Isotopic variations of Sm, Gd, Er and Yb found in planetary materials caused by neutron-capture reactions in nature

The isotopic shifts of 149 Sm– 150 Sm and 157 Gd– 158 Gd have often been observed in meteorites and lunar surface materials, because they result from the neutron-capture reactions associated with secondary neutrons produced by cosmic-ray irradiation. While the Sm and Gd isotopic shifts can mainly be used for the estimation of thermal neutron fluences that of 167 Er– 168 Er has recently been applied in the estimation of epithermal neutron fluences. The systematic isotopic dataset of Sm, Gd and Er helps us to consider the details of planetary materials’ cosmic-ray exposure conditions using the balance of the fluences between thermal and epithermal neutrons. This paper reviews a series of isotopic variations of Sm, Gd, and Er in association with neutron-capture reactions for the application of planetary sciences. As a new attempt and possibility for better understanding the neutron fluence and its energy distribution, the use of Yb isotopic variation is then discussed using two different data sources, namely lunar regolith and the Oklo natural reactors. Finally, the preliminary result for the precise isotopic measurement of Yb is presented from the viewpoint of chemical separation and instrumental improvement.


Introduction
The surfaces of airless bodies of solar planets are exposed to cosmic rays.Spallation reactions by the interactions of cosmic rays with planetary materials produce spallogenic products, such as 10 Be and 53 Mn.Such spallogenic products, called cosmogenic nuclides, have been effectively used for understanding the cosmic-ray exposure (CRE) conditions of planetary materials (e.g., Nishiizumi et al. 1996).At the occurrence of spallation reactions, neutrons are produced.Neutrons produced by spallation gradually reduce their energy down to epithermal (0.1 eV < E < 0.5 MeV) to thermal (E < 0.1 eV) energy regions by a collision cascade with the surrounding atoms in the planetary materials.Energy-lost neutrons then become more reactive with the nuclei consisting of the planetary materials.Neutron capture is one of the major reactions caused by cosmic-ray irradiation to the surficial parts of planetary bodies in space.
The total amount of neutrons produced in a target material by the cosmic-ray interaction and its energy distribution are highly dependent on the chemical composition and the size of the target material in space; therefore, their quantitative evaluations are important for better understanding the surficial changes of materials during the evolution processes of planets.
Several isotopes of some rare earth elements (REEs) have significantly large neutron-capture cross sections.In addition, isotopic abundances have changed as the neutron-capture reactions accumulate.For example, 149 Sm and 157 Gd react sensitively with thermal neutrons (E < 0.1 eV), and become 150 Sm and 158 Gd, respectively.The degrees of the 149 Sm-150 Sm and 157 Gd-158 Gd isotopic shifts can be used as a neutron dosimeter of the thermal neutrons produced in association with cosmicray irradiation.On the other hand, because 167 Er reacts with epithermal neutrons (0.1 eV < E < 500 keV) as well as thermal neutrons, the isotopic shift of 167 Er- 168 Er can be used for dosimetry of the epithermal neutrons.Systematic isotopic analyses of Sm, Gd, and Er collected from the same single material are planned to obtain information on neutron fluences in an energy range from the thermal to epithermal regions, which will provide information about the surface conditions of the cosmic-ray irradiated planetary materials.
This paper reviews a series of isotopic studies of Sm, Gd and Er for the application of planetary sciences and then, discusses new attempts to evaluate the occurrence of neutron-capture reactions in nature using Yb isotopic variations.Considering the nuclear properties of 168 Yb, the isotopic depletion degree of 168 Yb associated with the neutron-capture reaction of 168 Yb(n,γβ + ) 169 Tm could also be used in the application of an epithermal neutron dosimeter.The determination of Yb isotopic composition for planetary materials has been examined for a better understanding of nucleosynthetic heritage in the solar system (Shollenberger et al. 2018;Shollenberger and Brennecka 2020), mass-dependent fractionation in association with the condensation of the formation of planetary materials (Albalat et al. 2012(Albalat et al. , 2015)), and estimation for the β + decay of 176 Lu to 176 Yb (Amelin and Davis 2005).In this paper, however, the development of precise isotopic analysis of Yb is managed for the detection of the isotopic depletion of 168 Yb derived from the neutron-capture reaction of 168 Yb(n,γβ + ) 169 Tm.In association with the neutron-capture reactions, the Yb isotopic approach is somewhat more complicated for quantitative discussions than those of Sm, Gd, and Er, because the neutron-capture reaction of 168 Yb is not (n,γ)-type but (n,γβ + )-type reaction. 168Yb converts to a different element 169 Tm by the neutron-capture reaction.In addition, 169 Tm has a larger epithermal neutroncapture cross section, σ epi , than thermal neutron-capture cross section, σ th , and converts to 170 Yb by the neutroncapture reaction of 169 Tm(n,γβ − ) 170 Yb.As a reference, the Yb isotopic compositions of the Oklo natural fission reactor materials, which are known to be intensively irradiated with neutrons, show a small but significant deficit of 168 Yb by 168 Yb(n,γβ + ) 169 Tm and enrichment of 170 Yb produced from 169 Tm(n,γβ − ) 170 Yb (Holliger and Devillers 1981;Hidaka and Holliger 1998).It is interesting to find the isotopic variations of 168 Yb and 170 Yb in extraterrestrial materials and consider their application for neutron dosimetry in nature.Because the isotopic abundances of both 168 Yb and 170 Yb are originally small (0.13% and 3.04% of the total, respectively), careful and precise measurements should be required to detect their isotopic variations.Hidaka et al. (2020) examined the determination of Yb isotopic compositions of a series of lunar regolith samples collected from a 2.4 m-length drill stem at the Apollo 15 (A-15) landing site and reported the resolvable 168 Yb isotopic depletions in four of seven samples.

