One-photon physics

While the MCH result happens to be very close to the experimental result, that is clearly accidental, as there is a variation of up to 37 eV between the different potentials. In other fields of physics, one might be content with a one percent agreement with experiment, but for precision QED work it is clear that more physics needs to be considered, and we begin with one-photon physics. 

By far the easiest one-photon diagram to evaluate is photon exchange between the electrons, Fig. la, taken together with the counterterm diagram in Fig. lb. The associated formula is 

The phase factor in Eq. 22 leads to significant complications for the two-photon calculation, as that factor leads to a cut in the complex E plane. This factor is in general complex, and while we are interested in the real 

More difficult are the self-energy and vacuum-polarization diagrams of Fig. Ic and Id. The self-energy (SE) can be written as where (the self-mass counterterm is understood to be included) 

The most accurate calculations of the self-energy have been carried out in the point-nucleus Coulomb case by Mohr and collaborators [28]. Techniques that work for the general, non-Coulomb case have also been developed [29], and it is now possible to carry out a complete one-photon calculation for any potential with relative ease. We present the overall effect of the one-photon diagrams on the 2p3/2 — 2si/2 splitting in the second row of Table 1, and give a breakdown for the individual states in Tables 2 and 3. 

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Figure 1. Fe3mman diagrams associated with one-photon physics.

In photoluminescence one measures physical and chemical properties of materials by using photons to induce excited electronic states in the material system and analyzing the optical emission as these states relax. Typically, light is directed onto the sample for excitation, and the emitted luminescence is collected by a lens and passed through an optical spectrometer onto a photodetector. The spectral distribution and time dependence of the emission are related to electronic transition probabilities within the sample, and can be used to provide qualitative and, sometimes, quantitative information about chemical composition, structure (bonding, disorder, interfaces, quantum wells), impurities, kinetic processes, and energy transfer. 

Figure 8. Phase lag spectrum of HI in the vicinity of the 5d(n, 8) resonance. In panel (a), the circles show the phase lag between the ionization and dissociation channels. The diamonds and triangles separate the phase lag into contributions from each channel, using H2S ionization as a reference. Panels (b) and (c) show the conventional one-photon (m3) and three-photon (3a>i) photoionization spectra. (Reproduced with permission from Ref. 45, Copyright 2002 American Institute of Physics.)...

Figure 9. Phase lag spectrum of HI and DI in the vicinity of the 5sa resonance. The top panel shows the phase lag between photoionization and photodissociation of HI (filled circles) and DI (open circles), the phase lag between the photoionization of HI and DI (squares), and the phase lag between the photoionization of HI and H2S (triangles). The bottom two panels show the one-photon ionization spectra of HI and H2S. (Reproduced with permission from Ref. 30, Copyright 1999 American Physical Society.)...

Just as the absorption of UV or visible light causes electrons to excite between different electronic quantum states, so absorption of infrared photons causes excitation between allowed vibrational states, and absorbing microwave radiation causes excitation between allowed rotational states in the absorbing molecule. As a crude physical representation, these quantum states correspond to different angular velocities of rotation, so absorption of two photons of microwave radiation by a molecule results in a rotation that is twice as rapid as following absorption of one photon. 

The present chapter is devoted mainly to one of these new theories, in particular to its possible applications to photon physics and optics. This theory is based on the hypothesis of a nonzero divergence of the electric field in vacuo, in combination with the condition of Lorentz invariance. The nonzero electric field divergence, with an associated space-charge current density, introduces an extra degree of freedom that leads to new possible states of the electromagnetic field. This concept originated from some ideas by the author in the late 1960s, the first of which was published in a series of separate papers [10,12], and later in more complete forms and in reviews [13-20]. 

Photodissociation dynamics [89,90] is one of the most active fields of current research into chemical physics. As well as the scalar attributes of product state distributions, vector correlations between the dissociating parent molecule and its photofragments are now being explored [91-93]. The majority of studies have used one or more visible or ultraviolet photons to excite the molecule to a dissociative electronically excited state, and following dissociation the vibrational, rotational, translational, and fine-structure distributions of the fragments have been measured using a variety of pump-probe laser-based detection techniques (for recent examples see references 94-100). Vibrationally mediated photodissociation, in which one photon... 

Absorption of radiation is a one photon process. Absorption of one photon excites one atom or molecule in primary (initiating) step and all subsequent physical and chemical reactions follow from this excited species... 

For a given microwave frequency a , the right hand side of (6.2.47) is constant. Thus, (6.2.47) can be solved immediately with the result Pn(i) = exp(—A t). Therefore, A has the physical meaning of a one-photon decay rate to the continuum. The expression (6.2.48) is a form of Fermi s golden rule. 

Thus far, we have examined vibrational spectroscopy using IR absorption spectroscopy, what we called in Ch. 3 one photon method , a general type that encompasses most experiments in spectroscopy. There exist, however, other types of spectroscopy to observe vibrations. These are for instance Raman spectroscopy, which is also of a current use in chemical physics and may be considered a routine method. Other less known methods are modem time-resolved IR spectroscopies. All these methods are two-photon or multiphoton spectroscopies. They do not involve a single photon, as in absorption, but the simultaneous absorption and emission of two photons, as in Raman and in other scattering experiments, or the successive absorption(s) and emission(s) of photons that are coherently delayed in time, as in time-resolved nonlinear spectroscopies. By coherently , we assume the optical waves that carry these two photons keep a well-defined phase difference. In this latter type of spectroscopy, we include all modem set-ups that involve time-controlled laser spectroscopic techniques. We briefly sketch the interest of these various methods for the study of H-bonds in the following subsections. 

In other words, two photons can never be detected at two points separated by an odd number of X/lr 2, despite the fact that one photon can be detected anywhere. The vanishing of G 2 (Ri, t R2, f2) for two photons at widely separated points Ri and R2 is an example of quantum-mechanical nonlocality, that the outcome of a detection measurement at Ri appears to be influenced by where we have chosen to locate the R2 detector. At certain positions R2 we can never detect a photon at Ri when there is a photon detected at R2, whereas at other position R2 it is possible. The photon correlation argument shows clearly that quantum theory does not in general describe an objective physical reality independent of observation [17],... 

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