SR,

Vice using the questionable the Ground {Green Wire} of your
Household AC Power System.

Why not consider a simple Around-the-Room {Ceiling Level}
Horizontal [Flat] Loop Antenna. The Loop Antenna is consider
a 'blanced' Antenna that does not require a Ground and is
Horizontally Polarized so it generally pick-up less man made noise.

The "In-Door" Horizontal [Flat] Loop Antenna is easy to build;
usually is relatively long 40-60 Feet for an In-Door Antenna;
and relatively lower noise pick-up to an in-door vertical antenna
or long wire antenna.

The Radio or Receiver can be run off of AC with an AC Ground
connection via the AC Power Plug or DC without any Ground
connection at all.

something to consider - iane ~ RHF