  Superradiant decay is accompanied by two kinds of collective lineshifts, an
induced shift and the spontaneous "collective Lamb shift." Both form as sum of
dipole-dipole interaction-induced level shifts between atoms in the system. We
have developed a procedure to obtain numerical results on this model that
self-consistently incorporates the shifts. The induced shift displays large
non-zero values early in the system evolution. In addition, its effect on the
superradiant system is studied: there is only a very small dephasing effect on
the decay rate. While the induced shift is largely absent in not-too strongly
driven systems, this parameter region might provide a good experimental regime
for measuring the collective Lamb shift. These results can have important
consequences for highly sensitive systems, such as quantum information science
or atomic clocks.
