I guarantee its an 8 string bass playing a harmonic.
That bass is in stereo on both tracks. Its double tracked on the chris cornell track and has stereo chorus and reverb on it ....
Here I did this in about 10 minutes.
http://www.jasoncohenitservices.com/Snare.wav
6 tracks of bass
Track 1 - Harmonic at 5th fret g string panned 100 L
Track 2 - Harmonic at 5th fret g string panned 100 R
Track 3 - Harmonic at 17th fret g string panned 100 L
Track 4 - Harmonic at 17th fret g string panned 100 R
Track 5 - Open g string panned 100 L
Track 6 - Open g string panned 100 R
All bass tracks send to a bus with chorus and some verb, they were also gated with a release time matching the reverb I used on the snare
The snare had just a room reverb on it with a fairly long tail.
Its not mixed perfect and the bass tracks could be a bit louder but as the reverb on the snare tails off you can hear the bass harmonics. If I mixed the bass a tad louder to match the reverb volume it would be almost perfect.
This still won't sound exactly like it as I don't have the same snare and verb but this is my take on a similar sound just using verb and compression on the snare. The quality of the verb used on the OP track speaks for itself, I could not get a single ITB verb to sound that smooth.
I know its not 100% but it is similar?
http://dl.dropbox.com/u/10584477/Snare hit test.wav
What's the chord that comes after this effect in your song Morgan? I'm hearing that effect in Billie Jean as a D, which is a perfect fifth above the Am chord that comes after. You can't just choose whatever note if you want the same feel.
The only issue I see with your file is the "pitch" of the resonance isnt high enough. I can assure its a harmonic on the bass being played. If you check the bass tab for the song you will see it.
Thats how I know what it was.
Unfortunately I didnt save any of the work, but to recreate it just do what I said above.
Haven't got a song to use this on yet, but it's a really cool effect that I'd like to use in the future. A nice departure from the usual reverse cymbal/snare or a subdrop for emphasis.