I don't understand the type of antenna he / she built.

A half wave what? J Pole?

A little secret - take a television antenna - UHF / VHF, turn it on it's side if you want. You can even use a antenna pre amp. USE a antenna rotor.

Connect the antenna to some good RG 6 Quad Shield and run it into your house, into the power injector, into some more good Quad Shield and adapter to BNC.

Turn the antenna in the direction you desire to receive in.

I used a Winegard 8200U antenna and a Channel Master CM 7777 pre amp and Channel Master rotor @ 24' in my backyard and was able to hear stations that I could not hear with my Yaesu 8900 and my Diamond V2000 antenna nor my Cushcraft 4 element 2 meter beam antenna.

If all you want to do is receive, it does not matter if the cable is 50 ohm or 75 ohm nominal impedance.. You are not going to get standing waves from reception - only transmission.

Even better cable is the hardline that the TV cable company uses from pole to pole. I think its nominal resistance is about 77 Ohm's, but its loss rate is . 07 or something or another in like 100 feet @ 500 Mhz.

Enjoy the scanner, do not expect to hear much with a home brew vertical dipole antenna.