Calibration 33T

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Hyperfine field calibration: α-Fe standard at 33.0 T

Source: core/constants.py (LINE_POS_33T, _BASE_POSITIONS, fe57_sextet_positions)

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The problem of calibrating the BHF

In a magnetic Fe-57 sextet, the six lines separate proportionally to the hyperfine field $B_{hf}$. To convert the measured line positions (in mm/s) to a field in teslas a conversion factor is needed. There are two ways to obtain it:

1. From the nuclear moments ("textbook" calculation): using $\mu_N$, the ground- and excited-state $g$ factors, and the $\gamma$ energy. It gives theoretical positions.
2. From a published velocity standard: using the measured positions of a well-characterized reference material (metallic α-Fe at room temperature).

Fitbauer uses the second way, just like Normos.

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Why nuclear moments are NOT used

The theoretical calculation from the nuclear moments gives a magnetic splitting ~0.4 % smaller than the experimental α-Fe standard:

Origin	Outer-line separation (1–6)
Theoretical (nuclear moments)	~5.309 mm/s
Experimental (published α-Fe)	5.328 mm/s

If calibrated from theory, a real α-Fe spectrum would fit to a BHF ~0.1 T too high (systematic bias). That is why core/constants.py explicitly warns against replacing the published positions with theoretical values (see CHANGELOG v4.0.2 / v4.0.3).

The nuclear data (MU_N, E_GAMMA, G_GROUND, G_EXCITED) remain in the module as reference/documentation, but are NOT used for calibration.

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α-Fe velocity standard at 33.0 T

The hyperfine field of metallic α-Fe at room temperature is, by convention, 33.0 T. The published positions of its six lines (in mm/s, with respect to the center) are:

$$\pm 5.329 \quad \pm 3.084 \quad \pm 0.839 ;; \text{mm/s}$$

In the code, the base positions are already stored symmetrized:

_BASE_POSITIONS = np.array([-10.657, -6.167, -1.677, 1.677, 6.167, 10.657]) * 0.5
#                = [-5.3285, -3.0835, -0.8385, 0.8385, 3.0835, 5.3285] mm/s
LINE_POS_33T = fe57_sextet_positions(33.0)

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Linear scaling with the field

For an arbitrary field $B_{hf}$, the positions scale linearly with respect to the 33.0 T standard:

$$v_j(B_{hf}) = v_j^{(33\mathrm{T})} \cdot \frac{B_{hf}}{33.0}$$

implemented in fe57_sextet_positions(bhf_t). To this are then added the isomer shift $\delta$ and the first-order quadrupole pattern $q_j \cdot \Delta E_Q$ (see docs/manual_mossbauer.tex, sextet section):

$$v_{0,j} = \delta + q_j \Delta E_Q + v_j^{(33\mathrm{T})}\frac{B_{hf}}{33.0}$$

with the first-order quadrupole pattern:

LINE_QUAD_PATTERN = [0.5, -0.5, -0.5, -0.5, -0.5, 0.5]

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Related constants

Constant	Value	Use
BHF_DEFAULT_T	33.0	Reference field and default initial value
_BASE_POSITIONS	±5.329 / ±3.084 / ±0.839 (×internal scale)	Published α-Fe standard
LINE_POS_33T	fe57_sextet_positions(33.0)	Positions at 33 T used by the fit engine
LINE_QUAD_PATTERN	[+½,−½,−½,−½,−½,+½]	First-order quadrupole pattern
DIST_BHF_RANGE	(0.0, 60.0)	Default range of the P(BHF) grid

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Practical verification

To check the calibration: load data_sample/hierro_metalico_alphaFe.adt (or the ESRF calibration) and fit. The resulting BHF should come out very close to 33.0 T and the line positions should match the published standard. Any systematic deviation indicates a problem with $V_{\max}$ (velocity calibration) or with the folding point, not with the physical model.

Repository rule. The reference field is 33.0 T with the published α-Fe velocity standard (±0.839 / ±3.084 / ±5.329 mm/s). LINE_POS_33T lives in core.constants. Do not derive positions from the nuclear moments.