Neutron energy spectra
Considering the large thermal neutron-capture cross section of 149 Sm and 157 Gd, the isotopic variation of 150 Sm/ 149 Sm and/or 158 Gd/ 157 Gd have been used to evaluate the thermal neutron fluences in the target materials (Lingenfelter et al. 1972;Russ et al. 1972).Considering the variations in neutron fluence alongside energy, the neutron energy spectrum arising in the planetary materials by cosmic-ray irradiation is known to have dependencies on the chemical composition and the size of the target materials irradiated by cosmic rays (e.g., Spergel et al. 1986).In a previous study on the estimation of neutron fluences of planetary materials, thermal neutrons are considered to be more dominant than epithermal neutrons.However, there are few quantitative discussions about epithermal neutron fluences.Nevertheless, evaluation of the epithermal neutron fluence is also important, because the shape of neutron energy spectra largely changes, especially in the epithermal energy region (0.1 eV < E < 0.5 MeV).

Neutron energy-dependency of neutron-capture cross section of nuclides
The neutron-capture cross section of each nuclide is often characterized as a function of the neutron energy.On the other hand, it generally decreases along with the E −1/2 in the thermal energy region.Then, it has many sharp peaks, called resonance, in the epithermal energy region.For the evaluation of the reactivities of individual nuclides with neutrons in the resonance region, the resonance integral (RI) is defined as the following equation; where E c is a cut-off energy, typically used as 0.5 eV, and E max is the highest energy in the region of neutron-capture resonance, and σ(E) is a neutron-capture cross section as a function of energy.From Eq. (1), the epithermal neutroncapture cross section, σ epi , can be obtained as follows: Detailed data for the neutron energy spectrum, thermal neutron-capture cross section, and RI for each  1a shows a threeisotope diagram of Sm isotopic shifts found in a series of the A-15 lunar regolith core samples.In addition, as the quantitative correspondence between the isotopic decrements of 149 Sm and the increments of 150 Sm is balanced, the data points in the figure are plotted in a straight line with a slope of − 1.
Based on the variation degree of the Sm isotopic shift, the total number of thermal neutrons, thermal neutron fluence Ψ th (neutron number per square centimeter: n cm −2 ), arising in planetary materials can be evaluated from the Sm isotopic shift as the following equation; where R 0 = 150 Sm/ 149 Sm isotopic ratio without neutroncapture reactions (standard reference material), and R = 150 Sm/ 149 Sm isotopic ratio affected by neutron-capture reactions (Hidaka et al. 2020).
(3)  Gd isotopic shift of 157 Gd-158 Gd Gadolinium has seven stable isotopes with mass numbers 152, 154, 155, 156, 157, 158, and 160.Since 157 Gd has a very large σ th (2.5 × 10 5 barn at E = 0.0253 eV) and a small σ epi (1.2 × 10 2 barn at 0.5 eV < E < 300 eV), the isotopic shift of 157 Gd to 158 Gd can be treated similarly for the evaluation of Ψ th as in the case of 149 Sm-150 Sm. Figure 1b shows a three-isotope diagram of Gd for the A-15 lunar samples.When comparing the neutron-capture cross section between 149 Sm and 158 Gd in detail, however, 149 Sm has a large resonance peak at 0.0973 eV with a slightly higher value in the thermal energy region, which suggests that 