A Halo: The Trigger to a New Era of Nuclear Correlations

Abstract

In this contribution to the Halo-40 Proceedings, we discuss two topics regarding halo phenomena: The first is the pairing anti-halo effect on the neutron radius of halo nuclei and its restoration due to the coupling to the continuum; the second is the soft dipole excitation of deformed halo nuclei. We demonstrate the importance of Hartree-Fock-Bogoliubov and the relativistic Hartree-Bogoliubov theory in continuum for properly taking into account the halo nature of extended wave functions in calculations of neutron radii, as well as the soft dipole excitations of halo nuclei. It was shown that the anti-halo effect is very sensitive to the continuum coupling induced by Bogoliubov-type quasi-particles, which largely cancels the anti-halo effect on the neutron radius. The soft dipole excitations of deformed halo nuclei Ne-31 and Mg-37 are discussed within the deformed Woods-Saxon model. We point out that the sharp peak just above the threshold in the dipole response is created by the halo effect, and its strength can be used to identify the magnitude of deformation and the halo configuration in the Nilsson level scheme.

Figures (7)

• Figure 1: The matter radii of Li isotopes, deduced from the measured interaction cross sections with a carbon target at 790 MeV/nucleon Tani85. The solid line represents the systematic trend for stable nuclei, given by $R=1.18A^{1/3}$fm, where $A$ is the mass number.
• Figure 2: The HFB wave functions with a binding energy in a HF potential of $\varepsilon=-0.5$ MeV and the Fermi energy of $\lambda=-0.15$ MeV. Since the quasi-particle energy $E_i$ is larger than $|\lambda|$ for the loosely bound neutron, the wave function $u_i$ is non-localized, while $v_i$ is localized. These wave functions are compared with the BCS pair wave functions, which are obtained by multiplying factors to the HF wave functions. In the upper panel of the figure, the HFB and BCS wave functions $v_i$ show similar radial behavior, with the HFB wave function exhibiting some anti-halo effect. In the lower panel, the HFB wave function $u_i$ displays a typical non-localized behavior, in marked contrast to the BCS wave function, which remains always localized. Reproduced with permission from Ref. Sagawa2025. Copyright (2025) by Springer Nature.
• Figure 3: The mean square radii and the average pairing gap as a function of the single-particle energy $\varepsilon_{\rm WS}$ in a Woods-Saxon mean-field potential. The top panel shows the mean square radius of the 2p$_{3/2}$ wave function with and without the pairing correlation, denoted by HFB and Woods-Saxon, respectively. The middle panel shows the rms radii for $^{30}$Ne (the dotted line), $^{31}$Ne (the dashed line), and $^{32}$Ne (the solid line), obtained with the Hartree-Fock ($^{30}$Ne and $^{31}$Ne ) and the HFB ($^{32}$Ne) calculations. The bottom panel shows the results of the HFB calculations for the average pairing gap of $^{32}$Ne. Reproduced with permission from HS11. Copyright (2011) by the American Physical Society.
• Figure 4: The single-particle energy of the canonical basis, the occupation probability, the rms radius of each orbit, the rms radius multiplied by occupation probability, and the total neutron radius for $^{11}$Li and $^{32}$Ne, respectively calculated by the RCHB theory. Reprinted figure with permission from Ref. Chen2014. Copyright (2014) by the American Physical Society.
• Figure 5: Single-particle levels for neutrons in deformed Woods-Saxon potentials as a function of the quadrupole deformation parameter $\beta_{2}$. The potential depth $V_{\mathrm{WS}}$ is adjusted so that the binding energy of the 21st neutron of the prolate deformed nucleus $^{31}$Ne is 150 keV. The asymptotic quantum-numbers $[Nn_z\Lambda]\Omega$ are denoted for the single-particle levels. (Reproduced with permission from Xiao2025. Copyright (2025) by the American Physical Society.)