Evolution of Reduced Distribution Functions. IV. Momentum Moments of the One‐Body Function

1970 ◽  
Vol 52 (9) ◽  
pp. 4345-4354 ◽  
Author(s):  
Curtis F. Holmes ◽  
Robert G. Mortimer
Keyword(s):  
Distribution Functions ◽  
Body Function ◽  
The One ◽  
Reduced Distribution Functions

THE RESPONSE FUNCTION OF THE 4He, 16O AND 40Ca NUCLEI IN THE HARMONIC OSCILLATOR SHELL MODEL AND THE IMPULSE APPROXIMATIONS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350011
Author(s):  
M. MODARRES ◽  
Y. YOUNESIZADEH
Keyword(s):  
Harmonic Oscillator ◽  
Shell Model ◽  
Momentum Distribution ◽  
Impulse Approximation ◽  
Distribution Functions ◽  
Heavy Nuclei ◽  
Momentum Distribution Function ◽  
Oscillator Shell ◽  
Nucleus Scattering ◽  
The One

In this work, the response functions (RFs) of the 4 He , 16 O and 40 Ca nuclei are calculated in the harmonic oscillator shell model (HOSM) and the impulse approximation (IA). First, the one-body momentum distribution and the one-body spectral functions for these nuclei are written in the HOSM configuration. Then, their RFs are calculated, in the two frameworks, namely the spectral and the momentum distribution functions, within the IA. Unlike our previous work, no further assumption is made to reduce the analytical complications. For each nucleus, it is shown that the (RF) evaluated using the corresponding spectral function has a sizable shift, with respect to the one calculated in terms of the momentum distribution function. It is concluded that for the heavier nuclei, this shift increases and reaches nearly to a constant value (approximately 62 MeV), i.e., similar to that of nuclear matter. It is discussed that in the nuclei with the few nucleons, the above shift can approximately be ignored. This result reduces the theoretical complication for the explanation of the ongoing deep inelastic scattering (DIS) experiments of 3 H or 3 H nucleus target in the Jefferson Laboratory. On the other hand, it is observed that in the heavier nuclei, the RF heights (width) decrease (increase), i.e., the comparison between the theoretical and the experimental electron nucleus scattering cross-section is more sensible for heavy nuclei rather than the light ones.

Structural study of semi-crystalline blends of poly(vinylidene fluoride) and poly(methyl methacrylate) by means of linear correlation and interface distribution functions

e-Polymers ◽  
2005 ◽  
Vol 5 (1) ◽  
Author(s):  
Mohamed Fatnassi ◽  
Fadhel Ben Cheikh Larbi ◽  
André Dubault ◽  
Jean Louis Halary
Keyword(s):  
Methyl Methacrylate ◽  
Vinylidene Fluoride ◽  
Structural Parameters ◽  
Cylindrical Symmetry ◽  
Distribution Functions ◽  
Lamellar Thickness ◽  
Poly Methyl Methacrylate ◽  
Density Correlation ◽  
Poly Vinylidene Fluoride ◽  
The One

AbstractIn this article small-angle X-ray scattering (SAXS) is used to characterize the structural parameters of semi-crystalline blends of poly(vinylidene fluoride) (PVDF) and poly(methyl methacrylate). Different blend compositions from 100 to 50 wt.-% of PVDF were investigated. The samples were considered to be isotropic. As two-dimensional SAXS patterns with cylindrical symmetry were examined, a single direction in the SAXS pattern plane was chosen to collect and plot absolute intensities versus the scattering vector. Using the one-dimensional (linear) electron density correlation and interface distribution functions obtained, respectively, from the Fourier-transformed Lorentz-corrected experimental scattering intensity and from the interference function, structural parameters such as the minimal value and the most probable value of the long period, the average lamellar thickness, and the volume crystallinity were determined.

