Restoring the valence-shell stabilization in ${}^{140}\mathrm{Nd}$

A projectile Coulomb-excitation experiment was performed at the radioactive-ion beam facility HIE-ISOLDE at CERN to obtain $E2$ and $M1$ transition matrix elements of ${}^{140}\mathrm{Nd}$ using the multistep Coulomb-excitation code gosia. The absolute $M1$ strengths, $\mathrm{B}(M1;2_2^{+}\to 2_1^{+})=0.033\left(8\right){\mu }_{\mathrm{N}}^2,\mathrm{B}(M1;2_3^{+}\to 2_1^{+})=0.{26}_{-0.10}^{+0.11}{\mu }_{\mathrm{N}}^2$, and $\mathrm{B}(M1;2_4^{+}\to 2_1^{+})<0.04{\mu }_{\mathrm{N}}^2$, identify the $2_3^{+}$ state as the main fragment of the one-quadrupole-phonon proton-neutron mixed-symmetry state of ${}^{140}\mathrm{Nd}$. The degree of $F$-spin mixing in ${}^{140}\mathrm{Nd}$ was quantified with the determination of the mixing matrix element $V_{\mathrm{F}-\mathrm{mix}}<7_{-7}^{+13}\mathrm{keV}$.

Figure 1

The spectrum of the double-sided silicon strip detector shows the energy of the scattered heavy particles as a function of the scattering angle with respect to the beam axis (laboratory frame). Three different types of particles, heavy target, light target (contamination), and beam particles, are clearly separated. The gate for targetike particles is divided in single-hit (red) and double-hit (purple) events.

Figure 2

The time-random background subtracted, Doppler-corrected, beam-particles gated $\gamma$-ray singles spectrum (red) and the $\gamma$-ray coincidence spectrum (blue) with an additional gate on the $2_1^{+}\to 0_1^{+}$ transition of ${}^{140}\mathrm{Nd}$. Peaks are marked with the identified transition emitted following the CE of ${}^{140}\mathrm{Nd}$. Additionally, a peak at 840 keV was identified as a transition of the beam contaminant ${}^{140}\mathrm{Sm}$, which vanishes in the $\gamma$-ray coincidence spectrum. The binning changes after the dashed line for visibility.

Figure 3

The partial level scheme of ${}^{140}\mathrm{Nd}$. The widths of the transitions correspond to the observed intensities. The $2_1^{+}\to 0_1^{+}$ transition width is scaled down by a factor of 5 for visibility.

Figure 4

${\chi }^2$-surface distribution with respect to the diagonal and transitional matrix elements of the $2_3^{+}$ state. The dashed gray lines indicate the limits of the diagonal matrix element of the $2_1^{+}$ state, which is applied to the $2_3^{+}$ state.

Figure 5

The values for $\mathrm{B}(M1;2_{\mathrm{i}}^{+}\to 2_1^{+}),\mathrm{B}(E2;2_{\mathrm{i}}^{+}\to 2_1^{+})$, and $\mathrm{B}(E2;2_{\mathrm{i}}^{+}\to 0_1^{+})$ strengths of ${}^{140}\mathrm{Nd}$ are displayed in (a)–(c), respectively.

Figure 6

The $M1$ transition strengths $\mathrm{B}(M1;2_{\mathrm{i}}^{+}\to 2_1^{+})$ of the main and the small fragment of the $2_{1,\mathrm{ms}}^{+}$ state of the $N=80$ isotones are compared to a theoretical $\mathrm{B}(M1;2_{1,\mathrm{ms}}^{+}\to 2_1^{+})$ systematic (Sieja et al., Ref. [33]) in (a). The resulting $F$-spin mixing matrix elements ($\circ$) and upper limits ($\mathbf{\nabla }$) are shown in (b). $V_{\mathrm{F}-\mathrm{mix}}$ of ${}^{136}\mathrm{Ba}$ and ${}^{138}\mathrm{Ce}$ are taken from Ref. [9].