I: Systematic Uncertainties of Experiments and Data Evaluated Using Physical Criteria

The experimental data for photoneutron reaction cross sections for I obtained using beams of quasimonoenergetic annihilation photons and the method of neutron multiplicity-sorting at Livermore (USA) and Saclay (France) were analyzed using objective physical data reliability criteria. It was found that data of both laboratories contain significant systematic uncertainties and therefore are not reliable. New data for partial and total photoneutron reactions cross sections for 127 I satisfied physical criteria of data reliability were evaluated using experimental-theoretical method based on both experimental neutron yield reaction cross-section and results of calculation in the combined photonucleon reaction model (CPNRM). The neutron yield reaction cross-section obtained at Saclay (France) was used in evaluation procedure. The newly evaluated cross sections for partial (γ, 1n), (γ, 2n) and (γ, 3n) reactions for 127 I were used for discussion in detail the problems of significant disagreements between experimental data for many nuclei obtained at Saclay and Livermore. It was found that systematic uncertainties of experimental data for the (γ, 1n), (γ, 2n), and (γ, 3n) reactions cross sections for 127 I obtained at both laboratories are of different nature. One of the reasons of noticeable systematic uncertainties of cross sections obtained are the shortcomings of the procedures used to separate counts into 1n, 2n, and 3n events. At the same time it was shown that the main reason of significant disagreements between new evaluated data and data obtained at Livermore experiment for 127 I is the loss of many neutrons from the (γ, 1n) reaction. This situation is analogous to those in Livermore experiments for 75 As and 181 Ta.

There are three very interesting cases in the systematic under discussion: 75 As, 181 Ta, and 127 I. In the case of 75 As R int S/L ratios for both partial reactions (γ, 1n) and (γ, 2n) are relatively large and very close to each other (R int S/L (1n)=1.21, R int S/L (2n)=1. 22). In the case of 181 Ta those ratios are significantly different (R int S/L (1n)=1. 25  In the case of 127 I the ratio R int S/L (1n)=1.34 is the largest value in the systematic mentioned above.
At the same time the averaged disagreement between the neutron yield reaction cross-section, σ(γ, Sn)=σ(γ, 1n)+2σ(γ, 2n)+3σ(γ, 3n), (1) values obtained in various laboratories for many nuclei is about 10% [7][8][9]. It means that there are noticeable systematic uncertainties in partial reaction cross sections main reasons of which are the definite shortcomings of the neutron multiplicity-sorting method used. In order to resolve the problems of systematic disagreements between data obtained in various experiments the cases of 181 Ta [10] and 75 As [11,12] were investigated in detail using the experimental-theoretical method for evaluating the partial reaction cross sections [13]. In this method the experimental neutron yield reaction cross-section σ exp (γ, Sn), rather independent from the neutron multiplicity-sorting problems because all outgoing neutrons are included, is decomposed into partial reaction cross sections σ eval (γ, in) using the ratios, calculated for partial reactions (γ, in) with definite neutron multiplicity factors i=1, 2, 3,... in the combined photonucleon reaction model (CPNRM) [14,15]. The CPNRM is based on the statistical approach, uses a combination of preequilibrium exciton model and particle evaporation process to calculate probabilities of formation of specific final nuclei after absorption of a photon and additionally considers deformation of nucleus and isospin splitting of its giant dipole resonance. This treatment means that the competitions between partial reactions are in accordance with the CPNRM equations and their correspondent sum (1) σ eval (γ, Sn) is equal to the experimental once σ exp (γ, Sn).
The ratios F i exp determined in analogy to F i theor (3) were proposed [13] to be the objective physical criteria of partial photoneutron reaction cross-section data reliability. Follow the definitions (3) F i must not have values higher than 1.00, 0.50, 0.33 respectively for i=1, 2, 3. Larger F i exp values mean that experimental cross sections definitely have noticeable systematic uncertainties and therefore are not reliable. The second criterion of data reliability is that because the ratios F i include only the cross-section terms they must be definitely positive. The third reliability criterion was obtained after the comparison in detail the newly evaluated partial photoneutron reaction cross sections σ eval (γ, in) (2) for 181 Ta [10], 197 Au [12] and 209 Bi [16] with the results of measurements of multi-neutron reaction yields using bremsstrahlung beams and activation method [17][18][19], in which the direct identification of specific partial reaction is based on final nucleus features. It was found that for all three nuclei mentioned evaluated partial reaction cross sections σ eval (γ, in) agree with data obtained using activation method and therefore are reliable.
In this article systematic uncertainties of different nature existed in experimental data for 127 I because of using the method of photoneutron multiplicity sorting at Saclay and Livermore are discussed in detail.

