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Theoretical analysis of relativistic energy corrections, partition function and thermodynamic properties of spherically confined hydrogen atom

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Abstract

The relativistic energy corrections for the spherically confined hydrogen with penetrable wall are calculated for various orbitals as a function of pressure and confinement radius. The relativistic corrections at high pressures of the order of 108–109 atm are found to be more than thousand times higher than the corresponding values for the free atom. For calculating the energy eigenvalues, the efficient Numerov method is adopted. The partition function and other thermodynamic properties are also calculated for temperature range 104 K to 1010 K at low (0–10 atm) and high pressures (104–108 atm). We investigate the behaviour of partition function and thermodynamic parameters graphically with pressure and temperature. We discuss the effect of high temperature and reduction of confinement radius on these parameters. The present study will be useful in Industrial applications like development of hydrogen fuel and in various physics branches such as in fusion and astrophysical plasma, condensed matter, statistical mechanics and also in other research areas where we encounter atoms which are subjected to high pressures.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data generated or analysed during this study are included in this published article.]

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Acknowledgements

Rachna Joshi is thankful to AND College administration for constant motivation and encouragement. Arun Goyal is thankful to Shyamlal college for providing facilities and infrastructure for carrying out this work.

Author contribution statement

All authors contributed equally to the paper.

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Authors and Affiliations

  1. Department of Physics, Acharya Narendra Dev College, University of Delhi, New Delhi, 110019, India

    Rachna Joshi

  2. Department of Physics, Shyamlal College, University of Delhi, New Delhi, 110032, India

    Arun Goyal

  3. Department of Physics, Kirori Mal College, University of Delhi, New Delhi, 110007, India

    Pranav Kumar

  4. Department of Physics and Astrophysics, University of Delhi, New Delhi, 110007, India

    Man Mohan

Authors
  1. Rachna Joshi
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  2. Arun Goyal
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  3. Pranav Kumar
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  4. Man Mohan
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Correspondence to Arun Goyal.

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Joshi, R., Goyal, A., Kumar, P. et al. Theoretical analysis of relativistic energy corrections, partition function and thermodynamic properties of spherically confined hydrogen atom. Eur. Phys. J. D 76, 149 (2022). https://doi.org/10.1140/epjd/s10053-022-00484-6

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