Magnetic response of the halo nucleus ${}^{19}\mathrm{C}$ studied via lifetime measurement

The first lifetime measurement used to study the magnetic response of halo nuclei is presented. The lifetime of the first excited state of the one-neutron halo nucleus ${}^{19}\mathrm{C}$ has been measured by two complementary Doppler-shift techniques with the Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA). The $B(M1;3/2^{+}\to 1/2{}_{\mathrm{g}.\mathrm{s}.}^{+}$) strength of 3.21(25)$\times 10{}^{-3}{\mu }_N^2$ determined for this decay represents a strongly hindered $M1$ transition among light nuclei. Shell-model calculations predict a strong hindrance due to the near-degeneracy of the $s_{1/2}$ and $d_{5/2}$ orbitals among neutron-rich carbon isotopes, while tensor corrections and loosely bound effects are necessary to account for the remaining strength.

Figure 1

Data from (a) line-shape and (b) recoil-distance measurements are compared to simulated spectra (solid red histograms) which include scaled ${}^9\mathrm{Li}$ spectra as background contributions (dashed blue histograms). In (a), the dotted (dot-dashed) gray histogram shows a reference spectrum simulated with a mean lifetime of 0 ns (0.5 ns).

Figure 2

Experimental decay strengths in the mass region $A<40$ are plotted in W.u. for (a) the $M1$ transitions involving the ${1/2}^{+}$ state(s) and (b) all $M1$ transitions [38]. The red diamond highlights the present value for the ${3/2}^{+}\to {1/2}^{+}$ transition in ${}^{19}\mathrm{C}$, while the ${1/2}^{+}\to 3/2{}_{\mathrm{g}.\mathrm{s}.}^{+}$ decay strength in ${}^{17}\mathrm{C}$ [12] is shown by the blue triangle.

Figure 3

Comparison of the data with shell-model predictions (see text) for (a) the $B\left(M1\right)$ strength for the ${3/2}^{+}\to {1/2}^{+}$ transition and (b) the level scheme of ${}^{19}\mathrm{C}$. In (a), the solid bars are the results obtained with $g_s^{\mathrm{IV},\mathrm{eff}}/g_s^{\mathrm{IV}}$ = 0.95 and $\delta g_{\ell }^{\mathrm{IV}}$ = 0.15 [27], while the striped bars are obtained with the modified $M1$ operator as described in the text [42]. The level scheme in (b) shows the $5/2^{+}$ states (blue) suggested by previous experiments [23, 24] in addition to the presently studied ${3/2}^{+}$ state (red).

Figure 4

Results of the SFO-tls+lbe interaction [27] for the $M1$ strength between the ${3/2}^{+}$ and ${1/2}^{+}$ states in ${}^{19}\mathrm{C}$, calculated with the effective $g$ factors as described in the text [42]. The plot shows, from left to right, the values of the individual matrix elements ($M$) for the orbital, spin, tensor, and total components of the $M1$ operator for both the protons (red) and neutrons (blue). The proton tensor component has a negligible value compared to the other components.