Colliding heavy particles

The oldest and best known example of a Markov process in physics is the Brownian motion.510 A heavy particle is immersed in a fluid of light molecules, which collide with it in a random fashion. As a consequence the velocity of the heavy particle varies by a large number of small, and supposedly uncorrelated jumps. To facilitate the discussion we treat the motion as if it were one-dimensional. When the velocity has a certain value V, there will be on the average more collisions in front than from behind. Hence the probability for a certain change AV of the velocity in the next At depends on V, but not on earlier values of the velocity. Thus the velocity of the heavy particle is a Markov process. When the whole system is in equilibrium the process is stationary and its autocorrelation time is the time in which an initial velocity is damped out. This process is studied in detail in VIII.4. 

The relationship of the applied electric field to the resulting elevated electron temperature can be seen by a simple analysis. Consider a high velocity electron colliding with an initially stationary heavy particle, as shown below. 

A FIGU RE 21.5 The Relativistic Heavy Ion Collider. This particle accelerator is located at... 

There are two other simple ways of interaction of neutrinos with matter about which we have very little information. These are simple elastic collisions between the neutrino and heavy particles in the first case, electrons in the second case. All that the present information can yield in this connection are maximum cross sections. Whether the actual cross section is lower than this maximum by just a little bit, or by a very great amount is impossible to tell at this time. It seems worthwhile, therefore, to see under what conditions the neutrinos could be detected by these processes. If a neutrino collides with a nucleus of mass M, it transfers to it a maximum amoimt of energy... 

The Bohmian quantum-classical and QMF approaches [21,22] have been applied to a model intended as a simplified representation of gaseous oxygen interacting with a platinum surface, Ref. [13,91]. The model consists of a light particle q with mass m colliding with a heavier particle Q with mass M. The heavy particle is bound to an immobile surface. The total Hamiltonian for the system is given by... 

Here p is the radius of the effective cross-section, (v) is the average velocity of colliding particles, and p is their reduced mass. When rotational relaxation of heavy molecules in a solution of light particles is considered, the above criterion is well satisfied. In the opposite case the situation is quite different. Even if the relaxation is induced by collisions of similar particles (as in a one-component system), the fraction of molecules which remain adiabatically isolated from the heat reservoir is fairly large. For such molecules energy relaxation is much slower than that of angular momentum, i.e. xe/xj > 1. 

Neutron stars are important laboratories for the physics of high-density matter. Unlike particles in relativistic heavy-ion colliders, the matter in the cores of neutron stars has a thermal energy that is much less than its rest-mass energy. Various researchers have speculated whether neutron star cores contain primarily nucleons, or whether degrees of freedom such as hyperons, quark matter, or strange matter are prevalent (see Lattimer Prakash 2001 for a recent review of high-density equations of state). 

FIGURE 7.2 When a light particle collides with a heavy wall, very little energy is transferred. The component of the velocity perpendicular to the wall is reversed the other components are unaffected. 

The transuranium elements are synthesized by colliding accelerated charged particles with heavy atoms (i.e., curium and lead). In certain collisions the nuclei of the accelerated charged particles and the stationary heavy atoms will fuse to produce a n transuranium element. The lifetimes of these n elements are so short they often break down into other elements within fractions of a second and are detected only by their breakdown products, referred to as daughter elements. 

When colliding particles are heavy and their interactions are long range, the impact parameter method conveniently describes the problem (9, 10, 32, 57). This method is based on the concept that the motion of nucleus is described classically and that of electrons is described quantum mechanically. If the angular momentum of colliding system is larger than K, the trajectory of an incident or a scattered particle can be defined. The impact parameter method will be useful where the total scattering is determined mainly by these processes. 

Fig. 18.2 (a) Abstaice of reaction due to too little collision energy, (b) Successful reaction in a collision with high enough energy (for the sake of simplicity, we will imagine that all colliding particles— despite their differences in size—are equally heavy and equally fast). 

Rutherford thought this scattering happened when positive nuclei of the test particles collided and were then repelled by heavy positively charged gold nuclei. It was later proven that Rutherford s dense pit model was correct. When an accelerated alpha particle colUded with an electron of a gold atom in a gas, a proton was knocked out of the nucleus. 

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