Excited-state transition-rate measurements in ${}^{18}$C

Excited states in ${}^{18}$C were populated by the one-proton knockout reaction of an intermediate energy radioactive ${}^{19}$N beam. The lifetime of the first $2^{+}$ state was measured with the Köln/NSCL plunger via the recoil distance method to be $\tau \left(2_1^{+}\right)=22.4\pm 0.9{\left(\mathrm{stat}\right)}_{-2.2}^{+3.3}\left(\mathrm{syst}\right)$ ps, which corresponds to a reduced quadrupole transition strength of $B(E2;2_1^{+}\to 0_1^{+})=3.{64}_{-0.14}^{+0.15}{\left(\mathrm{stat}\right)}_{-0.47}^{+0.40}\left(\mathrm{syst}\right)$ e${}^2$fm${}^4$. In addition, an upper limit on the lifetime of a higher-lying state feeding the $2_1^{+}$ state was measured to be $\tau <4.6$ ps. The results are compared to large-scale ab initio no-core shell model calculations using two accurate nucleon-nucleon interactions and the importance-truncation scheme. The comparison provides strong evidence that the inclusion of three-body forces is needed to describe the low-lying excited-state properties of this $A=18$ system.

Figure 1

${}^{18}$C-gated and Doppler-corrected $\gamma$-ray energy spectra for the 30${}^{\circ }$ and 140${}^{\circ }$ rings of SeGA collected prior to installing the plunger degrader. The arrow widths of the inset level scheme are representative of the transition relative intensities measured after in-beam efficiency corrections.

Figure 2

Experimental $\gamma$-ray spectra with statistical uncertainties (solid black) and simulated line shapes (dashed red) generated with the best-fit lifetime $\tau =22.4$ ps for the 1585 keV transition in ${}^{18}$C for the ${30}^{\circ }$ and ${140}^{\circ }$ rings of SeGA and all five target-degrader distances. Doppler corrections were done with ${\beta }_{\mathrm{slow}}=0.2920$.

Figure 3

Summed experimental $\gamma$-ray spectra with statistical uncertainties (solid black) and simulated line shapes (dashed red) generated with the best-fit lifetime $\tau \left(2_2^{+}\right)=3.2$ ps for the 932 keV transition in ${}^{18}$C. As in Fig. 2, bins with experimental error bars indicate the region where the statistical analysis was carried out.

Figure 4

Select ab initio NCSM results with the CDB2K interaction. Filled symbols correspond to full space results. Open symbols illustrate the importance-truncated scheme results for $N_{\max }=6,8$ at $\hslash \Omega =12$. Each extrapolation curve corresponds to the sequence of results obtained at a fixed $\hslash \Omega$ value. The gray bounded regions were constructed by removing the two lowest (highest) $\hslash \Omega$ sequences from the constrained fit to produce upper (lower) limits as an estimate of the uncertainty.