Excitation of unnatural-parity states in (α, α′) scatterings on O¹⁶, Ne²⁰, Mg²⁴ and Si²⁸ at 28.5 MeV

Quasi-elastic (QEL) scattering measurements have been performed using a ²⁸Si projectile off a ⁹⁰Zr target at energies around the Coulomb barrier. A Bayesian analysis within the framework of coupled channels (CC) calculations is performed in a large parameter space of quadrupole and hexadecapole deformations (${\beta }_2$ and ${\beta }_4$) of ²⁸Si. Our results unambiguously show that ²⁸Si is an oblate shaped nucleus with ${\beta }_2$=-$0.38\pm 0.01$ which is in excellent agreement with results from electromagnetic probes. The sign and magnitude of quadrupole deformation along with a precise value of hexadecapole deformation (${\beta }_4$=+$0.03\pm 0.01$) of ²⁸Si have been determined for the first time using QEL scattering. A remarkable agreement is obtained between the experimental and calculated ${\beta }_4$ values of ²⁸Si based on Skyrme-Hartree-Fock method. The present results demonstrate the strong sensitivity of the quasi-elastic scattering to the sign and magnitude to the ground state deformation parameters, thus affirming its suitability to be used for rare exotic nuclei using low intensity RIBs.

The structure of excited states in ²⁸Si as well as the energy dependence of the reaction mechanism are investigated. Angular distributions related to the 0₁⁺, 2₁⁺, 4₁⁺, 0₂⁺, 3₁⁺, 2₂⁺ + 2₃⁺, 3₁⁻ + 4₂⁺ levels in the ²⁸Si(n, n′) reaction were measured at incident energies 6.8, 7.0, 8.0 … 12.0 MeV. The analysis was extended up to 14.8 MeV bombarding energy. The experimental cross sections are described by means of a coupled-channel calculation including compound nucleus contributions. The low-lying excited states can be interpreted by a rotational model with prolate but also with oblate g.s. deformation. For the higher-lying states various coupling schemes have been tested. Especially, a second rotational band could be described adopting an oblate deformation.

Angular distributions for the elastic and inelastic scattering of ¹⁶O from ²⁴Mg, exciting the 2₁⁺ (1.37 MeV), 4₁⁺ (4.12 MeV) and 2₂⁺ (4.24 MeV) states, have been measured at E_c.m. = 43.5 MeV, an energy at which resonance-like structure has been observed previously in the related ²⁴Mg(¹⁶O, ¹²C)²⁸Si reaction. In particular, the 4₁⁺, 2₂⁺ doublet has been resolved for the first time for heavy-ion projectiles. The data have been well described by coupled-channels calculations within the framework of a Davydov-Filippov asymmetric rotor model for the low-lying states of ²⁴Mg, which has been extended to include a symmetric hexadecapole shape component. The optical model potential for the ¹⁶O + ²⁴Mg interaction was found to have a moderate real well depth and some surface transparency. The shape parameters for the nuclear potential were determined to be β^(N)₂ = 0.25, γ = 22° and β₄^(N) = −0.065 and the corresponding deformation lengths are in good agreement with earlier light-ion results. The inclusion of a negative symmetric hexadecapole component leads to an improved description of the reduced transition rates. The triaxial structure of ²⁴Mg is discussed.

We have searched for the giant magnetic dipole resonance in ⁹⁰Zr and an associated state in ²⁰⁸Pb. Among the experimental techniques employed in this search was the detection of inelastically scattered protons in coincidence with ground-state de-excitation γ-rays, No state in ⁹⁰Zr up to an excitation of 10.5 MeV or in ²⁰⁸Pb between 5.0 to 6.0 MeV was observed with the desired characteristics. In ⁹⁰Zr, heretofore unidentified levels at 5.51, 5.89 and 6.42 MeV were determined to have J^π = 1⁻. In ²⁰⁸Pb J^π = 1⁻ states were observed at 5.29, 5.51 and 5.94 MeV. The implications of our observations are discussed.

Measurements of the differential cross sections for the elastic scattering of 30.5 MeV protons by ²⁴Mg and for the inelastic scattering to the 1.37, sum of 4.12 and 4.23, 5.22 and 6.0 MeV states are reported. Optical model fits to the elastic data, a distorted wave calculation for the first excited state, and coupled channel calculations are also presented.

The elastic and inelastic scattering of α-partieles by ²⁴Mg is investigated at bombarding energies between 15.4 and 19.1 MeV. Particular attention is given to the analysis of the inelastic scattering to the 3⁺ unnatural-parity state at 5.22 MeV. Both energy-averaged angular distributions and fine-energy-resolution excitation functions are used in the analysis. It is found that the inelastic scattering to the (3⁺, 5.22 MeV) state may be interpreted as pure compound nucleus scattering. This fact is used to investigate whether the incoherent addition of a compound nucleus cross section and a direct cross section, as has been done in recent analyses, is a realistic way to describe energy-averaged scattering data which contain both direct and compound contributions.