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Register a new userZero range potential for particles interacting via Coulomb potential: application to electron positron annihilation
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The zero range potential is constructed for a system of two particles interacting via the Coulomb potential. The singular part of the asymptote of the wave function at the origin which is caused by the common effect of the zero range potential singularity and of the Coulomb potential is explicitly calculated by using the Lippmann-Schwinger type integral equation. The singular pseudo potential is constructed from the requirement that it enforces the solution to the Coulomb Schrodinger equation to possess the calculated asymptotic behavior at the origin. This pseudo potential is then used for constructing a model of the imaginary absorbing potential which allows to treat the annihilation process in positron electron collisions on the basis of the non relativistic Schrodinger equation. The functional form of the pseudo potential constructed in this paper is analogous to the well known Fermi-Breit-Huang pseudo potential. The generalization of the optical theorem on the case of the imaginary absorbing potential in presence of the Coulomb force is given in terms of the partial wave series.
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In this paper we show that electron-positron pairs can be pumped inexhaustibly with a constant production rate from the one dimensional potential well with oscillating depth or width. Bound states embedded in the the Dirac sea can be pulled out and pushed to the positive continuum, and become scattering states. Pauli block, which dominant the saturation of pair creation in the static super-critical potential well, can be broken by the ejection of electrons. We find that the width oscillating mode is more efficient that the depth oscillating mode. In the adiabatic limit, pair number as a function of upper boundary of the oscillating, will reveal the diving of the bound states.
In a recent work, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential - for example, the interatomic potential at short ranges, and the electrostatic potential at long ranges. Here, we examine the proposed mechanics of turbulence formation in a simple model of two particles, which interact solely via a potential. Following the kinetic theory approach, we derive a hierarchy of the velocity moment transport equations, and then truncate it via a novel closure based on the high Reynolds number condition. While standard closures of the velocity moment hierarchy of the Boltzmann equation lead to the compressible Euler and Navier-Stokes systems of equations, our closure leads to a transport equation for the velocity alone, which is driven by the potential forcing. Starting from a large scale laminar shear flow, we numerically simulate the solutions of our velocity transport equation for the electrostatic, gravity, Thomas-Fermi and Lennard-Jones potentials, as well as the Vlasov-type large scale mean field potential. In all studied scenarios, the time-averaged Fourier spectra of the kinetic energy clearly exhibit Kolmogorovs five-thirds power decay rate.
We obtain the centre-of-mass frame effective potential from the zero-momentum potential in Ruijsenaars-Schneider type 1-dimensional relativistic mechanics using classical inverse scattering methods.
We calculate the cross section for the exclusive production of J^{PC}=0^{++} glueballs G_0 in association with the J/psi in e^+e^- annihilation using the pQCD factorization formalism. The required long-distance matrix element for the glueball is bounded by CUSB data from a search for resonances in radiative Upsilon decay. The cross section for e^+e^- -> J/psi+ G_0 at sqrt{s}=10.6 GeV is similar to exclusive charmonium-pair production e^+e^- -> J/psi+h for h=eta_c and chi_{c0}, and is larger by a factor 2 than that for h=eta_{c}(2S). As the subprocesses gamma^* -> (c c-bar) (c c-bar) and gamma^* -> (c c-bar) (g g) are of the same nominal order in perturbative QCD, it is possible that some portion of the anomalously large signal observed by Belle in e^+ e^- -> J/psi X may actually be due to the production of charmonium-glueball J/psi G_J pairs.
The Schrodinger equation incorporating the long-range Coulomb potential takes the form of a Fredholm equation whose kernel is singular on its diagonal when represented by a basis bearing a continuum of states, such as in a Fourier-Bessel transform. Several methods have been devised to tackle this difficulty, from simply removing the infinite-range of the Coulomb potential with a screening or cut function to using discretizing schemes which take advantage of the integrable character of Coulomb kernel singularities. However, they have never been tested in the context of Berggren bases, which allow many-body nuclear wave functions to be expanded, with halo or resonant properties within a shell model framework. It is thus the object of this paper to test different discretization schemes of the Coulomb potential kernel in the framework of complex-energy nuclear physics. For that, the Berggren basis expansion of proton states pertaining to the sd-shell arising in the A ~ 20 region, being typically resonant, will be effected. Apart from standard frameworks involving a cut function or analytical integration of singularities, a new method will be presented, which replaces diagonal singularities by finite off-diagonal terms. It will be shown that this methodology surpasses in precision the two former techniques.
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