149 Sm not only react with well-thermalized neutrons but also slightly energetic neutrons.However, the cross section of 157 Gd does not show such resonance peaks in the thermal energy region.Using this difference found in the cross section between 149 Sm and 155 Gd, an index, ε Sm /ε Gd , consisting of the combination of Sm and Gd isotopic shifts was applied to discuss the energy distribution of neutrons within the thermal region (Lingenfelter et al. 1972;Russ et al. 1972).The index ε Sm /ε Gd determining the thermalization degree of neutrons is given by the combination of Sm and Gd isotopic shifts as follows: The cross sections of 149 Sm and 157 Gd vary with the chemical compositions of individual samples (Lingenfelter et al. 1972); therefore, the index ε Sm /ε Gd is treated as a function of the effective total macroscopic cross section (Σ eff ) in consideration of the chemical composition of major elements, such as O, Si, Al, Fe, Ca, Mg, and Ti, and some effective trace elements, such as Cd, Eu, Sm, and Gd, in the matrixes of individual samples (Lingenfelter et al. 1972;Russ et al. 1972).

Er isotopic shift of 167 Er-168 Er
Erbium has six stable isotopes with mass numbers, 162, 164, 166, 167, 168, and 170.Since the neutron capture of 167 Er is also (n,γ)-type reaction, the history of neutron irradiation in each sample can be conveniently viewed by the three-isotope diagram between 167 Er/ 166 Er and 168 Er/ 166 Er.Comparing the size between σ th (6.49 × 10 2 barn) and σ epi (3.6 × 10 2 barn at 0.5 eV < E < 2000 eV) of 167 Er, 167 Er can react with not only thermal neutrons but also epithermal neutrons.In this study, a total neutron fluence (Ψ) and total neutron-capture cross section (σ) are simply treated as the sum of thermal and epithermal components for fluence (Ψ = Ψ th + Ψ epi ) and cross (4) section (σ = σ th + σ epi ), respectively.Modifying Eq. ( 3), the relationship between the Er isotopic shift R, Ψ, and σ is expressed as follows: where R 0 = 168 Er/ 167 Er isotopic ratio without neutroncapture reactions (standard reference material), and R = 168 Er/ 167 Er isotopic ratio affected by neutron-capture reactions (Hidaka et al. 2020).Here, σΨ can be simply treated as σΨ = σ th Ψ th + σ epi Ψ epi , because σ th Ψ epi and σ epi Ψ th are negligible.Because Ψ th can be evaluated from Sm and/or Gd isotopic shifts as expressed in Eq. ( 3), Ψ epi can be quantified by the subtraction of Ψ th from Ψ.Although the neutron-capture cross section of 167 Er is two orders of magnitude smaller than that of 149 Sm, the isotopic variations of 167 Er in the samples with Ψ > 10 16 n cm −2 are expected to be detectable and distinguishable between Ψ th and Ψ epi after subtraction of the contribution of Ψ th evaluated from the Sm isotopic variations (Hidaka et al. 2020). (5) The systematic isotopic study of Sm, Gd, and Er provides information on the evaluation of Ψ th and Ψ epi , and the energy balance of neutrons within the thermal region based on the index ε Sm /ε Gd .Considering the size of the neutron-capture cross section as listed in Table 1, the isotopic variations of 168 Yb and 170 Yb are also expected to apply for the use of Ψ epi dosimetry.Precise measurements of Yb isotopic composition are now being planned to establish the sensitive dosimeter for Ψ epi .Here, in this study, new attempts to evaluate the occurrence of neutron-capture reactions observed in Yb isotopic variations will discuss.

