Inverse scattering problem and the Schwinger approximation

1992 ◽  
Vol 70 (4) ◽  
pp. 282-288 ◽  
Author(s):  
M. A. Hooshyar ◽  
T. H. Lam ◽  
M. Razavy
Keyword(s):  
Scattering Amplitudes ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Nucleon Nucleon ◽  
S Wave ◽  
Physical Systems ◽  
Nucleus Scattering ◽  
The Stability

A new method of inversion of the S-wave scattering amplitude based on the Schwinger variational method is presented. This method is accurate and stable and is applicable to a number of interesting physical systems such as nucleon–nucleon or nucleon–nucleus scattering even when the data are known for a finite nonrelativistic range of energies. ⁁Examples of different scattering amplitudes and their corresponding potential functions are given to show the accuracy and the stability of the method.

INTEGRABLE MODELS OF FIELD THEORY AND SCATTERING ON QUANTUM HYPERBOLOIDS

1992 ◽  
Vol 07 (05) ◽  
pp. 441-446 ◽  
Author(s):  
A. ZABRODIN
Keyword(s):  
Field Theory ◽  
Symmetric Space ◽  
Quantum Group ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Free Particle ◽  
Compact Quantum Group ◽  
Integrable Models ◽  
S Wave

We consider the scattering of two dressed excitations in the antiferromagnetic XXZ spin-1/2 chain and show that it is equivalent to the S-wave scattering problem for a free particle on the certain quantum symmetric space “quantum hyperboloid” related to the non-compact quantum group SU q (1, 1).

Inverse scattering problem for transparent obstacles

1982 ◽  
Vol 92 (2) ◽  
pp. 361-367 ◽  
Author(s):  
Vesselin Petkov
Keyword(s):  
Inverse Scattering ◽  
Convex Domain ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Normal Derivative ◽  
Index Of Refraction ◽  
Image Position ◽  
Compact Boundary ◽  
Limiting Values

Let K ⊂ ℝ3 be an open bounded strictly convex domain with smooth connected compact boundary ∂K. SetWe wish to study the filtered scattering amplitude, related to the transmission problemHere w± are the limiting values of w on ∂Ω; from the Ω;± side, while ∂w±/∂n are the corresponding limiting values of the normal derivative ∂w?/∂n on ∂Ω;. The function α(x) ∈ C∞(K¯), called the index of refraction, has the property α(x) > 0 for x ∈ K¯.

Inverse scattering for three-dimensional quasi-linear biharmonic operator

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Markus Harju ◽  
Jaakko Kultima ◽  
Valery Serov
Keyword(s):  
Inverse Scattering ◽  
Space Variable ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Regularity Conditions ◽  
Biharmonic Operator ◽  
Essential Information ◽  
Complex Valued

Abstract We consider an inverse scattering problem of recovering the unknown coefficients of a quasi-linearly perturbed biharmonic operator in the three-dimensional case. These unknown complex-valued coefficients are assumed to satisfy some regularity conditions on their nonlinearity, but they can be discontinuous or singular in their space variable. We prove Saito’s formula and uniqueness theorem of recovering some essential information about the unknown coefficients from the knowledge of the high frequency scattering amplitude.

SEARCH FOR BOUND η-NUCLEUS STATES

2009 ◽  
Vol 24 (02n03) ◽  
pp. 206-213 ◽  
Author(s):  
◽  
J. URBÁN ◽  
A. BUDZANOWSKI ◽  
A. CHATTERJEE ◽  
P. HAWRANEK ◽  
...  
Keyword(s):  
Cross Section ◽  
Opposite Direction ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Length ◽  
Bound State ◽  
S Wave ◽  
Decay Products ◽  
Upper Limit ◽  
Zero Degree

The extracted s-wave scattering amplitude from both the polarized and unpolarized d + d → 4He + η reaction at 2385.5 MeV/c allowed to determine the scattering length which fulfills the requirements for bound η. In the p + 27Al → 3He + p + π- + X reaction studied at recoil free kinematics the η meson is produced almost at rest and so it can be bound with enhanced probability. This state proceeds via N*(1535) resonance and the decay products proton and pion emitted into opposite direction are detected in concidence with 3He produced at zero degree. Under these conditions some hints for bound state can be observed with an upper limit of the cross section of ≈ 0.5 nb.

Application of the Singularity Expansion Method to Elastic Wave Scattering

1990 ◽  
Vol 43 (10) ◽  
pp. 235-249 ◽  
Author(s):  
Herbert U¨berall ◽  
P. P. Delsanto ◽  
J. D. Alemar ◽  
E. Rosario ◽  
Anton Nagl
Keyword(s):  
Elastic Wave ◽  
Elastic Waves ◽  
Wave Scattering ◽  
Scattering Amplitude ◽  
Scattering Problem ◽  
Expansion Method ◽  
Complex Frequency ◽  
Elastic Wave Scattering ◽  
Physical Measurements ◽  
Scattering Of Elastic Waves

The singularity expansion method (SEM), established originally for electromagnetic-wave scattering by Carl Baum (Proc. IEEE 64, 1976, 1598), has later been applied also to acoustic scattering (H U¨berall, G C Gaunaurd, and J D Murphy, J Acoust Soc Am 72, 1982, 1014). In the present paper, we describe further applications of this method of analysis to the scattering of elastic waves from cavities or inclusions in solids. We first analyze the resonances that appear in the elastic-wave scattering amplitude, when plotted vs frequency, for evacuated or fluid-filled cylindrical and spherical cavities or for solid inclusions. These resonances are interpreted as being due to the phase matching, ie, the formation of standing waves, of surface waves that encircle the obstacle. The resonances are then traced to the existence of poles of the scattering amplitude in the fourth quadrant of the complex frequency plane, thus establishing the relation with the SEM. The usefulness of these concepts lies in their applicability for solving the inverse scattering problem, which is the central problem of NDE. Since for the case of inclusions, or of cavities with fluid fillers, the scattering of elastic waves gives rise to very prominent resonances in the scattering amplitude, it will be of advantage to analyze these with the help of the resonance scattering theory or RST (first formulated by L Flax, L R Dragonette, and H U¨berall, J Acoust Soc Am 63, 1978, 723). These resonances are caused by the proximity of the SEM poles to the real frequency axis, on which the frequencies of physical measurements are located. A brief history of the establishment of the RST is included here immediately following the Introduction.

NONLOCAL SEPARABLE SOLUTIONS OF THE INVERSE SCATTERING PROBLEM

1993 ◽  
Vol 08 (18) ◽  
pp. 3163-3184 ◽  
Author(s):  
TONY GHERGHETTA ◽  
YOICHIRO NAMBU
Keyword(s):  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Bound State ◽  
Separable Potential ◽  
Nonlocal Potential ◽  
S Wave ◽  
Weakly Bound ◽  
Square Well ◽  
Nonlocal Separable Potential

We extend the nonlocal separable potential solutions of Gourdin and Martin for the inverse scattering problem to the case where sin δ0 has more than N zeroes, δ0 being the s-wave scattering phase shift and δ0(0) − δ0(∞) = Nπ. As an example we construct the solution for the particular case of 4 He and show how to incorporate a weakly bound state. Using a local square well potential chosen to mimic the real 4 He potential, we compare the off-shell extension of the nonlocal potential solution with the exactly solvable square well. We then discuss how a nonlocal potential might be used to simplify the many-body problem of liquid 4 He .

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