Effective field theory analysis of boson-trimer bond lengths to next-to-leading order

Abstract

Cold Helium atoms are a unique system where a single excited three-body Efimov state occurs, naturally, without the need for an external magnetic field. While three-body bound state energies of cold Helium atoms have previously been investigated, recent experimental techniques have allowed their structure to also be studied. The weak interaction between Helium atoms leads to a helium-helium (dimer) scattering length, $a$, much larger than the helium-helium effective range of interaction, $r$. This feature is exploited in a theory that systematically expands observables in powers of $r/a$, known as short range effective field theory (srEFT), which has been used successfully to investigate properties of cold atom systems. Using srEFT we investigate the average bond length of atoms in the three-body ground state and excited Efimov state of cold Helium atoms. At leading-order (next-to-leading order) in srEFT, we find the average bond length of the $^4$He trimer ground state is 8.35(33) \r{A} (10.29(2) \r{A}) and the average bond length of the excited $^4$He trimer Efimov state is 103(4) \r{A} (105.3(2) \r{A}).