  The phase time in quantum tunneling can be disentangled into a dwell time
plus a term arising due to the interference of the reflected and incident waves
in front of the barrier. The interference term dominates at low energies and as
E --> 0, this term and hence the phase time becomes singular. With the s-wave
motion in three dimensions being equivalent to that of a one-dimensional motion
in the radial coordinate, a similar singularity shows up in the phase time
delay of s-wave resonances. Relating the scattering matrix in three dimensional
collisions to the reflection amplitude, the interference term in tunneling can
be identified as a term given in terms of the transition matrix in scattering.
Subtraction of this term from the phase time delay gives the dwell time delay
which is finite at all energies and is useful in characterizing s-wave
resonances such as the sigma meson and mesic nuclei near threshold.
