The Thomas-Ehrman shift for Be-11 and N-11 mirror nuclei, which was recentl
y observed as a differential energy shift between s and other orbital state
s, is investigated in terms of complex expectation values. In calculating t
he complex expectation values, we use a new method which was recently propo
sed within the framework of the complex scaling method. The physical origin
of the energy shift can be understood by considering the effects of the s-
wave halo and the Coulomb barrier top. These two effects are discussed as a
nother proof of a halo in addition to the observation of large matter radii
in the drip-line nuclei.