Abstract
We examine the effects of the long range Coulomb force on the three-body contact interaction in a pionless effective theory of 3He. The corresponding interaction in 3H exhibits limit-cycle behavior and we show that this is not altered by the 1/r singularity of the potential.
Highlights
In the limit where two-body scattering length a2 goes to infinity, infinitely many three-body bound states are accumulated at the three-body scattering threshold with a geometric spectrum
We report the results of our recent calculations of three nucleon bound states,3H and 3He, in pionless effective field theory including di-baryon fields at leading order, treating the Coulomb interaction nonperturbatively
The pionless effective field theory (EFT) including di-baryon fields has been applied to the study of spin doublet nd scattering and tritium [2]. (For a recent review, see, e.g., Ref. [3].) In the renormalization group (RG) analysis in that study, an oscillating behavior of the scattering amplitude in UV limit of a cutoff parameter is observed, and in order to make the amplitude cutoff independence, a nucleon-nucleon-di-baryon-di-baryon contact interaction is promoted to the leading order, which appears as a higher order term in the naive dimensional analysis
Summary
In the limit where two-body scattering length a2 (two-body binding energy B2) goes to infinity (nil), infinitely many three-body bound states are accumulated at the three-body scattering threshold with a geometric spectrum Those states are known as Efimov states [1]. We determine the strength of the three-body force needed to reproduce observed 3He binding energy The difference between this and the corresponding force needed for the triton is of the expected size for an electromagnetic effect.
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