Simulation of the isotopic variations of 168 Yb and 170 Yb
Ytterbium has seven isotopes with mass numbers 168, 170, 171, 172, 173, 174, and 176.Because the size of σ epi (3.56 × 10 3 barn at 0.5 eV < E < 200 eV) for 168 Yb is around one and a half times larger than that of σ th (2.30 × 10 3 barn), 168 Yb reacts more sensitively with epithermal rather than thermal neutrons.Because 168 Yb becomes 169 Tm by the neutron-capture reaction of Yb(n,γβ + ) 169 Tm, its reactivity can be evaluated from the isotopic depletion of 168 Yb.
On the other hand, Tm is a monoisotopic element having only one stable isotope 169 Tm.Because the size of σ epi (1.95 × 10 2 barn at 0.5 eV < E < 2000 eV) for 169 Tm is around two times larger than that of σ th (1.05 × 10 2 barn), 169 Tm reacts more sensitively with epithermal neutrons rather than thermal neutrons.As 169 Tm becomes 170 Yb through the neutron-capture reaction of 169 Tm(n,γβ − ) 170 Yb, its reactivity cannot be evaluated from the isotopic depletion of 169 Tm, but from the isotopic enrichment of 170 Yb.Evaluation of the epithermal neutron fluence arising in planetary materials can be expected from the possible detection of the quantitative degree of 170 Yb isotopic excess.
The disadvantageous point for the application of the presented two neutron-capture reactions is that their reactivities cannot be graphically viewed by a threeisotope diagram, because the two neutron-capture reactions are not (n,γ)-type.Considering the predominant reactivities of 168 Yb and 169 Tm with epithermal neutrons; however, precise measurements of Yb isotopic composition of cosmic-ray irradiated planetary materials are desired for the evaluation of Ψ epi from the detection of both isotopic depletion of 168 Yb and excess of 170 Yb.Hidaka et al. (2020) measured Yb isotopic compositions of the lunar regolith samples collected from the drill core at the A-15 landing site.A series of the core samples are known to be irradiated by a neutron fluence of (5.2-7.5)× 10 16 n cm −2 from the Sm isotopic shifts (Hidaka et al. 2000).As a result of Yb isotopic analyses of A-15 samples, four of seven samples in the A-15 core samples show isotopic depletions of 168 Yb, while the other three show less isotopic depletions than the analytical uncertainties.On the other hand, isotopic excesses of 170 Yb could not be identified in all seven samples from the A-15 core.One of the major reasons for unsatisfactory results in detecting the isotopic anomalies on 168 Yb and 170 Yb is insufficient analytical precisions of the isotopic measurements.Because the isotopic abundances of both 168 Yb and 170 Yb are originally small, 0.13% and 3.04% of the total, respectively, careful and precise measurements should be required to detect their variations.The expected variations for 168 Yb and 170 Yb isotopic abundances can be considered as follows: (6) where subscript 0 means a nonirradiated situation, Ψ is a total neutron fluence including thermal and epithermal fluence (Ψ = Ψ th + Ψ epi ); σ is the total neutron-capture cross section including thermal and epithermal neutron-capture cross section (σ = σ th + σ epi ).Here, σΨ can be simply treated as σΨ = σ th Ψ th + σ epi Ψ epi .In this study, using two examples for the detectable Yb isotopic variations caused by neutron-capture reactions, one from the A-15 lunar regolith samples (Hidaka et al. 2020) and the other from the Oklo natural fission reactor samples (Holliger and Devillers 1981; Hidaka and Holliger 1998), the relationship between Ψ, σ, and isotopic variations of 168 Yb and 170 Yb is discussed by comparing the measured and calculated isotopic data.

