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Computing Allowed Transitions

The LSJ transitions require a complete set of *.c *.w and *.j files for both: the initial and final state. The transitions between initial and final groups are computed by biotr and the transition are saved in a *.lsj file in the directory LSJ.

For transition probabilities the orbitals of the initial and final state need not be orthogonal. A biorthogonal transformation is used for the evaluation of matrix elements. For Breit-Pauli calculations, all operators may be included, spin-orbit, spin-other orbit, spin-spin, and orbit-orbit. In addition to transition rates of all types, isotope shifts and hyperfine constants can be computed as well as g_J factors.

set -x

# compute the LSJ transitions using biotr.

echo "computing *.j files"
# set n to desired value (this script will work for up to n=7)
n=4

#copy the files for initial and final state
cp E4.c I.c
cp O4.c F.c

# the script computes for Z=8,9 but provided that the wavefunctions and
# .j have already been computed for other Z's the line below can be modified
# to reflect different desired Z's
for Z in 8 9 
do
   (echo

   # copy the wave function files from ../E1 into I.w
   cp ../E1/E1.${Z}_${n}.w I.w
   
   #copy the *.j file 
   cp E1.${Z}.j I.j
   
   #copy the final wave function from O1 into F.w
   cp ../O1/O1.${Z}_${n}.w F.w
   cp O1.${Z}.j F.j
   
   # use input file in_biotr which is universal and it accepts as 
   # file names for initial and final states as I (needs I.w, I.c I.j) 
   # and final state F (needs F.w, F.c, F.j)
${ATSP}/bin/biotr<in_biotr
   
   # the LSJ transitions between groups E1 and O1 will be saved into 
   # a file with a unique name, note  that since Breit-Pauli is 
   # performed only for the most accurate calculation and $n does
   # not need to be incorporated into the *.lsj file name.
   mv I.F.lsj E1.O1.${Z}.lsj
      
   echo)
done


# remove not needed files
rm ?.?  fort*

After completion biotr will leave the following *.lsj files in the directory LSJ.

-rw-r--r--    1 georgio  georgio     11738 Aug 19 19:15 LSJ/E1.O1.8.lsj
-rw-r--r--    1 georgio  georgio     11738 Aug 19 19:15 LSJ/E1.O1.9.lsj

The script starts with copying the appropriate files and running biotr. The input file for biotr is shown below:

E1         # initial state
O1         # final state
n          # do not give a full printout (only for debugging)
y          # relativistic calculation
E1         # transition

The transitions between each two groups are saved in a .lsj file which contains essential data per transition:

   1  -74.35652224  2s(2).2p(3)2P1_2P
   1  -73.64006121  2s.2p(4)1S0_2S
  157239.63 CM-1       635.97 ANGS(VAC)       635.97 ANGS(AIR)
 E1  S =  4.87252D-01   GF =  2.32723D-01   AKI =  1.91900D+09
          4.71411D-01         2.25157D-01          1.85662D+09
The first two lines are blank, the next line is the initial state including the J value, the energy and the label. The same information for the final state is shown on the next line. The first line for the transition data is computed in the length form, whereas the second is the velocity form. The Breit-Pauli methods have not modified the transition operator for the lowest order relativistic corrections in the velocity form. These are not important for the allowed transitions, but are important in spin-forbidden transitions. Generally, the accuracy of a transition depends on the accuracy of the length and velocity form in the non-relativistic approximation, and the accuracy of the Breit-Pauli transition energy, with the normalized length form value preferred. For intercombination transition, accuracy also depends on other factors, such as the accuracy of the separation of the two terms important for the transition.


next up previous contents
Next: Computing Forbidden Transition Up: Computing Atomic Transitions Previous: Breit-Pauli calculations   Contents
2001-10-11