scholarly journals A New Approach to the Analytic Evaluation of Thermonuclear Reaction Rates

1981 ◽  
Vol 93 ◽  
pp. 317-317
Author(s):  
H. J. Haubold ◽  
R. W. John
Keyword(s):  
Closed Form ◽  
Reaction Rate ◽  
Special Function ◽  
Reaction Rates ◽  
Thermonuclear Reaction ◽  
Fusion Plasma ◽  
New Approach ◽  
Analytic Evaluation ◽  
Image Position ◽  
Form Evaluation

In our paper (Haubold and John 1978) we succeeded in a closed-form evaluation of the reaction rate by means of a special function, known as Meijer's G-function This representation of the rate is appropriate to perform analytical operations (e.g. for the computation of energy generation in a fusion plasma).

scholarly journals On a family of logarithmic and exponential integrals occurring in probability and reliability theory

1994 ◽  
Vol 35 (4) ◽  
pp. 469-478 ◽  
Author(s):  
M. Aslam Chaudhry
Keyword(s):  
Closed Form ◽  
Recurrence Relation ◽  
Reliability Theory ◽  
Integral Function ◽  
Integral Representations ◽  
Exponential Integral ◽  
Error Functions ◽  
Special Cases ◽  
Image Position ◽  
Form Evaluation

AbstractWe define an integral function Iμ(α, x; a, b) for non-negative integral values of μ byIt is proved that Iμ(α, x; a, b) satisfies a functional recurrence relation which is exploited to find a closed form evaluation of some incomplete integrals. New integral representations of the exponential integral and complementary error functions are found as special cases.

scholarly journals Screening effects on resonant thermonuclear reaction rates

2019 ◽  
Vol 11 ◽  
Author(s):  
T. Liolios ◽  
K. Langanke ◽  
W. Wiescher
Keyword(s):  
Reaction Rate ◽  
Nuclear Reactions ◽  
Reaction Network ◽  
Reaction Rates ◽  
Partial Width ◽  
Entrance Channel ◽  
Correction Factors ◽  
Thermonuclear Reaction ◽  
Hydrogen Burning ◽  
Stellar Reaction Rate

The reaction rate of several astrophysically important nuclear reactions is dominated by the contribution of narrow resonances at the astrophysically most effective energies. In the stellar plasma the partial width of the resonances in the entrance channel is modified due to screening corrections. This effect, so far ignored in stellar reaction network calculations, reduces the conventional Salpeterscreening enhancement of the reaction rate. We derive analytical screening correction factors for the contributions of narrow resonances to the stellar reaction rate and discuss the effects for UC (a, j)lsO, 150(a,7)19 Ne and other reactions of relevance to explosive hydrogen burning

scholarly journals Effect of Excited States on Thermonuclear Reaction Rates

1983 ◽  
Vol 36 (4) ◽  
pp. 583 ◽  
Author(s):  
DG Sargood
Keyword(s):  
Statistical Model ◽  
Excited States ◽  
Cross Sections ◽  
Reaction Rate ◽  
Ground States ◽  
Reaction Rates ◽  
Thermonuclear Reaction ◽  
Thermal Distribution ◽  
Naturally Occurring ◽  
Thermonuclear Reaction Rate

Values of the ratio of the thermonuclear reaction rate of a reaction, with target nuclei in a thermal distribution of energy states, to the reaction rate with all target nuclei in their ground states are tabulated for neutron, proton and (X-particle induced reactions on the naturally occurring nuclei from 2�Ne to 70Zn, at temperatures of 1, 2, 3�5 and 5 x 109 K. The ratios are determined from reaction rates based on statistical model cross sections.

scholarly journals Enhancement of Thermonuclear Reaction Rate due to Strong Screening

1981 ◽  
Vol 93 ◽  
pp. 318-319
Author(s):  
N. Itoh ◽  
H. Totsuji ◽  
S. Ichimaru ◽  
H.E. DeWitt
Keyword(s):  
Monte Carlo ◽  
Ignition Temperature ◽  
Enhancement Factor ◽  
Reaction Rate ◽  
Number Density ◽  
Thermonuclear Reaction ◽  
Thermonuclear Reactions ◽  
Image Position ◽  
Thermonuclear Reaction Rate ◽  
Highly Evolved

The enhancement factor for the rate of thermonuclear reactions which involve two kinds of nuclei with charges Zi and Zj in the strong-screening regime is given for general cases of surrounding nuclear plasmas by the formula, exp[1.25Γij −0.095τij(3Γij/τij)2]. Here, Γij = 2ZiZje2/(ai+aj)T; ai = [3Zi/4πΣkZknk]1/3; τij = [(27π2/4)(2μijZi2Zj2e4Th2)]1/3; μij is the reduced mass for the two reacting nuclei Zi and Zj; and nk is the number density of nuclei Zk. The calculation is based on the recent results of Monte Carlo computations for binary ion mixtures, which have shown that the screening functions hij(r) at intermediate distances [0.5 ≤ r/[(ai+aj)/2] ≤ 1.6] can be expressed to a good degree of accuracy by Application to the calculation of carbon ignition in the carbon-oxygen core of a highly evolved star is discussed. The carbon ignition temperature is found to be single-valued as a function of the density in contrast to the work of Graboske.

scholarly journals Fusion yield: Guderley model and Tsallis statistics

2010 ◽  
Vol 77 (1) ◽  
pp. 1-14 ◽  
Author(s):  
H. J. HAUBOLD ◽  
D. KUMAR
Keyword(s):  
Shock Wave ◽  
Reaction Rate ◽  
Fusion Energy ◽  
Plasma Phys ◽  
Thermonuclear Reaction ◽  
Fusion Plasma ◽  
Linear Differential ◽  
Plasma Shock Wave ◽  
Thermonuclear Reaction Rate ◽  
Fusion Yield

AbstractThe reaction rate probability integral is extended from Maxwell–Boltzmann approach to a more general approach by using the pathway model introduced by Mathai in 2005 (A pathway to matrix-variate gamma and normal densities. Linear Algebr. Appl.396, 317–328). The extended thermonuclear reaction rate is obtained in the closed form via a Meijer's G-function and the so-obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma-compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981 (Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave. Plasma Phys.23, 399–411). An interpretation for the pathway parameter is also given.

SEM analysis of the change in the reaction rates with deposit structures in the copper-iron cementation system

1978 ◽  
Vol 36 (1) ◽  
pp. 456-457
Author(s):  
V. Annamalai ◽  
L.E. Murr
Keyword(s):  
Structural Characteristics ◽  
Secondary Electron Emission ◽  
Copper Deposit ◽  
Reaction Rates ◽  
Sem Analysis ◽  
Experimental Conditions ◽  
Major Drawback ◽  
Emission Mode ◽  
Scrap Iron ◽  
Image Position

Economical recovery of copper metal from leach liquors has been carried out by the simple process of cementing copper onto a suitable substrate metal, such as scrap-iron, since the 16th century. The process has, however, a major drawback of consuming more iron than stoichiometrically needed by the reaction.Therefore, many research groups started looking into the process more closely. Though it is accepted that the structural characteristics of the resultant copper deposit cause changes in reaction rates for various experimental conditions, not many systems have been systematically investigated. This paper examines the deposit structures and the kinetic data, and explains the correlations between them.A simple cementation cell along with rotating discs of pure iron (99.9%) were employed in this study to obtain the kinetic results The resultant copper deposits were studied in a Hitachi Perkin-Elmer HHS-2R scanning electron microscope operated at 25kV in the secondary electron emission mode.

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