Inhaltszusammenfassung

The harmonic oscillator shell model with LS-coupling is studied from a group-theoretical point of view. Leaving aside for the moment the spin and isospin degrees of freedom the most general transformation group, which leaves the hamiltonian invariant, is determined to be the unitary group in 3A dimensions (U_3A), where A is the nucleon number. The following chain of subgroups is considered: U_3A > U_3 × U_A > O_3^(+) × U_A > O_3^(+) × S_A. (U_3 and U_A denote the unitary group in 3 and A di...The harmonic oscillator shell model with LS-coupling is studied from a group-theoretical point of view. Leaving aside for the moment the spin and isospin degrees of freedom the most general transformation group, which leaves the hamiltonian invariant, is determined to be the unitary group in 3A dimensions (U_3A), where A is the nucleon number. The following chain of subgroups is considered: U_3A > U_3 × U_A > O_3^(+) × U_A > O_3^(+) × S_A. (U_3 and U_A denote the unitary group in 3 and A dimensions, respectively, × means direct product, O_3^(+) rotation group in 3 dimensions, S_A group of all permutations of the A nucleons). The classification of the wavefunctions with respect to energy is equivalent to a classification according to irreducible representations of U_3A . Therefore we can classify the wavefunctions in each energy level with respect to irreducible representations of U3, O_3^(+) and S_A by studying the laws of decomposition of the irreducible representations of U_3A into those of the subgroups. Such a classification is of physical importance in connection with the Elliot model. The last step going from O_3^(+) × U_A to O_3^(+) × S_A leads in a natural way to the problem of center-of-mass motion and one obtaines a clear separation of the totality of wave-functions into “good” states and “spurious” states. The most appropriate mathematical tool to deal with this question is the theory of “inner plethysm”. » weiterlesen» einklappen

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Klassifikation

DFG Fachgebiet:
Teilchen, Kerne und Felder

DDC Sachgruppe:
Naturwissenschaften