Neutron Yield Reaction Cross-Section
Data for 127 I It was mentioned above that the averaged disagreement between neutron yield reaction cross sections (1) obtained in various experiments for many nuclei in general is relatively small, about 10%. For 127 I this is not in case. The correspondent cross sections σ(γ, Sn) are presented in Figure  1 in comparison with the results of calculation in the CPNRM [14,15].
It is very important to underline that there are significant disagreements between σ exp (γ, Sn) obtained at Livermore and Saclay in the energy range below the threshold of (γ, 2n) reaction B2n=Е int =16.29 MeV where only reaction (γ, 1n) exists and one have no neutron multiplicity-sorting problems. The values of respective integrated cross-section and center of gravity values are presented in Table 1 together with the relevant data calculated in the CPNRM. One can see that the disagreement between σ exp (γ, Sn) obtained at Livermore [27] and Saclay [28] is about 36% (1143.19/837.86).

The Objective Physical Criteria for 127 I Partial Photoneutron Reaction Data Reliability
As it was mentioned above the ratios F i exp obtained using experimental cross sections in analogy to the calculated F i theor (2) were proposed [13] as objective physical criteria of partial photonuclear reaction cross-section reliability. The ratios F 1, 2, 3 exp for 127 I obtained using the experimental data of Livermore [27] and Saclay [28] are presented in Figure 2 together with calculated F 1, 2 theor data [14,15]. One can see that F 1, 2 exp values obtained for Saclay data [28] [28].
Moreover ratios F 2 exp are systematically noticeably smaller in comparison with F 2 theor at energies higher ~22.0 MeV, though in agreement with definition (3) they must decrease starting at the energy of (γ, 3n) reaction threshold B3n=25.83 MeV. In the energy range ~22-29 MeV underestimations of (γ, 2n) reaction cross sections (F 2 exp < F 2 theor ) clearly correlate with overestimation of (γ, 1n) reaction cross sections (F 1 exp > F 1 theor ).   [27], triangles and [28], full squares from database [1,6], and calculated sum (1)  It is important to point out that σ(γ, 3n) was not obtained at Livermore [27] and therefore one has no relevant F 3 exp values. Because at energies higher B3n=25.83 MeV there are correlated overestimation of F 1 exp and underestimation of F 2 exp in comparison with the correspondent F 1, 2 theor and at the same time absence of F 3 exp , one can be forced to suspect that noticeable part of neutrons from (γ, 2n) reaction and all neutrons from (γ, 3n) reaction was unreliably (erroneously) identified as neutrons from (γ, 1n) reaction.

The Newly Reliable Partial Reaction Cross Sections Evaluated for 127 I Using the Experimental-Theoretical Method
The newly cross sections of partial (γ, 1n), (γ, 2n), and (γ, 3n) reactions and total photoneutron reaction, evaluated using experimental-theoretical method (2) and based on the corrected experimental Saclay data for σ exp (γ, Sn) [28] are compared with experimental data of Saclay and Livermore in Figure 3. The correspondent integrated cross-section values for all evaluated cross sections for 127 I under discussion are presented in Table 2. Some special notes are needed before discussion in detail the obtained data.
There are noticeable disagreements in the case of (γ, 3n) reaction. Although associated uncertainties are overlapping, all disagreements are systematic and therefore the relevant integrated cross sections (presented in last line of Table 2) definitely disagree.
In Figure 3 one can see that at Livermore [27] the experimental cross sections of the reactions (γ, Sn), (γ, tot), and (γ, 1n) are significantly smaller in comparison with correspondent evaluated cross sections in energy range before B2n=16. 29 MeV where there are no problems of neutron multiplicity-sorting. Vice versa at energies Eγ > 22 MeV the cross sections of σ exp (γ, tot) and σ exp (γ, 1n) reactions are systematically larger in comparison with respective evaluated cross sections.
Moreover though at energies up to B2n=16.29 MeV F 1 exp values for data obtained at Livermore are near unity ( Figure  2a), it could gives to one an opportunity to have in mind the idea that that the reason of significant difference between Livermore data and Saclay and evaluated data in principle could not be the simple error in normalization. Such relative proximity of experimental and evaluated values means that assumption of simple normalization error is not correct. After the simple normalization the normalized and evaluated (γ, 1n) reaction cross sections became agree at low energies but disagree at high energies and normalized (γ, 2n) reaction-section became significantly disagree with relevant evaluated once. *) Experimental neutron yield reaction cross-section σ exp (γ, Sn) [28] used as the initial one for the evaluation procedure (2). **) Normalized Livermore data [27] (look further).
It is very important to point out that the analogous situation with unreliable sorting of neutrons between obtained experimentally σ(γ, 2n) and not obtained σ(γ, 3n) was investigated in detail before for 159 Tb [29].

