  In this work, we investigate the effect of electromagnetic (EM) field on the
generation of 2e-2h states from 1e-2h states. One of the fundamental ways by
which electromagnetic (EM) waves interact with matter is by the generation of
excited electronic states. The interaction of EM field with atoms and molecules
is given by the field-dependent Hamiltonian. Excited states are intrinsically
transient in nature because they are not stationary states of the
field-dependent Hamiltonian. Consequently, the time-dependent dynamics of
excited states depend strongly on the external electromagnetic field. Starting
with the 1e-1h excitation in a general many-electron system, the system was
propagated in time using time-dependent perturbation theory (TDPT). The
expression for time-dependent transition probability of
$(1\mathrm{e}-1\mathrm{h}) \rightarrow (2\mathrm{e}-2\mathrm{h})$ was evaluated
for a given time $t$ up to second-order in TDPT using diagrammatic techniques.
The derivation does not assume any a priori approximations to the
electron-electron correlation operator and presents the derivation of a
complete set of contributing diagrams associated with the full configuration
interaction wave function. The result from this work show that the calculation
of time-dependent transition probability can be factored into a
time-independent and time-dependent components. This is a significant outcome
for efficient computation of the time-dependent transition probability because
it allows for pre-computation of time-independent components before the start
of the calculations.
