Lifetime measurements with improved precision in ${}^{30,32}\mathbf{S}$ and possible influence of large-scale clustering on the appearance of strongly deformed states

The formation of large size clusters and/or their relative motion as possible excitation mode are suggested to be closely related to the origin of deformation in specific cases. In ${}^{32}\mathrm{S}$, the consideration of some excitations in this nucleus as based on the existence of two doubly magic ${}^{16}\mathrm{O}$ clusters offers a possible solution to the long-standing problem of missing quadrupole collectivity in shell-model calculations aiming to describe electromagnetic $E2$ transition strengths and quadrupole moments. To experimentally check again this collectivity, lifetime measurements were performed on ${}^{30}\mathrm{S}$ and ${}^{32}\mathrm{S}$. In ${}^{32}\mathrm{S}$, at least, the reproduction of a number of observables supports the cluster scenario. Additionally, the superdeformed yrast band in ${}^{80}\mathrm{Zr}$ could find an explanation as based on the relative motion of two ${}^{40}\mathrm{Ca}$ clusters. Simultaneously, a necessity arises to revise experimentally some lifetimes derived in the past within the Blaugrund approximation when using the Doppler-shift attenuation method.

Figure 1

Spectrum gated on the $2_1{}^{+}\to 0_1{}^{+}$ transition in ${}^{30}\mathrm{S}$ using a matrix accumulating the statistics of all detectors (angles). A partial level scheme with data from Ref. [20] is also shown. The line of 1635 keV belongs to ${}^{14}\mathrm{N}$ obtained in a parasitic reaction on ${}^{12}\mathrm{C}$. See also text.

Figure 2

Line shape analysis of the $2_2{}^{+}\to 2_1{}^{+}$ transition in ${}^{30}\mathrm{S}$ at backward angles indicated in the two panels. See also text.

Figure 3

Line-shape analysis of the $2_1{}^{+}\to 0_1{}^{+}$ transition in ${}^{30}\mathrm{S}$ at four different observation angles [indicated in panels (a)–(d)] with respect to the beam axis. See also text.

Figure 4

Line-shape analysis and determination of the lifetime of the $2_1{}^{+}$ level in ${}^{32}\mathrm{S}$ within the GFA procedure with gates set on the shifted components of three direct feeders: [(a), (b)] the 2776-keV transition depopulating the $I^{\pi }=3^{-}$ lying at 5006 keV; [(c), (d)] the 3182-keV transition depopulating the $I^{\pi }=3^{+}$ lying at 5412 keV; and (e) the 1548-keV transition depopulating the $I^{\pi }=0^{+}$ lying at 3778 keV. 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 is indicated. The width of the energy channel is 1 keV. See also text.

Figure 5

Line-shape analysis (“singles-like”) for three levels in ${}^{32}\mathrm{S}$ using spectra gated on the full line shape of the $2_1{}^{+}\to 0_1{}^{+}$ transition: [(a), (b)] $I^{\pi }=0_2^{+}$ level at 3778 keV depopulated by the 1548-keV transition; (c) $I^{\pi }=2_2{}^{+}$ level at 4282 keV depopulated by the 2053-keV transition; (d) $I^{\pi }=2_3{}^{+}$ level at 5549 keV depopulated by the 3319-keV transition. Red arrows indicate the positions of the unshifted energies (emissions at rest) of the transitions in panels (c) and (d). Note the obvious change in the line shapes of these nearly completely shifted transitions when going from the $2_2{}^{+}$ case to the $2_3{}^{+}$ one. The $2_3{}^{+}$ level has about twice shorter lifetime, indeed.

Figure 6

Systematics of results available in the literature and from the present work on the lifetime of the $2_1{}^{+}$ level in ${}^{32}\mathrm{S}$. Labels indicate the direct or indirect method used for the lifetime determination. The literature sources used are as follows: Ka98 [18], Ch74 [37], Co72 [38], In71 [39], Th69 [40], Re71 [41], Ba02 [42], Ma64 [43], Lo64 [44], and Ba80 [45].

Figure 7

Analysis of the effect of varying the electronic stopping powers on the lifetime derived. Three ${\chi }^2$ curves characterizing the quality of the line-shape analysis are shown. The one represented by filled circles corresponds to the set of standard stopping powers. The curve represented by diamonds corresponds to a 10% increase of the stopping powers, leading to faster deceleration and a shorter lifetime. In the case of 10% decrease (the squares), the opposite effect is observed and lifetime becomes longer. See also text.

Figure 8

Line-shape analysis of the $2_2{}^{+}\to 2_1{}^{+}$ transition in ${}^{30}\mathrm{S}$ performed with a stopping matrix $P_{\theta }(t,v_{\theta })$ [cf. Eq. (1)] calculated within the Blaugrund approximation [35]. The lifetime is derived via a ${\chi }^2$ analysis. Other parameters are kept fixed as in the standard calculation. Compare with Fig. 2 and see also text.

Figure 9

Geometrical sketch of the two ${}^{16}\mathrm{O}$ cluster configuration in ${}^{32}\mathrm{S}$.

Figure 10

The experimental energies of the low-lying $I^{\pi }=0^{+}$ and $2^{+}$ states in ${}^{32}\mathrm{S}$ together with experimental $B\left(E2\right)$ transition strengths and the quadrupole moment of the $2_1{}^{+}$ level. Our new data are presented in red in framed boxes and in Weisskopf units. Previous data on the $B\left(E2\right)$'s are in framed dotted boxes and in black. The third number characterizing each transition (in green) is the result of the present two-level mixing calculation. The structure of the mixed wave functions is also indicated. The best fit to the data was obtained with the following values of the amplitudes: $b_{sh}=0.9768, b_{cl}=-0.2141, a_{sh}=0.9350,$ and $a_{cl}=-0.3546$. See also text.

Figure 11

Experimental level energies of some low-lying quadrupole states in a chain of S isotopes. The $B(E2;2_1{}^{+}\to 0_1{}^{+}$) transition strength is also indicated in Weisskopf units for each isotope on the bottom. Our new values are in the framed box, on the upper row and in red.