scholarly journals Showers produced by the penetrating cosmic radiation

1938 ◽  
Vol 166 (927) ◽  
pp. 529-543 ◽  
Keyword(s):  
Cross Sections ◽  
Cosmic Ray ◽  
Nuclear Forces ◽  
Qualitative Explanation ◽  
Rest Energy ◽  
Self Energy ◽  
Heavy Electron ◽  
Order Of Magnitude ◽  
Mathematical Difficulties ◽  
The One

In two recent papers by Fröhlich, Heitler and Kemmer (1938) and by Kemmer (1938) it has been shown that the properties of the nuclear particles proton and neutron can qualitatively be understood on the assumption that a proton (neutron) is capable of emitting a heavy positive ( negative ) electron (denoted by Y + , Y - ), transforming itself at the same time into a neutron (proton). The theory of the heavy electron—its wave equation and its interaction with the nuclear particles—was built up in close analogy to the theory of light and its interaction with an electron. We now apply this theory to the passage of a heavy electron through matter, and we shall find that it leads to a qualitative explanation of a number of cosmic-ray facts connected with the penetrating radiation. In applying the theory to collisions of fast heavy electrons with nuclei, there is, however, a serious difficulty from the start: From the discussion of the nuclear properties it has become evident that the theory in its present form can only claim validity for relative energies between the heavy electron and the nuclear particles not very much greater than the rest energy μc 2 of the heavy electron, i. e. up to at most a few times 10 8 e-volts. For higher energies the theory leads to serious mathematical difficulties (diverging self-energy, diverging nuclear forces of higher order, etc.). For cosmic rays the interesting region is just the one for energies greater than 10 8 e-volts. It may be justifiable, in spite of these facts, to apply the theory to cosmic-ray heavy electrons, for two reasons: In the first place it is to be expected that the processes derived from the theory for energies of the order μc 2 will exist also at higher energies and will preserve a number of their qualitative features. In the second place the theoretical cross-section obtained for these processes at energies of the order 10 8 e-volts will at least be right in the order of magnitude. On the other hand, we must not attach any significance to the way in which the cross-sections are found to depend on energy.

Theoretical studies on the one- and two-photon absorption of tetrabenzoporphyrins and phthalocyanines

2004 ◽  
Vol 82 (1) ◽  
pp. 19-26 ◽  
Author(s):  
Xin Zhou ◽  
Ai-Min Ren ◽  
Ji-Kang Feng ◽  
Xiao-Juan Liu
Keyword(s):  
Dipole Moment ◽  
Cross Sections ◽  
Density Functional ◽  
Transition Dipole Moment ◽  
Photon Absorption ◽  
Transition Dipole ◽  
Two Photon Absorption ◽  
Two Photon ◽  
Order Of Magnitude ◽  
The One

The one-photon absorption (OPA) properties of tetrabenzoporphyrins (TBPs) and phthalocyanines (Pcs) were studied using the semiempirical ZINDO method and time-dependent density functional theory (TDDFT), respectively. The compared results confirmed that the semiempirical ZINDO method was reasonably reliable when calculating the OPA of tetrabenzoporphyrins and phthalocyanines. On the basis of the OPA properties obtained from the ZINDO method, two-photon absorption (TPA) properties of two series of molecules were investigated, using ZINDO and sum-over-states (SOS) methods. The results showed that the TPA cross-sections of all molecules were in the range of 220.6 × 10–50 – 345.9 × 10–50 cm4·s·photon–1, which were in the same order of magnitude as the values reported in the literature. The relatively larger δ(ω) value for Pcs with respect to that for corresponding TBPs originates from larger intramolecular charge transfer, which can be characterized by the difference of dipole moment between S0 and S1 and the transition dipole moment between S1 and S5.Key words: two-photon absorption, ZINDO, sum-over-states, tetrabenzoporphyrin, phthalocyanines.

Considerations affecting the estimation of cosmic-ray age

1968 ◽  
Vol 46 (10) ◽  
pp. S561-S568 ◽  
Author(s):  
M. M. Shapiro ◽  
R. Silberberg
Keyword(s):  
Cosmic Rays ◽  
Cross Sections ◽  
Galactic Disk ◽  
Principal Component ◽  
Cosmic Ray ◽  
Light Nuclei ◽  
The Galaxy ◽  
Primary Cosmic Radiation ◽  
Order Of Magnitude ◽  
Medium Nuclei

