Calculation of theS1State of the Beryllium Atom in Hylleraas Coordinates

1968 ◽  
Vol 176 (1) ◽  
pp. 63-70 ◽  
Author(s):  
R. F. Gentner ◽  
E. A. Burke
Keyword(s):  
Hylleraas Coordinates

General methods for evaluating matrix elements of singular operators in two-electron systems

1994 ◽  
Vol 72 (11-12) ◽  
pp. 822-844 ◽  
Author(s):  
Zong-Chao Yan ◽  
G. W. F. Drake
Keyword(s):  
General Scheme ◽  
Triplet States ◽  
Electron Systems ◽  
Matrix Elements ◽  
Atomic Systems ◽  
Singular Operators ◽  
Wide Range ◽  
Qed Effects ◽  
Hylleraas Coordinates ◽  
Theory And Experiment

Due to the recent advances in both theory and experiment for the fine structure of two-electron atomic systems, it is necessary to include quantum electrodynamic (QED) effects through orders α6mc2, α7ln(Zα)mc2, and α7mc2, in order to match the experimental precision. These effects can be expressed in terms of a sum of singular operators. A general scheme is given for the evaluation of a wide range of matrix elements of high-order singular QED operators for two-electron atomic systems in Hylleraas coordinates. The scheme presented here can be applied to triplet states with arbitrary angular momentum. A number of useful expressions for the analytical evaluation of radial integrals are derived. An example is given in calculating the Douglas and Kroll terms, and the numerical values of the reduced matrix elements are presented for the 2 3PJ states of helium.

On the evaluation of two-electron integrals in Hylleraas coordinates

1996 ◽  
Vol 259 (1-2) ◽  
pp. 96-102 ◽  
Author(s):  
Zong-Chao Yan ◽  
G.W.F. Drake
Keyword(s):  
Hylleraas Coordinates

High-precision nonrelativistic polarizabilities of the nS state of helium

2018 ◽  
Vol 32 (27) ◽  
pp. 1850294
Author(s):  
Shao-Hui Xiang ◽  
Ke-Jie Ma ◽  
Hao-Xue Qiao
Keyword(s):  
High Precision ◽  
Infinite Mass ◽  
Hylleraas Coordinates ◽  
S States ◽  
Dipole Polarizabilities ◽  
Better Than

The static dipole polarizabilities of the 1 1S [Formula: see text] 51S, 23S [Formula: see text] 63S states of helium are presented. Our results are accurate up to at least eight digits. The majority of [Formula: see text]He (infinite mass helium) data are better than the data derived by Yan with Hylleraas coordinates,[Formula: see text] and close to the newest results achieved by another method.[Formula: see text] We demonstrate the results of 4He besides.

scholarly journals Transformation of the integral using Hylleraas coordinates in N-dimensions

2006 ◽  
Vol 84 (9) ◽  
pp. 857-859
Author(s):  
Soma Mukhopadhyay ◽  
Ashok Chatterjee
Keyword(s):  
Three Dimensional ◽  
Simple Derivation ◽  
Hylleraas Coordinates ◽  
Dimensional Integral

The integral ∫ F(r, r′, |r–r′|) dr dr′ where r and r′ are N-dimensional position vectors can be transformed into a simple three-dimensional integral using Hylleraas coordinates. A simple derivation of this result is presented. PACS Nos.: 31.15.–p; 31.15.Ja; 03.65.–w

Sign in / Sign up

Export Citation Format

Share Document