Some aspects of the interaction of light with matter

Part I. The shell model near 208Pb.
The nucleus 208Pb has a double closed shell of protons and neutrons. Because of the stability of this structure it is possible that a nucleus with a few extra particles outside the double closed shell can be described as a system in which these few particles move in an average central field produced by the 208Pb core. It is assumed that the individual particle levels are those predicted by the shell model, and that the nuclear forces acting between the extra particles can be treated as a perturbation on their station in the central field. The behaviour of vacancies in the closed shell is equivalent to the behaviour of particles in the same states. Thus nuclei with a few holes in the closed shell and nuclei with a few extra particles can be treated by identical methods. Similar considerations hold for nuclei with a few holes and a few extra particles except for some details in the coupling of the angular moments of holes and particles.
To investigate the effect of internucleon forces it is necessary to calculate matrix elements of the internucleon potential two-particle states. It has been hoped that in heavy nuclei, where the radius of the nucleus is large compared with the range of nuclear forces, the effect of the range of the forces would be small so that zero range forces could be used. The effect of the range of the forces has been investigated and a relatively simple expansion obtained for the matrix elements of the internucleon potential as a power series in the ratio of the range of the nuclear forces to the nuclear radius. Calculations have been extended to take the second term of the series into account, and it is found that, in many cases, the contribution of this term is very important. This is particularly so for Majorana forces in a two-particle state coupled to give a low spin. The zero range approximation gives too large an interaction in states of low spin, while it gives a good estimate of the interaction in states of high spin. In particle hole configurations this situation is exactly reversed.
As an example of the application of the model the energy levels of the four nuclei 210Bi, 208Te, 204Pb and 202Pb have been investigated. In 210Bi it is possible to classify the known low lying levels in terms of two particle neutron-proton configurations and in particular to predict a low lying isomeric state with I - 8. 208Te is of interest as it gives an example of a particle hole configuration. The even-even nuclei 204Pb and 202Pb have very similar level schemes each with a 9-isomeric state. These scemes can be understood on the basis of the above model.
Part II. Some reactions with neutrons.
Reactions with neutrons are of considerable importance in the study of heavy nuclei. The interaction producing the reaction is the short range nuclear force, the cross sections are large, and there is no Coulomb barrier to complicate the interpretation of the experiments. Two types of reaction have been considered. The first is a process of inelastic scattering in the 1 MeV region and the second resonance scattering at slow neutron energies.
The inelastic scattering of neutrons is usually thought of as a compound nucleus process. In regions of atomic weight A = 170 and A = 230, however, the nucleus is highly distorted and there is the possibility of a direct inelastic process which can be described as follows. The neutron strikes the target nucleus and on reflection from its surface the neutrons set the target nucleus into rotation (i.e. excite a surface rotational mode) and are scattered with reduced energy. The interaction of the neutron with the nucleus has been represented by a complex potential well (the 'optical model'} the complex parts of the potential giving an absorption to be identified with compound nucleus formation. It is known that the "optical model" gives large cross sections in the region of atomic weights A = 150 and A = 240 corresponding to S, D and P partial wave resonances inside the nucleus. In these regions of atomic weight it is found that the scattering cross section predicted by the direct process is comparable with the compound inelastic cross section, while in intermediate regions of atomic weight the direct process is unimportant. The two processes are incoherent and give different neutron and γ-ray angular distributions.
In recent years there has been an intensive experimental investigation of the properties of slow neutron resonances in many nuclei. These resonances correspond to virtual levels of the compound nucleus and the experiments tell us something about high nuclear states. In general these states will be a complicated mixture of single particle configurations and there is a possibility that their properties can be treated statistically. On this assumption the distribution function for reaction widths has been investigated and it is found that reduced partial widths have a distribution which is approximately exponential.
Photo capture of neutrons is the inverse process to the nuclear photo effect. The dipole photo effect is known to have a broad resonance at about 13 → 20 MeV where the width and position of this resonance very slowly with atomic weight and appear insensitive to details of nuclear structure. An equation to the resonance is assumed and used to calculate the expectation values of the dipole radiation widths of slow neutron resonances. The theory predicts radiation widths too large by a factor of 3; but gives the right variation with atomic weight. The variation of radiation width with the spin of the emitting state is considered and it is found, using a modified sum rule, that the total radiation with Γγ should be independent of spin. The spectral distribution of the emitted γ-rays and the dependence of the total width on the energy of the radiating state are investigated.