Low-energy bound states, resonances, and scattering of light ions

Abstract

We describe bound states, resonances and elastic scattering of light ions using a δ-shell potential. Focusing on low-energy data such as energies of bound states and resonances, charge radii, asymptotic normalization coefficients, effective-range parameters, and phase shifts, we adjust the two parameters of the potential to some of these observables and make predictions for the nuclear systems d + α, 3 He + α, 3 He + α, α + α, and p + 16 O. We identify relevant momentum scales for Coulomb halo nuclei and propose how to apply systematic corrections to the potentials. This allows us to quantify statistical and systematic uncertainties. We present a constructive criticism of Coulomb halo effective field theory and compute the unknown charge radius of 17 F.

S-factor and scattering-parameter extractions from ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}{ \rightarrow }^{7}\mathrm{Be}+\gamma $

“…2 this motivates resumming the r 0 piece of the effective-range-theory amplitude, yielding a LO amplitude that scales as 1/Q 2 [30,47,48]. (We note that cancellations between r p 1 2 0 2 and ReH(η) could in fact render the LO amplitude as large as 1/Q 3 [18].)…”

Resonant and scattering states in the α+α system from the nonlocalized cluster model

“…Various aspects of the α + α system have been studied theoretically by many authors using the RGM [44,45], the GCM [46][47][48][49], the quantum Monte Carlo method [50][51][52], the THSR wave function [11,12], the cluster effective field theory [53,54], the complex-scaled cluster model [55][56][57][58], the lattice effective field theory [59], the configuration interaction technique [60,61], the δ-shell potential method [62], etc. Also, the experience on studying the α + α system would help extend our method further to the α + α + α system, which could contain more exotic structures such as gaslike α-condensates [6], linear-chain structures [18], etc.…”

Nuclear Structure at the Crossroads

“…How important is a semi-quantitative result at leading order [25,26]? It is certainly important for schemes that only treat the leading order nonperturbatively and treat all higher orders in perturbation theory.…”

“…Whether the four-body force at NLO [42] can correct this remains to be seen. Further progress has been made in understanding the scale introduced by long-range Coulomb interactions, which leads to an enhancement of effective range effects [25,26].…”