The slow magnetosonic waves can, under certain conditions, have a disc
rete set of regular eigenmodes similar to the discrete Alfven wave sqe
ctrum (Sturmian or anti-Sturmian). The latter were shown to explain th
e short period (2-8 min) prominence loop oscillations as a global Alfv
en modes. Here, we slow that the anti-sturmian discrete slow wave spec
trum can explain the long period (24-84 min) oscillations of solar loo
p prominences. we have also estimated the Q(Q(-1) = I-m omega/omega) f
actor, due to electron and ion Cherenkov damping, for the loop cavity,
and found the value of Q similar to 6 which is compatible with the ob
servations of loop period oscillation and life time.