Electrons electron-muon interaction

A AH < kT has important consequences. As the temperature is lowered to where AHg, kT, strong electron-phonon interactions must manifest themselves. Direct evidence for mode softening and strong electron-phonon coupling in the internal Ty < T < 250 K has been provided by measurements of the Mdssbauer recoiless fraction and the X-ray Debye-Waller factor as well as of muon-spin rotation Therefore, it would be... 

Note that in the parenthesis we have parted with our usual practice of considering the muon as a particle with charge Ze, and assumed Z = 1. Technically this is inspired by the cancellation of certain contributions between the electron and muon polarization loops mentioned above, and from the physical point of view it is not necessary to preserve a nontrivial factor Z here, since we need it only as a reference to an interaction with the constituent muon and not with the one emerging in the polarization loops. 

The weak interaction contribution to hyperfine splitting is due to Z-boson exchange between the electron and muon in Fig. 6.7. Due to the large mass of the Z-boson this exchange is effectively described by the local four-fermion interaction Hamiltonian... 

With intensification of particle physics research, many more particles were discovered and a classification of these particles into five families was proposed—the photon family, electron family, muon family, meson family, and baryon family. Most of these particles are unstable and decay within a time which is often very small by normal standards, but which is many orders of magnitude larger than the time required for any of these particles to traverse a typical nuclear dimension. There is a wide variety of reactions between them, but they could be understood in terms of three basic interactions—the strong (or nuclear), electromagnetic, and weak interactions. 

Figure 4. Energy spectra for elemental groups a) protons, b) helium, and c) iron. Open symbols give results of direct measurements, for references see Horandel 2003a. Filled symbols represent data from air shower measurements KASCADE electrons/muons interpreted with two interaction models Ulrich et a1. 2004 (preliminary), KASCADE single hadrons Antoni et al. 2004c, and EAS-Top Navarra et al. 2003. The data are compared to 8 calculations by Kalmykov Pavlov 1999 ( ), Sveshnikova 2003 (—), and the Poly-Gonato model Horandel 2003a (—).

Like electrons, protons, muons, and quarks are formed by the interaction of gamma rays, photons, and neutrinos with a particular amount of energy. The situation for proton formation, for example, involves the interaction of gamma rays and neutrinos with a total energy of about 1,000 MeV ... 

Lepton - One of the class of elementary particles that do not take part in the strong interaction. Included are the electron, muon, and neutrino. All leptons have a spin of 1/2. 

The well-known proton, neutron, and electron are now thought to be members of a group that includes other fundamental particles that have been discovered or hypothesized by physicists. These very elemental particles, of which all matter is made, are now thought to belong to one of two families namely, quarks or leptons. Each of these two families consists of six particles. Also, there are four different force carriers that lead to interactions between particles. The six members or flavors of the quark family are called up, charm, top, down, strange, and bottom. The force carriers for the quarks are the gluon and the photon. The six members of the lepton family are the e neutrino, the mu neutrino, the tau neutrino, the electron, the muon particle, and the tau particle. The force carriers for these are the w boson and the z boson. Furthermore, it appears that each of these particles has an anti-particle that has an opposite electrical charge from the above particles. 

The fourth force is the one which is involved in the radioactive jS-decay of atoms and is known as the weak interaction force. Like the strong interaction, this weak interaction force operates over extremely short distances and is the force that is involved in the interaction of very light particle known as leptons (electrons, muons, and neutrinos) with each other and as well as their interaction with mesons, baryons, and nuclei. One characteristic of leptons is that they seem to be quite immune to the strong interaction force. The strong nuclear force is approximately 10 times greater than the Coulombic force, while the weak interaction force is smaller than the strong attraction by a factor of approximately 10. The carrier of the weak interaction force is still a matter of considerable research we will return to this point later. 

Charged particles such as electrons, muons, or a particles lose eneigy through Coulomb interaction with the electrons in the solid. Two categories can be defined ... 

In this zoo of particles, only the electron, which was discovered even before the atomic theory was proven and the atomic structure was known, is really unseeable, stable, and isolatable. The proton also is stable and isolatable, but it is made up of two quarks up (with charge -1-2/3) and one quark down (with charge —1/3). As for the quarks, while expected to be stable, they have not been isolated. The other particle constitutive of the atomic nucleus, the neutron, is also made up of three quarks, one up and two down, but it is not stable when isolated, decaying into a proton, an electron, and an antineutrino (with a 15-min lifetime). The fermions in each of the higher two classes of the electron family (muon and tau) and of the two quark families (strange charmed and bottom/top) are unstable (and not isolatable for the quarks). Only the elusive neutrinos in the three classes, which were postulated to ensure conservation laws in weak interaction processes, are also considered as being unseeable, stable, and isolatable. 

A plethora of experiments involving the neutrino revealed some remarkable properties for this new particle. The neutrino was found to have an intimate connection with the electron and muon, and indeed never appeared without the simultaneous appearance of one or other of these particles. A conservation law was postulated to explain this observation. Numbers were assigned to the electron, muon, and neutrino, so that during interactions these numbers were conserved i.e. their algebraic sums before and after these interactions were equal. 

Molecular dynamic information is obtained from a study of the variation of the muon spin relaxation rate with temperature. Reorientation depolarizes the muons by causing anisotropic or dipolar terms in the electron-muon hyperhne interaction to fluctuate. Peaks in the relaxation rate (analogous to 2i minima in NMR) occur when the reorientation rate matches the frequency of the dominant transition between the coupled muon-electron spin states. The correlation time, T, at each temperature can be obtained using the derivations of Cox and Sivia [14]. The measured relaxation rate X is given by the following expression ... 

The Mott cross-section is just the cross-section for the scattering of a spin 5 particle in the Coulomb field of a massive (spinless) target. The extra factors in (15.1.19) arise (i) because the target has spin 5 and there is a contribution due to the magnetic interaction between electron and muon, and (ii) because the target has finite mass and recoils. 

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