Waasmaier-Kirfel form factor coefficients lose precision due to missing Fortran kind specifiers

[bjmorgan]

Summary

The Waasmaier-Kirfel X-ray form factor coefficients in lib_f90/element_data_mod.f90 are declared as real(kind=PREC_DP) arrays, but the literal constants in the initialisers lack _PREC_DP (or D0) kind suffixes. This causes gfortran to parse them as default real (float32) before promoting to float64, silently discarding ~7 digits of precision. The practical impact on typical calculations is negligible (~1e-7 relative), but the fix is mechanical and affects every element and ion.

Minimal reproducer

program precision_test
  implicit none
  integer, parameter :: DP = selected_real_kind(15, 307)
  real(kind=DP), parameter :: with_kind = 17.958397999999998973_DP
  real(kind=DP), parameter :: without   = 17.958397999999998973

  write(*,'(a,ES25.18)') ' With kind suffix:    ', with_kind
  write(*,'(a,ES25.18)') ' Without kind suffix: ', without
  write(*,'(a,ES25.18)') ' Difference:          ', with_kind - without
end program

Output (gfortran 14):

 With kind suffix:     1.795839799999999897E+01
 Without kind suffix:  1.795839881896972656E+01
 Difference:          -8.189697275895468920E-07

Affected arrays

All per_wa1 through per_wa5, per_wb1 through per_wb5, and per_wc arrays (lines 325–610) use bare literals. The effect is ~1e-7 relative error per coefficient, propagating to ~1e-7 relative error in the computed form factors.

Suggested fix

Add _PREC_DP suffixes to all literal constants in the WK coefficient arrays. For example, change:

17.958397999999998973,   12.063053999999999277, ...

to:

17.958397999999998973_PREC_DP,   12.063053999999999277_PREC_DP, ...