A speculation about effective range formulas applicable to s-wave scattering under long range polarization potentials

1980 ◽  
Vol 58 (1) ◽  
pp. 134-137 ◽  
Author(s):  
Derek Paul
Keyword(s):  
Long Range ◽  
Series Expansion ◽  
Wave Scattering ◽  
Charged Particles ◽  
Double Series ◽  
Phase Shifts ◽  
Effective Range ◽  
S Wave

Known effective range expansions for s-wave scattering of charged particles from polarizable systems fail to fit sets of accurately known phase shifts δ0 for e+–H and e+–He scattering as accurately as simple modified formulas. Formulas are given in which k cot δ0 is multiplied by a factor having a zero for each expected pole in cot δ0. The resulting fits are shown and a double series expansion is suggested as a generally fruitful formula.

PRECISE MEASUREMENTS OF S-WAVE SCATTERING PHASE SHIFTS WITH A JUGGLING ATOMIC CLOCK

2009 ◽  
Author(s):  
STEVEN GENSEMER ◽  
RUSSELL HART ◽  
ROSS MARTIN ◽  
XINYE XU ◽  
RONALD LEGERE ◽  
...  
Keyword(s):  
Wave Scattering ◽  
Atomic Clock ◽  
Phase Shifts ◽  
S Wave ◽  
Scattering Phase ◽  
Scattering Phase Shifts

PRECISE MEASUREMENTS OF S-WAVE SCATTERING PHASE SHIFTS WITH A JUGGLING ATOMIC CLOCK

2009 ◽  
Author(s):  
STEVEN GENSEMER ◽  
RUSSELL HART ◽  
ROSS MARTIN ◽  
XINYE XU ◽  
RONALD LEGERE ◽  
...  
Keyword(s):  
Wave Scattering ◽  
Atomic Clock ◽  
Phase Shifts ◽  
S Wave ◽  
Scattering Phase ◽  
Scattering Phase Shifts

Phase separation of two-component Bose–Einstein condensates with monopolar interaction

2017 ◽  
Vol 31 (23) ◽  
pp. 1750215 ◽  
Author(s):  
Long Zhu ◽  
Jinbin Li
Keyword(s):  
Phase Separation ◽  
Long Range ◽  
Wave Scattering ◽  
Scattering Length ◽  
Repulsive Interaction ◽  
S Wave ◽  
Interaction Point ◽  
Density Profiles ◽  
Two Component ◽  
Bose Einstein

This paper analyzes the properties of the two-component Bose–Einstein condensates (BECs) with long-range monopolar interaction by means of Thomas–Fermi approximation (TFA). The effects of long-range monopolar interaction, inter-component short-range s-wave scattering, and particle numbers on the density profiles and phase separation of BECs are investigated. It is shown that atoms with the small intra-component s-wave scattering length are squeezed out when the monopolar interaction of these atoms is not large enough, and the density profile will be compressed when corresponding monopolar interaction is increased. Effective zero interaction point that the s-wave scattering repulsive interaction is neutralized by monopolar attractive interaction, is found. Varying of particle numbers will cause the transformation between phase separation and faint phase separation (or mixture).

scholarly journals PHASE SHIFTS AND RESONANCES IN THE DIRAC EQUATION

2004 ◽  
Vol 19 (21) ◽  
pp. 3557-3581 ◽  
Author(s):  
PIERS KENNEDY ◽  
NORMAN DOMBEY ◽  
RICHARD L. HALL
Keyword(s):  
Dirac Equation ◽  
Wave Scattering ◽  
Numerical Procedure ◽  
Phase Shifts ◽  
P Wave ◽  
S Wave ◽  
P Waves ◽  
Gaussian Potential ◽  
S Waves ◽  
Relativistic Scattering

We review the analytic results for the phase shifts δl(k) in nonrelativistic scattering from a spherical well. The conditions for the existence of resonances are established in terms of time-delays. Resonances are shown to exist for p-waves (and higher angular momenta) but not for s-waves. These resonances occur when the potential is not quite strong enough to support a bound p-wave of zero energy. We then examine relativistic scattering by spherical wells and barriers in the Dirac equation. In contrast to the nonrelativistic situation, s-waves are now seen to possess resonances in scattering from both wells and barriers. When s-wave resonances occur for scattering from a well, the potential is not quite strong enough to support a zero momentum s-wave solution at E=m. Resonances resulting from scattering from a barrier can be explained in terms of the "crossing" theorem linking s-wave scattering from barriers to p-wave scattering from wells. A numerical procedure to extract phase shifts for general short range potentials is introduced and illustrated by considering relativistic scattering from a Gaussian potential well and barrier.

LONG-RANGE CORRELATIONS IN THE PHASE-SHIFTS OF NUMERICAL SIMULATIONS OF BIOCHEMICAL OSCILLATIONS AND IN EXPERIMENTAL CARDIAC RHYTHMS

1999 ◽  
Vol 07 (02) ◽  
pp. 113-130 ◽  
Author(s):  
I. M. DE LA FUENTE ◽  
L. MARTINEZ ◽  
J. M. AGUIRREGABIRIA ◽  
J. VEGUILLAS ◽  
M. IRIARTE
Keyword(s):  
Phase Shift ◽  
Periodic Solutions ◽  
Long Range ◽  
Phase Shifts ◽  
Long Range Correlations ◽  
Rescaled Range ◽  
Biochemical Oscillations ◽  
Phase Shift Data ◽  
Relationship Of ◽  
The Relationship

In biochemical dynamical systems during each transition between periodical behaviors, all metabolic intermediaries of the system oscillate with the same frequency but with different phase-shifts. We have studied the behavior of phase-shift records obtained from random transitions between periodic solutions of a biochemical dynamical system. The phase-shift data were analyzed by means of Hurst's rescaled range method (introduced by Mandelbrot and Wallis). The results show the existence of persistent behavior: each value of the phase-shift depends not only on the recent transitions, but also on previous ones. In this paper, the different kind of periodic solutions were determined by different small values of the control parameter. It was assessed the significance of this results through extensive Monte Carlo simulations as well as quantifying the long-range correlations. We have also applied this type of analysis on cardiac rhythms, showing a clear persistent behavior. The relationship of the results with the cellular persistence phenomena conditioned by the past, widely evidenced in experimental observations, is discussed.

Estimating the error in variational scattering calculations

1978 ◽  
Vol 56 (10) ◽  
pp. 1358-1364 ◽  
Author(s):  
J. W. Darewych ◽  
R. Pooran
Keyword(s):  
Wave Scattering ◽  
Exponential Potential ◽  
S Wave ◽  
Order Error ◽  
Absolute Value ◽  
First Order ◽  
Scattering Phase ◽  
Square Well ◽  
Scattering Phase Shifts ◽  
Made In

We derive bounds to the absolute value of the error that is made in variational estimates of scattering phase shifts. These bounds, like the variational estimates, are second order in 'small' quantities and are, in this respect, an improvement on similar but first-order error bounds derived previously by Bardsley, Gerjuoy, and Sukumar. The s-wave scattering by a square well potential, in the Born approximation, and by an exponential potential, using a many parameter trial function, are used to illustrate the results.

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