Previous investigations by Daniel and Durgaprasad on the ratios Be/B and Be/Li in the primary cosmic radiation exploited the decay of 10Be produced in space to deduce a confinement time for cosmic rays in the galaxy. They concluded that this "age" T is at least 50 million years, and thence inferred that the cosmic-ray nuclei are trapped in a volume much larger than that of the galactic disk. These conclusions depended upon the values of fragmentation cross sections available in 1962 to Badhwar, Daniel, and Vijayalakshmi. Recent values of the Orsay group, however, reduce the calculated rates of 10Be and 9Be production by an order of magnitude; and an analysis based upon the latest cross sections leads to the following conclusions: (1) The possibility that cosmic rays are mainly confined to the disk of the galaxy and that T ≈ 106 years is not excluded. (2) The fragmentation parameter for medium nuclei [Formula: see text] into light nuclei [Formula: see text] is revised from 0.48 (the value of Badhwar et al.) to 0.34. (3) The mean path-length of 2.5 ± 0.5 g/cm2 of Badhwar et al. is revised to 4 ± 1 g/cm2. (4) 7Be now appears to be the principal component of cosmic-ray beryllium (about 70 or 80%, depending upon the cosmic-ray lifetime).

scholarly journals Tuning domain wall dynamics by shaping nanowires cross-sections

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Dora Altbir ◽  
Jakson M. Fonseca ◽  
Oksana Chubykalo-Fesenko ◽  
Rosa M. Corona ◽  
Roberto Moreno ◽  
...  
Keyword(s):  
Domain Wall ◽  
Cross Section ◽  
Cross Sections ◽  
Oscillatory Behavior ◽  
Magnetic Nanowires ◽  
Micromagnetic Simulations ◽  
Domain Wall Dynamics ◽  
Cross Section Area ◽  
Order Of Magnitude ◽  
The One

AbstractThe understanding of the domain wall (DW) dynamics along magnetic nanowires is crucial for spintronic applications. In this work, we perform a detailed analysis of the transverse DW motion along nanowires with polygonal cross-sections. If the DW displaces under a magnetic field above the Walker limit, the oscillatory motion of the DW is observed. The amplitude, the frequency of oscillations, and the DW velocity depend on the number of sides of the nanowire cross-section, being the DW velocity in a wire with a triangular cross-section one order of magnitude larger than that in a circular nanowire. The decrease in the nanowire cross-section area yields a DW behavior similar to the one presented in a cylindrical nanowire, which is explained using an analytical model based on the general kinetic momentum theorem. Micromagnetic simulations reveal that the oscillatory behavior of the DW comes from energy changes due to deformations of the DW shape during the rotation around the nanowire.

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

scholarly journals Method for assessment of matching of total ankle joint endoprostheses based on CT data

2020 ◽  
Vol 6 (3) ◽  
pp. 396-397
Author(s):  
Heiner Martin ◽  
Josephine Wittmüß ◽  
Thomas Mittlmeier ◽  
Niels Grabow
Keyword(s):  
Cross Sections ◽  
Spline Functions ◽  
Moments Of Inertia ◽  
Cad System ◽  
Principal Moments Of Inertia ◽  
Principal Axes ◽  
Ct Data ◽  
The One ◽  
Relative Differences ◽  
Systemic Design

AbstractThe investigation of matching of endoprosthesis tibial components to the bone cross section is of interest for the manufacturer as well as for the surgeon. On the one hand, a systemic design of the prosthesis and the assortment is possible, on the other hand, a better matching implantation is enabled on the basis of experience of this study. CT sections were segmented manually using a CAD system and fitted by spline functions, then superseded with cross sections of the tibial component of a modified Hintermann H3 prosthesis. The principal moments of inertia, the direction of the principal axes and the area of the section were evaluated. Based on the relative differences of the principal moments of inertia, recommendations for application of the different prosthesis size and its selection with the surgery can be made.

Anonymized Firm Data under Test: Evidence from a Replication Study

2005 ◽  
Vol 225 (5) ◽  
Author(s):  
Joachim Wagner
Keyword(s):  
Cross Sections ◽  
Statistical Significance ◽  
Original Data ◽  
Replication Study ◽  
Firm Level ◽  
Level Data ◽  
Practical Usefulness ◽  
Order Of Magnitude ◽  
Anonymized Data ◽  
Firm Data

SummaryThis paper contributes to the literature on the use of anonymized firm level data by reporting results from a replication study. To test for the practical usefulness of anonymized data I selected two of my published papers based on different cross sections of firm data. The data used there were anonymized by micro aggregation. I replicated the analyses reported in the papers with the anonymized data, and then compared the results to those produced with the original data. Frequently, the reported levels of statistical significance differ. Furthermore, statistically significant coefficients sometimes differ by order of magnitude. Therefore, at least for the moderate sample sizes used here micro-aggregated firm data should not be considered as a tool for empirical research.

