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.

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

scholarly journals COUPLED CHANNEL EFFECTS IN ππ S-WAVE INTERACTION

2005 ◽  
Vol 20 (08n09) ◽  
pp. 1905-1909 ◽  
Author(s):  
F. Q. WU ◽  
B. S. ZOU
Keyword(s):  
Wave Scattering ◽  
Wave Interaction ◽  
Matrix Formalism ◽  
S Wave ◽  
Coupled Channels ◽  
Channel Effects ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Coupled Channel ◽  
K Matrix

We study coupled channel effects upon isospin I=2 and I=0 ππ S-wave interaction. With introduction of the ππ→ρρ→ππ coupled channel box diagram contribution into ππ amplitude in addition to ρ and f2(1270) exchange, we reproduce the ππ I =2 S-wave and D-wave scattering phase shifts and inelasticities up to 2 GeV quite well in a K-matrix formalism. For I=0 case, the same ππ→ρρ→ππ box diagram is found to give the largest contribution for the inelasticity among all possible coupled channels including ππ→ωω→ππ, [Formula: see text]. We also show why the broad σ appears narrower in production processes than in ππ scattering process.

A note on bounds to central potential scattering parameters

1982 ◽  
Vol 60 (8) ◽  
pp. 1075-1078 ◽  
Author(s):  
J. W. Darewych
Keyword(s):  
Scattering Length ◽  
Potential Scattering ◽  
Radial Wave ◽  
Central Potential ◽  
Absolute Value ◽  
First Order ◽  
Scattering Phase ◽  
Screened Coulomb Potential ◽  
Scattering Phase Shifts ◽  
The Difference

We derive a bound to the absolute value of the difference between the exact and approximate values of central potential scattering phase shifts. This bound, which is first order in the difference between the exact and approximate radial wave functions, is applicable to a wide class of potentials and/or partial waves, namely those for which dU/dr < 2l(l + 1)/r3 It is illustrated by using it to obtain simple, analytic bounds to the scattering length and total cross section for a screened Coulomb potential.

scholarly journals Phase-shifts determination for nucleon–nucleon scattering using velocity-dependent potentials

2016 ◽  
Vol 94 (2) ◽  
pp. 231-235
Author(s):  
M.I. Sayyed
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Nucleon Nucleon ◽  
Phase Shifts ◽  
S Wave ◽  
Dependent Part ◽  
Dependent Potential ◽  
Scattering Phase ◽  
Square Well

The s-wave time-independent Schrödinger equation with an isotropic velocity-dependent potential is considered. We have used perturbation theory to calculate the scattering phase shifts when the energy is changed by a small amount ΔE from an arbitrary unperturbed value E0. The validity of our results was tested by comparing the perturbed phase shifts to those obtained exactly by solving the Schrödinger equation. We assumed the local potential to have the form of a finite square well and the velocity-dependent part of the potential to have the form of a Yukawa potential.

Comparative study of the energy dependent and independent two-nucleon interactions — A supersymmetric approach

2014 ◽  
Vol 23 (08) ◽  
pp. 1450039 ◽  
Author(s):  
U. Laha ◽  
J. Bhoi
Keyword(s):  
Factorization Method ◽  
Nucleon Nucleon ◽  
Wave Functions ◽  
S Wave ◽  
Starting Point ◽  
Phase Function Method ◽  
Scattering Phase ◽  
Scattering Phase Shifts ◽  
Energy Dependent ◽  
Supersymmetric Approach

By exploiting supersymmetry inspired factorization method nucleon–nucleon (n–n) potentials, both energy dependent and independent, in the partial waves 1P1 and 3P1 are generated by judicious use of appropriate ground state wave functions and interactions. The energy independent Hulthen and energy dependent equivalent local Yamaguchi potentials and their corresponding S-wave functions are used as the starting point of our calculation. The scattering phase shifts are computed for the constructed potentials through Phase Function Method (PFM) and compared with the standard results to examine the merit of our approach to the problem.

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