New lifetime measurements for the lowest quadrupole states in ${}^{20,22}\mathrm{Ne}$ and possible explanations of the high collectivity of the depopulating $E2$ transitions

Shell model and multiparticle-multihole configuration-mixing calculations indicate a missing quadrupole collectivity needed to explain the transition strengths in the even-even Ne isotopes. Even with a significant scaling of the effective charges all details of the data cannot be reproduced. The effect is very pronounced in ${}^{20,22}\mathrm{Ne}$. Therefore new lifetime measurements in these nuclei were undertaken by us with the Doppler-shift attenuation method to recheck experimentally earlier findings. They confirmed the previous result in the case of ${}^{20}\mathrm{Ne}$ while in ${}^{22}\mathrm{Ne}$ the $2_1^{+}$ level lifetime was found to be shorter by 43%. It turned out that in the latter nucleus the lifetime of the $4_1^{+}$ level also has to be corrected. The $B(E2;2_1^{+}\to 0_1^{+})$ reduced transition strengths derived from the newly determined lifetimes as well as those for the heavier Ne isotopes are reasonably described by involving a mixing of $\alpha$-cluster states of, e.g., the type $\alpha \otimes 16\mathrm{O}$ with normal, nearly spherical states. An extended version of the coupled-cluster effective interaction method published earlier describes well the spin dependence of the $B\left(E2\right)$'s in ${}^{20}\mathrm{Ne}$.

Figure 1

Comparison of the interpolated stopping power of ${}^{20}\mathrm{Ne}$ ions in Mg with the tabulated values of Northcliffe and Schilling [49] and SRIM [50]. These values were integrated over the foil thickness.

Figure 2

Line-shape analysis and determination of the lifetime of the $2_1^{+}$ level in ${}^{20}\mathrm{Ne}$ within the GFA procedure with different gates set on the shifted components of the feeding transition of 2614 keV from the $4_1^{+}$ level and at different beam energies. The gate in (a)–(c) is set at the forward ring of ${45}^{\circ }$ while in (d)–(f) the gate is set at the backward ring of $142.3^{\circ }$. The decomposition of the full line shape of the gated transition into shifted and unshifted components is shown and the derived lifetime for each case are indicated. The width of the energy channel is 1 keV. Note the smooth evolution of the line shapes with increasing beam energy characterized by a net increase of the plateau fraction. See also text.

Figure 3

Description of the line shape of the 2614 keV transition using a one-parameter fit of the $4_1^{+}$ level lifetime and a decay function representing a single exponential function. In the top panels (a), (b), the fits of the line shapes observed at the angles of ${143}^{\circ }$ and ${45}^{\circ }$ at the beam energy of 30 MeV are shown. The corresponding data at 33 MeV are shown in the bottom panels (c), (d). The effective lifetimes derived by the analysis of the ${\chi }^2$ curve are indicated. See also text.

Figure 4

Analysis within the SDM of the pair of subsequent transitions $4_1^{+}\to 2_1^{+}\to 0_1^{+}$ in ${}^{22}\mathrm{Ne}$ at the angles indicated. In the top panels (a), (d), the line shapes are displayed after background subtraction and conversion of the line shape of the 2083 keV transition on the range of the 1275 keV one. The fit of the line shape of the latter transition is also shown. In the middle panels (b), (e), the difference of the two line shapes from the top panels is shown with its fit. The lifetime derivation using the $\tau$ curve is illustrated in the bottom panels (c), (f). See also text.

Figure 5

The same as in Fig. 4 but for the pair of subsequent transitions $6_1^{+}\to 4_1^{+}\to 2_1^{+}$ at the angles indicated. Note the smaller Doppler shift at the backward angle, which makes the analysis more difficult. A small contamination at the far end of the shifted 2954 keV transition at ${45}^{\circ }$ leads to some drop in the spectral difference which of course cannot be reproduced by a fit (middle panel on the right). See also text.

Figure 6

Description of the line shape of the 1275 keV transition using a one-parameter fit of the $2_1^{+}$ level lifetime and a decay function representing a superposition of exponential functions with the participation also of the $4_1^{+}$ level (lifetime from the present work) and of the $6_1^{+}$ level (lifetime form [66]). See also text.

Figure 7

Analysis of the pairs of 1634 and 2614 keV in ${}^{20}\mathrm{Ne}$ at three different beam energies according to the SDM. The meaning of the information displayed is the same as in Fig. 4 but for the specific case presented here. See also text.

Figure 8

Experimental data on $B\left(E2\right)$ transition strengths from the present work (circles) and from the literature (squares) compared to different calculations as function of the mass number $A$. See also text.

Figure 9

Experimental data on $B\left(E2\right)$ transition strengths in ${}^{20}\mathrm{Ne}$ from the present work (circles) and from the literature (squares) compared to different calculations as function of the spin I. See also text.

Figure 10

The same as in Fig. 9 but for ${}^{22}\mathrm{Ne}$. See also text.

Figure 11

Schematic representation of the system of two overlapping spheres with different radii $R_1$ and $R_2$. The first one of them is associated with ${}^4\mathrm{He}$ while the second one is associated with ${}^{16}\mathrm{O}$. The distances to the intersection plane $d_1$ and $d_2$ are also indicated. See also text.

Figure 12

Calculation of the intrinsic quadrupole moments of the cluster states in ${}^{20-28}\mathrm{Ne}$ after solving Eq. (9) for them and for the whole range of possible squared amplitudes. In the far-most right on the bottom the range of possible values for ${}^{20}\mathrm{Ne}$ consistent with the results of Ref. [23] is indicated. In the insert, a systematics of the low-lying quadrupole states in ${}^{20-28}\mathrm{Ne}$ is presented. See also text.