ISOSPIN DECOMPOSITION OF pp → NNππ CROSS SECTIONS — DO WE SEE A SIGN OF Δ(1600) EXCITATION IN THE nnπ+π+ CHANNEL?

2009 ◽  
Vol 24 (02n03) ◽  
pp. 450-453
Author(s):  
◽  
T. SKORODKO ◽  
M. BASHKANOV ◽  
D. BOGOSLOWSKY ◽  
H. CALÉN ◽  
...  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Differential Cross ◽  
Pion Production ◽  
Significant Contribution ◽  
Differential Cross Sections ◽  
Pp Collisions ◽  
Theoretical Predictions ◽  
Order Of Magnitude ◽  
The Cross

The two-pion production in pp-collisions has been investigated in exclusive measurements from threshold up to Tp = 1.36 GeV . Total and differential cross sections have been obtained for the channels pnπ+π0, ppπ+π-, ppπ0π0 and also nnπ+π+. For intermediate incident energies Tp > 1 GeV , i.e. in the region, which is beyond the Roper excitation but at the onset of ΔΔ excitation the total ppπ0π0 cross section falls behind theoretical predictions by as much as an order of magnitude near 1.2 GeV, whereas the nnπ+π+ cross section is a factor of five larger than predicted. A model-unconstrained isospin decompostion of the cross section points to a significant contribution of an isospin 3/2 resonance other than the Δ(1232). As a possible candidate the Δ(1600) is discussed.

An unified approach to inelastic light scattering in Keldysh–Schwinger functional integral formalism

2015 ◽  
Vol 29 (07) ◽  
pp. 1550040 ◽  
Author(s):  
Hyun Cheol Lee
Keyword(s):  
Light Scattering ◽  
Cross Sections ◽  
Golden Rule ◽  
Functional Integral ◽  
Integral Formalism ◽  
Inelastic Light Scattering ◽  
Scattering Geometry ◽  
The One ◽  
Resonant Part ◽  
Functional Integral Formalism

We propose a theoretical framework which can treat the nonresonant and the resonant inelastic light scattering on an equal footing in the form of correlation function, employing Keldysh–Schwinger functional integral formalism. The interference between the nonresonant and the resonant process can be also incorporated in this framework. This approach is applied to the magnetic Raman scattering of two-dimensional antiferromagnetic insulators. The entire set of the scattering cross-sections are obtained at finite temperature, the result for the resonant part agrees with the one obtained by the conventional Fermi golden rule at zero temperature. The interference contribution is shown to be very sensitive to the scattering geometry and the band structure.

scholarly journals On the scattering of fast neutrons by protons

1947 ◽  
Vol 191 (1025) ◽  
pp. 195-209 ◽  
Keyword(s):  
Angular Distribution ◽  
Cross Section ◽  
Cosmic Ray ◽  
Fast Neutrons ◽  
Meson Mass ◽  
Nuclear Forces ◽  
Total Scattering ◽  
Empirical Results ◽  
Meson Theory ◽  
Total Scattering Cross Section

The features of the scattering of fast neutrons by protons are calculated using the Møller- Rosenfeld version of the meson theory of nuclear forces. The experimental results of Occhialini & Powell are used to check the predicted angular distribution of the scattered particles and to determine the mass of the meson; the meson mass indicated is about 215 electronic masses, which agrees with the mass of cosmic ray mesons. The total scattering cross-section predicted by the theory agrees with the empirical results.

RENORMALIZATION OF FERMI VELOCITY IN A COMPOSITE TWO DIMENSIONAL ELECTRON GAS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 87-94 ◽  
Author(s):  
M. WEGER ◽  
L. BURLACHKOV
Keyword(s):  
Electron Gas ◽  
Fermi Velocity ◽  
Bohr Radius ◽  
Dimensional Electron ◽  
Temperature Dependent ◽  
Two Dimensional Electron Gas ◽  
Self Energy ◽  
2D System ◽  
Dimensional Electron Gas ◽  
The One

We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a 0, where a 0 = ħ2∊1/ me 2 is the Bohr radius, separated by layers with a dielectric constant ∊2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters k F a 0 and k F c ∊2/∊1. We find that when ∊2/∊1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near k F , and v ( k F ) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δ k/k F is a few percent) and becomes sharper as ∊2/∊1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T 2. Preliminary measurements suggest an increase in v k in YBCO very close to k F .

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