Muon positive

Condition (ii) can be fulfilled in other crystal structures on occasion as well. An AFM state is usually a condition, since, as mentioned, the contact field will not vanish in a FM material (but is present only in conducting compounds). The important point is that in an AFM spontaneous spin precession can be absent although LRO of the spin system exists. The strict consequence of (ii) would be a non-depolarizing pSR signal in ZF. But in nearly all cases the field distribution (iii) exists and Lorentzian Kubo-Toyabe patterns are seen instead. It is important to realize that the width of the Lorentzian Kubo-Toyabe patterns is not simply connected to the size of the magnetic moments the concentration and nature of faults enters dominantly. A randomness of these faults (though probable) is not required since the muon positions woidd in any case be randomly distributed relative to them. We finally point out that the width of the field distribution is rather small (about 8 G for UAs) and in many cases not significantly different from that produced by nuclear dipoles. A distinction between the two can be cumbersome in some cases. 

In the ordered state, part of the fast relaxing signal component exhibits spontaneous spin precession for T < 9 K (i.e., in the commensurate AFM state) with only moderate depolarization (A 2 p.s ). The saturation precession frequency is V f (0) 183 MHz, corresponding to an internal field of 1.35 T. These values are of the same magnitude as those in AFM Ho and Dy metals (see fig. 33), which verifies a muon position close to... 

Ito, Y. Chemical Reactions Induced and Probed by Positive Muons. 157, 93-128 (1990). 

Table 2 Restricted Hartree-Fock energies (Hartrees) for Ceo and C70 and their muon adducts. AE is the difference in energy between the carbon allotrope and its adduct. In all cases, except where indicated by f, only the six carbon atoms in the immediate vicinity of the muon have had there positions optimised, f means that a full geometry optimisation has been carried out. The type specifies the defect and for C70 is identified in Table 1. is the spin density at the muon in atomic units (and the hyperfine coupling constant in MHz). JMuon constrained to lie in equatorial plane. indicates geometry not fully optimized.

FIGURE 3.1 Stopping power of water for various charged particles over a wide span of energy 1 electron, 2 (positive) muon, 3 proton, 4 carbon nucleus, and 5 fission (light) fragment. See text for details. Reproduced from Mozumder (1969), by permission of John Wiley Sons, Inc. ... 

The muon spin relaxation technique uses the implantation and subsequent decay of muons, n+, in matter. The muon has a polarized spin of 1/2 [22]. When implanted, the muons interact with the local magnetic field and decay (lifetime = 2.2 ps) by emitting a positron preferentially in the direction of polarization. Adequately positioned detectors are then used to determine the asymmetry of this decay as a function of time, A t). This function is thus dependant on the distribution of internal magnetic fields within a... 

The techniques of u.SR and p-LCR are based on the fact that parity is violated in weak interactions. Consequently, when a positive muon is created from stationary pion decay its spin is directed opposite to its momentum. This makes it possible to form a beam of low energy (4 MeV) positive muons with nearly 100% spin polarization at high intensity particle accelerators such as TRIUMF in Canada, the PSI in Switzerland, LAMPF and BNL in the USA, KEK in Japan, and RAL in England. Furthermore the direction of position emission from muon decay is positively correlated with the muon spin polarization direction at the time of decay. This allows the time evolution of the muon spin polarization vector in a sample to be monitored with a sensitivity unparalleled in conventional magnetic resonance. For example, only about 101 7 muon decay events are necessary to obtain a reasonable signal. Another important point is that //.SR is conventionally done such that only one muon is in the sample at a time, and for p,LCR, even with the highest available incident muon rates, the 2.2 fis mean lifetime of the muon implies that only a few muons are present at a given time. Consequently, muonium centers are inherently isolated from one another. 

Note that the position of the juLCR depends on the sign of the nuclear hyperfine parameter relative to that of the muon. Using degenerate perturbation theory one can calculate the effects of the level crossing on the... 

Much less is known about the charge states of muonium in silicon that are not neutral. The most likely ones of these are the positive and negative charge states, Mu+ and Mu. Both would have an even number of electrons and hence would quite likely be electronically diamagnetic. They presumably contribute to the p.SR line, usually labelled p+, which occurs at the Larmor frequency of a bare muon. Little else is known about these charge states other than that at high temperatures at least one of them is formed from neutral muonium, Mu and Mu. ... 

In diamond, Sahoo et al. (1983) investigated the hyperfine interaction using an unrestricted Hartree-Fock cluster method. The spin density of the muon was calculated as a function of its position in a potential well around the T site. Their value was within 10% of the experimental number. However, the energy profiles and spin densities calculated in this study were later shown to be cluster-size dependent (Estreicher et al., 1985). Estreicher et al., in their Hartree-Fock approach to the study of normal muonium in diamond (1986) and in Si (1987), found an enhancement of the spin density at the impurity over its vacuum value, in contradiction with experiment this overestimation was attributed to the neglect of correlation in the HF method. 

The opportunities for concentrating and detecting (probably primordial) quarks and the properties of adducts of atoms, ions and molecules with quarks are discussed. There is a pronounced difference between positive quarks located in the outer valence-regions (or in the conduction electrons of metals) and negative quarks so firmly bound to nuclei that they may not be mobile, and constitute a kind of new elements with (Z - 1/3). Analogies are drawn with neutrinos, muons and other well-established particles. 

Mu is a very light and unstable (ti/2 (half live) = 2 p,s) isotope of hydrogen consisting of a nucleus which is a positive muon (p,+) and an electron. The nuclear mass of Mu is 0.113 amu. For this isotope one would expect much larger KBoele values than those discussed above. 

The English physicist Cedi Powell discovered Yukawa s meson in 1947. Powell found evidence of its existence in photographic plates that had been exposed to cosmic rays in the Bolivian Andes. The particle was found to be a little heavier than the muon, and it interacted strongly with nuclei, as Yukawa s particle was expected to do. Unlike the muon, which always carried a negative charge, the new particle could have either a positive or a negative charge, or it could be electrically neutral. 

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