Overcoming Roundoff Errors In The First-Order Amplitude For General-State To -State Transitions In Hydrogen By Projectile Impact
Published In
Canadian Journal of Physics
Document Type
Citation
Publication Date
9-1-2013
Abstract
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.
Locate the Document
https://doi.org/10.1139/cjp-2013-0072
DOI
10.1139/cjp-2013-0072
Persistent Identifier
https://archives.pdx.edu/ds/psu/25899
Citation Details
Straton, J. C. (2013). Overcoming roundoff errors in the first-order amplitude for general state-to-state transitions in hydrogen by projectile impact. Canadian Journal of Physics, 91(9),