Finite rank approximation of wave operators for short‐range and Coulomb interactions

1984 ◽  
Vol 25 (6) ◽  
pp. 1875-1880 ◽  
Author(s):  
Helmut Kröger
Keyword(s):  
Finite Rank ◽  
Short Range ◽  
Coulomb Interactions ◽  
Wave Operators ◽  
Rank Approximation

On the finite-rank approximation of wave operators and the S matrix using Hermite expansion functions

1986 ◽  
Vol 64 (8) ◽  
pp. 872-875 ◽  
Author(s):  
Helmut Kröger
Keyword(s):  
Finite Rank ◽  
Hermite Functions ◽  
Quantum Mechanical ◽  
Weak Approximation ◽  
Body System ◽  
Hermite Expansion ◽  
Wave Operators ◽  
Finite Dimensional ◽  
S Matrix ◽  
Rank Approximation

For the quantum mechanical, nonrelativistic two-body system, wave operators can be approximated by exponentials of finite-rank operators obtained by finite-dimensional projections of the full and the asymptotic Hamiltonian onto a set of Hermite functions. This yields a weak approximation of the S matrix.

Inclusion of a Coulomb interaction potential in a variational model for positronium–helium scattering

2013 ◽  
Vol 91 (2) ◽  
pp. 188-190 ◽  
Author(s):  
Joseph DiRienzi ◽  
Richard J. Drachman
Keyword(s):  
Wave Function ◽  
Short Range ◽  
Scattering Length ◽  
Variational Model ◽  
Coulomb Interactions ◽  
Zero Energy ◽  
Close Coupling ◽  
Helium Atoms ◽  
Coupling Approximation ◽  
Variational Wave

While carrying out investigations on Ps–He scattering it was discovered that it would be possible to improve the results of a previous work on zero-energy scattering of ortho-positronium by helium atoms. The previous work used a model to account for exchange and also attempted to include the effect of short-range Coulomb interactions in the close-coupling approximation. The three terms that were then included did not produce a well-converged result but served to give some justification to the model. Now we improve the calculation by using a simple variational wave function, and derive a much better value of the scattering length. The new result is compared with other computed values, and when an approximate correction due to the van der Waals potential is included the total is consistent with an earlier conjecture.

Spherical harmonic expansion of short-range screened Coulomb interactions

2006 ◽  
Vol 39 (27) ◽  
pp. 8613-8630 ◽  
Author(s):  
János G Ángyán ◽  
Iann Gerber ◽  
Martijn Marsman
Keyword(s):  
Spherical Harmonic ◽  
Short Range ◽  
Spherical Harmonic Expansion ◽  
Coulomb Interactions
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