Diabatic and Adiabatic Collective Motion in a Model Pairing System

Large amplitude collective motion is investigated for a model pairing Hamiltonian containing an avoided level crossing. A classical theory of collective motion for the adiabatic limit is applied utilising either a time-dependent mean-field theory or a direct parametrisation of the time-dependent Schr\"odinger equation. A modified local harmonic equation is formulated to take account of the Nambu-Goldstone mode. It turns out that in some cases the system selects a diabatic path. Requantizing the collective Hamiltonian, a reasonable agreement with an exact calculation for the low-lying levels are obtained for both weak and strong pairing force. This improves on results of the conventional Born-Oppenheimer approximation.Comment: 23 pages, 7 ps figures. Latex, uses revtex and graphic

Collective coordinates, shape transitions and shape coexistence: a microscopic approach

We investigate a description of shape-mixing and shape-transitions using collective coordinates. To that end we apply a theory of adiabatic large-amplitude motion to a simplified nuclear shell-model, where the approximate results can be contrasted with exact diagonalisations. We find excellent agreement for different regimes, and contrast the results with those from a more standard calculation using a quadrupole constraint. We show that the method employed in this work selects diabatic (crossing) potential energy curves where these are appropriate, and discuss the implications for a microscopic study of shape coexistence.Comment: 20 pages, including 6 ps file

Quantising the B=2 and B=3 Skyrmion systems

We examine the quantisation of a collective Hamiltonian for the two-baryon system derived by us in a previous paper. We show that by increasing the sophistication of the approximations we can obtain a bound state - or a resonance - not too far removed from the threshold with the quantum numbers of the deuteron. The energy of this state is shown to depend very sensitively on the parameters of the model. Subsequently we construct part of a collective Hamiltonian for the three baryon system. Large-amplitude quantum fluctuations play an important r\^ole in the intrinsic wave function of the ground-state, changing its symmetry from octahedral to cubic. Apart from the tetrahedron describing the minimum of the potential, we identify a ``doughnut'' and a ``pretzel'' as the most important saddle points in the potential energy surface. We show that it is likely that inclusion of fluctuations through these saddle points lead to an energy close to the triton's value.Comment: 32 pages, 19 Postscript figures, uses epsfig.sty and elsart.st

Effective Interactions in a Graphene Layer Induced by the Proximity to a Ferromagnet

The proximity-induced couplings in graphene due to the vicinity of a ferromagnetic insulator are analyzed. We combine general symmetry principles and simple tight-binding descriptions to consider different orientations of the magnetization. We find that, in addition to a simple exchange field, a number of other terms arise. Some of these terms act as magnetic orbital couplings, and others are proximity-induced spin-orbit interactions. The couplings are of similar order of magnitude, and depend on the orientation of the magnetization. A variety of phases, and anomalous Hall effect regimes, are possible.Comment: 10 pages, 3 figures, 3 table