===========================================
Recombination data: (last updated: 2/27/00)
(Includes collisional ionization and charge
transfer rates as well.)
===========================================

Recombination coefficients for H I and He I-II are taken from
the file hherec.f.i It calculates recombination coeffs. for H I, He I, 
He II, C VI, N VII and O VIII for a vast temperature interval. To call 
the subroutine in Fortran you write (for hydrogen)

      call hherec(te,1,0,rec,otsp,cool)

where:
te = temperature
iz = charge for ionized hydrogen
ihe1 = 1 for He I, and 0 for other ions
rec = rec.coeff.
otsp = 0. for on-the-spot, and 2. for no on-the-spot (note that otsp
       is not an integer)
cool = recombination cooling

You have to multiply rec and cool by Ne and Nion to get the number of
recombinations per cm3 (and ergs/s/cm3 for the cooling), where Nion is the
number density of the recombining ion.

For He I you call on
      call hherec(te,1,1,rec,otsp,cool)
For He II you call on
      call hherec(te,2,0,rec,otsp,cool)
For C VI you call on
      call hherec(te,6,0,rec,otsp,cool)
etc.

Only H I, He I and He II should be treated on-the-spot.
Note that the routine includes dielectronic recomb. for Helium I, so
you should not add this outside the routine. hherec looks like:

C     ***************************************************************
      subroutine hherec(te,iz,ihe1,rec,otsp,cool)
C     ***************************************************************
C
C     Recombination coeff. for hydrogen-like ions and helium
C     te = temperature (K); iz = charge; ihe1 = Helium I identifier
C     (ihe=1 for He I); rec = recombination coeff.; otsp = on-the-spot
C     identifier (otsp =< 1.0 gives on-the-spot); cool = recomb.cooling
C
C     ***************************************************************
      implicit real*8(a-h,o-z)
etc.
etc.

During the course in 1998, two things were brought up which may be useful
to know:
1/ Do not attempt to put ``otsp'' exactly equal to 1. It should be
   strictly different from 1 for the routine to work correctly.
2/ The recombination emission coefficient ``cool'', which is a parameter
   calculated by the routine, is not the same as ``beta'' in Osterbrock's
   chapter 3.3. The coefficient in hherec routine includes ``kT'', which
   Osterbrock's expression doesn't.




Metal recombibation (except for H-like C, N and O):
===================================================

All data for C, N and O are gathered in the file tab_rec_coll
The format of this file is shown below for O I.
(Note that for hydrogen-like C, N and O, it is better though to use
hherec above.)

First there is an identifier: (8 = Oxygen, 1 means ionization stage I.)
Then follows 41 lines with 5 columns each. Column 1 is log(Temperature).
Column 2 is log(Recombination coefficient). Column 3 is log(collisional
ionization coefficient), i.e., same as the constant C above for He I and
He II. Columns 4 and 5 give log(charge transfer recombination coeff.=CREC)
and log(charge transfer ionization coeff.=CION), respectively.

Charge transfer recombination:
H I  +  O II  -->  H II  +  O I     Rate = N(H I) * N(O II) * CREC

Charge transfer ionization:
H II  +  O I  -->  H I  +  O II     Rate = N(H II) * N(O I) * CION

It's not important to include charge transfer rates in the rate equations 
for H, but they should be included in the rate equations for O. (In one
example you are asked to switch off charge transfer to see what the effect
is.)


Example from the file tab_rec_coll, valid for O I:

8   1
 2.0  -10.934  -50.000   -9.000  -11.048
 2.1  -11.019  -50.000   -9.000  -10.751
 2.2  -11.103  -50.000   -9.000  -10.497
 2.3  -11.188  -50.000   -9.000  -10.278
 2.4  -11.272  -50.000   -9.000  -10.087
 2.5  -11.357  -50.000   -9.000   -9.920
 2.6  -11.441  -50.000   -9.000   -9.772
 2.7  -11.526  -50.000   -9.000   -9.642
 2.8  -11.610  -50.000   -9.000   -9.527
 2.9  -11.695  -50.000   -9.000   -9.426
 3.0  -11.778  -50.000   -9.000   -9.339
 3.1  -11.861  -50.000   -9.000   -9.264
 3.2  -11.941  -50.000   -9.000   -9.203
 3.3  -12.019  -42.704   -9.000   -9.154
 3.4  -12.095  -35.581   -9.000   -9.117
 3.5  -12.169  -29.913   -9.000   -9.091
 3.6  -12.240  -25.400   -9.000   -9.074
 3.7  -12.303  -21.805   -9.000   -9.064
 3.8  -12.365  -18.940   -9.000   -9.057
 3.9  -12.425  -16.653   -9.000   -9.054
 4.0  -12.482  -14.827   -9.000   -9.051
 4.1  -12.537  -13.367   -9.000   -9.049
 4.2  -12.589  -12.196   -9.000   -9.047
 4.3  -12.636  -11.257   -9.000   -9.046
 4.4  -12.677  -10.501   -9.000   -9.045
 4.5  -12.712   -9.891   -9.000   -9.044
 4.6  -12.740   -9.397   -9.000   -9.043
 4.7  -11.548   -8.995   -9.000   -9.043
 4.8  -11.354   -8.667   -9.000   -9.043
 4.9  -11.276   -8.398   -9.000   -9.042
 5.0  -11.197   -8.175   -9.000   -9.042
 5.1  -11.202   -7.991   -9.000   -9.042
 5.2  -11.208   -7.837   -9.000   -9.042
 5.3  -11.268   -7.708   -9.000   -9.041
 5.4  -11.328   -7.600   -9.000   -9.041
 5.5  -11.418   -7.509   -9.000   -9.041
 5.6  -11.508   -7.433   -9.000   -9.041
 5.7  -11.623   -7.369   -9.000   -9.041
 5.8  -11.737   -7.317   -9.000   -9.041
 5.9  -11.867   -7.276   -9.000   -9.041
 6.0  -11.997   -7.244   -9.000   -9.041
8   2
etc. etc.


One thing brought up during the course in 1998 was:
1/ There are jumps in the recombination coeffs. as a function of temperature.
   In particular, there are jumps for O I, O II and O V between log(T)=
   4.6 and 4.7. This is correct, and reflects the uncertainty of today's
   knowledge about dielectronic recombination for oxygen. High-temperature
   dielectronic recombination has only been calculated down to 50,000 K.
   It would be dangerous to extrapolate this down to lower temperatures.
   Now, this is not a problem, since when you have included the right
   cooling, you will never reach these temperatures in your final models.
   So please, interpolate among the values in the tables as they are. That
   should work.