arXiv subjects

C. -L. Song

Publications and source records attributed to C. -L. Song.

3 recordsLinked to original sources

arXiv1999

Beyond the Shell Model: The Canonical Nuclear Many-Body Problem as an Effective Theory

We describe a strategy for attacking the canonical nuclear structure problem ---bound-state properties of a system of point nucleons interacting via a two-body potential---which involves an expansion in the number of particles scattering at high momenta, but is otherwise exact. The required self-consistent solutions of the Bloch-Horowitz equation for effective interactions and operators are obtained by an efficient Green's function method based on the Lanczos algorithm. We carry out this program for the simplest nuclei, d and $^3$He, to contrast a rigorous effective theory with the shell model, thereby illustrating several of the uncontrolled approximations in the latter.

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arXiv1999

The Canonical Nuclear Many-Body Problem as a Rigorous Effective Theory

The shell model is the standard tool for addressing the canonical nuclear many-body problem of nonrelativistic nucleons interacting through a static potential. We discuss several of the uncontrolled approximations that are made in this model to motivate a different approach, one based on an exact solution of the Bloch-Horowitz equation. We argue that the necessary self-consistent solutions of this equation can be obtained efficiently by a Green's function expansion based on the Lanczos algorithm. The resulting effective theory is carried out for the simplest nuclei, d and 3He, using realistic NN interactions such as the Argonne v18 and Reid93 potentials, in order to contrast the results with the shell model. We discuss the wave function normalization, the evolution of the wave function as the "shell model" space is varied, and the magnetic elastic effective operator. The numerical results show a simple renormalization group behavior that differs from effective field theory treatments of the two- and three-body problems. The likely origin of this scaling is discussed.

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arXiv1995

Large-basis shell model studies of light nuclei with a multi-valued G-matrix effective interaction

Large-basis shell model studies of low-lying excitations in light nuclei from 4He to 7Li have been performed with a multi-valued G-matrix effective interaction, as recently suggested by Haxton et al.. Calculations were performed relative to the vacuum (``no core") using very large, separable model spaces containing all excitations with unperturbed energies up to 8\hbarΩ. Using G matrices derived from a new Nijmegen potential, we achieve a very satisfactory description of these excitations.

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