I have a Snapper Hi-vac riding mower, with the large bagger on the back. First, i ride around and chop up the leaves, without the tube connected to the mower deck. Then, after i get a lot of them chopped smaller, i install the tube, and go around and vacuum them into the rear bagger.
Another method, is to leave the adapter chute off, tie up the flopper cover, and drive around and chop the leaves up much smaller, then do the normal pickup with the chute and bag.
That said: Go buy a Garden Rake! T.M. name. It has a cart that ya tow, an auxiliary engine/chopper that sets on the cart tongue, and a large flexible tube that runs from the deck to that engine, then from there into the enclosed cart! Two of my near neighbors have them! Those things suck up almost everything you can see, and some ya can't! If i could afford one, i'd have one!
Some machines have an extra feature--you can disconnect one tube and suck the leaves off yer shrubs, and outta yer garden--hence the name--Garden Rake. Expensive, but good investment.

Thanks so much for your reply. But we don't have a riding mower.
Sigh. Linda

Troy-Bilt makes two lawn leaf vacs. I have the non self propelled model and it, while able to handle lots of leaves, is a relatively heavy machine especially with a full bag of chopped leaves.This bag can weigh about 50# with some leaves.They make a self propelled model which should help with the job.