Article

1998 ◽  
Vol 76 (3) ◽  
pp. 169-172 ◽  
Author(s):  
S G Karshenboim
Keyword(s):  
Energy Level ◽  
Analytic Form ◽  
Muonic Atom ◽  
Closed Analytic Form

We examine the Uehling correction to the energy level of some states in the hydrogen-like muonic atom without any expansion over Zα. The result as a function on n is obtained in closed analytic form for a state with l=n-1 and j=l+1/2. PACS Nos.: 31.20D and 12.20D

scholarly journals Structure factors for generalized grey Browinian motion

2019 ◽  
Vol 22 (2) ◽  
pp. 396-411
Author(s):  
José L. da Silva ◽  
Ludwig Streit
Keyword(s):  
Gaussian Processes ◽  
Form Factors ◽  
Analytic Form ◽  
Debye Function ◽  
Asymptotic Decay ◽  
Structure Factors ◽  
Closed Analytic Form ◽  
Non Gaussian

Abstract In this paper we investigate the form factors of paths for a class of non Gaussian processes. These processes are characterized in terms of the Mittag-Leffler function. In particular, we obtain a closed analytic form for the form factors, the Debye function, and can study their asymptotic decay.

scholarly journals The Uehling correction to the energy levels in a pionic atom

2006 ◽  
Vol 84 (2) ◽  
pp. 107-113 ◽  
Author(s):  
S G Karshenboim ◽  
E Yu. Korzinin ◽  
V G Ivanov
Keyword(s):  
Free Electron ◽  
Vacuum Polarization ◽  
Energy Levels ◽  
Analytic Form ◽  
Electron Mass ◽  
Mass Ratio ◽  
Pionic Atom ◽  
Closed Analytic Form

We consider a correction to energy levels in a pionic atom induced by the Uehling potential, i.e., by a free electron vacuum-polarization loop. The calculation is performed for circular states (l = n–1). The result is obtained in a closed analytic form as a function of Zα and the pion-to-electron mass ratio. Certain asymptotics of the result are also presented.PACS Nos.: 12.20.Ds, 36.10.Gv

Non-homogeneous semi-Markov systems and maintainability of the state sizes

1992 ◽  
Vol 29 (3) ◽  
pp. 519-534 ◽  
Author(s):  
P.-C. G. Vassiliou ◽  
A. A. Papadopoulou
Keyword(s):  
Convex Set ◽  
Analytic Form ◽  
The State ◽  
Markov Systems ◽  
Markov System ◽  
Basic Parameters ◽  
Manpower System ◽  
Closed Analytic Form ◽  
First Time ◽  
Expected Duration

In this paper we introduce and define for the first time the concept of a non-homogeneous semi-Markov system (NHSMS). The problem of finding the expected population stucture is studied and a method is provided in order to find it in closed analytic form with the basic parameters of the system. Moreover, the problem of the expected duration structure in the state is studied. It is also proved that all maintainable expected duration structures by recruitment control belong to a convex set the vertices of which are specified. Finally an illustration is provided of the present results in a manpower system.

General state-to-state transitions in atoms for either Yukawa or Coulomb potentials via Fourier transforms

2015 ◽  
Vol 93 (3) ◽  
pp. 326-338 ◽  
Author(s):  
Jack C. Straton
Keyword(s):  
Fourier Transforms ◽  
Electron Transition ◽  
Analytic Form ◽  
Bound State ◽  
Impact Excitation ◽  
State Transitions ◽  
Final States ◽  
Quantum Numbers ◽  
Closed Analytic Form ◽  
Coulomb Potentials

In a previous paper we used our integro-differential extension of Gaussian transforms to find the closed analytic form for hydrogenic bound-state transitions with arbitrarily high quantum numbers due to projectile impact excitation via Coulomb potentials (in the intermediate representation). Here we extend that result to Yukawa potentials, but do so by utilizing Fourier transforms. The result is used to find the first-order cross section for proton impact excitation of hydrogen to the 2s–7s final states. Because the results hold for any initial and final quantum states, and the amplitude may be easily converted for use with pseudostates, it may be used to automatically calculate sums over intermediate pseudostate propagators whose (bound and free) principal and angular quantum numbers can become very large. This result may be extended to multi-electron transition amplitudes by representing initial and final states by configuration–interaction wave-functions.

