Structure of ${}^{11}\mathrm{Li}$(g.s.) and an excited $3/2^{-}$ state

New measurements of reaction cross sections for scattering of ${}^{11}\mathrm{Li}$ from H and C have provided a value for the radius of the neutron density distribution. By using the sensitivity of calculated radii to neutron configuration, I find that the $s^2$ fraction required to reproduce the new radius is $P\left(s^2\right)=0.{33}_{-0.05}^{+0.03}$, in agreement with an earlier estimate of 0.33(6). Calculations of relative cross sections for the reaction ${}^9\mathrm{Li}\left(t,p\right)$ (in reverse kinematics) suggest a method to observe an expected excited $3/2^{-}$ state and to independently determine $P\left(s^2\right)$.

Figure 1

The fraction of the $s^2$ configuration in ${}^{11}\mathrm{Li}$(g.s.) required to reproduce various radii: filled symbols from matter radius—diamond (previous) and square (new); open symbol from $R_{\mathrm{n}}$ and $x$ for weighted average. Labels correspond to those in Table 2.

Figure 2

For the reaction ${}^9\mathrm{Li}\left(t,p\right)$ ${}^{11}\mathrm{Li}$, the expected cross-section ratio for the (unknown) excited $3/2^{-}$ state to the g.s. is plotted vs $P\left(s^2\right)$, the fractional $s^2$ intensity in ${}^{11}\mathrm{Li}$(g.s.). The solid vertical line just above $P=0.3$ represents the value of $0.{31}_{-0.03}^{+0.02}$ extracted from the analysis herein. The dashed vertical line near 0.59 is at the lower limit of $P$ for which potential-model [1] and IMME [27] predictions for the ${}^{11}\mathrm{O}$(g.s.) mass agree.