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Proton-proton scattering without Coulomb force renormalization R. Skibiński, J. Golak, H. Witała, W. Glöckle
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tarix | 18.04.2018 | ölçüsü | 501 b. | | #39196 |
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R.Skibiński, J.Golak, H.Witała, W.Glöckle Renormalization and proton-proton scattering observables. The screened Coulomb t-matrix properties.
The brief introduction → short range methods (eg. exponential screening ) The direct limit R → ∞ of t does not exist Renormalization (t → te-2i, =(R,n,E….)) The renormalization factor is just a phase factor → it is not needed for observables ~|t|2
The pp scattering observables at Eplab=13 MeV for the exponential screening with n=4 and different values of R.
The pp scattering observables at Eplab=13 MeV for the exponential screening with R=120 fm and different values of n.
The 3-dimensional screened Coulomb t-matrix at Eplab=13 MeV, n=4, R=120 fm
The screening limit of the off-the-energy-shell screened Coulomb t-matrix elements The pure Coulomb t-matrix off-shell elements (L.P.Kok and H. van Haeringen; PRC21, 512 (1980)):
An example: the off-shell screened Coulomb t-matrix t(q=0.36 fm-1,q’,=45°) at Eplab=13 MeV, n=4
The screening limit of the half-the-energy-shell screened Coulomb t-matrix elements The pure Coulomb t-matrix half-shell elements (L.P.Kok and H. van Haeringen; PRL46, 1257 (1981)):
An example: the half-shell screened Coulomb t-matrix t(q0=0.4 fm-1,q’,=45°) at Eplab=13 MeV, n=4
The screening limit of the on-the-energy-shell screened Coulomb t-matrix element
An example: the on-shell screened Coulomb t-matrix t(q0=0.4 fm-1,q’0=0.4 fm-1,) at Eplab=13 MeV, n=4
Summary The screened Coulomb t-matrix can be obtained numerically with high precision ― application in three-body calculations The renormalization is useful to study the screening limit of half- and on-shell t-matrix elements The pp scattering observables can be obtained using screened Coulomb potential without renormalization More details: R.Skibiński, J.Golak, H.Witała, W.Glöckle, Eur. Phys. J. A40, 215 (2009)
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