Stopping power of gases for heavy ions

Pulse-height and time-of-flight methods have been used to measure the electronic stopping cross sections for projectiles of ¹²C, ¹⁶O, ¹⁹F, ²³Na, ²⁴Mg, and ²⁷Al, slowing in helium, neon, argon, krypton, and xenon. The ion energies were in the range 185 keV ≤ E ≤ 2560 keV.

A semiempirical calculation of the electronic stopping cross section for projectiles with atomic numbers between 6 and 13 passing through the inert gases has been performed using a modification of the Firsov model. Using Hartree-Slater-Fock orbitals, and summing over the losses for the individual charge states of the projectiles, good agreement has been obtained with the experimental data. The main features of the stopping cross section seen in the data, such as the Z₁ oscillation and the variation of the velocity dependence on Z₁ and Z₂, are present in the calculation. The inclusion of a modified form of the Bethe-Bloch formula as an additional term allows the increase of the velocity dependence for projectile velocities above v_o to be reproduced in the calculation.

Phase transitions from the solid state of monatomic elements

The principle aims of this thesis include the development of models of sublimation and melting from first principles and the application of these models to the rare gases.

A simple physical model is constructed to represent the sublimation of monatomic elements. According to this model, the solid and gas phases are two states of a single physical system. The nature of the phase transition is clearly revealed, and the relations between the vapor pressure, the latent heat, and the transition temperature are derived. The resulting theory is applied to argon, krypton, and xenon, and good agreement with experiment is found.

For the melting transition, the solid is represented by an anharmonic model and the liquid is described by the Percus-Yevick approximation. The behavior of the liquid at high densities is studied on the isotherms kT/∈ = 1.3, 1.8, and 2.0, where k is Boltzmann's constant, T is the temperature, and e is the well depth of the Lennard-Jones 12-6 pair potential. No solutions of the PercusYevick equation were found for ρσ³ above 1.3, where ρ is the particle density and σ is the radial parameter of the Lennard-Jones potential. The liquid structure is found to be very different from the solid structure near the melting line. The liquid pressures are about 50 percent low for experimental melting densities of argon. This discrepancy gives rise to melting pressures up to twice the experimental values.