R. Gerard wrote:
We have a heat pump. The compressor is outside; the air handler is
inside, in an unfinished attic. I.e., there is no flooring and access
is through a "hatch" reached by a ladder.

Every time someone goes up there, to service the air handler,
install an attic fan, etc., the heads of nails holding the ceiling to
the joists "pop" through the ceiling below, making a very noticeable
dimple in the paint, and occasionally breaking through. It's a real
drag having this happen every time someone goes up there.

Is there some way to prevent this from happening?

I thought that if I were able to floor part of the attic, i.e., the
areas where these servicemen need to walk in order to access the air
handler, might this spread the load somewhat and perhaps prevent these
dimples from forming every time they go up there?

If so, what thickness of particle board should I put down?

Particle board is a bad choice - for anything. If it's just a narrow
area where they have to walk use planks. Generally using 1/2" ply is
all that is needed for such an application, but the 1/2" ply is
probably a bit thin to distribute the load. Stiffness is proportional
to the thickness of the material. You have to balance that with not
adding too much weight - hence the planks. You don't need a high grade
of wood at all, and a couple of 1x8s next to each other will form a
sufficient walkway. It'll be easier to get planks up there anyway.
Don't have adjoining pieces break on the same joist - stagger them. A
lower grade cedar might be your best choice, balancing weight, strength
and cost. Plus they smell nice.

If folks think this won't do the trick, what might???

Pull those offending nails and use screws. They won't pop the same
way. Space them about 8" apart - 1.25" is all you need.

R