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.

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.

Low Energy n–16O Elastic Scattering Phase Shifts Derived from the Sussex Interaction

1975 ◽  
Vol 53 (3) ◽  
pp. 203-206
Author(s):  
M. Betz ◽  
J. P. Jeukenne ◽  
A. Lejeune
Keyword(s):  
Elastic Scattering ◽  
Body Force ◽  
Phase Shifts ◽  
Potential Scattering ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent Field ◽  
Scattering Phase ◽  
Scattering Phase Shifts

The properties of the Sussex interaction are tested in the study of the n–16O elastic scattering described by the potential scattering in the Hartree–Fock field. This force leads to an easy determination of the self-consistent field, but gives s1/2 and d3/2 phase shifts which are not very satisfactory. This results from the important gap separating bound and unbound states. Further, some uncertainty in the calculation arises from approximations necessary in order to obtain some nondiagonal matrix elements of the two body force which are necessary in the determination of the phase shifts.

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