  We discuss the creation of entanglement between two two-level atoms in the
dissipative process of spontaneous emission. 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. The amount of
entanglement created in the system is quantified by using two different
measures: concurrence and negativity. We find analytical formulas for the
evolution of concurrence and negativity in the system. We also find the
analytical relation between the two measures of entanglement. The system
consists of two two-level atoms which are separated by an arbitrary distance
$r_{12}$ and interact with each other via the dipole-dipole interaction, and
the antisymmetric state of the system is included throughout, even for small
inter-atomic separations, in contrast to the small sample model. It is shown
that for sufficiently large values of the dipole-dipole interaction initially
the entanglement exhibits oscillatory behaviour with considerable entanglement
in the peaks. For longer times the amount of entanglement is directly related
to the population of the slowly decaying antisymmetric state.
