Lifetime measurement for the $2_1^{+}$ state in ${}^{140}\mathrm{Sm}$ and the onset of collectivity in neutron-deficient Sm isotopes

Background: The chain of Sm isotopes exhibits a wide range of nuclear shapes and collective behavior. While the onset of deformation for $N>82$ has been well studied both experimentally and theoretically, fundamental data is lacking for some Sm isotopes with $N<82$.

Purpose: Electromagnetic transition rates represent a sensitive test of theoretical nuclear structure models. Lifetime measurements are furthermore complementary to Coulomb excitation experiments, and the two methods together can give access to spectroscopic quadrupole moments.

Method: The lifetime of the $2_1^{+}$ state in ${}^{140}\mathrm{Sm}$ was measured with the recoil-distance Doppler shift technique using the reaction ${}^{124}\mathrm{Te}({}^{20}\mathrm{Ne},4\mathrm{n}){}^{140}\mathrm{Sm}$ at 82 MeV. Theoretical calculations were performed based on a mapped collective Hamiltonian in five quadrupole coordinates (5DCH) and the Gogny D1S interaction.

Results: The lifetime of the $2_1^{+}$ state in ${}^{140}\mathrm{Sm}$ was found to be 9.1(6) ps, corresponding to a $B(E2;2_1^{+}\to 0_1^{+})$ value of 51(4) Weisskopf units. The theoretical calculations are in very good agreement with the experimental result.

Conclusions: The $B(E2;2_1^{+}\to 0_1^{+})$ value for ${}^{140}\mathrm{Sm}$ fits smoothly into the systematic trend for the chain of Sm isotopes. The new beyond-mean field calculations are able to correctly describe the onset of collectivity in the Sm isotopes below the $N=82$ shell closure for the first time.

Figure 1

Entry-state distribution for the reaction ${}^{124}\mathrm{Te}({}^{20}\mathrm{Ne},4\mathrm{n}){}^{140}\mathrm{Sm}$ at a projectile energy of 82 MeV calculated with the code compa [34].

Figure 2

Projections of the forward-forward matrix for a distance of $40\mu \mathrm{m}$ between the target and stopper foils. The top panel (a) shows a section of the total projection. The same section is shown in the middle panel (b) after applying a coincidence gate on the shifted component of the $4_1^{+}\to 2_1^{+}$ transition. The bottom panel (c) shows the same coincidence spectrum after the normalized subtraction of background gates as marked in the top panel.

Figure 3

Background-subtracted spectra observed under forward angles showing the two components of the $2_1^{+}\to 0_1^{+}$ transition after gating on the shifted component of the $4_1^{+}\to 2_1^{+}$ transition for the nine different distances between the target and stopper foils.

Figure 4

Decay curves for the $2_1^{+}\to 0_1^{+}$ transition showing the normalized intensities of the shifted (b) and unshifted (c) components of the transition as a function of distance. The resulting lifetimes for each distance and their mean value are shown in the top panel (a).

Figure 5

Systematics of $B(E2;2_1^{+}\to 0_1^{+})$ values for the even-even Sm isotopes. The data points show experimental values [29] including the one for ${}^{140}\mathrm{Sm}$ measured in this work. The line shows $B\left(E2\right)$ values obtained from the energies of the $2_1^{+}$ states by applying a modified Grodzins formula [39].

Figure 6

Experimental $B(E2;2_1^{+}\to 0_1^{+})$ values for ${}^{134-138}\mathrm{Sm}$ [29], ${}^{140}\mathrm{Sm}$ (present work), and the value for ${}^{142}\mathrm{Sm}$ [40] compared to theoretical calculations using the general Bohr Hamiltonian (BH) based on a Nilsson potential [41], the interacting boson approximation (IBA) [19], a simple rotational model based on a deformed Woods-Saxon potential (WS) [14], and the 5DCH calculations based on the Gogny D1S interaction from the present work.

Figure 7

Experimental excitation energy ratio $E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$ compared to the values from the 5DCH calculations based on the Gogny D1S interaction from the present work.