 2003

DOI:https://doi.org/10.1103/PhysRevC.69.044313