Розрахунок фаз нуклон-нуклонного розсіяння для потенціалу Reid93 за методом фазових функцій
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Date
2016
Authors
Жаба, Віктор
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Abstract
Для обрахунку фаз одноканального нуклон-нуклонного розсiяння розглянуто вiдомий метод фазових функцiй. За допомогою методу фазових функцiй чисельно отримано фазовi зсуви нуклон-нуклонного розсiяння: nn (1S0-, 3P0-, 3P1-, 1D2-, 3F3-станiв), pp (1S0-, 3P0-, 3P1-, 1D2-станiв) i np (1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-станiв). Розрахунки проведено для сучасного реалiстичного нуклон-нуклонного потенцiалу Reid93. Чисельно розрахованi фазовi зсуви добре узгоджуються з результатами, отриманими iншими методами. За розрахованими фазовими зсувами обчислено повний перерiз i парцiальну амплiтуду розсiяння, значення яких мало вiдрiзняються вiд величин, отриманих за вiдомими фазами в iнших роботах.
Description
For calculation of the single-channel nucleon-nucleon scattering a phase-functions method (PFM) has been considered. PFM is a special method to solve the radial Schr¨odinger equation, which is a second order linear
differential equation. It is quite convenient for obtaining scattering phases, because this method does not require calculating radial wave functions of scattering problem in a wide range firstly and then finding these phases by
their asymptotics. Using a phase-functions method the following phase shifts of a nucleon-nucleon scattering are calculated numerically: nn (1S0-, 3P0-, 3P1-, 1D2-, 3F3-state), pp (1S0-, 3P0-, 3P1-, 1D2-state) and np
(1S0-, 1P1-, 3P0-, 3P1-, 1D2-, 3D2-state). The calculations has been performed using realistic nucleon-nucleon potential Reid93. When calculating phases of scattering, one should consider the peculiarities of potentials
of internucleonic interaction. Obtained phase shifts are in good agreement with the results obtained in the framework of other methods. Calculations compared with the results of other operations: for the partial-wave
analysis and for potentials NijmI, NijmII, Argonne v18 (Av18) and CD-Bonn. If we compare the phase shifts of nucleon-nucleon scattering calculated for the same Nijmegen group potentials (for pp- and np- scatterings) by different methods — on the basis of a solution of Schr¨odinger equation and PFM, we may conclude that the discrepancy between the outcomes makes no more than two percent. The comparison of the calculation results of the phase shifts for Reid93 potential, obtained with the help of PFM, and the phase shifts for other potential
models (Argonne v18 and CD-Bonn) and for the partial-wave analysis indicates that the deviation between these data makes up to five percents. The Runge-Kutta method of the fourth order was chosen as the numerical
method of solving the phase equation. The phase shifts were at an output of the phase function δl(r) on an asymptotics at r = 10 fm. Using the obtained phase shifts we have calculated the full cross-section and the partial scattering amplitudes. Our results are in good agreement with those obtained by using known phases published in literature. The all results of numeral calculations are represented in the type of tables which are comfortable for comparison with the values got other methods or for other nucleon-nucleon potential models.
Keywords
метод фазових функцiй, нуклон-нуклонне розсiяння, нуклон-нуклонний стан, фазовi зсуви, потенцiал Reid93, стаття, phase-function method, nucleon-nucleon scattering, nucleon-nucleon state, phase shifts, potential Reid93
Citation
Жаба В. І. Розрахунок фаз нуклон-нуклонного розсіяння для потенціалу Reid93 за методом фазових функцій / Жаба В. І. // Наукові записки НаУКМА : Фізико-математичні науки. - 2016. - Т. 178. - С. 44-48.