Low-spin levels in ${}^{140}\mathrm{Sm}$: Five $0^{+}$ states and the question of softness against nonaxial deformation

Background: Investigation of the ${}_{62}{}^{140}\mathrm{Sm}_{78}$ nucleus, situated in the area close to the magic $N=82$ neutron shell, offers the opportunity to find and study interesting phenomena resulting from the interplay of collective and other degrees of freedom.

Purpose: Experimental identification of low-spin low-energy levels, particularly $0^{+}$, in ${}^{140}\mathrm{Sm}$ and theoretical interpretation within the collective general Bohr Hamiltonian (GBH) model.

Method: The $\gamma \text{−}\gamma$ angular correlation technique for $\gamma$ radiation after the $\beta$/EC decay of ${}^{140}\mathrm{Eu}\to {}^{140}\mathrm{Sm}$ and ${}^{140}\mathrm{Gd}\to {}^{140}\mathrm{Eu}\to {}^{140}\mathrm{Sm}$ was used to determine spins of excited states of ${}^{140}\mathrm{Sm}$. The ${}^{140}\mathrm{Gd}$ and ${}^{140}\mathrm{Eu}$ nuclei were produced in the ${}^{104}\mathrm{Pd}+{}^{40}\mathrm{Ar}$ reaction at the HIL UW cyclotron. In the theoretical part the full five-dimensional GBH model was applied in two variants: the simple phenomenological Warsaw model and the microscopic version with six inertial functions and a potential calculated from mean-field theory.

Results: The spin and parity of six low spin (0,1,2) low lying excited levels of ${}^{140}\mathrm{Sm}$ were measured. Two new states at around 2 MeV were identified. A analysis of the consequences of possible admixtures on the determination of the spin of a level was performed. The theoretical models applied successfully describe most of the spectrum of ${}^{140}\mathrm{Sm}$ giving hints on the origin of the states observed in the experiment.

Conclusions: Significant softness against nonaxial deformation seems to be essential to interpret the properties of ${}^{140}\mathrm{Sm}$. Further experimental studies are needed to check if some low-energy excitations are not deformation driven.

Figure 1

Theoretical cross sections (integrated over the target and degrader thickness) for the six strongest channels for the ${}^{104}\mathrm{Pd}+{}^{40}\mathrm{Ar}$ reaction.

Figure 2

Part of the $\gamma$-ray spectrum coincident with the 531.0 keV line. The expected position of the 1952.0 keV line ($I_{\gamma }=1.4$; [20]) is marked. The 2064.9 keV line ($I_{\gamma }=3.2$; [20]) is shown for comparison. Both intensities are normalized to $I_{\gamma }\left(531.0\right)=100$.

Figure 3

Part of the $\gamma$-ray spectrum coincident with the 459.9 keV line. The expected position of the 1491.3 keV line ($I_{\gamma }=2.1$; [20]) is marked. The 1293.6 keV line ($I_{\gamma }=1.2$; [20]) is shown for comparison.

Figure 4

Part of the $\gamma$ rays spectrum (with gate set on the 531.0 keV $\gamma$ line) showing that the 1420.3 keV line ($I_{\gamma }=1.2$; [20]) is in coincidence with the 531.0 keV transition. The 1491.3 keV line ($I_{\gamma }=2.1$; [20]) is shown for comparison.

Figure 5

The ratios of the $\gamma$ transition intensities obtained in this work to the intensities given in Ref. [20]. The red symbols show the experimental intensities, the red triangles correspond to the $0\to 2\to 0$ cascades. The thick red line represents the weighted mean value with an error $\sigma =12$. The four black lines deviate by $\pm 10\%$ and $\pm 20\%$ from the mean value.

Figure 6

Parametric plot of the $A_{22}$ and $A_{44}$ angular correlation coefficients. Full red symbols indicate the experimental points. The open black circle shows the theoretical $(A_{22}^{\text{t}},A_{44}^{\text{t}})$ point for the $0\to 2\to 0$ cascade. The full black circle points to the top of the $2\to 2\to 0$ contour. The arrow shows a transition from the top of the $2\to 2\to 0$ contour to the $0\to 2\to 0$ one which could possibly be caused by admixtures—for more information see Appendix.

Figure 7

Scheme of levels populated in the ${}^{140}\mathrm{Eu}\to {}^{140}\mathrm{Sm}$ decay. The scheme proposed in Refs. [12, 20, 21] has been modified in the present work. New data are marked as solid red lines and bold digits. Spin and parity assignments are based on the $\gamma \text{−}\gamma$ angular correlation and $logft$ values. For more details see text.

Figure 8

Potential energy surface for ${}^{140}\mathrm{Sm}$ calculated using the SLy4 Skyrme interaction and seniority-type pairing. Position of a minimum is marked with a black dot.

Figure 9

Experimental and theoretical energy levels of the ${}^{140}\mathrm{Sm}$ nucleus. The dotted lines connect levels for which a tentative correspondence is based on $B\left(E2\right)$ ratios only. For the $n_{\beta }$ and $\lambda$ labels see Sec. 3a.

Figure 10

Probability distributions for the five lowest $0^{+}$ states in the phenomenological model. Distance between contour lines is 0.2 (dimensionless). One can read the $n_{\beta }$ number from the number of knots in the radial ($\beta$) direction, while $\lambda =0,3$ is related with the number of knots in the angular ($\gamma$) direction.

Figure 11

Probability distributions for the five lowest $0^{+}$ states in the microscopic model.

Figure 12

The $A_{22}(\delta$), $A_{44}(\delta$) parametric plot for the $2\to 2\to 0$ and $1\to 2\to 0$ cascades. The ‘true’ values of ($A_{22}^{\text{t}}$, $A_{44}^{\text{t}}$) and ‘effective’ ones, i.e., the result of an admixture ($A_{22}^{\text{eff}}$, $A_{44}^{\text{eff}}$) are shown as open and full black circles, respectively. It is seen that the admixture can change the value of the mixing ratio ($\delta$) (the left-hand side of the drawing) as well as the spin assignment (the right-hand side of the drawing). In the latter case the true spin $I_i=2$ will be observed as $I_i=1$.