Dennis Bonatsos

Quantum algebraic description of vibrational molecular spectra

Abstract Vibrational spectra of diatomic molecules can be described in terms of the q-deformed anharmonic oscillator. The Hamiltonian has the Uq(2) ⊃ Oq(2) symmetry, where q is the parameter measuring its deviation from the usual U(2) ⊃ O(2) symmetry. The energy formula obtained is equivalent to an expansion in terms of powers of (υ + 1 2 , where υ is the vibrational quantum number, and corresponds to summing a Dunham expansion for vibrational molecular spectra.

Effects of short-range correlations on the self-energy in the optical model of finite nuclei

Abstract The real and imaginary parts for the self-energy of a nucleon interacting with a finite nucleus ( 16 O) are derived from a realistic one-boson-exchange potential including terms up to second order in the Brueckner G -matrix. Effects of 2-particle-1-hole and 3-particle-2-hole correlations on the optical model potential are evaluated. The studies are performed in a mixed representation, employing a basis of oscillator functions for the occupied hole states and plane wave states for the unoccupied particle states. Attempts are discussed to represent the resulting self-energies in terms of a local energy-dependent potential.

B(E2) transition probabilities in the q-rotator model with SUq(2) symmetry

The SUq(2) symmetry of the q-rotator model, which for rotational bands predicts squeezing of the energy levels equivalent to the variable moment of inertia (VMI) model, predicts an increase with angular momentum of the B(E2) transition probabilities among these levels, while the rigid rotor model predicts saturation and the interacting boson model predicts a decrease. Some evidence supporting the SUq(2) prediction is presented. The possible usefulness of the quantum algebraic method in extending the VMI concept to B(E2) transition probabilities is pointed out.

Discretization of the phase space for a q-deformed harmonic oscillator with q a root of unity

The “position” and “momentum” operators for the q-deformed oscillator with q being a root of unity are proved to have discrete eigenvalues which are roots of deformed Hermite polynomials. The Fourier transform connecting the “position” and “momentum” representations is also found. The phase space of this oscillator has a lattice structure, which is a non-uniformly distributed grid. Non-equidistant lattice structures also occur in the cases of the truncated harmonic oscillator and of the q-deformed parafermionic oscillator, while the parafermionic oscillator corresponds to a uniformly distributed grid.

Quantum algebraic description of the pairing correlations in a single-j nuclear shell

Pairing in a single-j shell is described in terms of two Q-oscillators, one describing the J=0 fermion pairs and the other corresponding to the J not=0 pairs, the deformation parameter T=ln Q being related to the inverse of the size of the shell. Using these two oscillators an SUQ(2) algebra is constructed, while a pairing Hamiltonian giving the correct energy eigenvalues up to terms of first order in the small parameter can be written in terms of the Casimir operators of the algebras appearing in the UQ(2) contains/implies UQ(1) chain, thus exhibiting a quantum algebraic dynamical symmetry. The additional terms introduced by the Q-oscillator are found to improve the agreement with the experimental data for the neutron pair separation energies of the Sn isotopes, with no extra parameter introduced.

Exact boson mappings for the proton-neutron nuclear p-shell with the symmetry Sp(12)⊃U(6)

Abstract The closed set of commutation relations obeyed by the fermion pair and multipole operators for a major shell of protons and neutrons in LST coupling is found. The case of a p-shell of protons and neutrons coupled to S =0 is studied in detail. The associated Lie algebra is the compact unitary symplectic algebra Sp(12). The corresponding multipole subalgebra is the unitary algebra U(6), which has an SU(3)⊗ U(1)⊗SU T (2) subalgebra. Number conserving exact boson mappings of both the Dyson and hermitian form are constructed and their group theoretical structure is emphasized. The method is directly generalizable to the case of an sd-shell of protons and neutrons and can lead to a link between the isospin invariant versions of the interacting boson model (IBM-3 and IBM-4) and the shell model. In addition it provides a bosonized version of the k -active limit of the isospin invariant form of the fermion dynamical symmetry model (FDSM).

Application of the commutator method for boson mapping

Abstract The boson mapping developed by Bonatsos, Klein and Li is applied to a single j -shell and the resulting energy levels are shown for a simple pairing plus quadrupole-quadrupole hamiltonian. The results are compared to the exact fermionic case, as well as to those obtained through use of the Otsuka-Arima-Iachello mapping and the Zirnbauer-Brink mapping. In all cases good results are obtained for the spherical and near-vibrational cases, while in the rotational limit the results are of lower quality.

Exact boson mappings for the nuclear single j = 32 shell of protons and neutrons with the symmetry SO(16) ⊃ U(8)

Abstract The closed set of commutation relations satisfied by the fermion pair and multipole operators for a system of many non-degenerate- j shells of protons and neutrons is found. The case of a single j = 3 2 shell of protons and neutrons with structure SO(16) ⊃ U(8) is studied in detail. An exact Dyson boson mapping is constructed first, which is subsequently hermitized. The present model is a generalization of Ginocchios SO(8) model for the case that protons and neutrons are simultaneously present and can serve as a tool in providing a shell-model justification of the interacting boson model in light nuclei.