<<I agree with the suggestion of constructing one's own antenna, for non-mobile. But dipoles are less than optimal due to their directiveness.>>
So you hang it up as a vertical dipole, with the wire connected to the braid of the co-ax pointing downwards. That way it becomes omni-directional.
Be forewarned - a lot of cheapo scanners will become overloaded with a more efficient antenna. It won't damage the set, but you may well hear transmissionns which you are not tuned to. Eg a taxi driving past, or the local CB or amateur transmitters may blast through well away from their transmit frequencies.
Lastly, remind yourself of the WT Act: See the sticky on the ATC forum.