Inversion of simulated positron annihilation lifetime spectra by moving boundary subspaces

Abstract

ABSTRACT:The retrieval of the density function for the positron annihilation lifetime spectrum is obtained from simulated data using the damped singular value decomposition. Two filters factors were discussed, for noise and noiseless data, and under the L curve criterion. The obtained density function is exact in the absence of noise. When noise is considered, the predicted peaks are at positions 1 ϭ 0.4167 ns Ϫ1 , 2 ϭ 2.418 ns Ϫ1 , whereas the exact results are 1 ϭ 0.5250 ns Ϫ1 and 2 ϭ 2.538 ns Ϫ1. The computed areas for these peaks are also in fair agreement when compared with the theoretical results. In this case, a filter factor that takes into account all the singular values was found appropriate. The current study shows that the damped singular value decomposition approach can be used to invert real laboratory data.

Probability density function from experimental positron annihilation lifetime spectra

“…This basis, as j increases, becomes a more oscillating function and it is not appropriate to describe the probability density function. That is the reason why one should impose the condition 8 , f (λ) > 0, for the inverted results obtained from equation 3.…”

“…6 The inversion of simulated positron annihilation spectra has been performed before by the singular value decomposition 7 and the Hopfield neural network, 8 on simulated data. Instead of dealing with simulated data, the present work will handle laboratory data for the Al(dpm) 3 system.…”

“…Instead of dealing with simulated data, the present work will handle laboratory data for the Al(dpm) 3 system. 9 The singular value decomposition method will be used, which has been proved to be very useful while inverting data in simulated data, both in positronium annihilation 8 and in thermodynamics 10 . Effects not considered before, the experimental noise in the data and the choice of zero time channel, will be also discussed.…”