Interaction electron-photon

Another kind of particle and another kind of interaction were discovered from a detailed study of beta radioactivity in which electrons with a continuous spectrum of energies are emitted by an unstable nucleus. The corresponding interactions could be viewed as being due to the virtual transmutation of a neutron into a proton, an electron, and a new neutral particle of vanishing mass called the neutrino. The theory provided such a successful systematization of beta decay rate data for several nuclei that the existence of the neutrino was well established more than 20 years before its experimental discovery. The beta decay interaction was very weak even compared to the electron-photon interaction. 

The Nuclear Force. The nuclear forces and the interactions between pions and nucleons are strong the electron-electron and electron-photon interactions are electromagnetic the beta decay interactions are weak... 

Fig. 1. Time-direct - (a) - and time-reverse - (b) - diagrams describing the process of inelastic scattering of a photon with the energy hu> and the wave vector k by an atom residing in the state ) (ui,k, ) —> (u>, k, f)). Solid lines stand for atomic states, dashed lines denote photons in the initial/final states, and filled circles designate the vertices of the electron-photon interaction V...

All fields and physical constants of the QED Hamiltonian have to be taken as renormalized to avoid divergencies of the electron-electron and electron-photon interaction integrals including the interaction with the external field [41]. Renormalization is independent of die external potential Vg, but requires correction terms, among them an energy correction <5E[Ve ]- Expectation values ( TI I T) of the renormalized QED Hamiltonian are finite for arbitrary N-... 

The carrier multiplication (CM) process generated as a result of a single photon absorption in a spherical quantum dot (QD) is explained as due to multiple,virtual band-to-band electron-photon quantum transitions. Only the electron-photon interaction is used as a perturbation without the participation of the Coulomb electron-electron interaction. The creation of an odd number of electron-hole (e-h) pairs in our model is characterized by the Lorentzian-type peaks, whereas the creation of an even number of e-h pairs is accompanied by the creation of one real photon in the frame of combinational Raman scattering process. Its absorption band is smooth and forms an absorption background without peak structure. It can explain the existence of a threshold on the frequency dependence of the carrier multiplication efficiency in the region corresponding to the creation of two e-h pairs. 

The first attempt to explain the mechanism of the CM process was made in [1-2]. An example with the creation of two electron-hole pairs as a result of one photon absorption, was considered in the second order of the perturbation theory. In its first step the Hamiltonian of the electron-photon interaction, giving rise to band-to-band transition, was used. The virtual state of the electron-hole (e-h) pair. lr ) was situated on the energy scale not far from the final state Ixr). The second virtual transition between the states lr ) and Irx) was calculated using the matrix element of the Coulomb electron-electron interaction, which describes the scattering of one particle with the simultaneous creation of an e-h pair. This matrix element is much smaller than the diagonal one. Nevertheless, the general enhancement of the Coulomb interaction introduced by the size confinement could favor to the realization of this mechanism. 

Side by side with it, one can discuss also another mechanism of carrier multiplication (CM) without participation of the Coulomb interaction. It is based on the successive, multiple application of the electron-photon interaction... 

Hamiltonian, which takes part in the first step of the perturbation theory. On this way we will need to discuss along with the creation of an odd number of e-h pairs, also the Raman scattering processes with the creation of an even number of e-h pairs and simultaneously of one real photon. The pure electron-photon interaction mechanism requires the introduction of the virtual and final states of two types one of them is the pure e-h states, when their number is n= 1,3,5,. Another type is the combined electron-hole-photon states, when an even number of e-h pairs =2,4,6,... is accompanied by the creation of one virtual or real photon. 

The Hamiltonian of the electron-photon interaction will be used in a very simplified form taking into account only the simplest band structure of a semiconductor with parabolic electron and hole bands without complications related to heavy and light holes, spin-orbit splitted hole band or with the Dirac model of the band structure in the case of small band gap semiconductors. In the case of simple parabolic band after their size quantization in a spherical symmetry quantum dots the electrons and holes are characterized by envelope wave functions with the quantum numbers I, n, m. An essential simplification of the future calculations is the fact that in the selected simple model the band-to-band transitions under the influence of the electron-photon interaction Hamiltonian take place with the creation of an e-h pair with exactly the same quantum numbers for electron and for hole as follows e l,n,m), h l,n,m). ... 

