A note on the quantum-tail effect on fusion reaction rate

Zubarev, Alexander L.

doi:10.1088/1751-8113/41/31/312004

Cited by 6 publications

(4 citation statements)

References 42 publications

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“…The accuracy of this approach is discussed further below where the results of calculations are shown for the full formula (2), simplified equation (17), and approximate analytical estimations (57) and (70). This eliminates the issues raised in the paper [16] on the validity of such a method.…”

Section: Analytical Estimates For Reaction Rates For Model Dis-tribut...mentioning

confidence: 95%

“…In the literature [16,17] there was some criticism, connected with the use of the asymptotical presentation of a single-particle distribution function for calculation of reaction rates, including fusion rates. The problem is that in reality we must use the product of distribution functions over momentum in the laboratory frame for both reacting particles and due to power low tails, not Maxwellian ones, it is hard to perform analytical integration of the reaction cross-section, depending on particles relative momentum in their center of mass.…”

Section: Introductionmentioning

confidence: 99%

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Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal plasma media

et al. 2012

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This study concerns a situation when measurements of the nonresonant cross-section of nuclear reactions appear highly dependent on the environment in which the particles interact. An appealing example discussed in the paper is the interaction of a deuteron beam with a target of deuterated metal Ta. In these experiments, the reaction cross section for d(d,p)t was shown to be orders of magnitude greater than what the conventional model predicts for the low-energy particles. In this paper we take into account the influence of quantum effects due to the Heisenberg uncertainty principle for particles in a non-ideal medium elastically interacting with the medium particles.In order to calculate the nuclear reaction rate in the non-ideal environment we apply both the Monte Carlo technique and approximate analytical calculation of the Feynman diagram using nonrelativistic kinetic Green's functions in the medium which correspond to the generalized energy and momentum distribution functions of interacting particles. We show a possibility to reduce the 12-fold integral corresponding to this diagram to a fivefold integral. This can significantly speed up the computation and control accuracy. Our calculations show that quantum effects significantly influence reaction rates such as p + 7 Be, 3 He + 4 He, p + 7 Li, and 12 C + 12 C. The new reaction rates may be much higher than the classical ones for the interior of the Sun and supernova stars. The possibility to observe the theoretical predictions under laboratory conditions is discussed.

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Section: Analytical Estimates For Reaction Rates For Model Dis-tribut...mentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal plasma media

et al. 2012

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“…For nonrelativistic Coulomb particles, γ(p) ∝ E −3/2 p , therefore the tail decays as w qt ∝ E −7/2 p . 1 This approach was criticized by Bahcall et al [5] and by Zubarev [41]. Bahcall for the reaction rate represents the density of states and should not be confused with the expectation values of particle momenta, distributed according to w mod (E p ).…”

Section: "Quantum Tail" In Energy Distributionmentioning

confidence: 99%

“…Zubarev [41] put forward another argument. He noted that the pp-fusion rates calculated with w B (E) and with w mod (E) differ by three orders of magnitude for the Sun, and concluded that in the second case "one has neglected the coupling between the various probability amplitudes of velocity which is introduced by the quantum uncertainty."…”

Section: "Quantum Tail" In Energy Distributionmentioning

confidence: 99%

Electron screening effect on stellar thermonuclear fusion

Potekhin,

Chabrier

2013

Preprint

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We study the impact of plasma correlation effects on nonresonant thermonuclear reactions for various stellar objects, namely in the liquid envelopes of neutron stars, and the interiors of white dwarfs, low-mass stars, and substellar objects. We examine in particular the effect of electron screening on the enhancement of thermonuclear reactions in dense plasmas within and beyond the linear mixing rule approximation as well as the corrections due to quantum effects at high density. In addition, we examine some recent unconventional theoretical results on stellar thermonuclear fusions and show that these scenarios do not apply to stellar conditions.

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Electron Screening Effect on Stellar Thermonuclear Fusion

Potekhin

Chabrier

2013

Contrib. Plasma Phys.

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We study the impact of plasma correlation effects on nonresonant thermonuclear reactions for various stellar objects, namely in the liquid envelopes of neutron stars, and the interiors of white dwarfs, low‐mass stars, and substellar objects. We examine in particular the effect of electron screening on the enhancement of thermonuclear reactions in dense plasmas within and beyond the linear mixing rule approximation as well as the corrections due to quantum effects at high density. In addition, we examine some recent unconventional theoretical results on stellar thermonuclear fusions and show that these scenarios do not apply to stellar conditions. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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A note on the quantum-tail effect on fusion reaction rate

Abstract: A study is made of the power-law tail effect in the quantum particle distribution over momentum on the nuclear fusion reactions. Our results do not support the idea of averaging the fusion reaction cross-section over the momentum distribution, postulated and used in many publications.

Cited by 6 publications

References 42 publications

Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal plasma media

Enhancement of fusion rates due to quantum effects in the particles momentum distribution in nonideal plasma media

Electron screening effect on stellar thermonuclear fusion

Electron Screening Effect on Stellar Thermonuclear Fusion

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