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 $ε_n$ 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 $\langle r^2_m \rangle/\langle r^2_c\rangle = A f(ε_n/B)$, where $A$ is the mass number of the core and $f$ is a function of the ratio $ε_n/B$ which we find explicitly. In particular, when $B\ggε_n$, $\langle r^2_m\rangle/\langle r^2_c\rangle = \frac23 A$. The shape of the the $E1$ dipole strength function also depends only on the ratio $ε_n/B$ 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.
Halo nuclei are characterized by a few weakly bound halo nucleons and a more tightly bound core. This separation of scales can be exploited in a few-body description of halo nuclei, since the detailed structure of the core is not resolved by the halo nucleons. We present an introduction to the effective (field) theory for low-energy properties of halo nuclei. The focus is on halos with S-wave interactions for which universal properties are most pronounced. The special role of the unitary limit is illustrated using the example of multineutron systems and the Efimov effect as a universal binding…
The clear separation of scales observed in halo nuclei between the extended halo and the compact core makes these exotic nuclei a perfect subject for Effective Field Theory (EFT). Such description leads to a systematic expansion of the core-halo Hamiltonian, which naturally orders the nuclear-structure observables. In this short review, I show the advantage there is to include Halo-EFT descriptions within precise models of reactions. It helps identifying the nuclear-structure observables that matter in the description of the reactions, and enables us to easily bridge predictions of nuclear-str…
The neutron skin and halo distributions in medium and heavy nuclei are calculated within the extended Thomas-Fermi approximation. Calculations are carried out for the effective Skyrme-like forces using the direct variational method. The analytical expression for the isovector shift of the rms radii $Δr_{np}$ as a sum of skin- and halo-like terms is obtained. The contribution of halo and skin terms to $Δr_{np}$ are found to be approximately equal.
Beta decay is a well-established and efficient probe of nuclear structure and provides important information also for halo nuclei. Detailed decay studies of near-dripline nuclei are challenging, but are now feasible due to the technical progress during the last decades in isotope production as well as detection capabilities. The halo structure can change the dynamics of the decay process, most noticably when decays proceed directly to continuum states as seems to be the case in beta-delayed deuteron emission, a process only observed until now for the halo nuclei $^6$He and $^{11}$Li. The prono…
It is known that nuclear deformation plays an important role in inducing the halo structure in neutron-rich nuclei by mixing several angular momentum components. While previous theoretical studies on this problem in the literature assume axially symmetric deformation, we here consider non-axially symmetric deformations. With triaxial deformation, the $Ω$ quantum number is admixed in a single-particle wave function, where $Ω$ is the projection of the single-particle angular momentum on the symmetric axis, and the halo structure may arise even when it is absent with the axially symmetric deforma…
Halo/Cluster Effective Field Theory describes halo/cluster nuclei in an expansion in the small ratio of the size of the core(s) to the size of the system. Even in the point-particle limit, neutron halo nuclei have a finite charge radius, because their center of mass does not coincide with their center of charge. This point-particle contribution decreases as $1/A_c$, where $A_c$ is the mass number of the core, and diminishes in importance compared to other effects, e.g., the size of the core to which the neutrons are bound. Here we propose that for heavy cores the EFT expansion should account f…
We explore the rotational feature of deformed halos by performing the angular momentum projection (AMP) on the ground state wave functions obtained from the deformed relativistic Hartree-Bogoliubov theory (DRHBc) in continuum. The DRHBc+AMP approach self-consistently describes the coupling between single particle bound states and the continuum not only in the ground state but also in rotational states. The rotational modes of deformed halos in $^{42}$Mg and $^{44}$Mg are investigated by studying properties of rotational states such as excitation energy, configuration, and density distribution.…
We propose a new quantum mechanical method to evaluate complete and incomplete fusion in collisions of weakly bound nuclei. The method is applied to the $^{7}{\rm Li}+^{209}{\rm Bi}$ system and the results are compared to experimental data. The overall agreement between theory and experiment is very good, above and below the Coulomb barrier.
