  Diffractive dissociation of quasi-real photons at a photon-proton centre of
mass energy of W ~ 200 GeV is studied with the ZEUS detector at HERA. The
process under consideration is gamma p -> X N, where X is the diffractively
dissociated photon system of mass M_X and N is either a proton or a nucleonic
system with mass M_N < 2GeV. The cross section for this process in the interval
3 < M_X < 24 GeV relative to the total photoproduction cross section was
measured to be sigma^partial_D / sigma_tot = 6.2 +- 0.2(stat) +- 1.4(syst)%.
After extrapolating this result to the mass interval of m_phi^2 < M_X^2 < 0.05
W^2 and correcting it for proton dissociation, the fraction of the total cross
section attributed to single diffractive photon dissociation, gamma p -> X p,
is found to be sigma_SD / sigma_tot = 13.3 +- 0.5(stat) +- 3.6(syst)%. The mass
spectrum of the dissociated photon system in the interval 8 < M_X < 24 GeV can
be described by the triple pomeron (PPP) diagram with an effective pomeron
intercept of alpha_P(0) = 1.12 +- 0.04(stat) +- 0.08(syst). The cross section
for photon dissociation in the range 3 < M_X < 8 GeV is significantly higher
than that expected from the triple pomeron amplitude describing the region 8 <
M_X < 24 GeV. Assuming that this discrepancy is due to a
pomeron-pomeron-reggeon (PPR) term, its contribution to the diffractive cross
section in the interval 3 < M_X < 24 GeV is estimated to be f_PPR = 26 +-
3(stat) +- 12(syst)%.
