  We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the
open-system spin dynamics of radical pairs subject to spin-selective
recombination reactions. For these systems, non-Lindbladian master equations
are widely employed, which account for recombination via the non
trace-preserving Haberkorn superoperator in combination with reaction-dependent
exchange and singlet-triplet dephasing terms. We show that this type of master
equation can be accommodated in the MCWF approach, by introducing a second type
of quantum jump that accounts for the reaction simply by suitably terminating
the propagation. In this way, we are able to evaluate approximate solutions to
the time-dependent radical pair survival probability for systems that have been
considered untreatable with the master equation approach until now. We
explicate the suggested approach with calculations for radical pair reactions
that have been suggested to be relevant for the quantum compass of birds and
related phenomena.