The Reasons of Disagreements Between Partial Reaction Cross Sections for 127 I
To find the possible reasons of disagreements between Saclay and Livermore 127 I data under discussion the comparison of competitions between various total and partial reactions was studied in detail using ratios of respective integrated cross-section values σ int eval /σ int exp , calculated for evaluated and experimental cross sections using the data presented in Table 2.
Because as was pointed out there are serious problems in the sorting of neutrons from all partial reactions at Livermore at energies higher B3n, the ratios σ int eval /σ int S [28] and σ int eval /σ int L [27] were calculated using relatively Saclay and Livermore data for energies between B2n and B3n in which the maximal competition between (γ, 1n) and (γ, 2n) reactions exists and are presented in Table 4. It is very important to point out that σ int eval /σ int exp values for all total and partial reaction cross sections obtained at Saclay and Livermore are quite different.
As was mentioned above, the disagreements under discussion could not be explained by relatively simple errors in normalization of data because decreasing the disagreement between cross sections of (γ, 1n) reaction will be followed by increasing the disagreement between cross sections of (γ, 2n) reaction. To confirm this assumption all experimental Livermore [27] cross sections were normalized to the Saclay [28] data by multiplying all to 1.36=1143.19/837.86 using the data of the Tables 1 and 2 for energy range before B2n=16. 29 MeV in which all cross sections must be identical.
The correspondent ratios σ int eval /σ int L [27] obtained using the corrected Livermore data are presented in the last column of Table 4. One can see that after such correction (normalization) the cross sections of (γ, Sn), (γ, tot), and (γ, 1n) reactions became much closer to the relevant evaluated data with relatively small (9%, 6%, and 3%) differences respectively, but at the same time the cross-section of (γ, 2n) reaction became significantly (up to 21%) larger in comparison with evaluated cross-section.
One can see that at energies before B2n=16.29 MeV the evaluated cross sections are relatively close to the Saclay data [28]. At higher energies some disagreements exist (Figure 4a). The differences ∆σ (5) obtained for Saclay data look as "reflected in a mirror" with average deviation from zero of about several mb. Although associated uncertainties are overlapping, all disagreements are systematic and therefore one can talk about definite disagreements. Those clearly demonstrate the reason of this kind "traditional" [10][11][12][13][16][17][18][19][20][21][22][23][24][25][26] systematic uncertainties in the experiments discussed, e.g., the unreliable uncertainties in sorting of a certain number of neutrons between 1n and 2n channels because of not direct dependence of measured neutron kinetic energy and its determined multiplicity.
For Livermore data [27] the situation is completely different. As it was shown above there is noticeable difference between σ(γ, 1n) obtained at Livermore and Saclay at energies below the threshold B2n (Figure 4b). The experimental (γ, 1n) reaction cross-section is significantly less in comparison with the evaluated cross-section with the biggest deviation ∆σ (γ, 1n) ~100 mb. But at energies higher than ~21 MeV the experimental (γ, 1n) reaction cross-section is vice versa noticeably larger in comparison with the evaluated one: the average deviation is about 30 mb, the biggest ones are ~40-50 mb. At the same time at all energies the difference ∆σ (γ, 2n) is relatively small (the average deviation is about several mb).
In Figure 4c the differences ∆σ (5) obtained using the corrected normalized Livermore σ exp (γ, Sn) [27], which is relatively close to that of Saclay, are presented. One can see that the energy dependencies of ∆σ(γ, 1n) and ∆σ(γ, 2n) look absolutely different in comparison with previous once (Figure 4b). At energies up to B2n=16. 29 MeV the difference ∆σ(γ, 1n) became significantly smaller in comparison with previous values, at energies between B2n and ~22 MeV ∆σ(γ, 1n) is relatively the same as before and at higher energies ∆σ(γ, 1n) has values noticeably larger in comparison with previous values. At the same time in complete agreement with previous conclusions the difference ∆σ(γ, 2n) has the values significantly larger in comparison with previous once: in the energy range between B2n and ~25 MeV the average value is ~25-30 mb, several extreme deviations are ~40, 50, 80 mb. It means that additional normalization of experimental Livermore data [27] does not exclude the traditional disagreements because of difference of procedures used to separate counts into 1n and 2n events.

