Continuum discretization using orthogonal polynomials
A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional ‘
Systematic calculation of molecular vibrational spectra through a complete Morse expansion
We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard-Jones oscillator, and to the ab initio potential of the H2 molecule. Global cm−1 accuracy is exhibited through the H2 spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi-dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
The Structure of Finite Nuclei in the Local Density Approximation.
A new theory is presented for calculating the structure of finite nuclei from the nucleon-nucleon interaction. The essential features of the reaction matrix in finite nuclei are obtained from nuclear-matter theory through the local-density approximation. The resulting density- and energy-dependent effective interaction is justified in detail, and it is shown that the tensor force plays an important role in saturation. The effective interaction is cast into two different forms, one convenient for use in calculating matrix elements and the other specialized for a Hartree-Fock calculation in position space. The density-dependent Hartree-Fock equations are derived by variation of the ground-state expectation value of the energy, and in addition to the usual Hartree-Fock terms, one obtains rearrangement terms arising from the variation of the density appearing in the density-dependent interaction. The appropriate angular-momentum reduction for closed $j$-shell nuclei is performed. The need for modifying the effective interaction to account for higher-order corrections is discussed, and the constraints imposed on this modification by the properties of nuclear matter are examined. The results of this theory for ${\mathrm{O}}^{16}$, ${\mathrm{Ca}}^{40}$, ${\mathrm{Ca}}^{48}$, ${\mathrm{Zr}}^{90}$, and ${\mathrm{Pr}}^{208}$ are shown to yield very satisfactory agreement with experimental binding energies, single-particle energies, and electron scattering cross sections. The rearrangement terms in the density-dependent theory are demonstrated to have two essential effects on nuclear structure: a significant reduction in the central density of the nucleus, and a modification of the usual Hartree-Fock relation between single-particle energies and the binding energy. Equivalent local single-particle potentials are calculated and are shown to have significant state dependence.