Universal Properties of Weakly Bound Two-Neutron Halo Nuclei

TL;DR

This paper develops an effective field theory describing weakly bound two-neutron halo nuclei, revealing universal properties and explicit relations between matter and charge radii, and dipole strength functions, in the double fine-tuning limit.

Contribution

It introduces a universal effective field theory for two-neutron halo nuclei without Efimov effect, providing explicit formulas for radii ratios and dipole strength functions.

Findings

The ratio of matter to charge radius depends on the ratio of neutron separation energy to virtual energy.

When the separation energy is much larger than virtual energy, the radius ratio approaches 2/3 times the core's mass number.

The shape of the E1 dipole strength function is explicitly derived as a function of the energy ratio.

Abstract

We construct an effective field theory of a two-neutron halo nucleus in the limit where the two-neutron separation energy $B$ and the neutron-neutron two-body virtual energy $\epsilon_n$ are smaller than any other energy scale in the problem, but the scattering between the core and a single neutron is not fine-tuned, and the Efimov effect does not operate. The theory has one dimensionless coupling which formally runs to a Landau pole in the ultraviolet. We show that many properties of the system are universal in the double fine-tuning limit. The ratio of the mean-square matter radius and charge radius is found to be $\langle r^2_m \rangle/\langle r^2_c\rangle = A f(\epsilon_n/B)$, where $A$ is the mass number of the core and $f$ is a function of the ratio $\epsilon_n/B$ which we find explicitly. In particular, when $B\gg\epsilon_n$, $\langle r^2_m\rangle/\langle r^2_c\rangle = \frac23 A$. The shape of the the $E1$ dipole strength function also depends only on the ratio $\epsilon_n/B$ and is derived in explicit analytic form. We estimate that for the $^{22}$C nucleus higher-order corrections to our theory are of order 20% or less if the two-neutron separation energy is less than 100 keV and the $s$-wave scattering length between a neutron and a $^{20}$C nucleus is less than 2.8 fm.