Abstract
We confirmed that the Coulomb phase shifts can not be given with a screened Coulomb potential by a monotonic increase of the range R . However, several screening “discrete range-bands” reproduce the Coulomb phase shift in a wide energy region. If the range-band of a proton-proton system for example is obtained, then the range-bands are generalized by three universal arguments: the universal range R (k )(≡ kR ), the Sommerfeld parameter η (k )(≡ Z 1 Z 2 e 2 ν /k ), and the universal asymptotic phase F (k )(≡ 2krc ). Finally, the phase shifts of any other systems from e− −e− to heavy ions such as 208 Pb−208 Pb can be reproduced automatically by an individual range R = R (k )/k on the universal range-bands R (k).
Highlights
The screened Coulomb potential can not reproduce the Coulomb phase shift by the monotonic increase-range method, the screened Coulomb potential itself reaches the Coulomb potential in the infinite range [1][2]
The Coulomb phase shift is analytically obtained in configuration space and expressed by σL(k) = arg Γ(L + 1 + iη(k)), (1)
The phase shift appears in the asymptotic Coulomb wave function, w(L±)(kr) = exp ± i kr − πL/2 − η(k) ln 2kr + σL(k), (2)
Summary
The screened Coulomb potential can not reproduce the Coulomb phase shift by the monotonic increase-range method, the screened Coulomb potential itself reaches the Coulomb potential in the infinite range [1][2]. The Coulomb phase shift is analytically obtained in configuration space and expressed by σL(k) = arg Γ(L + 1 + iη(k)), (1). The phase shift appears in the asymptotic Coulomb wave function, w(L±)(kr) = exp ± i kr − πL/2 − η(k) ln 2kr + σL(k) , (2). EPJ Web of Conferences where the r-dependent phase: η(k) ln 2kr differs from the one obtained from short-ranged potentials, h(L±)(kr) = exp ± i kr − πL/2 + δRL(k) , (3). Where δRL(k) is the phase shift with short range potential. Let us define a phase function by the ratio between both wave functions in the region r ≥ rc, where rc is a starting point of the asymptotic region, Y±L (kr)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
