English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

A generating integral for the matrix elements of the Coulomb Green's function with the Coulomb wave functions

MPS-Authors
/persons/resource/persons37691

Skoromnik,  O. D.
Division Prof. Dr. Christoph H. Keitel, MPI for Nuclear Physics, Max Planck Society,;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Dzikowski, K., & Skoromnik, O. D. (2020). A generating integral for the matrix elements of the Coulomb Green's function with the Coulomb wave functions. Journal of Mathematical Physics, 61(3): 032103. doi:10.1063/1.5119349.


Cite as: https://hdl.handle.net/21.11116/0000-0008-1E1E-7
Abstract
We analytically evaluate the generating integral Knl(beta,beta ')=integral 0 infinity integral 0 infinity e-beta r-beta ' r ' Gnl(r,r ')rqr ' q ' drdr ' and integral moments Jnl(beta,r)=integral 0 infinity dr ' Gnl(r,r ')r ' qe-beta r ' for the reduced Coulomb Green's function G(nl)(r, r ') for all values of the parameters q and q ', when the integrals are convergent. These results can be used in second-order perturbation theory to analytically obtain the complete energy spectra and local physical characteristics such as electronic densities of multi-electron atoms or ions.