case.ham (e.g. Ni22pP.ham) is the input file for ham.case, generating reduced matrix elements of the Hamiltonian for x-ray excited final states. The reduced matrix elements are used for the calculation of the spectral intensities. The input largely overlaps with the caseGS.ham for generating the Hamiltonian for final states. In most cases, copy the casaGS.ham and add configurations for final states (and intermediate states for second-order process, such as RIXS). Two entries, absent in the caseGS.ham input file, are explained below.

1. Configurations to be taken into account for describing x-ray excited final states
The configurations (bases) for describing the initial states are defined in caseGS.ham. In case.ham, we introduce the configurations describing the final states. Finding the configurations is “usually” rather straightforward. For example, for core-level XPS (say 2p core-level excitation), create a 2p core hole and a photoelectron (emitted from sample) for all configurations included in the initial-state calculation. For 2p core-level XAS, create a 2p core hole and an extra electron into the valence shell. For RIXS, we provide configurations for the intermediate states (which are (usually) the same ones for the XAS final states) and final states (which are the same with the initial-state calculation). Then, the users specify the paths between the configurations by the core-level excitation, which is straightforward once you determine the configurations to be included. This step is illustrated in figure below. (prep_xspec -i generates the paths automatically)

2. Intra-configuration interaction (multiplet interaction) including core-valence interaction
Here, the users define the intra-atomic interaction of the Hamiltonian, e.g. Coulomb multiplet interaction of valence-valence channel and core-valence channel, spin-orbit interaction, crystal field, magnetic field, see also caseGS.ham.In the presence of the core-hole, core-valence Coulomb interaction is activated. As for the valence-valence Coulomb interaction, the isotropic part of the core-valence Coulomb interaction U_dc is given in case.and (next step) since it depends only on the electron (and core-hole) filling, thus is absorbed into the configuration diagonal energies. Therefore in this case.ham file, only the multiplet part of the core-valence Coulomb interaction is specified.

case.ham (for XPS)

==========     Input for Hamil.f     ==========
    Symmetry  1     (0:SO3, 1:Oh, 2:D4h, 3:D2h, 4:D3d, 5:Td, -1: user-defined)   : symmetry 
    No_Conf   8     : number of configurations to be included in the calculation 
    No_Shell  5     : number of shells for active shells in the configurations
    PE-Shell  0     : index of photoelectron shell, if exists (option for experts only)
Configuration       : define configurations to be included in the ground-state calculation
      1  -1  -1  -1   1   : e/h rep. conversion (1: electron picture/ -1: hole picture)
   1 P 0 D 2 L 0 L 0 P 0    : |d8>
   2 P 0 D 1 L 1 L 0 P 0    : |d9L> 
   3 P 0 D 0 L 2 L 0 P 0    : |d10L2>
   4 P 0 D 0 L 1 L 1 P 0    : |d10LL>
   5 P 1 D 2 L 0 L 0 P 1    : |cd8>
   6 P 1 D 1 L 1 L 0 P 1    : |cd9L>
   7 P 1 D 0 L 2 L 0 P 1    : |cd10L2>
   8 P 1 D 0 L 1 L 1 P 1    : |cd10LL>
Diagonal Interaction (1:S-O  2:C.F.  3:Uvv  4:Ucv  5:M.F.)   : define intra-configuration interaction 
   1  3  3         1.00 1.00 1.00 1.00
     1 2     2 2         3 2
     0.083          10.338 6.461
   2  2  1         1.00 1.00 1.00 1.00
     1 2   2 2
     0.083
   3  0  0         1.00 1.00 1.00 1.00
   4  0  0         1.00 1.00 1.00 1.00
   5  5  7         1.00 1.00 0.80 0.80
     1 1      1 2   2 2      3 2             4 1 2
    11.506   0.112      10.338 6.461   8.350 6.332 3.603   ← F2, G1, G3 for |cd8> (Ni2+)  
   6  4  5         1.00 1.00 0.80 0.80
     1 1      1 2   2 2              4 1 2
    11.507   0.102             7.721 5.787 3.291           ← F2, G1, G3 for |cd9L> (Ni1+)  
   7  1  1         1.00 1.00 0.80 0.80
     1 1
    11.507
   8  1  1         1.00 1.00 0.80 0.80
     1 1
    11.507

CF and MIX param : No_params // Prameter-set for CF/ LD/ OP
        *** Delete Parameter lines if corresopnding No_Params=0 ***
   1  1  0
   1  0.32        : number of CF parameter = 1, 10Dq 
   2  1.0 1.0     : number of independent hybridization function = 2, for d system in Oh symmetry, eg and t2g orbitals 
Transition           (6:Mix  7:Rad  8:C.I.)  :   transitions between configurations (inter-configuration interaction)  
   6 6 6            : mixing-type transition (6), number of mixing paths (=6 for this example) 
    2 1 3 2 4 2     : path (<f|H|g>) (conf2-conf1), (conf3-conf2), (conf6-conf5) + (conf7-conf4), (conf7-conf6), (conf8-conf6) 
     1   1   1
   7 4 4            : radiative-type transition (7), number of x-ray excitation paths (=4 for this example)
    5 1 6 2 7 3 8 4 : path (<f|T|g>) (conf5-conf1), (conf6-conf2), (conf7-conf5) + (conf8-conf4)
    1.0 1.0 1.0 1.0
   777 0 0          (888: end / 777: GS_character / 555: Upd / 999: Lifetime)
   888 0 0
=====   End of input   =====

See caseGS.ham for spin-orbit interaction, crystal field, valence-valence Coulomb interaction, and user-defined operators.

Note. F⁰ part is included in U_dc (isotropic part), see H_imp above, which is given by users in case.and file (not in case.ham). In case.ham file only F², G¹, G³ integrals are provide by the users. This treatment (separation) is useful for fitting analysis of core-level spectra where U_dc is treated as a fitting parameter. Note U_dc contributes only to the configuration diagonal energy depending only on the electron (and hole) filling of the configurations (i.e. gives just a shift w.r.t other configurations). In core-level spectroscopy analysis, F², G¹, G³ parameters are usually evaluated by the atomic Hartree Fock calculation.