Related papers: Stability of Three- and Four-Body Coulomb Systems
We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the…
A brief review is presented of the stability domain of three- and four-charge ground-states when the constituent masses vary. Rigorous results are presented, based on the scaling behavior and the convexity properties deduced from the…
We consider the stability of three Coulomb charges $\{+1, -1, -1 \}$ with finite masses in the framework of nonrelativistic quantum mechanics. A simple physical condition on masses is derived to guarantee the absence of bound states below…
We have studied the general properties of the energy thresholds of stability for a three-particle system with short-range interaction. A wide region of the interaction constants and various ratios of the masses of particles are considered.…
A survey of the stability of matter problem is given, starting with the stability of the hydrogen atom. The stablity of bulk matter with Coulomb potentials, with or without relativistic mechanics, and with or without magnetic fields is…
In this paper, we present preliminary results on the stability of massless particles in two and three-planet systems. The results of our study may be used to address questions concerning the stability of terrestrial planets in these systems…
Confined to small regions, quantum systems exhibit electronic and structural properties different from their free space behavior. In Coulomb 3-body problems, configurations of close proximity of identically charged particles are classically…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…
In Coulomb 3-body problems, configurations of close proximity of the particles are classically unstable. In confined systems they might however exist as excited quantum states. Quantum control of such states by time changing electromagnetic…
The method of screening and renormalization for including the Coulomb interaction in the framework of momentum-space integral equations is applied to the three- and four-body nuclear reactions. The Coulomb effect on the observables and the…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
Three-body and four-body interactions have been directly measured in a colloidal system comprised of three (or four) charged colloidal particles. Two of the particles have been confined by means of a scanned laser tweezers to a line-shaped…
We consider the problem of $n$ points with positive masses interacting pairwise with forces inversely proportional to the distance between them. In particular, it is the classical gravitational, Coulomb or photo-gravitational $n$-body…
Coulomb bubbles, though stable against monopole displacement, are unstable at least with respect to quadrupole and octupole distortions. We show that there exists a temperature at which the pressure of the vapor filling the bubble…
The thermodynamic properties of nuclei are studied in a mean field model using a Skryme interaction. Properties of two component systems are investigated over the complete range of proton fraction from a system of pure neutrons to a system…
The Coulomb energy of a charge that is uniformly distributed on some set is maximized (among sets of given volume) by balls. It is shown here that near-maximizers are close to balls.
In the framework of nonrelativistic quantum mechanics we derive a necessary condition for four Coulomb charges $(m_{1}^+, m_{2}^-, m_{3}^+, m_{4}^-)$, where all masses are assumed finite, to form the stable system. The obtained stability…
The time evolution of the continuous measure symmetry for the system built of the three bodies interacting via the potential U(r)~1/r is reported. Gravitational and electrostatic interactions between the point bodies were addressed. In the…
We consider three one dimensional quantum, charged and spinless particles interacting through delta potentials. We derive sufficient conditions which guarantee the existence of at least one bound state.