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

4. Results for the astrophysical S-factor, rate and flux of neutrino

The results of calculation of the astrophysical S-factor (Eq. (11)) with the considered potentials are: with the Gauss potentials

Yukawa potential

M-T potential

Reid potential

The difference between wave functions at small distance does not occur on the rate of pp reaction which is shown in Fig. 3. We see that the deuteron fusion reaction to occur inside of the core of the Sun does not exceed one third of the solar radius.

Fig.3. The rate of pp reaction vs the interior radius of the Sun. The calculated rate by the Gauss, Yukawa, M-T , and Reid potentials are almost the same.

The modern devices for the measurement of the flux of neutrino from pp reaction is not possible owing smallest energy of neutrino. However, there are the several theoretical prediction for this flux. We present the results for the flux of neutrino obtained by us at 1 AU with application of the Standard Solar Model BS2005-OP.

The Gauss potential: Φ_pp = 6.196×10¹⁰ cm^-2s^-1;

The Yukawa potential: Φ_pp = 6.070×10¹⁰ cm^-2s^-1;

The M-T potential: Φ_pp = 6.156×10¹⁰ cm^-2s^-1;

The Reid potential: Φ_pp = 6.135×10¹⁰ cm^-2s^-1.

The Bahcall et. al [6] applied the simple approach without using any nucleon-nucleon potential and got the result for the flux: Φ_pp = (5.987± 0.052)×10¹⁰ cm^-2s^-1.
3. Conclusion

The obtained results for the astrophysical S-factor defined only by the description of elementary pp process confirm the independence on the type to the nucleon-nucleon potential. Calculations with the most widely used NN potentials like the Paris, the Argonne AV18, the CD-Bonn and the Nijmegan potentials must give the same result for astrophysical S-factor as we received using the Gauss, Yukawa, M-T and Reid potentials, because the small distance between nucleon at the considered energies gives very small contribution into overlap integral. The flux of neutrinos obtained by us coincides with the Bahcal’s results if we take into account the d-part of the deuteron wave function. We mention that the survival probability of solar neutrino from pp reaction is under question.

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