1.2.1 Reaction via Giant Dipole Resonance

Nuclear transmutation with laser Compton scattering uses photonuclear reactions via GDR because the cross section of GDR is quite large and the total cross section is a smooth function of mass number. GDR is a collective excitation of a nucleus involving almost all nucleons, which is interpreted classically as a macroscopic oscillation of a bulk of protons against that of neutrons. The total cross section °gDR, the resonance energy ER, and the width rR are given by [4]

4dR = 60(1 + к) NZ mb • MeV,

Er = 31.2A~1/3 + 20.6A~1/6MeV, (1Л)

Tr = 0.0026ER91 MeV,

where N and Z are the neutron and proton numbers, A = N+Z is the mass number, and к, which is roughly equal to 0.2 for medium nuclides, is a correction coefficient for the pion exchange.

When a target nucleus is irradiated with a photon and excited to GDR, it often forms a compound nucleus with only a small contribution of a pre-equilibrium reaction [5]. The compound nucleus is an excited state in which the energy brought

Fig. 1.1 Schematic illustration of nuclear transmutation with laser Compton scattering

by the incident particle is shared among all degrees of freedom of the nucleus. The reaction cross section from an initial channel a to a final channel в proceeding through a compound nucleus state of spin J can be written by the Hauser-Feshbach formula as

(1.2)

where ka is the wave number in the initial channel, gJ is a statistical factor, T is a transmission coefficient, and (T) is the energy average of T. The statistical factor is

where ia and Ia are the projectile and target spins.

Calculations of reaction cross sections are performed using the nuclear model code TALYS (version 1.4) [6]. The neutron transmission coefficients are calculated via the global optical potential [7]. The gamma-ray transmission coefficients are calculated through the energy-dependent gamma-ray strength function according to Brink [8] and Axel [9]. We employed the level density given by Gilbert and Cameron [10].

Figure 1.2 shows the photonuclear reaction cross sections of 137Cs calculated using the TALYS code. In the incident photon energy B(n) < EY < B(2n), where B (n) and B(2n) are the one — and two-neutron binding energies, respectively, we can see that the (y, n) reaction mainly occurs. Because the resonance energy of GDR ER is 15-18 MeV, which is roughly equal to B(2n) for medium nuclides, about half the reactions via GDR are (y, n) reactions, which occur at B(n) < EY < B(2n).