Structure of low-lying states in ${}^{140}\mathrm{Sm}$ studied by Coulomb excitation

The electromagnetic structure of ${}^{140}\mathrm{Sm}$ was studied in a low-energy Coulomb excitation experiment with a radioactive ion beam from the REX-ISOLDE facility at CERN. The $2^{+}$ and $4^{+}$ states of the ground-state band and a second $2^{+}$ state were populated by multistep excitation. The analysis of the differential Coulomb excitation cross sections yielded reduced transition probabilities between all observed states and the spectroscopic quadrupole moment for the $2_1^{+}$ state. The experimental results are compared to large-scale shell model calculations and beyond-mean-field calculations based on the Gogny D1S interaction with a five-dimensional collective Hamiltonian formalism. Simpler geometric and algebraic models are also employed to interpret the experimental data. The results indicate that ${}^{140}\mathrm{Sm}$ shows considerable $\gamma$ softness, but in contrast to earlier speculation no signs of shape coexistence at low excitation energy. This work sheds more light on the onset of deformation and collectivity in this mass region.

Figure 1

Partial level scheme showing low-lying states in ${}^{140}\mathrm{Sm}$. The spin assignments for the excited states at 990 and 1599 keV are taken from a recent angular correlation measurement [14].

Figure 2

Particle-$\gamma$ coincidence time spectrum. A normalized fraction of the random gate was used for background subtraction.

Figure 3

Energy spectra of particles detected in the DSSSD as a function of the laboratory scattering angle. The cuts to select between detected ${}^{140}\mathrm{Sm}$ projectiles and recoiling ${}^{94}\mathrm{Mo}$ target nuclei are marked. Ring number 1 corresponds to laboratory angle $19.7^{\circ }$ and ring 16 to laboratory angle $58.4^{\circ }$.

Figure 4

Background subtracted $\gamma$-ray spectrum in coincidence with a particle in the DSSSD, with Doppler correction for ${}^{140}\mathrm{Sm}$. The $2_1^{+}\to 0_1^{+}$ transition at 531 keV, the $4_1^{+}\to 2_1^{+}$ transition at 715 keV, and the $2_2^{+}\to 2_1^{+}$ transition at 460 keV are visible. The broad structure originates from the 871 keV $2_1^{+}\to 0_1^{+}$ transition in ${}^{94}\mathrm{Mo}$. The purple arrow marks the $2_1^{+}\to 0_1^{+}$ transition of the potential beam contaminant ${}^{140}\mathrm{Nd}$.

Figure 5

Background subtracted $\gamma$-ray spectrum in coincidence with a particle in the DSSSD, with Doppler correction for the ${}^{94}\mathrm{Mo}$ recoils. The $2_1^{+}\to 0_1^{+}$ transition in ${}^{94}\mathrm{Mo}$ was observed at 871 keV. The inset shows an enlarged part of the same spectrum, where the $3/2^{+}\to 5/2_{\mathrm{gs}}^{+}$ transition in the target contaminant ${}^{95}\mathrm{Mo}$ is seen at 204 keV.

Figure 6

Gamma-ray spectra obtained with and without RILIS laser ionization in a measurement during which the lasers were periodically switched on and off. The spectra are Doppler corrected for the ${}^{140}\mathrm{Sm}$ projectiles.

Figure 7

Gamma-ray spectra for five separate ranges of center-of-mass scattering angles with Doppler correction for $\gamma$ emission from the ${}^{140}\mathrm{Sm}$ projectiles.

Figure 8

Illustration of the iterative procedure to fit the reduced matrix elements using the codes gosia and gosia2, with parts (a), (b), and (c) corresponding to steps 2, 3, and 4 as described in the text. The level schemes indicate which matrix elements were included in the fit as free parameters, as fixed values, or as free parameters with spectroscopic data to constrain the fit. Iterations between step 3 and step 4 were performed until the solution converged.

Figure 9

Result of the ${\chi }^2$ minimization for the $\langle 0_1^{+}\parallel E2\parallel 2_1^{+}\rangle$ and $\langle 2_1^{+}\parallel E2\parallel 2_1^{+}\rangle$ matrix elements in ${}^{140}\mathrm{Sm}$ obtained after the last iteration of step 4 of the fitting procedure using target normalization. Note that the final uncertainties of all matrix elements were obtained after one more iteration of step 3.

Figure 10

Comparison of the experimental excitation energies (in keV) of the low-lying states in ${}^{140}\mathrm{Sm}$ with predictions from beyond-mean-field calculations based on the Gogny D1S interaction, the shell model (SM), the interacting boson approximation (IBA), and expectations for a nucleus with E(5) critical point symmetry (see text for explanations).

Figure 11

Potential energy surface for ${}^{140}\mathrm{Sm}$ from constrained deformed Hartree-Fock minimization in the shell-model basis.

Figure 12

Potential energy surface for the ground state of ${}^{140}\mathrm{Sm}$ obtained in the CHFB calculations with the Gogny D1S interaction.