Anyone have any experience of this?

My neighbour's beech tree is shedding thousands of beech seed cases and
seeds on my lawn (I reciprocate with ash seeds...). The lawn mower
picks some up, but not enough. The leaf vacuum also picks some up, but
the density of the seed cases is just about on the cusp as to whether or
not the vac picks them up.

So I was wondering if a lawn raker would be up to the job of picking up
the open seed cases. I'm not worried about the seed; the leaf vac picks
up some of that, and if any germinates the lawn mower or a selective
(broad-leaf) herbicide will deal with it. I know that the collection
boxes are pretty small, but it's better than nothing.

Also, can the seed cases be composted, or should they be burnt?

--

Jeff