Stability of complex-scaled continuum-continuum transition matrix elements against rotation angle
Author: Chrysos M.
Source: Journal of Physics B: Atomic, Molecular and Optical Physics, Volume 33, Number 15, 2000 , pp. 2875-2879(5)
Publisher: Institute of Physics Publishing
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Abstract:
The complex plane methodology for computing continuum-continuum matrix elements (CCME) can be useful in practical applications, even when a huge number of CCME are required for a converged calculation. This conclusion arises as a consequence of the substantial stability against [iopmath latex="$\theta $"] [/iopmath] of the complex matrix elements' real and imaginary parts, [iopmath latex="$Y_{\rm R}$"] YR [/iopmath] and [iopmath latex="$Y_{\rm I}$"] YI [/iopmath] , enabling one to economically evaluate CCME. For more refined values, the criterion [iopmath latex="$\rmd Y_{\rm R}(\theta)/\rmd \theta =0$"] dYR()/d = 0 [/iopmath] (and separately [iopmath latex="$\rmd Y_{\rm I}(\theta )/\rmd\theta =0$"] dYI()/d = 0 [/iopmath] for the `irregular' integral, if necessary) may be superior to the cusp-condition, since the latter would imply that the two quantities [iopmath latex="$ Y_{\rm R}$"] YR [/iopmath] and [iopmath latex="$Y_{\rm I}$"] YI [/iopmath] , which should represent the values of two conceptually independent integrals, were optimized as if they were correlated.
Language: English
Document Type: Miscellaneous
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