Biomedical subjects
Publications and source records attributed to P Van Isacker.
The complete exact solution of the T = 1 neutron-proton pairing Hamiltonian is presented in the context of the SO(5) Richardson-Gaudin model with nondegenerate single-particle levels and including isospin symmetry-breaking terms. The power of the method is illustrated with a numerical calculation for for 64Ge for a pf + g9/2 model space which is out of reach of modern shell-model codes.
An analytic solution of the Gross-Pitaevskii equation for a rotating Bose-Einstein condensate of trapped atoms describes the onset of vorticity when the rotational speed is increased, starting with the entry of the first vortex and followed by the formation of growing symmetric Wigner molecules. It explains the staircase of angular momentum jumps and the behavior of the bosonic occupancies observed in numerical studies. The similarity of this behavior and mesoscopic superconductors is discussed.
Predictions are obtained for T=0 and T=1 deuteron-transfer intensities between self-conjugate N=Z nuclei on the basis of a simplified interacting boson model which considers bosons without orbital angular momentum but with full spin-isospin structure. These transfer predictions can be correlated with nuclear binding energies in specific regions of the mass table.
In a k-dimensional system of weakly interacting Bose atoms trapped by a spherically symmetric and harmonic external potential, an exact expression is obtained for the rotating ground states at a fixed angular momentum. The result is valid for arbitrary interactions obeying minimal physical requirements. Depending on the sign of a modified scattering length, it reduces to either a collective rotation or a condensed vortex state, with no alternative. The ground state can undergo a kind of quantum phase transition when the shape of the interaction potential is smoothly varied.
The number of levels of a many-fermion system confined by a harmonic-oscillator potential is computed as a function of excitation energy. Because of its exact nature, the formalism accounts for effects of shell structure on the level density. The method is easily extended to a variety of situations as is illustrated with the inclusion of isospin and deformation effects as well as a calculation of the number of spurious states.
We introduce the notion of a generalized partial dynamical-symmetry for which part of the eigenstates have part of the dynamical symmetry. This general concept is illustrated with the example of Hamiltonians with a partial dynamical O(6) symmetry in the framework of the interacting boson model. The resulting spectrum and electromagnetic transitions are compared with empirical data in 162Dy.