Asymptotic Form of the Electron Capture Cross Section in First Born and Distorted Wave Approximations PDF Download
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Author: R. A. Mapleton Publisher: ISBN: Category : Cross sections (Nuclear physics) Languages : en Pages : 22
Book Description
The first Born approximation with both the proton-proton and proton-electron interaction is used to calculate the high energy electron capture cross section. It is shown that the high energy proton-nucleus amplitude has a dominant peak for backward scattering (centre-of-mass system). As a consequence of this peak, if the protons are treated as distinguishable particles, the cross section depends upon the impact energy E as E(3- ) in contrast to the commonly accepted E(6- ) dependence. When the protons are treated as indistinguishable particles, the electron capture cross section is not defined at sufficiently high energies. This same cross section is also calculated using the distorted wave approximation as developed by Bassel and Gerjuoy in 1960. It is shown that the proton-nucleus amplitude is only cancelled in the forward direction, and consequently the electron capture cross section is again not defined at high energies. (Author).
Author: R. A. Mapleton Publisher: ISBN: Category : Cross sections (Nuclear physics) Languages : en Pages : 22
Book Description
The first Born approximation with both the proton-proton and proton-electron interaction is used to calculate the high energy electron capture cross section. It is shown that the high energy proton-nucleus amplitude has a dominant peak for backward scattering (centre-of-mass system). As a consequence of this peak, if the protons are treated as distinguishable particles, the cross section depends upon the impact energy E as E(3- ) in contrast to the commonly accepted E(6- ) dependence. When the protons are treated as indistinguishable particles, the electron capture cross section is not defined at sufficiently high energies. This same cross section is also calculated using the distorted wave approximation as developed by Bassel and Gerjuoy in 1960. It is shown that the proton-nucleus amplitude is only cancelled in the forward direction, and consequently the electron capture cross section is again not defined at high energies. (Author).
Author: R. A. Mapleton Publisher: ISBN: Category : Cross sections (Nuclear physics) Languages : en Pages : 0
Book Description
The first Born approximation with both the proton-proton and proton-electron interaction is used to calculate the high energy electron capture cross section. It is shown that the high energy proton-nucleus amplitude has a dominant peak for backward scattering (centre-of-mass system). As a consequence of this peak, if the protons are treated as distinguishable particles, the cross section depends upon the impact energy E as E(3- ) in contrast to the commonly accepted E(6- ) dependence. When the protons are treated as indistinguishable particles, the electron capture cross section is not defined at sufficiently high energies. This same cross section is also calculated using the distorted wave approximation as developed by Bassel and Gerjuoy in 1960. It is shown that the proton-nucleus amplitude is only cancelled in the forward direction, and consequently the electron capture cross section is again not defined at high energies. (Author)
Author: D. R. Bates Publisher: ISBN: Category : Languages : en Pages : 6
Book Description
It has been shown that if the protons are regarded as distinguishable particles the asymptotic form of the cross section for H(+) + H(1s) to H(1s) + H(+) in the (nonrelativistic) First Born and distorted wave approximations is Q(1s-1s) = 2Mpi(a-squared) /3m (E-cubed), where E is the energy of the incident proton in atomic units, M is its mass and m is the mass of the electron. A simple classical treatment of this problem is given.
Author: John N. Pierce Publisher: ISBN: Category : Alphabets Languages : en Pages : 38
Book Description
The performance of a plurality-count diversity combiner for fading M-ary transmissions is analyzed, and calculated error probabilities are presented graphically for alphabet sizes of 2, 8, and 32. The performance is shown to be within 3 dB of that of an optimum square-law combiner for moderate alphabet sizes when there is no restriction on the allowable number of diversity branches. It is shown that a worthwhile saving in transmitted power can be effected by using nonbinary alphabets with plurality-count combining for the transmission of binary data. The availability of extra information from the combiner for use with error-correction is discussed.
Author: C. C. Leiby (Jr.) Publisher: ISBN: Category : Electrophoresis Languages : en Pages : 42
Book Description
Druyvesteyn's solutions for electrophoretically induced gas flows in electrical discharges in gases were extended over a larger pressure range and corrected for the influence of Debye shielding effects. The effects of molecular or 'slip' flow were also taken into account. These more accurate and general solutions were applied to the reverse phenomenon of space charge field generation arising from the flow of a thermally ionized cesium plasma through a tube. Under such flow conditions, a non-linear differential equation for the axial pressure distribution was obtained but not solved. However, it was possible to obtain estimates of the ranges of cesium pressure, temperature and tube radii which would be required for sensible levels of electric power generation. Anaphoretic flow power levels of the order of 0.1 to 10 watts, in tubes of laboratory dimensions (radii of 10 cm or less), appear feasible at temperatures from 1700 to 2400K. Sensible power generation levels at lower temperatures require very large diameter tubes, and therefore are not feasible. (Author).
Author: E. Folke Bolinder Publisher: ISBN: Category : Electric circuits Languages : en Pages : 34
Book Description
A discussion of a recent significant advance in network synthesis theory is presented. This 'breakthrough' was accomplished by D. Hazony of the Case Institute of Technology and by D. C. Youla of the Polytechnic Institute of Brooklyn, who independently of each other developed methods for unifying the theory of two-port cascade synthesis. Both methods are based on Richards' theorem, and both introduce the gyrator artificually. Different methods of proof are used, however. A valuable 'cookbook recipe' was developed by Youla. Hazony managed to extend the method to n-ports. In all, this epoch-making achievement has resulted in an important, simple, and beautiful method of network synthesis. (Author).
Author: Stephen J. Kahne Publisher: ISBN: Category : Control theory Languages : en Pages : 30
Book Description
The application of Bellman's dynamic programming technique to realistic control problems has generally been precluded by excessive storage requirements inherent in the method. In this paper, the notion of state mobility is described and shown to be valuable in reducing certain classes of dynamic programming calculations to manageable size. The scheme requires one simple calculation at each stage of the process. IN many cases even this calculation may be omitted. It results in the reduction of the range of allowable state variables to be scanned. The amount of reduction varies from problem to problem. A simple example exhibits a fifty percent reduction. This corresponds to a fifty percent reduction in storage requirements for the problem. Reductions of one or two orders of magnitude appear possible for certain classes of problems.
Author: R. A. Mapleton
Author: R. A. Mapleton
Author: R. A. Mapleton
Author: D. R. Bates
Author: R. A. Mapleton
Author: John N. Pierce
Author: C. C. Leiby (Jr.)
Author: Lorenzo Calabi
Author: E. Folke Bolinder
Author: Heinz J. Fischer
Author: Stephen J. Kahne