Quasi-elastic (QEL) scattering measurements have been performed using a $^{28}$Si projectile off a $^{90}$Zr 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 ( and ) of $^{28}$Si. Our results unambiguously show that $^{28}$Si is an oblate shaped nucleus with =- 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 (=+) of $^{28}$Si have been determined for the first time using QEL scattering. A remarkable agreement is obtained between the experimental and calculated values of $^{28}$Si 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.
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"value": "Quasi-elastic (QEL) scattering measurements have been performed using a $^{28}$Si projectile off a $^{90}$Zr 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 (<math><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>2</mn></mrow></msub></math> and <math><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>4</mn></mrow></msub></math>) of $^{28}$Si. Our results unambiguously show that $^{28}$Si is an oblate shaped nucleus with <math><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>2</mn></mrow></msub></math>=-<math><mn>0.38</mn><mo>\u00b1</mo><mn>0.01</mn></math> 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 (<math><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>4</mn></mrow></msub></math>=+<math><mn>0.03</mn><mo>\u00b1</mo><mn>0.01</mn></math>) of $^{28}$Si have been determined for the first time using QEL scattering. A remarkable agreement is obtained between the experimental and calculated <math><msub><mrow><mi>\u03b2</mi></mrow><mrow><mn>4</mn></mrow></msub></math> values of $^{28}$Si 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."
}
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