Chemical separation of individual REEs for isotopic analyses
For the precise determination of Yb isotopic composition by mass spectrometric techniques, it is required to purify the Yb component after the separation of Er and Lu in the individual samples to completely avoid the isobaric interferences of all Yb isotopes on the mass spectra.Mizutani et al. (2020) established a chemical separation method for La, Ce, Nd, Sm, Gd, Dy, Er, Yb, and Lu without any isobaric interferences from other elements using column chromatography with lanthanide-specific (LN) resin (particle size of 20-50 μm) and HCl as the eluent.This method has been used conveniently for the chemical separation of Sm, Gd, Er, and Yb in a sequential procedure.In this technique, the elution behaviors of Pr, Eu, Tb, Ho, and Tm were not examined, because such five elements do not provide any isobaric interferences with the other elements on the mass spectra.Even if there are no isobaric interferences, the presence of impurities in a target element fraction significantly reduces the ionization efficiency during the isotopic analysis by a thermal ionization mass spectrometer.Therefore, it is desirable to separate any impurity elements from the target element as much as possible for better isotopic analyses.In this study, a part of the chemical separation technique for individual REEs given by Mizutani et al. ( 2020) was improved for better purification of Sm, Gd, Er and Yb fractions by the fine adjustments of the concentrations and flow volumes of HCl for Ln-resin packed column.

Isotopic analyses of Yb
Before starting this study, the isotopic measurement of Yb was given by the normal mode of a TRITON Plus thermal ionization mass spectrometer (TIMS) equipped with nine Faraday cups connected to individual 10 11 Ω resistor amplifiers (Mizutani et al. 2020;Hidaka et al. 2020).This study used two of nine amplifiers modified to 10 13 Ω resistor amplifiers for the detection of 168 Yb and 170 Yb isotopes and the rest seven 10 11 Ω resistor amplifiers for the detection of other five 171, 172, 173, 174, 176 Yb isotopes and for the monitoring of 167 Er and 175 Lu to correct isobaric interferences to perform high-accuracy and precise Yb isotopic analyses.

