Continuum Lowering -- A New Perspective

TL;DR

This paper clarifies the concept of continuum lowering and ionization potential depression (IPD) in Coulomb systems, distinguishing between equilibrium and non-equilibrium processes, and introduces an analytical, thermodynamically consistent approach that aligns well with spectroscopic data.

Contribution

It presents a new analytical framework for calculating thermodynamic and spectroscopic IPDs in multicomponent Coulomb systems, resolving discrepancies with experimental measurements.

Findings

Spectroscopic IPD aligns best with measurements.

Thermodynamic and spectroscopic IPDs differ in interpretation.

A self-consistent free energy-based equation of state is developed.

Abstract

What is meant by continuum lowering and ionization potential depression (IPD) in a Coulomb system depends upon precisely what question is being asked. It is shown that equilibrium (equation-of-state) phenomena and non-equilibrium dynamical processes like photoionization are characterised 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 such an IPD is that of 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, 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 to calculating thermodynamic and spectroscopic (adiabatic) IPDs in multicomponent Coulomb systems of arbitrary coupling strength. The ramifications are carefully examined in order to elucidate the roles of the various IPD forms. A formulation in terms of free energy leads to an analytical equation of state (EoS) that is thermodynamically self-consistent, provided that the bound and free electrons are dynamically separable. Of the various proposed formulae, the Spectroscopic (adiabatic) IPD gives the most consistent agreement with spectroscopic measurements.