On the quantum statistics of bound states within the Rutherford model of matter

Abstract

The quantum statistical treatment of the Rutherford model, considering matter as a system of point charges (electrons and nuclei) is analyzed. First, in the historical context, the solutions of different fundamental problems, such as the divergence of the partition function, elaborated by Herzfeld, Planck, Brillouin and Rompe - most of the relevant papers published in the Annalen der Physik, are discussed. Beyond this, the modern state of art is presented and new results are given which explain, why bound states according to a discrete part of the spectra occur only in a valley in the temperature-density plane. Based on the actual state of the quantum statistics of Coulomb systems, virial expansions within the canonical ensemble and the grand ensemble and combinations are derived. The following transitions along isotherms are studied: (i) the formation of bound states occurring by increasing the density from low to moderate values, (ii) the disappearance of bound state effects at higher densities due to medium effects. Within the physical picture we calculate isotherms of pressure for Hydrogen in a broad density region and show that in the region between $20000$ K and $100000$ K and particle densities below $10^{22}$ cm${}^{-3}$ the cross-over from full to partial ionization may be well described by the contributions of extended ring diagrams and ladder diagrams.

20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1110.1962

References in corpus (3)

• Equation of state of metallic hydrogen from Coupled Electron-Ion Monte Carlo simulations
• The influence of Pauli blocking effects on the properties of dense hydrogen
• Bound States in Coulomb Systems - Old Problems and New Solutions

Cited by in corpus (5)

• The equation of state of partially ionized hydrogen and deuterium plasma revisited
• Virial theorem and Gibbs thermodynamic potential for Coulomb systems
• Semiempirical $\text{ab initio}$ modeling of bound states of deep defects in semiconductor quantum technologies
• Statistical theory of charged particle systems including triple bound states -- and the Collaboration Lviv-Rostock
• Screened activity expansion for the pressure of a quantum multi-component plasma and consistency with the local charge neutrality