Angular Correlations of Bosons and Fermions

Walter Greiner

A.‐S. F. Obada, M. M. A. Ahmed

The generalized boson-fermion interacting system is described by transforming the angular momentum operators into boson operators. Using the Holstein-Primakoff model, the forms for the expectation values of the different number operators are obtained. The second-order correlation function is calculated in different state representations.

Euan J. Squires, Steve Mackman

José Barea, R. Bijker, Alejandro Frank

The observed preponderance of ground states with angular momentum $L=0$ in many-body quantum systems with random two-body interactions is analyzed in terms of correlation coefficients (covariances) among different eigenstates. It is shown that the geometric analysis of Chau et al. can be interpreted in terms of correlations (covariances) between energy eigenvalues, thus providing an entirely statistical explanation of the distribution of ground state angular momenta of randomly interacting quantum systems that, in principle, is valid for both fermionic and bosonic systems. The method is illustrated for the interacting boson model.

D Bonatsis

In a single-j shell the author considers fermion pair and multipole operators coupled to zero angular momentum. The commutation relations of these operators can be satisfied up to first-order corrections by suitably defined q-bosons, onto which the fermion pair operators are mapped. After performing the same mapping to a simple pairing Hamiltonian, it is proved that the pairing energies are also correctly reproduced up to the same order. The small parameter used (T=In Q) is found to be inversely proportional to the size of the shell.