Intermediate-energy Coulomb excitation of ${}^{30}\mathrm{Na}$

The neutron-rich nucleus ${}^{30}\mathrm{Na}$ in the vicinity of the “Island of Inversion” was investigated using intermediate-energy Coulomb excitation. A single $\gamma$-ray transition was observed and attributed to the $3_1^{+}\to 2_{\mathrm{gs}}^{+}$ decay. A transition probability of $B(E2;2_{\mathrm{gs}}^{+}\to 3_1^{+})=147(21)\hspace{0.5em}{e}^2\hspace{0.5em}{\mathrm{fm}}^4$ was determined and found in agreement with a previous experiment and with large-scale shell-model calculations. Evidence for the strong excitation of the $4_1^{+}$ state predicted by the shell-model calculations was not observed.

Figure 1

(a) Energy loss vs TOF for the reacted projectiles emerging from the ${}^{209}\mathrm{Bi}$ target. ${}^{30}\mathrm{Na}$ can be cleanly identified from the other constituents of the cocktail beam. (b) Energy loss vs dispersive position in the S800 focal plane gated on the ${}^{30}\mathrm{Na}$ projectiles identified via (a). Shown is the entire acceptance of the spectrograph in the dispersive direction. A tail of the ${}^{29}\mathrm{Na}$ distribution originating from the (weak) one-neutron knockout channel enters the spectrograph at the edge of the acceptance. ${}^{30}\mathrm{Na}$ can be cleanly separated.

Figure 2

(a) $\gamma$-ray spectrum in coincidence with scattered ${}^{30}\mathrm{Na}$ (maximum scattering angle ${\theta }_{\mathrm{c}.\mathrm{m}.}^{\max }=2.{90}^{°}$). The γ rays detected in the laboratory were event-by-event Doppler reconstructed into the rest frame of the projectile. (b) Same as (a) but without a software gate applied that restricts events to $\theta ⩽{\theta }^{\max }$. (c) Same as (b) only for the SeGA detector pair at ${24}^{°}$ with respect to the beam axis.

Figure 3

ECIS95 calculations for ${}^{30}\mathrm{Na}{+}^{209}\mathrm{Bi}$ at 80 MeV/nucleon. Given are differential cross sections for the $2_{\mathrm{gs}}^{+}\to 3_1^{+}$ excitation as a function of the center-of-mass angle for solely Coulomb excitation (blue, dashed line) and for Coulomb excitation plus nuclear contribution (black, solid line). The optical potential from Ref. [25] was used for this plot.

Figure 4

Calculated $B(E2;2_{\mathrm{gs}}^{+}\to J^{+})$ strengths within the MCSM using the SDPF-M effective interaction compared to the experimental result.