Abstract
A simplified method to calculate the electronic partition functions and the corresponding thermodynamic properties of atomic species is presented and applied to C(I) up to C(VI) ions. The method consists in reducing the complex structure of an atom to three lumped levels. The ground level of the lumped model describes the ground term of the real atom, while the second lumped level represents the low lying states and the last one groups all the other atomic levels. It is also shown that for the purpose of thermodynamic function calculation, the energy and the statistical weight of the upper lumped level, describing highlying excited atomic states, can be satisfactorily approximated by an analytic hydrogenlike formula. The results of the simplified method are in good agreement with those obtained by direct summation over a complete set (i.e., including all possible terms and configurations below a given cutoff energy) of atomic energy levels. The method can be generalized to include more lumped levels in order to improve the accuracy.
We thank the students of the “Plasma Chemistry” course held in 2012 in the Chemistry department of the University of Bari for help in the present calculations.
I. INTRODUCTION
II. METHOD OF CALCULATION
III. RESULTS
IV. CONCLUSIONS
Key Topics
 Excited states
 20.0
 Ionization
 9.0
 High pressure
 7.0
 Electrons
 6.0
 Atomic ionization
 5.0
Figures
Partition function of the carbon ions as a function of temperature for different values of the ionization energy lowering . Curves are calculated using the threegroup partition function, symbols are the reference data. ^{ 22 }
Partition function of the carbon ions as a function of temperature for different values of the ionization energy lowering . Curves are calculated using the threegroup partition function, symbols are the reference data. ^{ 22 }
Internal plus translational energy ( ) divided by RT of the carbon ions as a function of temperature for different values of the ionization energy lowering . Curves are calculated using the threegroup model, symbols are the reference data. ^{ 22 }
Internal plus translational energy ( ) divided by RT of the carbon ions as a function of temperature for different values of the ionization energy lowering . Curves are calculated using the threegroup model, symbols are the reference data. ^{ 22 }
Internal plus translational specific heat ( ) divided by R of the carbon ions as a function of temperature for different values of the ionization energy lowering . Curves are calculated using the threegroup model, symbols are the reference data. ^{ 22 }
Internal plus translational specific heat ( ) divided by R of the carbon ions as a function of temperature for different values of the ionization energy lowering . Curves are calculated using the threegroup model, symbols are the reference data. ^{ 22 }
Tables
Ground state terms of the C(I)C(VI) ions.
Ground state terms of the C(I)C(VI) ions.
Lowlying terms of the C(I)C(IV) ions. The terms in bold have been used to construct the first excited lumped level of the threelevel model.
Lowlying terms of the C(I)C(IV) ions. The terms in bold have been used to construct the first excited lumped level of the threelevel model.
Parameters of the ground and first excited lumped levels of the threelevels model for C(I)C(VI) ions.
Parameters of the ground and first excited lumped levels of the threelevels model for C(I)C(VI) ions.
Parameters needed for the calculation of the hydrogenlike statistical weight ( ) and energy ( ) of the second excited lumped level of the threelevels model for C(I)C(VI) ions.
Parameters needed for the calculation of the hydrogenlike statistical weight ( ) and energy ( ) of the second excited lumped level of the threelevels model for C(I)C(VI) ions.
Parameters for the hydrogenlike lumped level of the two and threelevels model for the C(I)C(VI) ions.
Parameters for the hydrogenlike lumped level of the two and threelevels model for the C(I)C(VI) ions.
Maximum relative error of thermodynamic quantities as a function of for the two and threelevel model.
Maximum relative error of thermodynamic quantities as a function of for the two and threelevel model.
Maximum relative error of thermodynamic quantities as a function of , using a reduced partition with independent lumped levels for each spectroscopic term in Table II and an higher hydrogenlike lumped level.
Maximum relative error of thermodynamic quantities as a function of , using a reduced partition with independent lumped levels for each spectroscopic term in Table II and an higher hydrogenlike lumped level.
Article metrics loading...
Full text loading...
Most read this month
Most cited this month










Electron, photon, and ion beams from the relativistic interaction of Petawatt laser pulses with solid targets
Stephen P. Hatchett, Curtis G. Brown, Thomas E. Cowan, Eugene A. Henry, Joy S. Johnson, Michael H. Key, Jeffrey A. Koch, A. Bruce Langdon, Barbara F. Lasinski, Richard W. Lee, Andrew J. Mackinnon, Deanna M. Pennington, Michael D. Perry, Thomas W. Phillips, Markus Roth, T. Craig Sangster, Mike S. Singh, Richard A. Snavely, Mark A. Stoyer, Scott C. Wilks and Kazuhito Yasuike

Commenting has been disabled for this content