Volkov states

A Volkov state is obtained from the solution of the time-dependent Schrodinger equation for a free particle in an external plane-wave laser field. Such states were first derived by Volkov, in a relativistic context [21]. 

For the computation of the amplitude (4.1), the Volkov time-evolution operator is usually expanded in terms of the Volkov states (4.2),... 

The Coulomb attraction of the electrons in the intermediate state and in the final Volkov states by the ion, as well as the Coulomb repulsion between the two final electrons are missing from the theory developed thus far. A rigorous treatment of the first issue has so far resisted any efforts. It is much easier to deal with the Coulomb repulsion of the two electrons in the final state, depicted in the right-hand panel of Fig. 4.1, since the product of two Volkov states (4.2) can be extended exactly to incorporate the Coulomb repulsion [22]. This is possible because in the long-wavelength approximation the laser couples to the sum rq I rq of the two electron coordinates while the Coulomb repulsion affects their difference r = rq — r2 just like in the absence of the laser held. The state reads [22]... 

For the case cited above, the ponderomotive energy is approximately 1 eV. For typical short pulse experiments today, this energy can easily be hundreds of electron volts. Therefore the wave function of a photoelectron in an intense laser field does not resemble that of the normal field-free Coulomb state, but is dressed by the field, becoming, in the absence of a binding potential, a Volkov state [5], This complex motion of the photoelectrons in the continuum is very difficult to reproduce in terms of the field-free atomic basis functions, so that we have chosen to define our electron wave functions on a finite difference grid. These numerical wave functions have the flexibility to represent both the bound and continuum states in the laser field accurately. 

These equations allow the main features of observed ATI spectra to be computed in a simple way. The method is referred to as the Keldysh-Faisal-Reiss (KFR) theory. Note that the final states are Volkov states, and therefore contain no information about the atom. In this sense, we are dealing with a model of type (i) in section 9.18. Very little atomic physics is required only the ionisation potential of the atom, the angular momentum acquired by the emerging electron and the properties of the... 

Volkov and Sushko [335] described a technique that is based on the use of nets. This method provides direct absorption spectra, but is very complex to perform The net must be placed in a chamber that ensures a pure inert atmosphere so as to avoid hydrolysis of the melt, and the temperature and geometry of the net must be kept very stable. Other major limitations of the method are the requirements that the surface tension of the melt be such that its position on the net is ensured, and that the vapor pressure of the material in molten state be as low as possible... 

Volkov (1994) has given a state-of-the-art review on pervaporation. A number of industrial plants exist for dehydration of ethanol-water and (.vwpropanol-water azeotropes, dehydration of ethyl acetate, etc. There is considerable potential in removing dissolved water from benzene by pervaporation. The recovery of dis.solved organics like CH2CI2, CHCI3, CCI4, etc. from aqueous waste streams also lends itself for pervaporation and pilot plants already exist. 

Every interface is more or less electrically charged, unless special care is exercised experimentally [26]. The energy of the system containing the interface hence depends on its electrical state. The thermodynamics of interfaces that explicitly takes account of the contribution of the phase-boundary potential is called the thermodynamics of electrocapillarity [27]. Thermodynamic treatments of the electrocapillary phenomena at the electrode solution interface have been generalized to the polarized as well as nonpolarized liquid liquid interface by Kakiuchi [28] and further by Markin and Volkov [29]. We summarize the essential idea of the electrocapillary equation, so far as it will be required in the following. The electrocapillary equation for a polarized liquid-liquid interface has the form... 

We will focus on static spherically symmetric stars which are described by the Tolman-Oppenheimer-Volkov equations. At low densities, up to a few times nuclear density no, matter consists of interacting hadrons. Theoretical models for this state have to start from various assumptions, as for the included states and their interactions. Naturally, the results for the hadronic equation of state become notably model dependent at densities exceeding approximately 2/io- This is reflected in uncertainties of the predictions for the shell structure of neutron stars, cf. [18]. 

For a linear equation of state, the Tolman-Oppenheimer-Volkov equations imply a scaling property for the total mass and the radius of the star,... 

Novozhilova IV, Volkov AV, Coppens P (2003) Theoretical analysis of the triplet excited state of the [Pt2(H2P205)4] ion and comparison with time-resolved X-ray and spectroscopic results. J Am Chem Soc 125 1079-1087... 

Fig. 4.1. Feynman diagrams corresponding to the transition amplitude (4.1), a without and b with electron-electron repulsion between the two electrons in the final state. The vertical wavy line and the dots in b indicate the Coulomb interaction, which is exactly accounted for by the two-electron Volkov solution. The dashed vertical line represents the electron-electron interaction Vi2 by which the second electron is set free...

Volkov II, Rozanov AG, Demidova TP (1992) Reduced inorganic sulphur species and dissolved manganese in the water of the Black Sea. In Vinogradov ME (ed) Winter state of the ecosystem of the open part of the Black Sea, Shirshov Institute of Oceanology RAS, Moscow, p 38 (in Russian)... 

Prosser, R.S., Volkov, V.B., and Shiyanovskaya, I.V. (1998) Solid-state NMR studies of magnetically aligned phospholipid membranes taming lanthanides for membrane protein studies, Biochemistry and Cell Biology 76, 443-454. 

In aquatic settings, sulfate reducers are intimately associated with various heterotrophs and autotrophs. These include purple and green sulfur bacteria and thiobacUli which affect the availability of organic matter and alter the distribution of sulfur compounds in their various valence states. In the majority of the sites where elemental sulfur is formed (see Chapter 6.2), oxidation to sulfate also occurs and other intermediate oxidation states may also be found. For example, Volkov et al. (1972) reported the presence of thiosulfate in waters of some sediments from the Pacific Ocean east of Japan. These are interpreted as oxidation products of sulfide rather than intermediates of sulfate reduction since their concentration increased with increasing free sulfide ion content. 

F. S. Bergeret, B. Huckestein, and A. F. Volkov, Current-voltage characteristics and the zero-resistance state in a two-dimensional electron gas, Phys. Rev. B 67, 241303 (2003). 

The method works particularly well for ATI spectra excited by circularly polarised light. The reason for this is as follows an atom which absorbs N photons then acquires Nh units of angular momentum. The emerging electron is then subject to a repulsive centrifugal barrier (see chapter 5) and does not therefore penetrate into the core. Consequently, most atomic effects are suppressed, and a final state representation as a Volkov wavefunction is a reasonable approximation. This is also why intensity suppression occurs near threshold in this case the effect is very similar to delayed onset in single-photon ionisation to continua of high angular momentum. 

Fig. 9.7. Comparison between experimental data and KFR calculations, which demonstrates that the main features of ATI for circularly polarised light (including angular momentum barrier effects) are well accounted for in a non-perturbative model using Volkov final states (after H. Reiss [496]).

Volkov AN, Ubbink M, van Nuland NA (2010) Mapping the encounter state of a transient protein complex by PRE NMR spectroscopy. J Biomol NMR 48 225-236... 

StiU, Tikhonov and Volkov repeatedly observed the above shift in the ratio of water spin isomers after contacting water vapor with the polymeric adsorbent both under dynamic (Fig. 10.19) and static conditions [30]. Activated carbons, zeolites, and sifica gels generated similar effects. The adsorbed water was strongly para-enriched. Interestingly, water samples enriched in the ortho- or para-isomers were found to be stable in the form of ice, but equilibrated to the ratio of 3 1 in the hquid state at room temperature within 20—30 min. As the separation takes place at the... 

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