Yb isotopic data of the A-15 lunar regolith materials
The isotopic variations of 168 Yb/ 174 Yb and 170 Yb/ 174 Yb for individual samples are expressed as the deviation relative to those for the Yb standard reference material in ε-unit.
The ε expression is defined as follows: where i = 168 or 170, the subscripts "std" and "meas" mean standard reference materials without neutron irradiation and each sample used in this study, respectively.
(8) The calculated ε values from the expected Ψ th + Ψ epi and the measured ε values for seven samples from the A-15 lunar regolith samples are listed in Table 2. Considering the contribution of only Ψ th estimated from the Sm isotopic shifts (Hidaka et al. 2000), the ε 168Yb values range from − 1.2 to − 1.7, which are much fewer variations compared with those of the A-15 samples by measurements (− 12.7 to − 27.9).The ε 168Yb values for the A-15 samples can be well reproduced by the contribution of Ψ epi in addition to Ψ th .Although the measured ε 168Yb data include large analytical uncertainties (± 9 to 21 in ε unit), the estimated ε 168Yb ranges from − 20 to − 31 which is almost consistent with the measured ε 168Yb values within the analytical uncertainties.
The measured ε 170Yb excesses over the analytical uncertainties were not clearly detected in all of the A-15 samples (Hidaka et al. 2020).Considering the contribution of Ψ th only, the ε 170Yb values estimated from Eq. ( 7) are less than + 0.42 for all seven samples.These excesses cannot be detected by the current techniques, because the analytical uncertainties (± 0.47 to 0.77 in ε unit) are over Table 2 Comparison of the isotopic variations of (a) 168  b The calculations were done under consideration of the contribution of Ψ th only.The Ψ th values (in 10 16 n cm −2 unit) were given by Hidaka et al. (2000) c The calculations were done under consideration of the contributions of both Ψ th and Ψ epi .Both Ψ th and Ψ epi values (in 10 16 n cm −2 unit) were given by Hidaka et  the range of the estimated ε 170Yb .Considering the contributions of both Ψ epi and Ψ th (see Table 2), however, the estimated ε 170Yb ranging from + 5.9 to + 8.9 should be detectable enough even with the current analytical uncertainties.
The results from the comparison between the measured and calculated Yb isotopic variations reveal that 168 Yb is affected by both Ψ th and Ψ epi , and that 170 Yb is affected by only Ψ th .How should this inconsistency be interpreted?One of the ideas to explain this issue is the estimation of σ epi by Eq. ( 2).In this study, σ epi is simply calculated from Eq. ( 2) based on individual RI and E max values.The measured isotopic data of 170 Yb/ 174 Yb suggest that epithermal neutrons did not interact sufficiently with 169 Tm.The resonance region of the neutron-capture cross section for 169 Tm is wider (0.1 < RI < 2000 eV) than that of 168 Yb (0.5 < RI < 200 eV); therefore, if the energy distribution of epithermal neutrons at the lunar surface is deviated to the lower energy region rather than 2000 eV, the effective σ epi for 169 Tm should be less than our estimation.If the energy of most neutrons arising on the lunar surface does not reach 2000 eV, the effective cross section of 169 Tm should be estimated to be less than 1.95 × 10 2 barn.
In the current situation, it is experimentally unclear whether the 170 Yb isotope reacts sufficiently with epithermal neutrons.Through the isotopic study of the A-15 regolith core, Ψ is estimated to be of the 10 16 order (Russ et al. 1972;Hidaka et al. 2000).In the second example, it is interesting to consider the relationship between Ψ, σ th , and σ epi for the Oklo natural reactor materials.The total neutron fluences of the Oklo reactors, including thermal and epithermal neutrons, are estimated to be in the range of 10 20 to 10 21 n cm −2 (Holliger and Devillers 1981;Gauthier-Lafaye et al. 1996;Hidaka and Holliger 1998).The isotopic variations of 168 Yb and 170 Yb can be clearly shown in the Oklo natural reactor materials.In the case of the Oklo reactor samples, their isotopic variations are so large that it is convenient to discuss using isotopic ratios instead of ε-notation.