CLOSED ANALYTIC FORM FOR EVALUATION OF RELATIVISTIC BOUND-UNBOUND AND UNBOUND-UNBOUND TRANSITION MATRIX ELEMENTS OF HYDROGENIC ATOMS

2008 ◽  
Vol 22 (29) ◽  
pp. 5095-5102
Author(s):  
A. V. SOLDATOV ◽  
J. SEKE ◽  
G. ADAM ◽  
M. POLAK
Keyword(s):  
Electromagnetic Field ◽  
Plane Wave ◽  
Vector Potential ◽  
Transition Matrix ◽  
Analytic Form ◽  
Field Vector ◽  
Matrix Elements ◽  
Plane Wave Expansion ◽  
Transition Matrix Elements ◽  
Closed Analytic Form

A closed analytic form for relativistic bound-unbound and unbound-unbound transition matrix elements of hydrogenic atoms by using the plane-wave expansion for the electromagnetic-field vector potential is derived. By applying the obtained formulae, these transition matrix elements can be evaluated analytically and numerically.

scholarly journals The heterogeneous energy landscape expression of KWW relaxation

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
J. H. Wu ◽  
Q. Jia
Keyword(s):  
Energy Landscape ◽  
General Characteristic ◽  
Analytic Form ◽  
Threshold Value ◽  
Characteristic Relaxation Time ◽  
Relaxation Time Distribution ◽  
Frequency Domains ◽  
Apparent Correlation ◽  
Closed Analytic Form ◽  
Distribution Equation

Abstract Here we show a heterogeneous energy landscape approach to describing the Kohlrausch-Williams-Watts (KWW) relaxation function. For a homogeneous dynamic process, the distribution of free energy landscape is first proposed, revealing the significance of rugged fluctuations. In view of the heterogeneous relaxation given in two dynamic phases and the transmission coefficient in a rate process, we obtain a general characteristic relaxation time distribution equation for the KWW function in a closed, analytic form. Analyses of numerical computation show excellent accuracy, both in time and frequency domains, in the convergent performance of the heterogeneous energy landscape expression and shunning the catastrophic truncations reported in the previous work. The stretched exponential β, closely associated to temperature and apparent correlation with one dynamic phase, reveals a threshold value of 1/2 defining different behavior of the probability density functions. Our work may contribute, for example, to in-depth comprehension of the dynamic mechanism of glass transition, which cannot be provided by existing approaches.

The effect of an extranuclear electron on the muonic atom

1968 ◽  
Vol 46 (10) ◽  
pp. 1253-1254
Author(s):  
B. G. Best ◽  
D. Y. Kim
Keyword(s):  
Energy Level ◽  
Variational Method ◽  
Total Energy ◽  
Ground State ◽  
Muonic Atom ◽  
Level Shift ◽  
Energy Level Shift

The effect of an extranuclear electron on the hydrogenic muonic atom in the ground state has been evaluated by means of a variational method. The energy-level shift due to this effect was found to be about 0.5% of the total energy of the muonic atom.

PARITY AND TIME REVERSAL VIOLATION IN RESONANCE NEUTRON TOTAL CROSS SECTIONS WITH POLARIZED TARGETS

1990 ◽  
Vol 05 (11) ◽  
pp. 2181-2194 ◽  
Author(s):  
C. R. GOULD ◽  
D. G. HAASE ◽  
N. R. ROBERSON ◽  
H. POSTMA ◽  
J. D. BOWMAN
Keyword(s):  
Cross Sections ◽  
Time Reversal ◽  
Analytic Form ◽  
Spin Representation ◽  
Resonance Neutron ◽  
Total Cross Sections ◽  
Polarized Target ◽  
Complete Set ◽  
Closed Analytic Form ◽  
Polarized Targets

The formalism for evaluating parity and time reversal violating terms in total cross sections of polarized targets and low energy resonance neutrons is reviewed. A complete set of symmetry violating terms (P-odd, T-even; P-odd, T-odd; and P-even, T-odd) is obtained by analyzing the dependence of the cross section on the statistical tensors describing the beam and target. Results are tabulated in numerical and closed analytic form, using the j-spin representation. P-odd, T-even experiments are classified, with emphasis on experiments with an unpolarized beam and a polarized target where the effect of induced polarization is found to be small. Different combinations of partial neutron widths are shown to enter when P-odd, T-odd effects are compared to P-odd, T-even effects. The results for P-even, T-odd experiments for single level and two level mixing are summarized.

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