Related papers: Some Remarks on Effective Range Formula in Potenti…
We construct the potentials that describe the spectrum and decay of electromagnetic bound states of hadrons, and are consistent with ChPT. These potentials satisfy the matching condition which enables one to express the parameters of the…
The validity range of the widely used traditional effective range expansion can be severely limited by the presence of a left-hand cut near the two-particle threshold. Such a left-hand cut emerges in two-particle scattering processes…
We analyze how a short distance boundary condition for the Schrodinger equation must change as a function of the boundary radius by imposing the physical requirement of phase shift independence on the boundary condition. The resulting…
In the phenomenological study of exotic hadrons, the sign of the effective range, $r_0$, is invoked as a criterion to distinguish between compact multiquark configurations (associated with $r_0 < 0$) and loosely bound hadronic molecules…
This work is a short communication where phase function method has been applied to obtain the phase shifts using Effective Range Approximation potential for $^3S_1-np$, $^1S_0-nn$, $^1S_0-np$, and $^1S_0-pp$ states. No free fitting…
One-dimensional scattering problems are of wide physical interest and are encountered in many diverse applications. In this article I establish some very general bounds for reflection and transmission coefficients for one-dimensional…
Probability of reflection $R(E)$ off a finite attractive scattering potential at zero or low energies is ordinarily supposed to be 1. However, a fully attractive potential presents a paradoxical result that $R(0)=0$ or $R(0)<1$, when an…
When high energy strings scatter at fixed angle, their amplitudes characteristically fall off exponentially with energy, ${\cal A} \sim \exp(-s \times const.)$. We show that in a compact space this suppression disappears for certain…
We report on our determination of the values of the one and two loop low energy constants appearing in the Chiral Perturbation Theory calculation of the pi-pi scattering amplitude. For this we use a precise sum rule determination of…
For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f(\vec{k}', \vec{k})$. The result is $f=\sqrt{\frac{\pi}{2}}\{1/log k)+O(1/(log k)^2)$. The only…
For a class of negative slowly decaying potentials, including $V(x):=-\gamma|x|^{-\mu}$ with $0<\mu<2$, we study the quantum mechanical scattering theory in the low-energy regime. Using modifiers of the Isozaki-Kitada type we show that…
Many low energy hadrons, such as the rho, can be observed as resonances in scattering experiments. A proposal by L\"uscher enables one to determine infinite volume elastic scattering phases from the two-particle energy spectrum measured…
The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target…
We examine the convergence properties of the 2-nucleon Effective Range Expansion as used in Effective Theories (ET-ERE's) for 3-nucleon calculations. We accomplish this by accounting for the 2-body dynamics with a simple rank-1 separable…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
Scattering amplitudes in quantum field theories are of widespread interest, due to a large number of theoretical and phenomenological applications. Much is known about the possible behaviour of amplitudes, that is independent of the details…
We are concerned with the acoustic scattering problem by many small rigid obstacles of arbitrary shapes. We give a sufficient condition on the number $M$ and the diameter $a$ of the obstacles as well as the minimum distance $d$ between them…
In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products…
We consider phaseless inverse scattering for the Schr\"odinger equation with compactly supported potential in dimension $d\ge 2$. We give explicit formulas for solving this problem from appropriate data at high energies. As a corollary, we…
Universal low-energy behaviour ${2 m c}\over{\ln |s-4m^2|}$ of the scattering function of particles of positive mass m near the threshold $s=4m^2$, and ${\pi} \over {\ln |s-4m^2|}$ for the corresponding S-wave phase-shift, is established…