Stark effect in a hydrogenic atom or ion 1st edition by Nanny Froman, Per Olof Froman ISBN 186094924X 978-1860949241

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ISBN 10: 186094924X
ISBN 13: 978-1860949241
Author: Nanny Froman, Per Olof Froman 

This book treats the Stark effect of a hydrogenic atom or ion in a homogeneous electric field. It begins with a thorough review of previous work in this field since 1926. After the Schrödinger equation has been separated with respect to time dependence, centre of mass motion and internal motion, followed by a discussion of its eigenfunctions, the exact development in time of the probability amplitude for a decaying state is obtained by means of a formula analogous to the Fock-Krylov theorem. From this formula one obtains by means of the phase-integral approximation generated from a particular base function non-relativistic formulas for profiles, energies and half-widths of the Stark levels. These formulas are then transformed into formulas expressed in terms of complete elliptic integrals. The formulas thus obtained are used for the calculation of energies and half-widths of 198 different Stark states, which are compared with the corresponding results obtained by other authors with the use of other methods. An analysis of this material indicates that the energy values obtained by the phase-integral method are at least as accurate as those obtained by other methods in more than half of the 198 cases. The book presents one of the most comprehensive asymptotic treatments of the Stark effect in atomic hydrogen that have been published.

Stark effect in a hydrogenic atom or ion 1st Table of contents:

1 Introduction

Brief review of di.erent aspects studied and various methods used

Brief account of the background of this book

Publications with relevance to this book

Treatment in this book

Brief account of the contents of this book

2 Schr¨odinger Equation, its Separation and its Exact Eigenfunctions

2.1 Separation of the time-independent Schr¨odinger equation for the internal motion

2.2 Properties of the eigenfunctions of the time-independent Schr¨odinger equation for the internal

3 Development in Time of the Probability Amplitude for a Decaying State

4 Phase-Integral Method

4.1 Phase-integral approximation generated from an unspecified base function

4.2 Connection formulas associated with a single transition point

4.2.1 Connection formulas pertaining to a first-order transition zero on the real axis

4.2.2 Connection formula pertaining to a first-order transition pole at the origin

4.3 Connection formula for a real, smooth, single-hump potential barrier

4.3.1 Wave function given as a standing wave

4.3.2 Supplementary quantity φ

4.4 Quantization conditions for single-well potentials

5 Derivation of Phase-Integral Formulas for Profiles, Energies and Half-Widths of Stark Levels

5.1 Positions of the Stark levels

5.2 Formulas for the calculation of dL/dE, dK2n/dE and dK/dE

5.3 Half-widths of the Stark levels

6 Procedure for Transformation of the Phase-Integral Formulas into Formulas Involving Complete Ellip

Adjoined Papers by Anders H¨okback and Per Olof Fr¨oman

7 Phase-Inegral Quantities and Their Partial Derivatives with Respect to E and Z1 Expressed in Terms

7.1 The ξ-equation

7.2 The η-equation in the sub-barrier case

7.3 The η-equation in the super-barrier case

8 Numerical Results

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Tags: Nanny Froman, Per Olof Froman, Stark effect, hydrogenic atom