3.1.4. POPRATIO
This is the main module that actually computes the rate coefficients for the processes described in section 2 (after reading the related atomic data from a separate input file) and then solves the system of equations of statistical equilibrium.
It begins defining a few useful constants to the evaluation of the rate coefficients and three new types:
This module also declares several global variables that are visible to the main program. Table 1 shows the correspondence between most important variables and the mathematical quantities given in section 2.
Variable | Mathematical quantity |
E(i) | E_{i} |
g(i) | g_{i} |
A(i,j) | A_{ij} |
B(i,j) | B_{ij} |
u(i,j) | u_{ij} |
CD(k)%q(i,j) | q^{k}_{ij} |
gam(i,j) | _{ij} |
matrix(i,j) | M_{ij} |
indep(i) | I_{i} |
X(i) | X_{i} |
We also have the following routines:
The redshift is used to set the temperature of the Cosmic Microwave Background Radiation (CMBR), as given by the following relation predicted by the standard Big Bang cosmology (see, for instance, Kolb and Turner [8]):
where T_{0} = 2.728 ± 0.002 K is the current value of the CMBR temperature [9, 10]. The effect of the CMBR blackbody radiation field is then included in the energy densities:
where c is the speed of light. Alternatively, there are models that generalize the standard temperature law of the CMBR (19) by introducing a free parameter [11]:
where is within the range 0 1. If this parameter is not entered via the optional parameter BETA, it is assumed zero. POPULATIONRATIO calls function TCMBR to evaluate the temperature of the CMBR, and next function PLANCK to evaluate its contribution to the energy densities. If the user does not wish to take the CMBR into account, the redshift Z should be entered with the value -1.0_WP.
POPULATIONRATIO also adds to the energy densities the contribution from a radiation field defined by the user in function URAD. The optional parameter F multiplies the radiation field defined in URAD by a constant factor f. If F is not entered, it is assumed 1.