scholarly journals Effective Interactions: Resonances and Off-Shell Characteristics

2019 ◽  
Vol 10 ◽  
pp. 93
Author(s):  
S. E. Massen ◽  
S. A. Sofianos ◽  
S. A. Rakityansky ◽  
S. Oryu
Keyword(s):  
Inverse Scattering ◽  
Nuclear Reactions ◽  
Bound State ◽  
Inverse Scattering Method ◽  
Wave Functions ◽  
Scattering Method ◽  
Effective Interactions ◽  
Analytical Properties ◽  
Jost Functions ◽  
Jost Solutions

The influence of resonances on the analytical properties and off-shell characteristics of effective interactions has been investigated. This requires, among others, the knowledge of the Jost function in regions of physical interest on the complex kplane when the potentials are given in a tabular form. The latter are encountered in inverse scattering and supersymmetric transformations. To investigate the effects of resonances on the analytical properties of the potential, we employed the Marchenko inverse scattering method to construct, phase and bound state equivalent local potentials but with different resonance spectra. It is shown that the inclusion of resonances changes the shape, strength, and range of the potential which in turn would modify the bound and scattering wave functions in the interior region. This could have important consequences in calculations of transition amplitudes in nuclear reactions, which strongly depend on the behaviour of the wave functions at short distances. Finally, an exact method to obtain the Jost solutions and the Jost functions for a repulsive singular potential is presented. The effectiveness of the method is demonstrated using the Lennard-Jones (12,6) potential.

SUPERSYMMETRY, REFLECTIONLESS SYMMETRIC POTENTIALS AND THE INVERSE METHOD

1990 ◽  
Vol 05 (09) ◽  
pp. 1763-1772 ◽  
Author(s):  
B. BAGCHI
Keyword(s):  
Inverse Scattering ◽  
Schrodinger Equation ◽  
Inverse Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Inverse Scattering Method ◽  
Wave Functions ◽  
Scattering Method ◽  
De Vries

The role of inverse scattering method is illustrated to examine the connection between the multi-soliton solutions of Korteweg-de Vries (KdV) equation and discrete eigenvalues of Schrödinger equation. The necessity of normalization of the Schrödinger wave functions, which are constructed purely from a supersymmetric consideration is pointed out.

scholarly journals Integrable extended Hubbard models with boundary Kondo impurities

2001 ◽  
Vol 64 (3) ◽  
pp. 445-467
Author(s):  
Anthony J. Bracken ◽  
Xiang-Yu Ge ◽  
Mark D. Gould ◽  
Huan-Qiang Zhou
Keyword(s):  
Hilbert Space ◽  
Bethe Ansatz ◽  
Inverse Scattering ◽  
Magnetic Moments ◽  
Inverse Scattering Method ◽  
Scattering Method ◽  
Ansatz Method ◽  
One Dimensional ◽  
Hubbard Models ◽  
Kondo Impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z2-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

An inverse scattering method in time-domain electromagnetics

1981 ◽  
Vol 59 (10) ◽  
pp. 1348-1353
Author(s):  
Sujeet K. Chaudhuri
Keyword(s):  
Inverse Scattering ◽  
Time Domain ◽  
Random Noise ◽  
Power Series Expansion ◽  
Inverse Scattering Method ◽  
Wave Number ◽  
Moment Condition ◽  
Scattering Method ◽  
Fourth Moment ◽  
Rayleigh Coefficient

An inverse scattering model, based on the time-domain concepts of electromagnetic theory is developed. Using the first five (zeroth to fourth) moment condition integrals, the Rayleigh coefficient and the next higher order nonzero coefficient of the power series expansion in k (wave number) of the object backscattering response are recovered. The Rayleigh coefficient and the other coefficient thus recovered are used (with the ellipsoidal assumption for the object shape) to determine the dimensions and orientation of the object.Some numerical results of the application of this coefficient recovery technique to conducting ellipsoidal scatterers are presented. The performance of the software system in the presence of normally distributed random noise is also studied.

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