Proton-proton reaction rate

Tognelli, Degl'Innocenti, Marcucci, Prada Moroni

Physics Letters B 742 (2015), 189

The code

The fortran code - developed by Laura E. Marcucci - provides the proton-proton weak capture reaction rate [cm³mol^-1s^-1)] presented in Tognelli, Degl'Innocenti, Marcucci, Prada Moroni, Physics Letters B 742 (2015), pp. 189-194. The reaction rate is accurate at the level of few per mil. Two subroutines (flux and b5) are needed to calculate the flux for the proton-proton weak capture reaction, given the star temperature in 10⁹ K. It is based on the following articles:

• Marcucci et al., Phys. Rev. Lett. 110, 192503 (2013)
• NACRE II, Nucl. Phys. A 918, 61 (2013) [ Eq.(3) ]

• the initial p-p wave function can include only the S-wave contribution or also all the P-wave contributions. The S+P waves is what has been suggested in Marcucci et al., the S-wave contribution is what has been used so far in the literature;
• the user can calculate the flux using the calculated values for the p-p astrophysical S-factor on an energy grid of 101 points of step = 1 keV, or alternatively use the values of S(0), Sⁿ⁽⁰⁾, [Sⁿ⁽⁰⁾ is the n-th derivative of S(E) calculated at zero energy] up to n=3, and tabulate S(E) with the preferred steps. In this second case, in parameter, the user needs to adjust he and ne_int (see below).

How to compile the code

The code should be compiled as:

• gfortran -O4 -o flux flux.f
• ifort -O4 -o flux flux.f

Usage

The user needs to know only the following inputs indices:

• iprint = 1/0 for printing/not printing intermediate results
• t9 = star temperature in 10⁹ K
• ic =
  • 1 for S+P waves
  • 2 for only S-waves
• inter =
  • 1 for using the calculated S-factor
  • 2 for using the fitted values for S(0), S^'(0), S^''(0) and S^'''(0) and then tabulating the S(E) as preferred. In this case, in parameter the user should fix:
    • he = 1.e-3 ne_int = 101 : step (given in MeV) of 1 keV
    • he = 1.e-4 ne_int = 1001: step (given in MeV0 of 0.1 keV
    • etc...

In output, the user finds:

• flx = flux in cm³ mol^-1 s^-1
• dflx = theoretical uncertainty on the flux

In the ReadMe an example and tests are available.