Comparison of Data for 127 I with
Those for 181 Ta and 75 As As it was mentioned above, there are three interesting cases in the systematic of disagreements between Livermore and Saclay data, 127 I, 181 Ta, and 75 As.
The cases of 181 Ta [10] and 75 As [12] were investigated in detail before. It was shown that for both nuclei additionally to the traditional [10][11][12][13][16][17][18][19][20][21][22][23][24][25][26] disagreements between the partial reaction cross sections obtained at Livermore and Saclay because of difference of procedures used to separate counts into 1n and 2n events, one can see the presence of systematic uncertainties of other nature. It was found that in both cases there are the significant disagreements for (γ, 1n) reaction cross sections but at the same time relatively proximity of data for (γ, 2n) reaction cross sections. It was shown that in the relevant Livermore experiments for 75 As [30] and 181 Ta [31] the competitions of the ratios of integrated cross sections σ int eval /σ int S/L calculated using evaluated and experimental data presented in Table 5 are generally very similar to those found in the case of 127 I.
In the absolute analogy to the case of 127 I for both 75 As and 181 Ta the evaluated data are in general closer to experimental Saclay [32,33] not to Livermore [30,31] data. For both 181 Ta and 75 As similar to that was found for 127 I the larger the fraction of the σ(γ, 1n) reaction in the cross-section for the reactions (γ, Sn), (γ, tot), and (γ, 1n), the higher the degree to which the latter is underestimated (1.24 → 1.30 → 1.46 in the case of 181 Ta and 1.27 → 1.30 → 1.34 in the case of 75 As). For σ(γ, 2n) the σ int eval /σ int L are significantly smaller -1.05 in the case of 181 Ta and 1.14 in the case of 75 As. The very important difference between the cases of 127 I and 181 Ta and 75 As is that differences ∆σ(γ, 2n) between evaluated and experimental data are relatively small (2% and 5%, correspondingly) for the first two nuclei and noticeably large (14%) for the third one. Because in accordance with all things discussed above one is forced to conclude that at Livermore in the cases of 127 I [27] and 181 Ta [30] many neutrons from (γ, 1n) reactions were lost, in the case of 75 As [31] many neutrons not only from (γ, 1n) but from (γ, 2n) reaction also were lost. Therefore it can be concluded that experimental Livermore data for 75 As [31], 127 I [27], and 181 Ta [30] are in general unreliable.
It was found additionally that the competitions of the ratios σ int eval /σ int exp of integrated cross sections of the reactions (γ, Sn), (γ, tot), (γ, 1n) and (γ, 2n) calculated for energies before B3n using data obtained at Saclay and Livermore are quite different.
At Saclay all ratios σ int eval /σ int S [28] are near unity. At Livermore the ratio σ int eval /σ int L [27] is near unity only for (γ, 2n) reaction. For other reactions those ratios are significantly larger. Moreover the larger the fraction of the σ(γ, 1n) reaction, the higher the degree to which the latter is underestimated, 1.20 → 1.25 → 1.33 for the reactions (γ, Sn), (γ, tot), and (γ, 1n), correspondingly. Using those data and data for the differences ∆σ=σ eval -σ exp (5) between evaluated and experimental cross sections it was shown that the main reason of such significant systematic uncertainties of data obtained in Livermore is that many neutrons from the reaction 127 I(γ, 1n) [27] were lost in analogy to the situations for reactions 75 As(γ, 1n) [30] and 181 Ta(γ, 1n) [31].
So, one is forced to conclude that the experimental cross sections of (γ, Sn), (γ, tot), and (γ, 1n) reactions obtained at Livermore for 127 I [27] contain significant uncertainties not only because the definite shortcomings of the procedures used to separate counts into 1n and 2n events but also because the loss of many neutrons from (γ, 1n) reaction.
So one is forced to conclude that experimental Livermore data for 127 I [27] similar to those for 75 As [30] and 181 Ta [31] obtained using the photoneutron multiplicity-sorting method are obviously unreliable because of the presence of significant systematic uncertainties from erroneous transportation of many neutrons from one partial channel to another and additionally from the loss of many neutrons. Therefore the results obtained using alternative experimental methods are needed [11,12].