Related papers: The Escape Rate of a Molecule
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
The scattering of two and more particles at low energies is described by the so called effective-range expansion. The leading terms of this expansion are the scattering length and effective range. The analytic expressions for both of the…
A Brownian particle with diffusion coefficient $D$ is confined to a bounded domain of volume $V$ in $\rR^3$ by a reflecting boundary, except for a small absorbing window. The mean time to absorption diverges as the window shrinks, thus…
Diffusion of a particle in the N-dimensional external potential which is periodic in one dimension and unbounded in the other N-1 dimensions is investigated. We find an analytical expression for the overdamped diffusion and study…
Accurately determining escape rates from a planet's atmosphere is critical for determining its evolution. Escape can be driven by upward thermal conduction of energy deposited well below the exobase, as well as by non-thermal processes…
We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the…
A model investigating the role of geometry on the alpha dose rate of spent nuclear fuel has been developed. This novel approach utilises a new piecewise function to describe the probability of alpha escape as a function of particulate…
The r\^{o}le of inelastic diffraction in elastic scattering of nuclei is studied in the formalism of \emph{diffractive limit}. The results obtained for scattering of the $\alpha$--particles on light nuclei show that the nucleonic…
The rotational constant parametrizes the relative spacing between a molecule's rotational energy levels. It depends on the molecule's classical moments of inertia, which, in all studies, are expressed by treating the constituent nuclei as…
In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
We calculate the differential scattering rate for thermal neutrinos in a hot and dilute gas of interacting neutrons using linear response theory. The dynamical structure factors for density and spin fluctuations of the strongly interacting…
We study the thermal escape problem in the moderate-to-high and high damping regime of a system with a parabolic barrier. We present a formula that matches our numerical results accounting for finite barrier effects, and compare it with…
Numerous small bodies inevitably lead to cratering impacts on large planetary bodies during planet formation and evolution. As a consequence of these small impacts, a fraction of the target material escapes from the gravity of the large…
In this paper, based on a canonical quantization scheme, we study the effect of the relativistic motion of an excited atom on its decay rate in the presence of absorbing and dispersive media. For this purpose, we introduce an appropriate…
The narrow escape problem concerns the time needed for a diffusing particle to exit a confining domain through a small hole in the boundary. While this problem is now well-understood, determining the escape time for a particle that must…
Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are…
The bolometric radiation from a central body is potentially a powerful driver of atmospheric escape from planets or satellites. When heated above their equilibrium temperatures those satellites, due to their low surface gravity, are be…
A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point…
Neutrinos are perhaps the most elusive known particles in the universe. We know they have some nonzero mass, but unlike all other particles, the absolute scale remains unknown. In addition, their fundamental nature is uncertain; they can…