  Atomic Kapitza-Dirac Bragg regime scattering is a multiphoton process in
which a neutral atom undergoes a change of momentum through an interaction with
a coherent light source. When the Bragg conditions are met, the outgoing atom
beams are spatially quantized. Counterpropagating lasers act as pump and probe
scattering from far-off-resonant excited intermediate electronic states,
leaving the atoms in the electronic ground state with quantized transverse
momentum. Each nontrivial scattering event imparts transverse velocity and
therefore kinetic energy to the deflected atoms through recoil. In the Bragg
regime, the loss of energy in the light fields is equal to the gain of kinetic
energy in the atom. Energy nonconserving intermediate states, which are
described by nonadiabatic contributions, are not accounted for by first-order
off-resonant states. By comparing the solutions of increasing orders of
off-resonant intermediate states, it becomes clear that calculating the correct
Pendell\"{o}sung frequencies and phases requires including an ever increasing
number of off-resonant states in proportion to the square root of the field
strength.
