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

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

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