αα scattering in halo effective field theory

Abstract

We study the two-alpha-particle (αα) system in an Effective Field Theory (EFT) for halo-like systems. We propose a power counting that incorporates the subtle interplay of strong and electromagnetic forces leading to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT expansion in detail, and compare its results with existing low-energy αα phase shifts and previously determined effective-range parameters. Good description of the data is obtained with a surprising amount of fine-tuning. This scenario can be viewed as an expansion around the limit where, when electromagnetic interactions are turned off, the 8 Be ground state is at threshold and exhibits conformal invariance. We also discuss possible extensions to systems with more than two alpha particles.

Ab initio alpha–alpha scattering

“…We find that the calculated 8 Be ground state is bound at NNLO, though only a small fraction of an MeV away from threshold. For further comparison, we show in the inset next-to-leading-order results using halo effective field theory with point-like alpha particles [32]. We note that the norm matrix in Eq.…”

Reexamination of the astrophysicalSfactor for theα+d→6Li

“…Using these equations one can fit the experimental scattering phase shift at given partial wave and find the bound state pole and its residue [6,7]. We note that effective field theory can also be applied to obtain binding energy (if necessary) and the ANC [8][9][10]. In principle, if experimental data are quite accurate, such an extrapolation can provide the location of the bound state pole (binding energy) and its residue, which is expressed in terms of the ANC [11][12][13].…”

Coulomb interactions within halo EFT

“…1) and find agreement in the effective range parameters [5] except for a 0 , whose inverse is very sensitive to big cancellations that occur between strong and electromagnetic contributions [3]. However, the order of magnitude is the same, which indicates a lot of fine-tuning in the αα system that remains to be understood.…”

“…Analyses of scattering data using effective range theory reveal an incredibly large scattering length, a 0 ∼ 10 3 fm [5], thus implying that our power counting needs more fine-tuning than naively expected. In [3] we developed a power counting for the αα, wich results in a very large scattering length, a 0 ∼ M hi /M 2 lo , and a non-perturbative (but still of natural size) effective range r 0 ∼ 1/M hi . Coulomb interactions were dealt non-perturbatively along the lines of [4] and the inverse of the amplitude becomes proportional to…”