120vac input, 12vdc output plus more

I want to use a series of flood light type P.I.R. motion sensors to activate a chime or door bell. so far I have several motion sensors with the output trigger wires connected together and these work well together for turning on the same 120vac light bulb.

how can I change this 120vac output (that is basically constant since the lowest setting for on duration is 5 minutes) to a 5 - 12 vdc pulse output?

Im thinking I need a 120vac Normaly Open, SPST relay but I dont know exactly which one or how to determine this. can anyone help me with this?

from there, I think adding this 12vdc assemblage:
will change the constant output to momentary so that I can utilize a peizo or bell chime but is there a simpler way?

Ive only ever dealt with 12vdc relays, 120vac is all new to me!

thanks

or, can anyone suggest where else to ask or know a specific search term I could use to find more info somewhere?

seems pretty simple until you try it ;-)