Precise determination of quadrupole and hexadecapole deformation parameters of the $sd$-shell nucleus, $^{28}$Si

Y. K. Gupta; V. B. Katariy; G. K. Prajapati; K. Hagino; D. Patel; V. Ranga; L. S. Danu; A. Pal; B. N. Joshi; S. Dubey; V. V. Desai; S. Panwar; U. Garg; N. Kumar; S. Mukhopadhyay; Pawan Singh; N. Sirswal; R. Sariyal; I. Mazumdar; B. V. John

arXiv · 2303.12495

Precise determination of quadrupole and hexadecapole deformation parameters of the $sd$-shell nucleus, $^{28}$Si

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Abstract

Quasi-elastic (QEL) scattering measurements have been performed using $^{28}$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 ($\beta_{2}$ and $\beta_{4}$) of $^{28}$Si. Our results clearly show that $^{28}$Si is an oblate shaped nucleus with $\beta_{2}$=-$0.38 \pm 0.01$ which is in excellent agreement with electromagnetic probes. A precise value of hexadecapole deformation for $^{28}$Si, $\beta_{4}$=+$0.03 \pm 0.01$, along with a consistent value of quadrupole deformation has now been determined for the first time using QEL scattering. A remarkable agreement between the experimental $\beta_{4}$ value of $^{28}$Si and Skyrme-Hartree-Fock based calculations is obtained. The QEL results obtained previously for $^{24}$Mg (prolate) and the present result for $^{28}$Si (oblate) hereby affirm the strong sensitivity of the quasi-elastic scattering to ground state deformations, thus reinforcing its suitability as a potential probe for rare exotic nuclei.

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Y. K. Gupta, V. B. Katariy, G. K. Prajapati, K. Hagino, D. Patel, V. Ranga, L. S. Danu, A. Pal, B. N. Joshi, S. Dubey, V. V. Desai, S. Panwar, U. Garg, N. Kumar, S. Mukhopadhyay, Pawan Singh, N. Sirswal, R. Sariyal, I. Mazumdar, B. V. John. 2023-03-22. Precise determination of quadrupole and hexadecapole deformation parameters of the $sd$-shell nucleus, $^{28}$Si. https://arxiv.org/abs/2303.12495

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