Bethe, mechanism

Both reactions occur, though the Bethe mechanism requires a higher temperature and therefore predominates in the central regions of large stars. 

Bethe H A and Salpeter E E 1957 Quantum Mechanics of One- and Two-electron Atoms (Berlin Springer)... 

Bethe provided the theoretical basis for understanding the scattering of fast electrons by atoms and molecules [3, 4]. We give below an outline of the quantum-mechanical approach to calculating the scattermg cross section. 

H. A. Bethe and E. E. Salpeter, Quantum Mechanics of One and Two Electron Atoms, Henurn/ Rosetta, New York, 1977. 

In 1938 Bethe formulated the mechanism for energy generation in stars. This research grew out of his participation at the third Washington conference on theoretical physics in April 1938. The reaction... 

Bethe, H. A., and Salpeter, E. E., Handbuch der Physik, Springer, Berlin, 1957, Band XXXV. Quantum mechanics of one-and two-electron systems. ... 

Eugen Merzbacher, Quantum Mechanics, Chapter 21, John Wiley and Sons, Inc., New York, 1961 Schweber, Bethe, and de Hoffmann, Mesons and Fields, Vol. 1, Section 8a, Harper and Row, New York, 1955. 

H. A. Bethe and E. E. Salpeter (1957) Quantum Mechanics of One- and Two-Electron Atoms (Springer, Berlin Academic Press, New York reprinted by Plenum, New York, 1977). A comprehensive non-relativistic and relativistic treatment of the hydrogen and helium atoms with and without external fields. 

I like to emphasize that Fig. 1 is not meant to indicate any fundamental limitation of quantum mechanics both Bohr s and Bethe s formulae invoke mathematical approximations to the underlying physical models, and Bethe s formula in particular relies on first-order perturbation theory for both distant and close collisions. 

Despite the fact that Bohr s stopping power theory is useful for heavy charged particles such as fission fragments, Rutherford s collision cross section on which it is based is not accurate unless both the incident particle velocity and that of the ejected electron are much greater than that of the atomic electrons. The quantum mechanical theory of Bethe, with energy and momentum transfers as kinematic variables, is based on the first Born approximation and certain other approximations [1,2]. This theory also requires high incident velocity. At relatively moderate velocities certain modifications, shell corrections, can be made to extend the validity of the approximation. Other corrections for relativistic effects and polarization screening (density effects) are easily made. Nevertheless, the Bethe-Born approximation... 

A weakly bound state is necessarily nonrelativistic, v Za (see discussion of the electron in the field of a Coulomb center above). Hence, there are two small parameters in a weakly bound state, namely, the fine structure constant a. and nonrelativistic velocity v Za. In the leading approximation weakly bound states are essentially quantum mechanical systems, and do not require quantum field theory for their description. But a nonrelativistic quantum mechanical description does not provide an unambiguous way for calculation of higher order corrections, when recoil and many particle effects become important. On the other hand the Bethe-Salpeter equation provides an explicit quantum field theory framework for discussion of bound states, both weakly and strongly bound. Just due to generality of the Bethe-Salpeter formalism separation of the basic nonrelativistic dynamics for weakly bound states becomes difficult, and systematic extraction of high order corrections over a and V Za becomes prohibitively complicated. 

This experimental development was matched by rapid theoretical progress, and the comparison and interplay between theory and experiment has been important in the field of metrology, leading to higher precision in the determination of the fundamental constants. We feel that now is a good time to review modern bound state theory. The theory of hydrogenic bound states is widely described in the literature. The basics of nonrelativistic theory are contained in any textbook on quantum mechanics, and the relativistic Dirac equation and the Lamb shift are discussed in any textbook on quantum electrodynamics and quantum field theory. An excellent source for the early results is the classic book by Bethe and Salpeter [6]. A number of excellent reviews contain more recent theoretical results, and a representative, but far from exhaustive, list of these reviews includes [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. 

Bethe, H. A., and R. W. Jackiw, Intermediate Quantum Mechanics, Second Edition, Benjamin, New York, 1968. 

From the theorist s point of view, the work of Sommerfeld on the Electron Theory of Metals was most seminal. It was eventually reviewed on a quantum mechanical basis in a famous article in the Handbuch der Physik , Vol. XXIV/2 [A. Sommerfeld, H. Bethe (1933)]. Two years before, Heisenberg had introduced the electron hole . A. H. Wilson worked on the Lheory of semiconductors, and it was understood that at T - OK their valence band was completely filled with electrons, whereas the conduction band was empty. At T> 0 K, electrons are thermally excited from the valence band into the conduction band. 

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