Projection operators for simple lie groups

Electromagnetic meson exchange currents

Projection operators for simple lie groups: II. General scheme for constructing lowering operators. The groups SU(n)

Projection operators are an important tool in nuclear structure theory, because in many circumstances it is useful to construct wave-functions ψ which are not eigenfunctions of some operator Λ, although it is apparent that the physical states must be eigenstates of that operator. Thus one first constructs ψ and then projects from it onto eigenfunctions of Λ. We discuss the cases of angular momentum, isospin, centre of mass energy, particle number and antisymmetry. We describe the integral projection operator, an expansion in shift operators, the product operator of Lowdin and another product operator (the cosine product). Certain methods which appear in the literature are seen to be equivalent to one or the other of these. We consider factors that influence the choice of an appropriate method. Projection occurs frequently in the context of a variational method (such as Hartree-Fock or BCS). We consider the question of projection before or after variation.

Projection operators in nuclear structure calculations

The continuum shell model represents a merger of the traditional shell model, the tool for understanding nuclear structure, with the physics of reactions. In this work a new time-dependent approach to the continuum shell model is presented, where construction and application of the time-dependent evolution operator culminate in an effective and successful strategy for tackling the nonstationary many-body dynamics. Details behind the technique and methods to overcome general problems associated with quantum many-body physics on the verge of stability are discussed. Topics presented include the construction of the time-dependent Green's function, the full propagator from the exact solution of Dyson's equation, a treatment of decays and virtual self-energy terms, the explicit time dependence and survival probability of states, the strength function and collective features of unstable systems, the center-of-mass problem, computation of the cross section and its Blatt-Biedenharn angular decomposition, Coulomb amplitudes, and interference. An extensive comparison with the R-matrix approach is offered. Realistic examples are used to demonstrate the techniques.

F.C. Khanna

Papers

Meson-exchange currents in thermal n-3He radiative capture

A projection operator for the spurious centre-of-mass motion