Elastic Constants of Binary Liquid Crystalline Mixtures

1998 ◽  
Vol 53 (12) ◽  
pp. 963-976
Author(s):  
A. Kapanowski ◽  
K. Sokalski
Keyword(s):  
Phase Diagram ◽  
Elastic Constants ◽  
Short Range ◽  
Liquid Crystalline ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Binary Liquid ◽  
Small Density ◽  
Nematic Phases ◽  
The One

Abstract Microscopic expressions for the elastic constants of binary liquid crystalline mixtures composed of short rigid uniaxial molecules are derived in the thermodynamic limit at small distorsions and a small density. Uniaxial and biaxial nematic phases are considered. The expressions involve the one-particle distribution functions and the potential energy of two-body short-range interactions. The theory is used to calculate the phase diagram of a mixture of rigid prolate and oblate molecules. The concentration dependence of the order parameters and the elastic constants are obtained. The possibility of phase separation is not investigated.

scholarly journals Remark on the Kinematics of the One-Photon Production in Electron–Proton Scattering

1997 ◽  
Vol 12 (21) ◽  
pp. 1553-1559
Author(s):  
Wei Lu
Keyword(s):  
Phase Space ◽  
Deeply Virtual Compton Scattering ◽  
Quark Distribution ◽  
Photon Production ◽  
Distribution Functions ◽  
Proton Scattering ◽  
Diquark Model ◽  
Space Factor ◽  
The Cross ◽  
The One

We clarify some misleading mistakes in the literature about the phase space for the one-photon production in electron–proton scattering and present the correct overall phase space factor in the cross-section formula. Our conclusion is that the earlier diquark model predictions for the cross-sections of the one-photon production in electron–proton scattering are unreliable. Furthermore, we specify the phase space boundaries. In relation to the recent proposal to measure the off-diagonal quark distribution functions in the deeply virtual Compton scattering off the proton, we point out that the kinematics strongly disfavors such experiments.

On the theory of electromagnetic waves and instabilities in multi-species weakly ionized plasmas in external d.c. electric field

1987 ◽  
Vol 38 (1) ◽  
pp. 53-77 ◽  
Author(s):  
B. S. Milić ◽  
S. R. Krstić
Keyword(s):  
Electric Field ◽  
Electromagnetic Waves ◽  
Kinetic Equations ◽  
Mean Free Path ◽  
Short Wave ◽  
Distribution Functions ◽  
Bgk Model ◽  
Ionized Plasmas ◽  
Weakly Ionized ◽  
The One

Electromagnetic modes with the electric vector of the wave lying in the plane defined by the wave vector and the external d.c. electric field are studied theoretically in weakly ionized plasmas with several sorts of ions. The corresponding instability criteria are also given. The analysis is based on kinetic equations with BGK model collision integrais for the one-particle distribution functions of the charged constituents (electrons and all sorts of ions). The linear theory of perturbation is applied. Special attention is given to the long-wave domain (modal wavelengths much larger than the electron mean free path): it is in this domain that the instabilities are found to set in first as the electron drift is gradually increased. The increments of these instabilities are, however, smaller than in the short-wave domain which was mainly studied before. Apart from the modes which exist in weakly ionized plasmas with only one ion species, and which re-appear in the case studied here with somewhat altered characteristics, a new slow mode, specifie for multi-species weakly ionized plasmas, is found. Its phase velocity is below the electron thermal velocity, and its existence, as well as the conditions of excitation of the corresponding instability, depend on the plasma composition and non-isothermality (viz. the ratio Te/Ti). In some situations, two such modes are possible. The analysis of the instabilities is completed by a brief description of two (sometimes three) branches of ion acoustic instability, specific for the multi-species plasmas and propagating strictly along the direction of the external electric field.

A note on the variance-ratio distribution

1950 ◽  
Vol 10 (01) ◽  
pp. 62-64
Author(s):  
M. T. L. Bizley
Keyword(s):  
Simple Formula ◽  
Distribution Functions ◽  
Ratio Test ◽  
Variance Ratio ◽  
Ratio Distribution ◽  
Variance Ratio Test ◽  
Elementary Methods ◽  
The One

In his paper (J.S.S.Vol. VI, p. 172) Dr Wishart showed that the variance-ratio test can be very easily used with the aid of the appropriate tables. It may not have been obvious to the reader of that paper that, unlike most distribution functions, the one in question can be evaluated by elementary methods and that a simple formula can be established to give the required probability independently of any table. It is not suggested that the use of the formula to be demonstrated in this note is preferable to the ordinary employment of tables. It may be remarked, however, that in certain cases where a probability has to be directly calculated the formula has a big advantage, since the tables give only the values of F (orz) corresponding to a few specific ‘probability points’ and interpolation between these must be very unsatisfactory, as is obvious from a glance at Table 3 of Dr Wishart's paper.

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