++ne reaction in the Sun does not depend on the form of nn potential?

Why the rate of p+p®d+e^++ne reaction in the Sun does not depend on the form of NN potential? B.F. Irgaziev^*, Z. Kanakov, F. Safarov National University of Uzbekistan ^*Corresponding Author: E-mail [e-mail]

Abstract The proton-proton reaction is a key reaction in the Sun and many stars which luminosity lies on main-sequence of the Hertzsprung–Russell diagram. We have calculated the astrophysical S-factors and the rate of proton-proton reaction going in the core of the Sun as well as the flux of neutrino at the distance 1AU (astronomic unit) applying the simplest nucleon-nucleon (NN) potentials (Gauss and Yukawa types) being only attractive, and two potential having the repulsive core at small distance between nucleons (Malfliet-Tjon and Reid potentials). Application of all considered potentials describes well the effective range parameters. Analyzing of this reaction shows that all calculated data is not sensitive to the type of NN potential if we apply the parameters under the conditions created in the core of the Sun. Keywords: weak interaction, pp-chain, neutrino flux, nucleon-nucleon potentials

1. Introduction

It is known that the main source of radiated energy by stars of mass equal to or less than the mass of the Sun is the nuclear chain converting four protons into one helium nucleus:

(1)

The generated energy in the cycle is Q=26.73 MeV. This chain starts from reaction

(2)

where kinetic energy of 0.42 MeV is distributed between positron and neutrino. We note the reaction (2) as pp reaction. For the first time this reaction, going through a weak interaction, was considered by Bethe and Critchfield [1]. The detailed analysis of this reaction was carried out in the work [2]. We have calculated the reaction of (2) (see Ref. [3]) with a few number of the simple attractive nucleon-nucleon potentials, while in the calculations performed by Bachall and May the wave functions of the relative motion of the protons and the wave function of the deuteron were based on the theory of the effective range. The reaction (2) was assumed independent on the type of nucleon-nucleon potential according to approach applied by Bachall and May.

The present work was undertaken to perform accurate calculation of the rate reaction (1) and flux of neutrinos at one astronomic unit (AU) and to check its sensitivity to form of the nucleon-nucleon potential. We applied Gauss, Yukawa, Malfliet-Tjon (M-T) [4] and Reid [5] potentials.