Factor Lorentz

This term is normally combined with the atomic scattering polarization term  

Consider the 100 reflection from a cubic lattice. In the powder specimen, some of the crystals will be so oriented that reflection can occur from their (100) planes. Other crystals of different orientation may be in such a position that reflection can occur from their (010) or (001) planes. Since all these planes have the same spacing, the beams diffracted by them all form part of the same cone. Now consider the 111 reflection. There are four sets of planes of the form 111 which have the same spacing but different orientation, namely, (111), (HT), (ITT), and (iTl), whereas there are only three sets of the form 100. Therefore, the probability that 111 planes will be correctly oriented for reflection is f the probability that 100 planes will be correctly oriented. It follows that the intensity of the 111 reflection will be f that of the 100 reflection, other things being equal. 

This relative proportion of planes contributing to the same reflection enters the intensity equation as the quantity p, the multiplicity factor, which may be defined as the number of different planes in a form having the same spacing. Parallel planes with different Miller indices, such as (100) and (TOO), are counted separately as different planes, yielding numbers which are double those given in the preceding paragraph. Thus the multiplicity factor for the 100 planes of a cubic crystal is 6 and for the 111 planes 8. 

The value of p depends on the crystal system in a tetragonal crystal, the (100) and (001) planes do not have the same spacing, so that the value of p for 100 planes is reduced to 4 and the value for 001 planes to 2. Values of the multiplicity factor as a function of hkl and crystal system are given in Appendix 13. 

The integrated intensity of a reflection depends on the particular value of Og 

By expanding the cosine terms and setting sin Ad equal to Ad, since the latter is small, we find  

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The atomic amplitude functions take account of the atomic F- factor, the temperature factor, the Lorentz factor, and the polarization factor. 

The used S5mbols are K, scale factor n, number of Bragg peaks A, correction factor for absorption P, polarization factor Jk, multiplicity factor Lk, Lorentz factor Ok, preferred orientation correction Fk squared structure factor for the kth reflection, including the Debye-Waller factor profile function describing the profile of the k h reflection. 

Before going further, it may be noted that the flipping ratio does not depend either on the Lorentz factor or on absorption in the sample. Certain instrumental parameters such as the polarisation of the neutron beam for the two spin states, the half wavelength contamination of the neutron beam and the dead-time detector can readily be taken into account when analysing the data. On the other hand, the extinction which may occur in the scattering process is not so easy to assess, but must also be included [14]. Sometimes, it is even possible to determine the magnetisation density of twinned crystals [15]. 

Recently this approach was extended by inclusion of the isovector-scalar partner, the 5-meson, of the isoscalar scalar a-meson [22], Unfortunately the value of the coupling for the 5-meson cannot be determined well by fitting properties of stable nuclei. Also in its simplest, density independent form, the inclusion of the 5-meson leads to an even larger net value for po. This happens because of the presence of the Lorentz factor m /E in the scalar potential... 

A second hard constraint is the so-called baryon loading problem . The attainable bulk Lorentz factor is determined by the ratio of available energy and rest mass energy. If an energy of 1051 erg is available the fireball cannot contain more than 10 5 M in baryonic material, otherwise the required Lorentz-factors will not be reached. This poses a hard problem for central engine models how can a stellar mass object pump so much energy into a region that is essentially devoid of baryons ... 

The above reasoning has led to the fireball internal-external shocks model. This model is rather independent of the nature of the central engine. The latter one is just required to produce highly relativistic outflow, either in the form of kinetic energy or as Poynting flux. The radiation is produced in (collisionless) shocks. These can either occur due to interaction of the outflow with the cir-cumstellar material ( external shocks ) or due to interactions of different portions of the outflow with different Lorentz-factors, so-called internal shocks . 

Figure 4 The annihilation of neutrino-antineutrino pairs above the remnant of a neutron star merger drives relativistic jets along the original binary rotation axis (only upper half-plane is shown). The x-axis lies in the original binary orbital plane, the dark oval around the origin is the newly formed, probably unstable, supermassive neutron star formed in the coalescence. Color-coded is the asymptotic Lorentz-factor. Details can be found in Rosswog et al. 2003.

Or from the physics side by which physical mechanisms are jets launched from accretion disks How are the ejecta accelerated to Lorentz factors beyond 100 How are the magnetic fields at the emission site created Are they... 

The central assumption underlying the standard approach to tachyon theory is that the usual Lorentz transformation also applies to the superluminal case. One therefore simply takes the Lorentz factor [1 — (v/c)2)]1/2 and substitutes v > c into it [27,74]. This leads directly to an imaginary rest mass and propagation time for tachyons, with many difficulties of interpretation [74]. 

GRBs emit photons in pulses containing photons with a combination of different wavelengths, whose sources are believed to be ultrarelativistic shocks with Lorentz factor y = (9(100) [28]. Let us consider a wavepacket of photons emitted with a Gaussian distribution in x at the time t = 0. One has to find out how such a pulse would be modified at the observation point at a subsequent time t, because of the propagation through the spacetime foam, as a result of the refractive index. This is similar to the motion of a wavepacket in a conventional dispersive medium. The Gaussian wavepacket may be expressed at t 0 as the real part of... 

Owing to the Lorentz factor in formula (4.54), when v approaches c, we have b etf—meaning that a molecule can be excited by a very distant passing particle, which is in contradiction with reality. This is a consequence of the fact that in our derivation (as in Ref. 150) we made no allowance for the weakening of the interaction between a charged particle and molecule when b> a, which is due to the polarization of the medium. The account of dielectric properties of the medium should lead to finite values of b eff even at v = c. 

In the program Corspot, the Lorentz factor used was of the form for precession camera data,... 

It is very difficult to mount a specimen in an X-ray fibre camera such that it is precisely normal to the beam. Indeed, frequently the fibre must be tilted deliberately by a nominal amount to observe specific meridional reflections. Because the tilt angle p features in the Lorentz factor and other expressions given in section 7, it is necessary to obtain a value for it using the microdensitometer data. AXIS provides two methods for calculating /3 both are similar to procedures outlined by Fraser et al. (4) and, superficially, resemble those described in section 6 for calculating 5. The first method again requires the user to specify the positions of pairs of equivalent spots from a data file. This time, however, both members of a pair must be... 

There are other factors affecting the intensity of the peaks on a x-ray diffraction profile of a powdered sample. We have analyzed the structure factor, the polarization factor, and the broadening of the lines because of the dimensions of the crystallites. Now, we will analyze the multiplicity factor, the Lorentz factor, the absorption factor, the temperature factor, and the texture factor [21,22,24,26],... 

Abstract. The Coulomb interaction which occurs in the final state between two particles with opposite charges allows for creation of the bound state of these particles. In the case when particles are generated with large momentum in lab frame, the Lorentz factors of the bound state will also be much larger than one. The relativistic velocity of the atoms provides the oppotrunity to observe bound states of (-n+fx ), (7r+7r ) and (7x+K ) with a lifetime as short as 10-16 s, and to measure their parameters. The ultrarelativistic positronium atoms (.4oe) allow us to observe the effect of superpenetration in matter, to study the effects caused by the formation time of A e. from virtual e+e pairs and to investigate the process of transformation of two virtual particles into the bound state. 

The mechanism of Aab creation is the Coulomb interaction in the final state (between a+ and b ), formatting from two virtual particles a+ and b, the bound state Aab (Fig. 1). This mechanism, in principle, allows for creation of all types of bound states and if a+ and b are relativistic particles, then Aab will also be relativistic. For ultra-relativistic atoms, there are effects caused by final time of atom formation and new phenomena during atom interaction with matter. High value of the Lorentz factors of atoms also allows for the detection new short lived bound states An, Ao and A k, consisting accordingly from (7r+p ), (7r+7r ) and (tt+ K ) mesons and to measure their parameters. 

At high values of Lorentz factors the probability of passage of an atom through a layer of matter becomes greater than the one that follows from the usual exponential dependence. This phenomenon was predicted in [8] and was given the name superpenetration . The quantitative theory of superpenetration was developed in [9,10,11]. For ultrarelativistic A2e, the time of formation from the virtual electron-positron pair is strongly dependent on the thickness of the target [12],... 

Positronium in the ground state and first exited state (n = 2) can exist if his Lorentz factor j, velocity v (3 = v/c) and the strength H of the magnetic field in the lab frame satisfy the inequality... 

The Ewald series for the three-dimensional crystal can also be differentiated. The first derivative yields expressions for the Madelung electric field Fm (due to local charges). The second derivative yields the Madelung field gradient, or, equivalently, the internal or dipolar or Lorentz field FD (due to local dipoles) [68-71],This second derivative can also generates the dimensionless 3x3 Lorentz factor tensor L with its nine components Lv/t ... 

The Lorentz factor, a geometrical factor that describes how the crystal is moved through the diffraction condition. 

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