ASTM E944-19

3.2.1 The symbols introduced in this section will be used throughout the guide.

3.2.2 Dosimetry measurements are given as a set of reaction rates (or equivalent) denoted by the following symbols:

These data are, at present, obtained primarily from radiometric dosimeters, but other types of sensors may be included (see 4.1).

3.2.3 The neutron spectrum (see Terminology E170) at the dosimeter location, fluence or fluence rate Φ(E) as a function of neutron energy where:
3.2.4 The reaction cross sections of the dosimetry sensors are obtained from an evaluated cross section file. The cross section for the i-th reaction as a function of energy Used in connection with the group fluences, Eq 2, are the calculated group-averaged cross sections σ_ij. These values are defined through the following equation:

3.2.5 Uncertainty information in the form of variances and covariances must be provided for all input data. Appropriate corrections must be made if the uncertainties are due to bias producing effects (for example, effects of photo reactions).

3.3.1 An adjustment algorithm modifies the set of input data as defined in 3.2 in the following manner (adjusted quantities are indicated by a tilde, for example, ã_i):

or for group fluence rates

or for group-averaged cross sections

The adjusted quantities must satisfy the following conditions:

or in the form of group fluence rates

Since the number of equations in Eq 11 is much smaller than the number of adjustments, there exists no unique solution to the problem unless it is further restricted. The mathematical algorithms in current adjustment codes are intended to make the adjustments as small as possible relative to the uncertainties of the corresponding input data. Codes like STAY'SL, FERRET, LEPRICON, and LSL-M2 (see Table 1) are based explicitly on the statistical principles such as “Maximum Likelihood Principle” or “Bayes Theorem,” which are generalizations of the well-known least squares principle, and are taking into account variances and correlations of the input fluence, dosimetry, and cross section data (see 4.1.1, 4.2.2, and 4.3.3). A detailed discussion of the mathematical derivations can be found in NUREG/CR-2222 and EPRI NP-2188. Even the older codes, notably SAND-II and CRYSTAL BALL, apply a minimization algorithm although the statistical assumptions are not spelled out explicitly in the supporting documentation. Table 1 lists some of the available unfolding codes; however, the first four codes listed: SAND-II, SPECTRA, IUNFLD/UNFOLD, and WINDOWS have severe limitations in that they do not typically provide uncertainty characterization of the resulting unfolded spectrum and the adjusted damage exposure parameters.