The considered model is based on the use as a perturbation only the electron-photon interaction, on introduction of the photon states as virtual and real states along with the states of many e-h pairs. Only the e-h pairs with the same quantum numbers I, n, m for both partners were considered. The combinational Raman scattering process with the creation of an even number of e-h pairs is the main treasure of the presented model. The influence of the Coulomb electron-electron interaction must be also taken into account. 

Excluding non-linear optical phenomena by the neglect of the -term in eq. (2) and taking into account the use of Coulomb gauge, we may identify the term responsible for the electron-photon interaction ... 

The exact quantum theoretical treatment of the dispersion effect involves quantizing matter and electromagnetic fields as well. The coupled electron-photon system is to be treated on the basis of quantum electrodynamics. Using the method of second quantization, it is possible to build up the total Hamiltonian from an electron Hamiltonian H, a photon Hamiltonian and an electron-photon interaction operator Hin,. The dispersion energy between two particles now results in fourth order perturbation. Each contribution is due to the interaction of two electrons with, fwo photons. 

The Hamiltonian describing this electron-photon interaction is conveniently given in terms of second quantization... 

The third term in Eq. (8.1) gives the electron-photon interaction. An electron in orbital i) is annihilated, an electron in orbital fc> is created. This electron transition is coupled to the emission or absorption of a photon q. The respective coupling parameters are denoted by V ikiq) and U kiq). They are independent of the position of photon emission and absorption only if the photons correspond to planar modes. 

In the absence of the electron-photon interaction term in Eq. (8.1), we may represent the eigenvectors of... 

In spite of considering two-photon processes, we still find the energy levels (8.17) to be equidistant with respect to the photon occupation numbers n, -I- i. This suggests that it is permissible to neglect the effect of the electron-photon interaction on statistics and to occupy the electron states and the photon states according to Fermi statistics and to Bose statistics. We shall check this question in Section 8.4 by studying the creation and annihilation operators of the resulting quasi-electrons and quasi-photons. 

However, since the statistic weight of the excited states is affected by the electron-photon interaction, there might well arise a free energy of attraction from the energy terms of order zero and two. We have to check whether with decreasing separation there is a redistribution of occupied states, which gives rise to an energy of interaction of order four in U kiq) as well. 

The proposed successive summation over all electron states i involves the cancellation of terms quadratic in the electron-photon interaction parameter [/ (kiq) each time, whereas the terms of the fourth order which depend on the separation of particles 1 and 2 are retained. This procedure incures the unnecessary risk of omitting terms quadratic in U-(kiq) in the electron and photon distribution functions of the separated particles 1 and 2. In order to obtain the energy of attraction correctly up to terms of the sixth order in the interaction parameters we now sum the partition function (8.33) more rigorously. 

Equation (8.46) holds with respect to all orders in the electron-photon interaction parameter. Substituting Eq. (8.46) into (8.39), we expand the exponential term with respect to the mixed contribution E Vi V2 , which... 

Bolometer with hot electrons Photons interact with free electrons in semiconduchn and transfer their momentum to them, thus changing their effective temptaature... 

Up to this moment we ignored we electron-photon interaction. Taking it into account we should substitute exp( — itox) in Eq. (6) by exp( — i-J, dx )(x)). Then, Eq. (6) takes the following form [6,19] ... 

Solid-state physicists, on the other hand, got inspiration from the quantum field treatment of electron-photon interactions, and by jumping over nuclei, atoms, molecules, transferred these ideas into the field of solid-state condensed matter physics in the sophisticated form of a many-body treatment based on the electron-phonon interaction, in spite of the fact that its limits of validity were never investigated, particularly with respect to the COM problem. 

To make a diagonal indirect transition, both an appropriate energy photon and an appropriate momentum phonon must be present together with the electron. This is referred to as a three-body interaction because there are three particles (electron, phonon, and photon) participating. Such collisions are over 1000 times less likely than a simple electron-photon interaction at common temperatures. This means that electrons and holes of different momenta do not recombine rapidly. Typically, electrons and holes in pure direct-gap semiconductors last no more than 10 s. 

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