The command DIFCRS allows you to compute from previously determined S-matrix elements the

• differential cross sections
• diagonal quadrupole and octupole alignment moments $A_0^{(2)}$ and $A_0^{(4)}$
• off-diagonal alignment moment $A_2^{(2)}$
• m-dependent cross sections
• steric (oriented) cross sections.

The units of the cross setions are square Angstroms. The moments are dimensionless. The definition of the moments $A_0^{(2)}$ and $A_0^{(4)}$ is given in C. H. Greene and R. N. Zare, J. Chem. Phys. 78, 6741 (1983). The off-diagonal alignment moment $A_2^{(2)}$ is defined here.

difcrs,{jobname},j1,in1,j2,in2,ang1,ang2,dang,ienerg,jtotend,ipr,mflag,stflag,$\alpha$,$\beta$

where

• {jobnam} the jobname under which the S matrices have been stored {jobname}n.smt. Here n denotes the value of the parameter ienerg (see below). These S matrices must have been previously generated using
  • JLPAR = 0 (this generates S matrices for both parities)
  • JTOT1 = 1 (ensuring the determination of S-matrices at every partial wave)
  • WRSMAT = .true. (ensuring that the S-matrices are written to file {jobname}.smt). The default value of {jobname} is the value you have set with the command JOB, or, if no value has been set, {jobname}=JOB

• j1,in1 rotational quantum number and additional index for the initial state

• j2,in2 rotational quantum number and additional index for the final state

• ang1,ang2 initial and final angle (in degrees)

• dang step size (in degrees) for scan through angles.

• ienerg the cardinal value of the energy for which the differential cross section is computed. i.e. if ienerg = 2, then the second energy S matrices [{jobname}2.smt] are used

• jtotend the maximum value of $\mathbf{J}_{\rm tot}$ included in determining the scattering amplitude. The value of jtotend can not be larger than the variable JTOT2 used in the initial calculation

• ipr:
  • If ipr = 0 (the default) the degeneracy-averaged differential cross sections and product rotational alignment and hexapole moments are NOT printed to the normal output file but only to the file {jobnam}n.dcs
  • if ipr .ne. 0, the differential cross sections and the alignment (A0(2)) and hexapole moments (A0(4)) of the products are also printed to the normal output file and to stdout.
• mflag:
  • If mflag = 0 (the default) only the degeneracy-averaged differential cross section and the alignment (A0(2)) and hexapole moments (A0(4)) of the products are calculated.
  • If mflag .ne. 0, then
    • All m→m’ differential cross sections are calculated and printed. Quantization is in the collision frame, where the initial relative velocity vector defines the z axis.
    • The integral m→ m’ cross sections are determined, by integration from ang1 to ang2 in steps of dang.
    • The diagonal (ρm,m) and the real part of the 2nd supra-diagonal (ρm,m+2) elements of the rotational density matrix of the scattered products are output into file <jobnam>n.rho. These quantities are defined here in terms of the scattering amplitudes.
• stflag:
  • stflag = 0 is the default. If stflag .ne. 0, then “heads” and “tails” steric cross sections are calculated (see M. H. Alexander, Faraday Discuss. 113, 437 (1999). This is only allowed if FLAGHF = .true. and BASISTY = 3 (doublet pi). If stflag .ne. 0, then the following two parameters must be defined:
    • $\alpha, \beta$ parameters which define the mixture of e and f lamda-doublet states in the “heads” or “tails” orientation.

NB: the “heads” state for m-initial negative is defined as:

heads > = α

jme > - β

jmf >

and for m-initial positive as | heads > = α | jme > + β | jmf >