Infinite Nuclear Mass Research Articles

Neutral hydrogen-like system in a magnetic field

Explicit formulae are derived relating the energies and the ionisation potentials of an arbitrary neutral two-particle system in a magnetic field B to the energies and the ionisation potentials of a hydrogen atom of infinite nuclear mass in a magnetic field ( m e/μ) 2 B.

Variance minimization. A variational principle for accurate lower and upper bounds of the eigenvalues of a selfadjoint operator, bounded below

In connection with Temple's formula variance minimization yields accurate values especially for groundstate energies of Schrodinger operators with a discrete spectrum. The result in a.u. for the groundstate E 0 of the He-atom in the infinite nuclear mass approximation is −2.90372438655≤E 0≤−2.90372437696 i.e. E 0 is determined with an absolute error smaller than 0.0022 cm−1.

Negativity of ground-state interaction energies of atom-excess-electron systems

Any atom—excess-electron system confined to an arbitrary finite region of space that is free of external fields and which can be characterized by a non-relativistic spin-free hamiltonian has, in the limit of infinite nuclear mass of the atom, an exact ground-state expectation value of the atom—electron interaction hamiltonian that is negative-definite.

Asymptotic behavior of atomic bound state wave functions

In the present paper we investigate the asymptotic properties of an exact bound state wave function φ of an n-electron atomic system within the infinite nuclear mass approximation and neglecting relativistic effects. An explicit upper bound is derived for ‖riμφ‖, where ri denotes the distance of the ith electron from the nucleus and μ = 1,2,3,⋯. We are then able to derive upper bounds for expressions like ‖h(ri)φ‖, where h (x) is an exponentially increasing function. We finally indicate an exponentially decreasing pointwise bound for φ.

Correction to the Rydberg Constant for Finite Nuclear Mass

If the problem of the hydrogen-like atom is done with the assumption that the nucleus is at rest, the resulting energy levels are proportional to the Rydberg constant for infinite mass. It is traditional to obtain the Rydberg constant for finite mass of the nucleus by a simple substitution of the reduced mass of the system for the electron mass in the expression for the Rydberg constant for infinite nuclear mass. Realization that such a substitution (which is drawn from classical mechanics) does not give a correct transformation to the center-of-mass coordinate system in the case of charged particles, leads one to significant corrections for the Rydberg constants of finite nuclear masses. The corrections are drawn from classical, non-relativistic physics. Also, an interesting conjecture about the energy levels of hydrogen-like atoms, under the assumptions of Bohr theory and classical physics, is obtained.

The (2s)21S State Solution of the Non-relativistic Schr dinger Equation for Helium and the Negative Hydrogen Ion

A finite set of possible Slater determinants with spatial part constructed from an orthonormal complete one-electron set of associated Laguerre functions in the radial coordinates, and Legendre functions in the angular coordinates, has been introduced into the minimal sequence of the Ritz variational principle applied to the (2s)2 state solution (L = 0) of the two-electron wave equation for infinite nuclear mass. The sequence converges on a certain limiting eigen-function of the energy state. The numerical solution of the function and the corresponding energy value are given for helium as well as the negative hydrogen ion. The identification of certain helium lines in the vacuum ultra-violet is discussed.

Ground-State Solution of the Nonrelativistic Equation for Helium

By the inclusion of half-integral powers in the Hylleraas functions for the ground state of the helium atom, it is possible to obtain more rapid convergence in the Ritz variational method applied to the nonrelativistic Schr\"odinger equation (for infinite nuclear mass), as shown by results of calculations involving from four to thirteen parameters. The energy obtained with 13 parameters, -2.903719 a.u., is the lowest so far published. The coefficients for the normalized wave functions are given.