  Efimov states are a sequence of shallow 3-body bound states that arise when
the 2-body scattering length is large. Efimov showed that the binding energies
of these states can be calculated in terms of the scattering length and a
3-body parameter by solving a transcendental equation involving a universal
function of one variable. We calculate this universal function using effective
field theory and use it to describe the three-body system of 4He atoms. We also
extend Efimov's theory to include the effects of deep 2-body bound states,
which give widths to the Efimov states.
