Cold helium atoms are a unique system in which a single excited three-body Efimov bound 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 bound state of cold helium atoms. At leading-order (next-to-leading order) in SREFT, we find the average bond length of the $^{4}\mathrm{He}$ trimer ground state is 8.35(33) $\AA{}$ (10.29(2) $\AA{}$ ) and the average bond length of the excited $^{4}\mathrm{He}$ trimer Efimov bound state is 103(4) $\AA{}$ (105.3(2) $\AA{}$ ).Cold helium atoms are a unique system in which a single excited three-body Efimov bound 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 bound state of cold helium atoms. At leading-order (next-to-leading order) in SREFT, we find the average bond length of the $^{4}\mathrm{He}$ trimer ground state is 8.35(33) $\AA{}$ (10.29(2) $\AA{}$) and the average bond length of the excited $^{4}\mathrm{He}$ trimer Efimov bound state is 103(4) $\AA{}$ (105.3(2) $\AA{}$).

arXiv:2010.06105Physical Review AFeb 25, 20212 citations

The helium trimer has no bound rotational excited states

Teck-Ghee Lee, Brett D. Esry, Bingcong Gou +1 more

We have searched for bound states of helium trimers with nonzero angular momenta. Including only pair interactions between helium atoms, we solved the Schrödinger equation in hyperspherical coordinates in the adiabatic approximation. From the resulting potential curves - which are mostly repulsive for nonzero angular momenta - we conclude that there are no bound rotational excited states in any of the isotopes of the helium trimer. The symmetry properties of the trimer wavefunctions in the body-fixed frame are also analysed.We have searched for bound states of helium trimers with nonzero angular momenta. Including only pair interactions between helium atoms, we solved the Schrödinger equation in hyperspherical coordinates in the adiabatic approximation. From the resulting potential curves - which are mostly repulsive for nonzero angular momenta - we conclude that there are no bound rotational excited states in any of the isotopes of the helium trimer. The symmetry properties of the trimer wavefunctions in the body-fixed frame are also analysed.

Journal of Physics B Atomic Molecular and Optical PhysicsMar 22, 200121 citations

Long-range interactions between two helium atoms

Jun-Yi Zhang, Zong-Chao Yan, D. Vrinceanu +1 more

Bulletin of the American Physical SocietyMay 18, 20050 citations

Threshold Condition for Forming an Atomic4He Trimer

H. W. Graben, Kai-Ning Chang

The Rayleigh-Ritz variational principle is used to formulate a rigorous bound on the threshold conditions under which three helium four atoms will form a bound state when their pair interaction is represented by the Lennard-Jones (n, 6) model and their nonadditive interaction is taken to be the Muto-Axilrod-Teller triple-dipole potential. The accepted parameter values of the model with n equal to 12 predict a bound-state trimer. The oversight, that of failing to use the (12, 6) parameter values of Kihara, Midzuno and Shizume in the extensive work on liquid helium, is pointed out.The Rayleigh-Ritz variational principle is used to formulate a rigorous bound on the threshold conditions under which three helium four atoms will form a bound state when their pair interaction is represented by the Lennard-Jones (n, 6) model and their nonadditive interaction is taken to be the Muto-Axilrod-Teller triple-dipole potential. The accepted parameter values of the model with n equal to 12 predict a bound-state trimer. The oversight, that of failing to use the (12, 6) parameter values of Kihara, Midzuno and Shizume in the extensive work on liquid helium, is pointed out.

Journal of the Physical Society of JapanMar 15, 19800 citations

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 bound state of cold helium atoms. At leading-order (next-to-leading order) in SREFT, we find the average bond length of the

^{4}\mathrm{He}

trimer ground state is 8.35(33)

\AA{}

(10.29(2)

\AA{}

) and the average bond length of the excited

^{4}\mathrm{He}

trimer Efimov bound state is 103(4)

\AA{}

(105.3(2)

\AA{}