Kato Cusp Research Articles

Calculations of the one- and two-body densities in two-electron atomic systems

We study the single-particle and the electron-pair densities for the ground state of two-electron atomic systems by means of wavefunctions which provide very good values for the energy. Special attention is paid to the convergence of some properties of the densities when we increase the dimension of the used basis. The best results obtained for the densities and for Kato's cusp conditions indicate that we have really got a quite good description for the ground-state wavefunction.

Roothaan-Hartree-Fock Ground-State Atomic Wave Functions: Slater-Type Orbital Expansions and Expectation Values for Z = 2-54

Roothaan-Hartree-Fock orbitals expressed in a Slater-type basis are reported for the ground states of He through Xe. Energy accuracy ranges between 8 and 10 significant figures, reducing by between 21 and 2770 times the energy errors of the previous such compilation (E. Clementi and C. Roetti, Atomic Data and Nuclear Data Tables 14, 177, 1974). For each atom, the total energy, kinetic energy, potential energy, virial ratio, electron density at the nucleus, and the Kato cusp are given together with radial expectation values 〈rn〉 with n from −3 to 2 for each orbital, orbital energies, and orbital expansion coefficients.

Erratum: Partially linearized Thomas-Fermi-Weizsäcker theory for screening and stopping of charged particles in jellium

A partially linearized Thomas-Fermi-Weizsaecker theory is proposed to study charged particles interacting with jellium. This simple theory can be derived by linearizing contributions involving the Thomas-Fermi kinetic-energy density. The calculations are based on a nonlinear inhomogeneous integrodifferential equation that includes the potential along the lines suggested by the original Thomas-Fermi-Weizsaecker theory. Exchange-correlation effects are neglected. The coefficient of the von Weizsaecker term is prescribed according to Kato's cusp condition in order to investigate both heavy and light particles in jellium. This theoretical framework is applied to compute the stopping power of a jellium for slow protons and antiprotons, induced electron densities, positron annihilation rates, and the electron-correlation function for antiparallel spin. Illustrative comparisons with the results of other theories are also made.

Partially linearized Thomas-Fermi-Weizsäcker theory for screening and stopping of charged particles in jellium.

A partially linearized Thomas-Fermi-Weizs\"acker theory is proposed to study charged particles interacting with jellium. This simple theory can be derived by linearizing contributions involving the Thomas-Fermi kinetic-energy density. The calculations are based on a nonlinear inhomogeneous integrodifferential equation that includes the potential along the lines suggested by the original Thomas-Fermi-Weizs\"acker theory. Exchange-correlation effects are neglected. The coefficient of the von Weizs\"acker term is prescribed according to Kato's cusp condition in order to investigate both heavy and light particles in jellium. This theoretical framework is applied to compute the stopping power of a jellium for slow protons and antiprotons, induced electron densities, positron annihilation rates, and the electron-correlation function for antiparallel spin. Illustrative comparisons with the results of other theories are also made.

Fock's expansion, Kato's cusp conditions, and the exponential ansatz.

We have examined the recent solution of the Fock expansion through O(${\mathit{r}}^{2}$) for the ground state of the helium atom and have verified that it correctly treats the discontinuity in the local energy characteristic of the triple-collision point. We have also developed an exponential representation of the Fock expansion that satisfies Kato's cusp conditions for two-particle collisions even when the expansion is truncated at a finite order.

A two-parameter model for the screening of a proton in an electron gas

A simple two-parameter model for the electron density fluctuation induced by a slow proton intruder is examined. The model satisfies both Friedel's sum rule and Kato's cusp condition. The results obtained for the electron density fluctuation at the proton site and the transport collision frequency are in fair agreement with those given by self-consistent calculations.