Lately, researchers from the Institute of Modern Physics (IMP) of the Chinese Academy of Sciences and Peking University applied the Gamow shell model to analyze the two-neutron halo structure of ³¹F. The results were published in Physical Review C as a Rapid Communication.  

Due to their well-bound character, the nuclei of the valley of stability can be very precisely modelled by closed-quantum systems. This situation drastically changes when one departs from the valley of stability to reach the so-called proton and neutron drip-lines. Indeed, for extreme value of proton-to-neutron ratios, nuclei become less and less bound as protons or neutrons are added, and become unbound at proton and neutron drip-lines.  

The most striking feature occurring at drip-lines is the appearance of so-called halos. Even though halo nuclei are bound and cannot emit nucleons, their very small binding energy and large spatial extension imply that they are energetically coupled to the "continuum", that is to unbound nuclear configurations, which are mixed by the nucleon-nucleon interaction. 

Halo nuclei can be found for example in ¹¹Be, or ⁸B and the first excited state of ¹⁷F, which are one-neutron and one-proton halos, respectively. Two-nucleon halos exist, with the examples of ⁶He, ¹¹Li, where a two-neutron halo develops, and ¹⁷Ne, bearing a two-proton halo. These are the most difficult to study theoretically, because the two external nucleons are bound due to inter-nucleon correlations in the asymptotic region. The ³¹F isotope is of particular interest for that matter. Indeed, ³¹F is very loosely bound and possesses a large neutron-to-proton ratio, so that experimentalists suspect that it is a two-neutron halo. 

A powerful tool to describe halo nuclei is the Gamow shell model (GSM), which is an extension of the standard shell model of well-bound nuclei. In the standard shell model, the nuclear many-body wave function is represented by a linear combination of independent-particle configurations. However, the nuclear configurations used are well bound, so that the study of halo nuclei is precluded therein. This problem has been solved in GSM by using weakly bound, resonance and scattering configurations instead of well-bound configurations.  

Thus, in order to check the halo character of ³¹F, researchers from IMP and Peking University calculated the ³¹F isotope ground state wave function using GSM. For this, they fitted effective Hamiltonians, denoted as GSM-EFT and GSM-FHT, which reproduce the known experimental energies of ^25-31F.   

They calculated the nucleon densities and neutron root-mean-square radius of ^27,29,31F to state the spatial extension of Fluorine isotopes at neutron drip-line. Clearly, the ³¹F wave function is very extended in space, whereas ^27,29F are localized.

The researchers also checked that the two-neutron density of ³¹F is important in the asymptotic region, contrary to those of ^27,29F. Therefore, according to GSM calculations, ³¹F is a two-neutron halo nucleus.  

They then suggest experimentalists to further study ³¹F in order to prove or disprove its two-neutron halo character. The ³¹F isotope would then be the heaviest known two-neutron halo nucleus.

Fig. 1. One-nucleon densities (in fm^-3) of the bound ^27,29,31F isotopes calculated with the GSM-EFT in the valence space as a function of r (in fm). (Image by N. Michel)