Looks very much like a Cooey 64 that uses a plastic magazine. The plastic magazine has a corresponding groove on it's back half. Hate to seem too fussy...do you have a side view as well? I'm pretty sure it's a Cooey 64 though
Little bit of metal showing looks pretty nice too.
You could try to find a plastic magazine, or convert it to use modern (50 years running) magazines. To convert it:
-Acquire metal mag well (it's a pot metal part, that replaces your current magazine retainer)
-Take down your rifle (in your picture, it's the bigger screw) by removing the stock
(these rifles need to be clean to cycle well so get used to these steps. every 500-1000 rds)
-The takedown screw you removed to remove the stock fits into another screw. This screw holds your barrel retaining clip (and soon to be new mag well) in place. Remove the barrel retaining clip
-remove the 2 screws at the front of your trigger group (these screws will also retain your new magazine well), and the single screw at the back of the trigger group (not nec. if you're adding your new mag well, bet nec. if you're removing the bolt for cleaning)
-Remove your barrel (can be a chore, you can use the bolt to get it moving from the inside) Hold your barrel vertically with one hand, and tap with something nice (I have used hardwood rolling pins, soft mallets, even made a hardwood bushing) around the receiver. Have something soft under your receiver for it to land on. Avoid knocking your rear sights around too
-slide bolt forward, and pull outward/away on charging handle, the charging handle will come out, and the bolt will slide free of the receiver
Clean it all up. Do not lubricate the working parts unless you're trying to prevent rust during storage...run it dry. Also choose a round nosed ammo (I like Fed Champions, CCI Blazers, American Eagle...) you may have to try a few to find one that cycles nice in yours'.
Reassemble using your new magazine well. Kepp in mind the depth of the 2 screws at the front of the trigger group...if they go too deep into the receiver your bolt will bind. They should have lock washers...use them! Prone to getting loose n' lost.
Will try to snap some pictures when I clean mine next time if that will help.
Load it up and enjoy. I've only seen bolt actions marked as Sureshot.