The value of an isomeric ratio (IR) in N = 81 isotones (Ba-137, Ce-139, Nd-
141, and Sm-143) is studied by means of the (gamma,n) reaction. This quanti
ty measures a probability to populate the isomeric state in respect to the
ground state population. In (gamma,n) reactions, the giant dipole resonance
(GDR) is excited and after its decay by a neutron emission, the nucleus ha
s an excitation energy of a few MeV. The forthcoming gamma decay by direct
or cascade transitions deexcites the nucleus into an isomeric or ground sta
te. It has been observed experimentally that the IR for Ba-137 and Ce-139 e
quals about 0.13 while in two heavier isotones it is even less than half th
e size. To explain this effect, the structure of the excited states in the
energy region up to 6.5 MeV has been calculated within the quasiparticle ph
onon model. Many stales are found connected to the ground and isomeric stat
es by E1, E2, and M1 transitions. The single-particle component of the wave
function is responsible for the large values of the transitions. The calcu
lated value of the isomeric ratio is in very good agreement with the experi
mental data for all isotones. A slightly different value of maximum energy
with which the nuclei rest after neutron decay of the GDR is responsible fo
r the reported effect of the A dependence of the IR.