The Eikonal-SVEAS analytic closed forms for single-photon superradiance

Using the Slowly Varying Envelope Approximation in Space and the Eikonal Approximation, we obtain closed-form analytic expressions for the single-photon superradiance from a spherical cloud of two-level atoms in the scalar photon theory. The value 0.171, calculated in this approximation for the value of the maximum probability of secondary excited states, agrees with those obtained from the eigenmode analysis method and from the Debye-refined method.