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Gamow [3] first solved the one-dimensional case of quantum tunneling using the WKB approximation.Considering a wave function of a particle of mass m, we take area 1 to be where a wave is emitted, area 2 the potential barrier which has height V and width l (at < <), and area 3 its other side, where the wave is arriving, partly transmitted and partly reflected.
Since this integration has an exponential damping at high energies of the form and at low energies from the Gamow factor, the integral almost vanished everywhere except around the peak, called Gamow peak, [37]: 185 at E 0, where: =
= (/) / is the Gamow peak energy, dependent on E G, the Gamow factor. Additionally, S ( E )/E is the reaction cross section, n is number density, m R = m A ⋅ m B / ( m A + m B ) {\displaystyle m_{R}=m_{A}\cdot m_{B}/(m_{A}+m_{B})} is the reduced mass for the particle collision, and A , B are the two species participating in the limiting ...
R. A. Alpher, H. A. Bethe, G. Gamow, The Origin of Chemical Elements Archived 2013-02-07 at the Wayback Machine, Physical Review 73 (1948), 803. The so-called αβγ paper, in which Alpher and Gamow suggested that the light elements were created by hydrogen ions capturing neutrons in the hot, dense early universe. Bethe's name was added for ...
In practice, temperatures needed to overcome the Coulomb barrier turned out to be smaller than expected due to quantum mechanical tunnelling, as established by Gamow. The consideration of barrier-penetration through tunnelling and the speed distribution gives rise to a limited range of conditions where fusion can take place, known as the Gamow ...
All three researchers were familiar with the works on field emission, [10] and Gamow was aware of Mandelstam and Leontovich's findings. [16] In the early days of quantum theory, the term tunnel effect was not used, and the effect was instead referred to as penetration of, or leaking through, a barrier.
George Gamow (sometimes Gammoff; born Georgiy Antonovich Gamov; Russian: Георгий Антонович Гамов; 4 March 1904 – 19 August 1968) was a Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Georges Lemaître's Big Bang theory.
As the density increases, the Gamow peak increases in height and shifts towards lower energy, while the potential barriers are depressed. If the potential barriers are depressed by the amount of E 0 {\displaystyle E_{0}} , the Gamow peak is shifted across the origin, making the reactions density-dependent, as the Gamow peak energy is much ...