The Coulomb interaction in Helium-3: Interplay of strong short-range and weak long-range potentials

J. Kirscher*, D. Gazit

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Quantum chromodynamics and the electroweak theory at low energies are prominent instances of the combination of a short-range and a long-range interaction. For the description of light nuclei, the large nucleon-nucleon scattering lengths produced by the strong interaction, and the reduction of the weak interaction to the Coulomb potential, play a crucial role. Helium-3 is the first bound nucleus comprised of more than one proton in which this combination of forces can be studied.We demonstrate a proper renormalization of Helium-3 using the pionless effective field theory as the formal representation of the nuclear regime as strongly interacting fermions. The theory is found consistent at leading and next-to-leading order without isospin-symmetry-breaking 3-nucleon interactions and a non-perturbative treatment of the Coulomb interaction. The conclusion highlights the significance of the regularization method since a comparison to previous work is contradictory if the difference in those methods is not considered.With a perturbative Coulomb interaction, as suggested by dimensional analysis, we find the Helium-3 system properly renormalized, too.For both treatments, renormalization-scheme independence of the effective field theory is demonstrated by regulating the potential and a variation of the associated cutoff.

Original languageAmerican English
Pages (from-to)253-260
Number of pages8
JournalPhysics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
StatePublished - 10 Apr 2016

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© 2016 The Authors.


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