New Numerical Approach to Calculate Microstates of Equivalent and Non-Equivalent Electrons


  • Misha Shafi Department of Physics, University of Karachi, Karachi, Pakistan
  • Saba Javaid Department of Physics, Federal Urdu University of Arts, Science & Technology, Karachi, Pakistan
  • Roohi Zafar Department of Physics, NED University of Engineering & Technology, Karachi, Pakistan
  • Ahmed Ali Rajput Department of Physics, University of Karachi, Karachi, Pakistan
  • Muhammad Mustaqeem Zahid Department of Physics, University of Karachi, Karachi, Pakistan
  • Muhammad Daniyal Department of Physics, University of Karachi, Karachi, Pakistan



Microstates, Term Symbols, Equivalent and Non-Equivalent Electrons, Pauli Exclusion Principle, L-S Coupling


A term symbol is used to describe atomic microstate states, which give the multiplicity and total angular momentum of the atomic state. Russel Sauder coupling scheme is used to generate terms of equivalent and non-equivalent electronic configurations. For equivalent electrons, the terms are calculated using Pauli’s principle, and the number of terms is limited and is calculated by the combination rule. The total possible electrons and total available electrons are used in the combination formula. In case of non-equivalent electrons, the number of terms are found by the permutation rule. The number of terms for equivalent electrons is less than the terms for non-equivalent electrons. The number of possible microstates for p2 and d5  configurations are 15 and 252 respectively. While the number of final microstates for 1p2p and 3d4d configurations are 36 and 100.  In the proposed study, a Python programme was developed that generates the microstate according to filled and half-filled subshell electronic configurations for equivalent, non-equivalent, and combinations of both. Examples of microstates for non-equivalent electrons of configuration 1s2s, sp, sd, ss, 2p3p, pd, pf, 3d4d, df, 4f5f and for equivalent electrons of configuration su, pv, dx, and f y are presented.


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How to Cite

Misha Shafi, Saba Javaid, Roohi Zafar, Ahmed Ali Rajput, Muhammad Mustaqeem Zahid, & Muhammad Daniyal. (2023). New Numerical Approach to Calculate Microstates of Equivalent and Non-Equivalent Electrons. Proceedings of the Pakistan Academy of Sciences: A. Physical and Computational Sciences, 60(4), 29–33.



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