Quasi-elastic scattering for the nuclear ground state structure: An intriguing case of $^{30}$Si

Abstract

Quasi-elastic (QEL) scattering measurements have been performed using the $^{28, 30}$Si projectiles off the $^{90}$Zr target at energies around the Coulomb barrier. Coupled-channels (CC) calculations were carried out in a large parameter space of quadrupole and hexadecapole deformations for the N=Z, $^{28}$Si and N=Z+2, $^{30}$Si nuclei. $^{28}$Si at the N=Z line is observed to be uniquely oblate shaped in its ground state. In contrast, for $^{30}$Si with just two additional neutrons -- oblate, prolate, and spherical CC descriptions are equally compatible with the measurements. To further investigate the nuclear structure evolution with varying neutron number, shell-model calculations were performed. These calculations reveal a sudden change in the nuclear structure aspects at $^{30}$Si in going from $^{28}$Si to $^{30}$Si. Combined reaction and structure analyses consistently indicate that $^{30}$Si does not possess a well-defined intrinsic shape, and it is a potential candidate for ``shape fluctuations" in its ground state.

Figures (7)

• Figure 1: Typical backward-angle (160$^{\circ}$) energy spectra for $^{28}$Si and $^{30}$Si at four beam energies. The filled curves above 15 MeV mark the QEL events, while those below 10 MeV arise mainly from evaporated light charged particles (see text).
• Figure 2: Quasi-elastic excitation function (panel (a)) and determined quasi-elastic barrier distribution (panel (b)) at four backward angles for $^{28, 30}$Si + $^{90}$Zr reactions. The dash-dotted lines are shown to guide the eye.
• Figure 3: Quasi-elastic excitation function for $^{30}$Si + $^{90}$Zr reaction. The dash-dotted (blue) and solid lines (red) show CC calculations for the two respective cases: (i) both $^{30}$Si and $^{90}$Zr nuclei are inert and (ii) $^{30}$Si is an inert nucleus and vibrational couplings of $^{90}$Zr including (2$^{+}$) state at 2.18 MeV and the octupole (3$^{-}$) state at 2.75 MeV.
• Figure 4: A reduced $\chi^{2}$ distribution in the two dimensional space of $\beta_{2}$ and $\beta_{4}$ of $^{30}$Si, determined by comparing experimental QEL excitation function for $^{30}$Si+$^{90}$Zr scattering with CC calculations (see text).
• Figure 5: Two-dimensional probability distributions for $\beta_2$ and $\beta_4$ of for $^{30}$Si, resulting from the MCMC simulations ykgplb2020. The left and right side simulations correspond to oblate and prolate minima, respectively (see Fig. \ref{['Chisq']}).