Continuum lowering – A new perspective

Abstract

What is meant by continuum lowering and ionization potential depression (IPD) in a Coulomb system depends very much upon precisely what question is being asked. It is shown that equilibrium (equation of state) phenomena and non-equilibrium dynamical processes like photoionization are characterized by different values of the IPD. In the former, the ionization potential of an atom embedded in matter is the difference in the free energy of the many-body system between states of thermodynamic equilibrium differing by the ionization state of just one atom. Typically, this energy is less than that required to ionize the same atom in vacuo. Probably, the best known example of this is the IPD given by Stewart and Pyatt (SP). However, it is a common misconception that this formula should apply directly to the energy of a photon causing photoionization, since this is a local adiabatic process that occurs in the absence of a response from the surrounding plasma. To achieve the prescribed final equilibrium state, in general, additional energy, in the form of heat and work, is transferred between the atom and its surroundings. This additional relaxation energy is sufficient to explain the discrepancy between recent spectroscopic measurements of IPD in dense plasmas and the predictions of the SP formula. This paper provides a detailed account of an analytical approach, based on SP, to calculating thermodynamic and spectroscopic (adiabatic) IPDs in multicomponent Coulomb systems of arbitrary coupling strength with Te ≠ Ti. The ramifications for equilibrium Coulomb systems are examined in order to elucidate the roles of the various forms of the IPD and any possible connection with the plasma microfield. The formulation embodies an analytical equation of state (EoS) that is thermodynamically self-consistent, provided that the bound and free electrons are dynamically separable, meaning that the system is not undergoing pressure ionization. Apart from this restriction, the model is applicable in all coupling regimes. The Saha equation, which is generally considered to apply to weakly-coupled non-pressure-ionizing systems, is found to depend on the Thermodynamic IPD (TIPD), a form of the IPD which takes account of entropy changes. The average Static Continuum Lowering (SCL) of SP relates to changes in potential energy alone and features in EoS formulas that depend on the variation of the mean ionization state with respect to changes in volume or temperature. Of the various proposed formulas, the Spectroscopic (adiabatic) IPD (SIPD) gives the most consistent agreement with spectroscopic measurements.