Yb isotopic data of the Oklo natural fission reactor
The Oklo uranium deposit in the Republic of Gabon, Central Africa, is known as a fossil of natural fission reactor.The isotopic compositions of many elements have varied with the occurrence of several types of nuclear reactions in the reactor zones.Two major reactions occurred in the Oklo reactors: a fission reaction mainly of 235 U induced by thermal neutrons and the neutron-capture reactions of many nuclides existing in the reactor with neutrons released by the fission reactions.The neutron fluences arising in the Oklo reactors are quantitatively estimated to be 10 20 -10 21 n cm −2 (Gauthier- Lafaye et al. 1996;Hidaka and Holliger 1998).Since the nuclides with mass numbers 130 to 150 corresponding to lighter to middle REEs such as La, Ce, Pr and Nd have high fission product yields by fission reactions, significant amounts of fissiogenic components were produced and mixed with originally existing components that had been included since the ore formation.As a result, isotopic compositions of lighter to middle REEs vary not only with the contribution of neutron-capture reactions but also with the contribution of fission reactions.On the other hand, isotopic compositions of heavier REEs like Er, Yb, and Lu in the Oklo reactor materials were affected mainly by neutroncapture reactions because of the extremely low fission product yields of the nuclides with mass numbers over 150 belonging to Er, Yb and Lu.The isotopic composition of Yb from the Oklo reactor materials is the best example of the isotopic shifts associated with neutron-capture reactions under intensive neutron irradiations.
In previous studies, Yb isotopic analyses were performed on nine samples collected from several locations of the natural fission reactors (Holliger and Devillers 1981;Hidaka and Holliger 1998).The results of 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios for the nine samples are listed in Table 3.All nine samples have clear variations of the depletion of 168 Yb and the excess of 170 Yb for individual samples, although 168 Yb/ 174 Yb isotopic ratios for six of nine samples show the detection limits below 0.001 because of the intense depletions of 168 Yb isotope.The Ψ values of individual reactor samples were already obtained from previous studies; hence, the 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios could be simulated by substituting the estimated Ψ values into Eqs.( 6) and ( 7).The Ψ values used for the calculation are also listed in the table.As a result of the calculation, any Ψ values used for the calculation were insufficient to satisfy the isotopic variations of both 168 Yb and 170 Yb.The difference between the measured and calculated isotopic variations of both 168 Yb and 170 Yb for each sample is considered to be corrected by the addition of the Ψ epi value.The additional Ψ epi values to satisfy the variations of 168 Yb and 170 Yb for individual samples are calculated based on Eqs. ( 6) and ( 7).The results are listed in Table 3.
In the Oklo studies, the neutron-capture reaction of 143 Nd has been conventionally used to estimate the neutron fluence arising in the reactor (Ruffenach et al. 1976).In this estimation of the neutron fluence, the proportion of epithermal neutrons to thermal neutrons has been quantified as a neutron spectrum index.Previous studies suggested that the neutrons generated in the Oklo reactors were well-thermalized and that the thermalized neutrons worked sufficiently to sustain the criticality for fission.As shown in Table 3, the proportion of Ψ epi to Ψ by conventional method was at least 10%.However, according to our calculation in this study, the isotopic variations of both 168 Yb and 170 Yb cannot be produced only from the Ψ estimated by previous studies, but require additional neutron-capture reactions supported by an additional amount of Ψ epi .
In this study, the evaluations of Ψ th and Ψ epi for the Oklo reactor materials only from the Yb isotopic data were examined as a new attempt.The data for the 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios listed in Table 3 were substituted into Eqs.( 6) and ( 7).As a result, the neutron fluences of Ψ th = (1.3-3.0)× 10 20 and Ψ epi = (2.1-7.3)× 10 18 n cm −2 are evaluated for three of nine samples, SC55, KN245, and KN250.On the other hand, the neutron fluences of the other six samples cannot be fixed because of a lack of the proper 168 Yb/ 174 Yb ratios.These isotopic data were given by classic mass spectrometric techniques more than 25 years ago.Assuming the 168 Yb/ 174 Yb isotopic ratios of the Oklo reactor materials can be determined precisely, the isotopic variations of the pair of 168 Yb and 170 Yb may be Table 3 The results of calculated 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios from the estimated neutron fluences (Ψ:10 20 n cm −2 ) and calculated neutron fluences from the measured Yb isotopic ratios for nine of the Oklo natural reactor materials STD means a standard reference materials of Yb Ψ th and Ψ epi are expressed in 10 20 (n cm −2 ) unit a The data for the estimated Ψ th and Ψ epi , and measured isotopic ratios of 168 Yb/ 174 Yb and 170 Yb/ 174 Yb are given by Holliger and Devillers (1981) and Hidaka and Holliger (1998) b The isotopic ratios were calculated by substituting the estimated Ψ th and Ψ epi into Eqs.( 6) and ( 7) c The neutron fluences were calculated by substituting the measured 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios into Eqs.( 6) and ( 7)  used as the dosimetry for Ψ th and Ψ epi .The Yb isotopic variation of the sample SD37 and its relationship with the neutron fluences is of particular interest, because SD37 locating at the reactor zone 13 at Oklo is considered to have experienced the highest neutron including fast neutrons studied from some isotopic studies (Meshik et al. 2004;Groopman et al. 2018;Hidaka et al. 2023).

