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

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 10 8 –10 9 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 10 4 K to 10 10 K at low (0–10 atm) and high pressures (10 4 –10 8 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. Graphical abstract