Effects of rotation and valence nucleons in molecular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-chain nuclei
D. D. Zhang, Z. X. Ren, P. W. Zhao, D. Vretenar, Tamara Nikšić, Jie Meng
Abstract
Effects of rotation and valence nucleons in molecular linear $\ensuremath{\alpha}$-chain nuclei are analyzed using a three-dimensional lattice cranking model based on covariant density functional theory. The structure of the mirror nuclei $^{16}\mathrm{C}$ and $^{16}\mathrm{Ne}$ is investigated as a function of rotational frequency. The valence nucleons, with respect to the $3\ensuremath{\alpha}$ linear chain core of $^{12}\mathrm{C}$, at low frequency occupy the $\ensuremath{\pi}$ molecular orbital. With increasing rotational frequency these nucleons transition from the $\ensuremath{\pi}$ orbital to the $\ensuremath{\sigma}$ molecular orbital, thus stabilizing the $3\ensuremath{\alpha}$ linear chain structure. It is predicted that the valence protons in $^{16}\mathrm{Ne}$ change occupation from the $\ensuremath{\pi}$ to the $\ensuremath{\sigma}$ molecular orbital at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}1.3$ MeV, a lower rotational frequency compared to $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}1.7$ MeV for the valence neutrons in $^{16}\mathrm{C}$. The same effects of valence protons are found in $^{20}\mathrm{Mg}$, compared to the four valence neutrons in $^{20}\mathrm{O}$. The model is also used to examine the effect of alignment of valence nucleons on the relative positions and size of the three $\ensuremath{\alpha}$ clusters in the mirror nuclei $^{16}\mathrm{C}$ and $^{16}\mathrm{Ne}$.