Impact of pion tensor force on alpha clustering in $^{20}$Ne

Abstract

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 $α$-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 quadruple deformation, and the role of tensor force embedded in the Fock diagram of $π$-pseudovector ($π$-PV) coupling is revealed. It is shown that the level branches from the degenerated spherical orbits at the deformed prolate case are enlarged due to the extra contribution from pion-exchanged tensor force. Correspondingly, the excitation energy in this 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 $2α$ decay mode of $^{20}$Ne. Possible $α$-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. The results reveal the extra role of the tensor force, correlated to the evolved single-particle levels with nuclear deformation, in the formation and stability of nuclear clustering.

Figures (4)

• Figure 1: Binding energies as a function of the quadruple deformation $\beta$ for $^{20}$Ne. The results are calculated by the D-RHFB model with Lagrangians PKO1, PKO2, PKO3 and PKDD. The circles represent the ground state (G.S.) of $^{20}$Ne, while the triangles denote the excited state (E.S.). The experimental binding energy $E_B^{\textrm{exp.}}$ for the ground state of $^{20}$Ne is taken from Ref. CPCKondev_2021, and the referred threshold for the two-alpha decay mode of $^{20}$Ne is shown by the dashed line 10.1143/PTPS.E68.464. For comparison, the result with PKO1 but excluding tensor force component of $\pi$-PV contributions from the nucleon self-energy (according to Eq.\ref{['eq:4']}) is given by the dash-dotted line as well.
• Figure 2: Neutron canonical single particle energies $E(m_{\nu}^\pi)$ for both G.S. and E.S. of $^{20}$Ne, calculated by the D-RHFB model with Lagrangians PKO1, PKO2 and PKDD. The positive(negative) parity levels are plotted by the red(blue) bars, respectively. For PKO1, the shadowed area illustrate the contribution due to extra tensor force of $\pi$-PV coupling in Fock terms.
• Figure 3: Figures (a) and (b) are calculated by the D-RHFB model with Lagrangians PKDD, figures (c) and (d) are calculated with the Lagrangians PKO1, while figures (e) and (f) show the results of the Lagrangians PKO1 with tensor force component of $\pi$-PV contribution removed from the nucleon self-energy (PKO1 w.o. $V_{\pi-PV}^T$). The top row displays the results of ground state, while the bottom row shows excited state. The left half of each sub-figure shows the distribution of the single-particle level density along the $z$-axis $(\rho_z)$ for the $^{20}$Ne, while the right half shows the contour plot of the density distribution $(\rho)$ of the $^{20}$Ne. The tensor force promotes cluster dissociation by adjusting the spatial distribution of single-particle orbitals (the $1/2^-_2$ expands outward).
• Figure 4: The energy functional integral element $\varepsilon$ of Fock terms as a function of $r$ distribution (left figure) and the contour plot of the nucleonic localization function (right figure), both are calculated by the D-RHFB model with Lagrangians PKO1. The upper figures represent the ground state of $^{20}$Ne, while the lower figures represent the excited state. The gray line represents the distribution of the energy functional integral element for $\pi$-PV coupling with respect to $r$, while the red line represents the distribution for the sum of the coupling channels $\sigma$, $\omega$, and $\rho$. The distribution of $\varepsilon$ reveals the strong attractive effect of the $\pi$-PV in the $\alpha$ cluster region ($z\approx$4 fm) and the mechanism of its long-range cancellation of Coulomb repulsion. The while dash lines indicate the region of ${C_{q\sigma }\geq 0.9}$.