deltas.rst

Delta Values

For all integrals, δ-values can be calculated automatically as described in the usage documentation <../pkg/usage>. Delta values are always calculated (1) with respect to the major isotope and (2) using the NIST database of the iniabu package. If no value can be calculated, i.e., because the isotope is unknown to iniabu or because the natural abundance of the specified isotope is unknown, np.nan will be returned as the δ-value.

Note

All δ-values are reported in per mil (‰).

Calculation δ-value

Be i and j the number of counts in the nominator and denominator isotopes, respectively, and r the NIST isotopic ratio of the same isotopes. The δ-value can then be calculated as:

$$\delta = \left( \frac{i/j}{r} - 1 \right) \times 1000 \qquad (‰)$$

Uncertainties

Be σ_i and σ_j the uncertainties of values i and j, respectively. The uncertainty of the δ-value σ_δ can be calculated as:

$$\sigma_{\delta} = \frac{1000}{r} \left[ \left(\frac{\sigma_i}{j}\right)^2 + \left(\frac{i\sigma_j}{j^2}\right)^2 \right]^{1/2} \qquad (‰)$$