where (P) is the pressure, (n) is the number density of the gas, (Eq.) is elastic or

inelastic collision cross-section, (Eq.) is the average speed of reduced mass (Eq.).

The energetic ion when traverse through the material medium it losses its energy either in displacing atoms (of the sample) by elastic collisions or ionizing the atoms by

inelastic collision. The former is the dominant process at low energies whereas the

inelastic collisions dominate at high energies where the displacements of atoms due to elastic collisions are insignificant.

The theoretical analysis [6], which was based on the interpretations from super K data that the neutrino oscillations between flavors could only occur if the neutrino had a rest mass, was cast in terms of a net transfer of linear momentum, but since it is now known that the neutrino always possesses left-handed helicity, and since it is reported that upon

inelastic collision between a neutrino at v ~ c, and a proton or a neutron, the flavor of the neutrino has a very high probability to change--thus the spin magnetic moment property of the particle changes--the analysis is broadened herein to include total angular momentum.

[N.sub.p] stands for the fast proton density, x is the ratio of the pion energy to proton energy, and [[sigma].sup.inel.sub.pp] is the proton-proton

inelastic collision cross section.

Dual parton model (DPM) and quark gluon string model (QGSM) are multiple-scattering models in which each

inelastic collision results from the superposition of two strings and the weights of the various multiple-scattering contributions are represented by a perturbative Reggeon field theory.

This author's insight that inter-gas collisions may generally be inelastic requires that radiation is given off during such collisions thus enabling

inelastic collisions to adhere to conservation of energy [1].

According to the prescription of Cooper-Frye [34], as the temperature drops to the freeze-out temperature [T.sub.FO], the

inelastic collisions among hadrons cease.

In a one-dimensional space the Boltzmann-Grad limit is not trivial in case of hard sphere dynamics with

inelastic collisions [38].

where [v.sub.h], [v.sub.h] and [v.sub.d] are the input collision integral frequencies of the elastic hard, soft, and diffraction scattering collisions, respectively, and the Lorentzian collision half-width at half-height [gamma] contains the contributions of elastic and

inelastic collisions. If the above frequencies enter into a model collision integral explicitly, then the line profile derived from the respective muster equation for a density matrix will contain these frequencies as adjustable parameters [9, 10].

where [[??].sub.e] is the electron stream density, [n.sub.[epsilon]] is the volumetric energy density of the electrons, [D.sub.[epsilon]], [[mu].sub.[epsilon]] are the electrons' diffusion coefficient and mobility coefficient for the energy, [R.sub.e] is the intensity of the electron source, [R.sub.[epsilon]] is the electrons' energy source (describes the energy loss due to

inelastic collisions), and [??] is the electric field vector.