Electric structure of shallow D-wave states in Halo EFT

Abstract

We compute the electric form factors of one-neutron halo nuclei with shallow D-wave states up to nextto-leading order and the E2 transition from the S-wave to the D-wave state up to leading order in Halo Effective Field Theory (Halo EFT). The relevant degrees of freedom are the core and the halo neutron. The EFT expansion is carried out in powers of R core /R halo , where R core and R halo denote the length scales of the core and the halo, respectively. We propose a power counting scenario for weakly-bound states in one-neutron Halo EFT and discuss its implications for higher partial waves in terms of universality. The scenario is applied to the 5 2 + first excited state and the 1 2 + ground state of 15 C. We obtain several universal correlations between electric observables and use data for the E2 transition 5 2 + → 1 2 + together with ab initio results from the No-Core Shell Model to predict the quadrupole moment.

Low-energy deuteron–alpha elastic scattering in cluster effective field theory

“…Theoretically, this resonance can be constructed only by including the D-wave effects in the cross section. Also, the dominant contribution of the deuteron radiative capture by alpha particles at energy above 0.5 MeV comes from E2 transition with incoming D-wave states [40,47,48]. Therefore, we consider the D-wave scattering amplitudes of the d − α system in the present low-energy study.…”

“…For the LO calculation of the D waves, taking into account η [ξ] = ±1, we should include three EFT LECs in our Lagrangian (17), namely, ∆ [ξ] , g [ξ] , and h [ξ] corresponding to the scattering length, effective range, and shape parameter. The additional second-order kinetic term constant h [ξ] is needed to renormalize the interacting D-wave propagator which contains up to quintic divergences [48]. According to this suggested scheme, the LO contribution of the scattering amplitude in channels ξ = 3 S 1 , 3 P 0 , 3 P 1 , and 3 P 2 is constructed by both their scattering lengths and effective ranges and their shape parameter influences are considered as NLO correction.…”

Theory of Halo Nuclei

“…A more formal method of keeping the normalization F nc (0) = 1 involves imposing gauge invariance of the Lagrangian in the presence of an external gauge field. For a discussion of external gauge fields as well as the form factors of bound states with higher angular momenta, we refer the reader to Hammer and Phillips (2011); Braun et al (2019).…”

Halo EFT for 31Ne in a spherical formalism

“…The corresponding bound state pole conditions for an S-and D-wave halo nucleus at leading order can be found in [26,35], respectively. They read g -= a 1 0, 14 0 0 ( )…”