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Data Evaluation Procedure

Multichannel Quantum Defect Theory (MQDT) is used to organize, manage and evaluate the data in the Atomic Engineering system (AES). MQDT is a unified theory connecting the Rydberg states of spectroscopy and the autoionizing states of collisional processes in atoms and small molecules. It organizes atomic structures in terms of channel sets and structural parameters. A "channel set" is defined as a set of discrete and continuum states of an electron plus ion core. Each state differs in the energy of the excited electron. Subsequently, an atomic structure is characterized by three sets of quantum defect parameters:
  1. eigen-quantum defect Mq
  2. channel mixing angle 0q
  3. dipole transition matrix element dq
These parameters can be obtained by fitting the analytic relations to the discrete energy levels, oscillator strengths and photoionization cross sections. These parameters may also be calculated. Relativistic MQDT is used to characterize high Z ions.

Highly efficient and powerful algorithms based on the structure parameters have been developed to organize and evaluate the data: energy levels, oscillator strength / intensities / transition probabilities, life-times, photoionization cross sections and quantum defect of isoelectronic sequences. For example, the whole Rydberg series and autoionizing structures, as well as photoelectron angular distribution of the noble gases (Ne, Ar, Kr, Xe, and Rn), are characterized by five interaction channels with five eigen-quantum defect parameters, five dipole matrix elements, and 10 channel mixing angle parameters.

We developed the following procedures to evaluate Transition Probability, Intensity, and Life-time. Expression of transition probability Aul, intensity Iul and life-time tu of upper energy level Eu, are related by the following expression:

Aul=(Iul/∑l'Iul')/tu

(where l' refers to all the lower energy levels to which the upper level u decays)

The intensity data are taken using hollow cathode discharge and measured by high resolution Fourier Transform Spectrometer at National Solar Observatory at Kitt Peak, Arizona, USA. The intensity is measured by an automated AEC software MCCS system that fits a line profile and the integrated area. The analysis of the spectral lines in terms of energy levels, J values and assignments are also carried out using MCCS software.

The life-time is obtained using published data by laser-induced flourescence from atoms and ions in a beam. We have developed an evaluation procedure for life-time measurement based on the threshold laser induced flourescence measurements as a function of beam density and laser intensity.

Transition probability is obtained from the equation above. Most of the up-to-date data on transition probability are obtained by this method.

In the absence of life-time data, we obtain the reliable intensity by normalizing the intensity to the known data of transition probability. The normalized intensity carries the similar weight of reliability as the transition probability in terms of concentration measurement. For example, there is no reliable transition probability available for 257.601 nm line of Mn-II. However, it was seen in the LIBS spectrum. Following the above procedure, we determined that the normalized intensity of 257.601 nm line to be 35.

Copyright 2005