Development of precise isotopic measurements of Yb
For the chemical separation of Sm, Gd, Er and Yb, an Ln-resin packed column (particle size of 20-50 mm, column volume of 0.5 mL, column size of 110 mm-length and 2.5 mm-diameter) was used in this study.Figure 2 shows the elution behaviors of individual REEs from Sm to Lu after several adjustments to achieve better conditions.The purifications of Sm, Gd, Er, and Yb are much improved by the complete separation of isobaric interferences as well as the other elements as much as possible.
The recovery yields of Sm, Gd, Er, and Yb are more than 98%.The detailed procedures for the collection of Sm, Gd, Er and Yb are given in Table 4.
Table 5 shows a preliminary result of comparison for the Yb isotopic data set collected by the use of all nine 10 11 Ω resistor amplifiers and the use of two 10 13 Ω resistor amplifiers plus seven 10 11 Ω resistor amplifiers.In addition to the results of 5 repeated analytical runs of Yb standard material (1000 mg/L of single-element standard solution for the ICP-MS and ICP-AES analyses provided by SPEX CertiPrep), their analytical uncertainties of the average values are shown in 2SD (standard deviation) in the table.As a result of a simple comparison between two data sets, the analytical precisions for 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios using 10 13 Ω resistor amplifiers show about five and two times better, respectively, than those by the conventional method.Assuming these analytical precisions can be practically reproduced for planetary materials, the neutron fluence of Ψ > 2 × 10 16 n cm −2 can be detectable.While the Table 4 The procedures of column chemistry for the separation of Sm, Gd, Er and Yb use of 10 13 Ω resistor amplifiers has the advantage to enhance the abundance sensitivity for the detection of small ion beam like 168, 170 Yb isotopes, it has disadvantage to reduce the precision of gain factors of 10 11 Ω resistor amplifiers for the detection of other five 171,172,173,174,176 Yb isotopes because of the replacement of conventional gain calibration board supplying a current of 330 pA into a new one supplying 3.3 pA.In addition, significant time variations of the electronic baseline noise and relative gain factors during a few months after the installation are also reported (Torrano et al. 2023).Further studies are required to achieve higher precision of 168 Yb/ 174 Yb and 170 Yb/ 174 Yb isotopic ratios.

Summary
Several nuclear reactions that occurred in nature have been applied for the characterization of planetary materials.In this paper, isotopic variations caused by neutroncapture reactions were examined from the viewpoint of the interaction of cosmic-ray with planetary surfaces in space.The combination of isotopic shifts of 149 Sm-150 Sm, 157 Gd-158 Gd and/or 167 Er-168 Er in association with neutron-capture reactions has been used to estimate the neutron fluence and energy balance between thermal and epithermal neutrons.The results can be effectively used to understand the CRE history and situations for individual planetary materials.Although it is still in the process of developing precise isotopic measurement of Yb, the possibility and potential of effective use of Yb isotopic variations in association with neutron-capture reactions are quantitatively discussed from the numerical simulation using isotopic data from the A-15 lunar regolith and the Oklo natural reactor materials.

Fig. 1
Fig.1Correlation diagrams a between 149 Sm/ 152 Sm and 150 Sm/ 152 Sm (Sm three-isotope plot) and b between 157 Gd/ 160 Gd and 158 Gd/ 160 Gd (Gd three-isotope plot) for a series of lunar regolith samples collected from the A-15 drill stem.The isotopic data are given byHidaka et al. (2000) Yb/ 174 Yb and (b)170 Yb/ 174 Yb between measured and calculated values for seven of lunar regolith materials from the A-15 drill stem STD means standard reference materials of Yb a The data fromHidaka et al.(2020)

Fig. 2
Fig.2Elution behaviors of individual REEs by 7-step of sequential separation using an Ln-resin packed column with HCl.The method partialy modified previous study byMizutani et al. (2020)

Table 1
The data for neutron-capture reactions of the selected nuclides in this study aThe epithermal cross section (σ epi ) is calculated from the Eq.(2) (see text) with the parameters RI and ε max in the table σ th (barn) RI (barn) E max (eV) σ epi (barn) a

Table 5
Comparison of the data sets for Yb isotopic ratios collected from two different methods The numbers of uncertainties for individual analytical runs are shown as 2SE The numbers of uncertainties for the average values are shown as 2SD *Use of 10 11 Ω resistor amplifiers for detection of all Yb isotopes **Use of two 10 13 Ω resistor amplifiers for detection of 168 Yb and 170 Yb isotopes and use of seven 10 11 Ω resistor amplifiers for detection of other five Yb isotopes and two background