Overcoming roundoff errors in the first-order amplitude for general state-to-state transitions in hydrogen by projectile impact

A computer program to calculate the amplitude for general state-to-state transitions in hydrogen from the analytical result has the potential for significant numerical round-off errors whenever the sum of the angular momenta of the two states is greater than four and the projectile’s impact paramete...

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Bibliographic Details
Published inCanadian journal of physics Vol. 91; no. 9; pp. 682 - 688
Main Author Straton, Jack C
Format Journal Article
LanguageEnglish
Published Ottawa NRC Research Press 01.09.2013
Canadian Science Publishing NRC Research Press
Subjects
02.30.Gp
34.10.+x
34.50.Fa
Amplitudes
Angular velocity
Errors
Hydrogen
Mathematical analysis
Mathematical functions
Mathematical models
Multiplication
Phase transformations (Statistical physics)
Phase transitions
Polynomials
Projectiles
Properties
Theorems
United States
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Summary:A computer program to calculate the amplitude for general state-to-state transitions in hydrogen from the analytical result has the potential for significant numerical round-off errors whenever the sum of the angular momenta of the two states is greater than four and the projectile’s impact parameter is less than the ratio of its energy to velocity. This arises from high-order cancellation of terms in the MacDonald functions in that analytical result, whose polynomial portions have been found to obey a new multiplication theorem. The cost for correcting this instability is the replacement of a finite series of MacDonald functions by an infinite series via the multiplication theorem for the full MacDonald function.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0008-4204
1208-6045
DOI:10.1139/cjp-2013-0072