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A Unified Treatment Of The Non-Relativistic And Relativistic Hydrogen Atom Ii: The Green Functions, R. A. Swainson, Gordon W. F. Drake
A Unified Treatment Of The Non-Relativistic And Relativistic Hydrogen Atom Ii: The Green Functions, R. A. Swainson, Gordon W. F. Drake
Physics Publications
This is the second in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. In this paper the nonrelativistic Green function is examined in detail; new functional forms are presented and a clear mathematical progression is shown to link these and most other known forms. A linear transformation of the four radial parts of the relativistic Green function is given which allows for the presentation of this function as a simple generalization of the non-relativistic Green function. …
A Unified Treatment Of The Non-Relativistic And Relativistic Hydrogen Atom: Iii. The Reduced Green Functions, R. A. Swainson, Gordon W. F. Drake
A Unified Treatment Of The Non-Relativistic And Relativistic Hydrogen Atom: Iii. The Reduced Green Functions, R. A. Swainson, Gordon W. F. Drake
Physics Publications
The last in a series of three papers in which it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. The work presented here is concerned with the reduced Green functions which arise in second-order stationary state perturbation theory. Using a simple linear transformation of the four radial parts of the relativistic reduced Green function it is shown how the non-relativistic and relativistic functions are special instances of the solution of a general second-order differential equation. The general solution of this equation is exhibited in …
A Unified Treatment Of The Non-Relativistic And Relativistic Hydrogen Atom I: The Wavefunctions, R. A. Swainson, Gordon W. F. Drake
A Unified Treatment Of The Non-Relativistic And Relativistic Hydrogen Atom I: The Wavefunctions, R. A. Swainson, Gordon W. F. Drake
Physics Publications
In this and the following two papers in this series it is shown how the radial part of non-relativistic and relativistic hydrogenic bound-state calculations involving the Green functions can be presented in a unified manner. The angular part of such calculations, being well understood, is performed in the standard way. In this, the first paper, it is shown how a suitable linear transformation of the two relativistic radial wavefunctions allows the pair of relativistic coupled differential equations to be written as two uncoupled second-order equations which are simple generalizations of the corresponding non-relativistic equation. This transformation is presented in a …
Erratum: Expectation Values Of Rp For Arbitrary Hydrogenic States (Physical Review A (1991) 43, 11, (6432)), Gordon W. F. Drake, R. A. Swainson
Erratum: Expectation Values Of Rp For Arbitrary Hydrogenic States (Physical Review A (1991) 43, 11, (6432)), Gordon W. F. Drake, R. A. Swainson
Physics Publications
No abstract provided.
Variational Calculation For The Ground State Of Lithium And The Qed Corrections For Li-Like Ions, D. K. Mckenzie, Gordon W. F. Drake
Variational Calculation For The Ground State Of Lithium And The Qed Corrections For Li-Like Ions, D. K. Mckenzie, Gordon W. F. Drake
Physics Publications
High-precision variational calculations using multiple basis sets in Hylleraas coordinates are presented for the 1s22s 2S state of lithium. The variational bound of -7.478 060 326(10) a.u. for the nonrelativistic energy is in good agreement with our revised experimental value of -7.47 806 034(20) a.u., thereby resolving a long-standing disrepancy. Two-electron calculations of the QED corrections are extended to three-electron systems and compared with other results. The comparison for Li-like ions up to U89+ suggests a simple interpretation for the ''screening of the Lamb shift'' recently calculated by Cheng, Johnson, and Sapirstein [Phys. Rev. Lett. 66, 2960 (1991)]. © 1991 …
Quantum Defects And The 1/N Dependence Of Rydberg Energies: Second-Order Polarization Effects, Gordon W. F. Drake, R. A. Swainson
Quantum Defects And The 1/N Dependence Of Rydberg Energies: Second-Order Polarization Effects, Gordon W. F. Drake, R. A. Swainson
Physics Publications
The principal result of this paper is a general expression for the second-order dipole polarization energy of a Rydberg electron resulting from the term -1/r4 in the asymptotic potential, where 1 is the core polarizability. It is shown that the second-order term contributes even as well as odd powers of 1/n in a 1/n expansion of the energies for Rydberg states. The results are used to extend the interpretation of the terms in a quantum-defect expansion. It is shown that the Ritz expansion for the quantum defect, which contains only even inverse powers of the effective quantum number n*, provides …
Measurement Of The N=2 Lamb Shift In He+ By The Anisotropy Method, A. Van Wijngaarden, J. Kwela, Gordon W. F. Drake
Measurement Of The N=2 Lamb Shift In He+ By The Anisotropy Method, A. Van Wijngaarden, J. Kwela, Gordon W. F. Drake
Physics Publications
A high-precision measurement of the 2s 2S1/22p 2P1/2 Lamb shift in He+ by the quenching-anisotropy method is reported. The theory and experimental method are described in detail. The measured value of 14042.520.16 MHz (11 parts per million) rivals the accuracy of Lamb-shift measurements in hydrogen by microwave resonance. By subtracting the known low-order terms in the Lamb shift, we interpret the results as a measurement of the order (Z)6mc2 and higher contributions to the electron self-energy GSE(Z). The various contributions to the Lamb shift are discussed, and a revised value for GSE(Z) at low Z is extracted from high-Z calculations. …