  The QCD axion and axion-like particles are compelling candidates for galactic
dark matter. Theoretically, axions can convert into photons in the presence of
a strong external magnetic field, which means it is possible to search for them
experimentally. One approach is to use radio telescopes with high-resolution
spectrometers to look for axion-photon conversion in the magnetospheres of
neutron stars. In this paper, we describe the results obtained using a novel
approach where we used the Green Bank Telescope (GBT) to search for radio
transients produced by collisions between neutron stars and dark matter clumps
known as axion miniclusters. We used the VErsatile GBT Astronomical
Spectrometer (VEGAS) and the X-band receiver (8 to 10 GHz) to observe the core
of Andromeda. Our measurements are sensitive to axions with masses between 33
and 42 $\mu$eV with $\Delta$$m_a$ = 3.8$\times10^{-4}$ $\mu$eV. This paper
gives a description of the search method we developed, including observation
and analysis strategies. Given our analysis algorithm choices and the
instrument sensitivity ($\sim$2 mJy in each spectral channel), we did not find
any candidate signals greater than 5$\sigma$. We are currently implementing
this search method in other spectral bands.
