When a target nucleus X is irradiated with a photon beam with energy Ey, it forms a compound nucleus, which releases one neutron and becomes its isotope X0. The reaction rate of X(Y, n)X0 at time t is given by

B(2n)

rX—X'(t) = J d£y dEx ffX! X, (Ey)nx(t)a, (1.6)

B(n) Y

where ffX —x>(Ey) is the reaction cross section of X(y, n)X’, nx( t) is the number of target nucleus per unit area at time t, and a is the attenuation factor of incident photons through a thick target. dNy/dEy is expressed with Eq. (1.5) and aX — X’ (Ey) is calculated from Eq. (1.2) using the TALYS code.

Figure 1.4 shows a calculation in which the photon beam is generated by the laser Compton scattering of 1.2 GeV electrons and 0.7 eV laser beams. We assume that the cylindrical target of 137Cs of 1 g is irradiated with a photon beam with energy B(n) < EY < B(2n) within a radius r « 0.8 mm at 2 m from the interaction point. When a target of 137Cs is irradiated with photons and is excited to GDR, the (Y, Y), (Y, n) and (y, 2n) reactions mainly occur. We consider 137Cs, 136Cs, 135Cs, and 134Cs as the isotopes generated by the transmutation. The numbers of these isotopes are expressed as

П137 (t + At) = П137 (t)e 7,137At — r137!136(t) — r137!135(t), (1.7)

П136(t + At) = n136(t)e 7136At + Г137 —^136(t) — Г136!135(t) — П36—134(t), (1.8)

n135 (t + At) = n 135 (t)e 7135At + r 137—135 (t) + r 136—135 (t) — r 135—134 C’1) . (1.9)

n134(t + At) = n134(t)e ^1344t + r 136—134(t) + r 135—134(t). (1.10)

One can calculate the number of each isotopes by solving these equations with the Runge-Kutta method.