The proton-proton scattering without Coulomb force renormalization

R Skibiński,W Glöckle,H Witała,J Golak

doi:10.1051/epjconf/20100305014

R Skibiński, W Glöckle + Show 2 more

Open Access

https://doi.org/10.1051/epjconf/20100305014

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Abstract

We demonstrate numerically that proton-proton (pp) scattering observables can be determined directly by standard short range methods using a screened pp Coulomb force without renormalization. We numerically investigate solutions of the 3-dimensional Lippmann-Schwinger (LS) equation for an exponentially screened Coulomb potential. For the limit of large screening radii we conﬁrm analytically predicted properties for oﬀ-shell, half-shell and on-shell elements of the Coulomb t-matrix.

Highlights

[1], we proposed a method to obtain pp scattering observables using a screened Coulomb force in the standard framework of short range interactions
Despite the fact that the screening limit of the on-shell scattering amplitude does not exist and acquires an oscillating phase factor if the screening radius goes to infinity [2,3,4,5], it is still possible to obtain pp observables without renormalization of the scattering amplitude
In a series of papers [6, 7] related to the pd system, the screened Coulomb t-matrix was used in two forms: in the partial wave decomposition and in the direct 3-dimensional form < p ′|tcR(E)|p >

Summary

Introduction

[1], we proposed a method to obtain pp scattering observables using a screened Coulomb force in the standard framework of short range interactions. The off-the-energy-shell, half-shell and on-shell properties of the screened Coulomb t-matrix have been studied analytically in the past [2,3,4,8,9,10] These investigations, mostly rely on insight gained for fixed number of partial wave states. We study numerically the screening limit of < p ′|tcR(E)|p > for the off-, half- and onshell matrix elements and compare obtained results with the unscreened pure Coulomb force predictions. The resulting limiting values agree very well with the exact standard predictions obtained using the Vincent-Phatak method [12]. For this energy the screening limit for observables is achieved at R = 120 fm.

The 3-dimensional Lippmann-Schwinger equation

The off-shell elements

The half-shell elements

The on-shell elements

Findings

Summary