Impact of pion tensor force on alpha clustering in 20Ne

The nuclear clustering, as a quantum phase transition phenomenon governed by strong interactions, exhibits characteristics that are highly sensitive to the specific features of nuclear forces. Here, we examine how nuclear deformation and tensor forces influence $\alpha$-cluster formation in light nuclei. The axially deformed relativistic Hartree-Fock-Bogoliubov model is utilized to investigate the clustering structure of the ${}^{20}$Ne nucleus, at both the ground state and the excited state with a superdeformed prolate. The nuclear binding energies and the canonical single particle levels are obtained at different quadrupole deformation, and the role of tensor force embedded in the Fock diagram of $\pi$-pseudovector ($\pi$-PV) coupling is revealed. While the deformation induces level splittings from the degenerate spherical orbits, the pion-exchanged tensor force provides an additional contribution that increases them in the prolate case. Correspondingly, the excitation energy in the superdeformed prolate state is reduced due to the noncentral tensor interaction, leading to a predicted value which is much closer to the referred threshold for the $2\alpha$ decay mode of ${}^{20}$Ne. Possible $\alpha$-clustering configurations in ${}^{20}$Ne are then characterized by examining the nucleonic localization function. Although the contribution to the ground state is relatively small, the density profile and nucleonic localization are significantly changed by the pion tensor force for the superdeformed prolate excited state, as further evidenced by characterising the level mixing in the spherical basis components. It is found that the pion tensor force, through its long-range attraction, counteracts cluster dissolution by balancing against Coulomb repulsion. Thus, the results reveal the extra role of the tensor force, correlated to the evolved single-particle levels with nuclear deformation, in the formation, localization and stability of nuclear clustering.