Stark Energy Research Articles

Dispersion relations for stark energy shifts in hydrogen atom

On the basis of an approximate but nonperturbative expression for the energy shift δE in the ground state of the hydrogen atom in the presence of an electric field of strength E , we deduce that δE has a branch point at E = 0, and an asymptotic behavior δE → −1 2 E ln E as E → ∞. These properties lead to a twice-subtracted dispersion relation for δE as a function of E . The dispersion relations in conjunction with the WKB approximation and the perturbation series allow us to (i) deduce the large- n behavior of the coefficient of E n in the perturbation series for δE( E ) including 1 n corrections and (ii) obtain the energy shift and the level width of the ground state for a large range of values of E . The agreement with the earlier numerical calculations is very satisfactory.

Ring-type state selector and space focuser for molecules with a positive induced dipole moment

It is shown experimentally that an annular system of electrodes as commonly used in molecular beam maser studies, may also be employed to state select and focus molecules that posses a negative Stark energy ( μ eff>0).

Classical Stark ionisation threshold electric field and energy for hydrogenic ions

Values of the critical electric field and energy of a highly excited hydrogenic ion in a strong uniform electric field are presented using the recent classical adiabatic theory of Banks and Leopold (1978). Comparisons are made with the data available in the literature. For highly excited states the classical theory should provide a realistic approximation.

Dispersion relations and AC stark shifts

It is pointed out that AC Stark energy level shifts in a laser field can be calculated from experimental photo-absorption data via a dispersion relation. Explicit calculation is carried out for the ground state of helium.

A variational theory for high Rydberg Stark ionization threshold scaling laws in atomic hydrogen

We examine hydrogen atom Stark energies calculated with nonlinear variational theory using square-integrable wavefunctions. The trial function for each state has a characteristic critical field (F*) above which the variational energy is complex. F* approximates the experimentally important Stark ionization threshold for Rydberg states and typifies critical fields encountered in mathematical ’’catastrophe theory.’’ Zero-field wavefunctions yield analytic formulas for both threshold fields and energies in terms of parabolic quantum numbers. Aspects of the model suggest a ’’law of corresponding states’’ for Stark ionization near the critical field. The threshold fields scale as n−4 for all high Rydberg Stark states, while threshold energies scale as n−2 for the most unstable Stark components, and as n−8/3 for the most stable components. This variationally determined threshold behavior is compared with existing classical ionization criteria, perturbation theory, and semiclassical threshold orderings for different Stark components.

Stark energies for molecules with vibrationally induced dipole moments

For the various classes of molecules capable of having vibrationally induced electric dipole moments, explicit expressions for the resultant Stark energies are derived. In addition, the change in the vibrationally induced Stark effect with isotopic substitution of the B atoms in a tetrahedral AB4 molecule is considered.

Fourth order perturbation theoretic Stark energy levels in linear rotators

Fourth order perturbation theoretic Stark energy levels in linear rotators

Neutron Crystal-Field Spectroscopy in Rare-Earth Metallic Compounds

The technique of inelastic neutron scattering has been applied to the problem of crystal fields in rare-earth metallic compounds. It is shown that in compounds where the Stark energies are somewhat greater than exchange energies, the complete energy-level diagram can be readily obtained from the inelastic neutron spectra and hence the corresponding crystal-field parameters may be deduced. In this paper we illustrate this by a series of measurements which we have performed on the praseodymium monopnictides, PrBi, PrSb, PrAs, PrP, and monochalcogenides PrTe, PrSe, PrS. It is found that the spectra can be reproduced in detail using ordinary crystal-field theory together with a simple approximation to the instrumental resolution function. In addition, all of the crystal-field levels in all seven compounds studied can be quantitatively accounted for using a nearest-neighbor point charge model with an effective charge of −2. This is in spite of marked variations in covalency, carrier concentration and, indeed, in the widths of the crystal-field transitions themselves over the series.

The theory of the Stark effect in multiplet states of diatomic polar molecules

The theory of the Stark effect in Hund's case (a) for strong and intermediate field strengths is developed when the lambda-doubling is included. A simplification of the secular problem is worked through for the cases of constant lambda-doubling, and small lambda-doubling for moderately strong fields. The errors resulting from the use of a limited set of basis functions when calculating the energy changes due to the field, are discussed. For completeness a brief review of the Stark effect for Hund's case (a) in the weak field case is given. A general formula is derived for the weak field Stark energy of molecules in multiplet Sigma -states. In the strong and intermediate field cases for molecules in multiplet Sigma -states it is shown that it is convenient first to consider the effect of the electric field and thereafter take the spin interactions into account. Formulae expressing the Stark interaction between the lambda components are given for molecules which can be described by a coupling scheme intermediate between Hund's cases (a) and (b). The equations and formulae derived are for a rigid molecule. Hyperfine interactions are neglected in the treatment.

Microwave Spectrum, Internal Rotation, Dipole Moment, Quadrupole Coupling, and Structure of Nitrosomethane

The microwave spectra of CH3NO and CD3NO have been observed and analyzed. The barriers to internal rotation are 1137 ± 5 and 1095 ± 7 cal/mole for CH3NO and CD3NO, respectively, a difference of 42 cal/mole which is thought to be real. The barriers were calculated by the internal-axis method with retention of higher terms in the usual Fourier expansion of the rotational energy and computation of the torsional integrals in the harmonic-oscillator approximation. The theoretical parameters were fitted to the data by a least-squares method and the uncertainties reported are standard deviations. Transitions having comparable Stark and quadrupole energies were used to calculate the dipole moment. Secular equations of second or third order were solved for each of the data points. The dipole moment components are μa = 2.240 ± 0.001 D, μb = 0.522 ± 0.006 D, and μtotal = 2.300 ± 0.002 D. The quadrupole coupling constants of CH3NO are 0.50 ± 0.16, −6.016 ± 0.031, and 5.518 ± 0.031 for the components along the a, b, and c axes, respectively. The corresponding values for CD3NO are 0.60 ± 0.07, −6.007 ± 0.020, and 5.411 ± 0.020. The N=O and C–N distances are not well determined by the data. The CNO angle is 112.6 ± 1.0°.

Stark Energy Levels of Symmetric-Top Molecules

Calculations have been performed to determine the Stark energy levels of rigid symmetric-top molecules. The continued fraction expression for the eigenvalues of the energy matrix is presented and techniques of evaluation described. Tables of reduced energy levels as a function of electric field are given for all rotational states through J=4. Graphs of these values and the effective dipole moments are included.

On the Stark Effect of Helium In Strong Electric Field (II)

To explain the resonance phenomena of the Stark lines of He atom, a general method is found in the paper (I) to solve the secular equations, taking into account of the matrix elements between the states with different principal quantum numbers, n and n '. Along the line of this general method, we performed the numerical computations for the ortho-helium in the case of n =6 and n '=7. Numerical tables and diagrams representing the relations of the Stark energies and field strengthes are obtained for the respective values of magnetic quantum numbers, m =1, 2, 3 and 4. From these results we find that the pair of levels approaching nearest and repelling each other is as follows:

On the Stark Effect of Helium in Strong Electric Field (I)

To explain the resonance phenomena of the Stark lines of He atom, a general method is found in the paper (I) to solve the secular equations, taking into account of the matrix elements between the states with different principal quantum numbers, n and n '. Along the line of this general method, we performed the numerical computations for the ortho-helium in the case of n =6 and n '=7. Numerical tables and diagrams representing the relations of the Stark energies and field strengthes are obtained for the respective values of magnetic quantum numbers, m =1, 2, 3 and 4. From these results we find that the pair of levels approaching nearest and repelling each other is as follows: