Lab frame

In the Lab frame, the projectile is scattered by 0 and the target, originally at rest, recoils tlirough angle 9g. The number of particles scattered into each solid angle in each frame remains the same, the relative speed v is now and j- = N v in each frame. Hence... 

The scattering and recoil angles 0 and 0g in die Lab frame are related to the CM scattering angle by... 

The elastic cross sections for scattering and recoil in the Lab-frame are related to the cross section in the CM-frame by... 

A phenomenological description of the differential cross-section for emission of photoelectrons into solid angle O in the lab frame can be written, assuming random molecular orientation and an axis of cylindrical symmetry defined by the photon polarization, as... 

It may be worthwhile to compare briefly the PECD phenomenon discussed here, which relates to randomly oriented chiral molecular targets, with the likely more familiar Circular Dichroism in the Angular Distribution (CDAD) that is observed with oriented, achiral species [44 7]. Both approaches measure a photoemission circular dichroism brought about by an asymmetry in the lab frame electron angular distribution. Both phenomena arise in the electric dipole approximation and so create exceptionally large asymmetries, but these similarities are perhaps a little superficial. 

We consider the expression of the lab frame photoelectron angular distribution for a randomly oriented molecular sample. The frozen core, electric dipole approximation for the differential cross-section for electron emission into a solid angle about a direction k can be written as... 

TOF spectra of the H atom products have been measured at 18 laboratory angles (from 117.5° to —50° at about 10° intervals). Figure 19 shows a typical TOF spectrum at the laboratory (LAB) angle of —50° (forward direction). By definition, the forwardness and backwardness of the OH product is defined here relative to the 0(7D) beam direction. The TOF spectrum in Fig. 19 consists of a lot of sharp structures. All these sharp structures clearly correspond to individual rotational states of the OH product, indicating that these TOF spectra have indeed achieved rotational state resolution for the 0(1D)+H2 — OH+H reaction. By converting these TOF spectra from the laboratory (LAB) frame to the center-of-mass (CM) frame... 

The angular distributions of the 0(3P2) fragments show the degree of correlation between the product recoil velocity (v) with the electric vector of the dissociating light and are typically characterized by the lab frame anisotropy parameter (/ ) given in the equation,52,53... 

From a theoretical perspective, since the designation of the lab-fixed axes is arbitrary, what is relevant is the relative orientation of the polarizations of the excitation and scattered light. Thus the line shape for excitation light polarized along axis p, and scattered light polarized along axis q (p or q denote X, Y, or Z axes in the lab frame) is called Ipq(co). When p = q this is lyy, and when p q this is IVH. Mixed quantum/classical formulae for Ipq(co) are identical to those for the IR spectmm, except mPi is replaced by apqP which is the pq tensor element of the transition polarizability for chromophore i. Thus we have, for example [6],... 

Likewise, let QL(t) denote the orientation of the emission dipole in the lab frame, and iK t) — [ (/), (/)] its orientation in the molecular frame. Using the transformation property of the Wigner rotation functions,... 

As mentioned above, the electron spin system is strongly coupled to the classical degrees of freedom, in the first place the orientation of a molecule-fixed frame with respect to the lab frame, through anisotropic interactions. We concentrate here on the case of S > 1, where the main anisotropic interaction is denoted as the zero-field splitting, ZFS. In the language of spin Hamiltonians (8,80), the ZFS interaction is written ... 

Spin-lattice relaxation of C nuclei is, in principle, very attractive for it is determined by local fluctuations at to c or cuof (rotating or lab frame respectively) spin diffusion among nuclei does not average relaxation rates among chemically distinct carbons. In solids one must append a cautionary note. 

Figure 11. Time-resolved PADs from ionization of DABCO for linearly polarized pump and probe pulses. Here, the optically bright S E state internally converts to the dark 5i state on picosecond time scales, (a) PADs at 200 fs time delay for pump and probe polarization vector both parallel to the spectrometer axis. The difference in electronic symmetry between S2 and Si leads to significant changes in the form of the PAD. (b) The PADs at 200 fs time delay for pump polarization parallel and probe polarization perpendicular to the spectrometer axis, showing the effects of lab frame molecular alignment, (c) and (d) The PADs evolve as a function of time due to molecular axis rotational wavepacket dynamics. Taken with permission from C. C. Hayden, unpublished.

Figure 18. (a) Inverse Abel transformed photoelectron image showing the lab frame PAD for... 

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. 

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... 

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