Doppler Shift as a Tool for Studies of Isobaric Analog States of Neutron-Rich Nuclei: Application to ${}^7\mathrm{He}$

We have developed a new technique to study exotic neutron-rich nuclei via their isobaric analog states (IAS). We populate high-isospin states in resonant reactions of radioactive ion beams with protons. Characteristic $\gamma$ rays emitted from excited decay products were used to identify the population of the IAS. We show that information on the differential and total cross section for formation of the IAS can be extracted from the energy spectrum of the Doppler-shifted $\gamma$ rays. This technique was applied to the study of $T=3/2$ states in ${}^7\mathrm{Li}$, which are analogs of states in ${}^7\mathrm{He}$. The analog of the ${}^7\mathrm{He}$ ground state was clearly observed, whereas the presence of the analog of a narrow $1/2^{-}$ state at 0.6 MeV excitation in ${}^7\mathrm{He}$ reported by M. Meister et al. [Phys. Rev. Lett. 88, 102501 (2002)] was excluded at the 90% confidence level. Evidence is presented for a broad $1/2^{-}$ state at a higher excitation energy in ${}^7\mathrm{He}$.

Figure 1

(a) Decay pathways for the $T=3/2$ resonance in ${}^7\mathrm{Li}$, and (b) the successive kinematics stages of the studied reaction.

Figure 2

(a) Part of the $\gamma$-ray spectrum from the 90° Ge detector. The solid curve was obtained with a ${\mathrm{CH}}_2$ target; the dotted curve was taken with a carbon target. (b) The spectrum in the 0° Clover detector obtained by subtraction of the carbon contribution; the dotted curve was taken with a carbon target. The Compton background is approximated by a straight line as shown. (c) The final spectrum of the Doppler-shifted 3.56 MeV $\gamma$ rays. The solid line shows the contribution from the known $T=3/2$, $J^{\pi }=3/2^{-}$ state in ${}^7\mathrm{Li}$. The dotted line includes the effect of $T=1/2$ resonances. The dash-dotted line close to the abscissa axis shows the contribution of the direct charge-exchange process.

Figure 3

(a) The solid curve shows a calculation of the $\gamma$-ray spectrum including the analog of the ${}^7\mathrm{He}$ g.s. and a $J^{\pi }=1/2^{-}$, $E_{\mathrm{ex}}=3.1\mathrm{MeV}$, $\Gamma =10\mathrm{MeV}$ excited state. The dotted line is the effect from the g.s. resonance plus a state at $E_{\mathrm{ex}}\simeq 0.6\mathrm{MeV}$ having $\Gamma \simeq 1\mathrm{MeV}$. (b) Plot of the probable resonance parameters for the $T=3/2$, $J^{\pi }=1/2^{-}$ state. The shaded area shows the 50% confidence level of the ${\chi }^2$ fit. For excitation energies higher than 2.1 MeV, only a lower limit is set for the resonance width.