PhononSimple_process, Phonon_simple: scale the one-phonon cross-section to Squires 3.120

[henrikjacobsenfys]

Fixes #2792.

PhononSimple_process (Union) and Phonon_simple (samples) traced 1/(4π × 1.00866) ≈ 0.0789 of the one-phonon cross-section they implement (Squires Eq. 3.120). Two factors, one line each:

• 4π. PhononSimple_process now returns μ = 4πρ dσ/dΩ, which is what Union's ΔΩ/4π direction weighting expects. Phonon_simple drops the / (4 * PI) from its focusing factor p2.
• m_n/u. The recoil ħ²κ²/2m_n was divided by M as if it were in neutron masses. Both headers document M as an atomic mass, so the constant gains 1.00866 (m_n/u). The %P unit of M now reads [amu] in both components.

b stays the scattering length in fm, so existing instruments need no parameter change. Their phonon intensity goes up by 12.675.

Test targets

The test targets recorded at the old scale are updated, along with the generated READMEs that repeat them:

• Samples_Phonon, both %Example lines.
• Test_Dispersion_relation_TAS, the three phonon %Example lines and the phonon %Scan.
  • Its generate_phonon_dispersion.py deliberately reproduces Phonon_simple's cross-section, so it gets the same two factors. Otherwise Dispersion_relation and Phonon_simple would no longer agree.
  • The formula and the two phonon scan totals in its .md are updated to match.
• Test_inhomogenous_process, sample=phonon.

For Phonon_simple, the fix rescales every ray's weight by a constant without touching the random number sequence. So at a fixed seed each result scales by exactly 4π × 1.00866 = 12.6752. I ran every affected example at mctest's settings (seed 1000, 1e6 rays, no MPI), before and after:

• The ratio was 12.6752 for both Samples_Phonon lines, the three TAS examples, and all 25 points of the TAS %Scan. The same 17 points are zero before and after.
• The new targets are therefore the old targets × 12.6752, rounded to the significant figures each had. I didn't replace them with numbers from my own platform.

The Union test is not a pure rescaling, because μ also changes which process Union picks. Its target moves by the measured ratio, +4.6% (0.00505839 → 0.00529178).

The magnon examples (sample_choice=2, 3) are unaffected.

Absolute check

A monochromatic 100 meV beam on a thin fcc Ni sample, with four 0.2 × 0.4 m detector elements 6 m away at 2θ = 20°, 35°, 50° and 65°. dσ/dΩ per atom from the monitors, compared with Squires 3.120:

	before	after
PhononSimple_process (Union box, 4 seeds × 5e4)	0.0790	0.9995 ± 0.0025
Phonon_simple (cylinder, 2θ = 50°, 20 seeds × 1e6)	0.0790 ± 0.0001	1.0004 ± 0.0009

Tested, and not

• Tested: Windows 11, MSVC, conda-forge McStas 3.8.7, with this branch's components and test instruments, plus main's Union library files. In that setup the unpatched runs reproduce the committed targets (e.g. lin_det_I 0.00507 against 0.00506), which suggests the mix is sound.
• Not tested: Linux, macOS, GPU, and a build of main itself.
• Not touched:
  • The smaller issues listed in [BUG]: PhononSimple_process and Phonon_simple` scatter 1/(4π × 1.00866) of the one-phonon cross-section they implement #2792 (the line-349 metric, the missing 2π/a, the uninitialised slot, the printf, the root search, the int function that returns nothing).
  • The stale comment under the Union constant.
  • hk_scan.png in the TAS docs, whose shared colour scale is now 12.7× too small.

🤖 Generated with Claude Code

[willend]

@henrikjacobsenfys thanks! As I remember @Lomholy recently looked into benchmarking of multiple inelastic comps, so I've requested him to review.

[Lomholy]

@willend thank you for putting me on this. I will see when I have mental bandwidth to see if the factor 4 pi is supposed to be there or not, but i expect that it might be some time before i get to it!

[willend]

@henrikjacobsenfys current failures are a result of a not completely succesful merge with new content on main. I will fix that.