  We investigate the role of the collective antisymmetric state in entanglement
creation by spontaneous emission in a system of two non-overlapping two-level
atoms. We calculate and illustrate graphically populations of the collective
atomic states and the Wootters entanglement measure (concurrence) for two sets
of initial atomic conditions. Our calculations include the dipole-dipole
interaction and a spatial separation between the atoms that the antisymmetric
state of the system is included throughout even for small interatomic
separations. It is shown that spontaneous emission can lead to a transient
entanglement between the atoms even if the atoms were prepared initially in an
unentangled state. We find that the ability of spontaneous emission to create
the transient entanglement relies on the absence of population in the
collective symmetric state of the system. For the initial state of only one
atom excited, the entanglement builds up rapidly in time and reaches a maximum
for the parameter values corresponding roughly to zero population in the
symmetric state. On the other hand, for the initial condition of both atoms
excited, the atoms remain unentangled until the symmetric state is depopulated.
A simple physical interpretation of these results is given in terms of the
diagonal states of the density matrix of the system. We also study entanglement
creation in a system of two non-identical atoms of different transition
frequencies. It is found that the entanglement between the atoms can be
enhanced compared to that for identical atoms, and can decay with two different
time scales resulting from the coherent transfer of the population from the
symmetric to the antisymmetric state. In addition, we find that a decaying
initial entanglement between the atoms can display a revival behaviour.
