This is a really cool and rare made in 1977  white (faded nitro finish coat that becomes a bit yellow )  
Originally introduced as an upgrade to the Rickenbacker 4000, the Rickenbacker 4001 is one of the all-time classic rock basses. 
Offered with a combination of a fat Rickenbacker bass pickup at the bridge and a smaller bar pickup at the neck, the 4001 gave bassists a wide range of big bass tones to work with. Starting in 1971, stereo “Rick-O-Sound” outputs became standard on the 4001. 
This piece has a slight crack on the pickguard 
Two little hole that has been made for a thumb rest  piece that is delivered with the bass in her original case