The Thomas-Reiche-Kuhn Sum Rule and the Rigid Rotator

It is shown that the Thomas-Reiche-Kuhn sum rule, associated with the photoabsorption cross section from quantum systems, appears to be violated in the case of the quantized rigid rotator, The origin of the apparent violation is investigated, and its resolution is presented on the basis of a related system, i.e., a particle in a spherical delta-function potential whose energy spectrum approaches that of the rigid rotator when the strength of the potential becomes large. (C) 1997 American Association of Physics Teachers

Isospin structure of one- and two-phonon GDR excitations

Isospin is included in the description of Coulomb excitation of multiple giant isovector dipole resonances. In the excitation of even-even nuclei, a relevant portion of the excitation strength is shown to be associated with 1+ two-phonon states, which tends to be hindered or completely supressed in calculations in which the isospin degree of freedom is not considered. We find that the excitation cross sections is strongly dependent on the ground state isospin.Comment: 8 pages, 2 figure

Connection Between Conserved Quantities and Degeneracies in Quantum Systems

In the framework of quantum theory, we present one theorem and three corollaries regarding the direct connection between constants of motion of a physical system and degeneracies of its energy eigenvalues. It is shown that this connection emerges when there exist quantum operators which commute with the Hamiltonian, but not with each other. Further it is shown that if the commutator of these operators is a nonvanishing constant number then (a) all the eigenvalues of the system are degenerate, and (b) the degree of degeneracy is infinite. A number of examples are discussed including the parity degeneracy of the hydrogen atom and the infinite degeneracy of the Landau levels of a charged particle in a constant magnetic field. (C) 1995 American Association of Physics Teachers

Nuclear excitations and reaction mechanisms

The main theme of this report is the study and interpretation of the sequence of events that occur during the collisions of nuclear particles. Some of the processes discussed in parts A and B involve short range interactions; others involve interactions of long range. In most of part A one of the particles in the initial or in the final state (or in both) is a photon, which serves as a probe of the second particle, which may be a nucleus, a proton, a pion or any other hadron. The complexity of the processes taking place during the collisions makes it necessary to simplify some aspects of the physical problem. This leads to the introduction of modals which are used to describe a limited number of features in as much detail as possible. The main interest is the understanding of the hadronic excitations which result from the absorption of a photon and the determination of the fundamental structure constants of the target particle. In part B, all the particles are hadrons. The purpose here is to develop and apply optimal quantal methods appropriate for describing the interacting systems. Of particular interest are three-particle collision systems in which the final state consists of three free particles. Part B also considers the process of nuclear fusion as catalyzed by bound muons