Evaluation of neutron nuclear data for Technetium-99

Abstract

Neutron nuclear data of ⁹⁹Tc was evaluated, considering cross-sections and spectra provided from recent experiments. The evaluation was made in the incident neutron energy range from 1 keV to 20 MeV, using the optical model and nuclear reaction models. The optical model calculation based on the coupled-channels method was performed for the interaction of neutrons with ⁹⁹Tc, and potential parameters appropriately chosen reasonably explain the measured data of total cross-section. The cross-section of inelastic scattering, capture, (n, 2n), (n, p), (n, α) and (n, n′α) reactions, and γ-ray emission spectra were calculated on the basis of statistical model with preequilibrium and direct components, and they were compared with available experimental data. It is found that the presently evaluated cross-sections and γ-ray emission spectra well reproduce those experimental values and that there is a large discrepancy among the present result and evaluated data for neutron emission spectra. The obtained capture cross-section increases at the energies below 1 MeV, relative to that in JENDL-4.0. This makes the transmutation efficiency of ⁹⁹Tc into stable ¹⁰⁰Ru by accelerator driven system enhanced. The production cross-section of ⁹⁹Mo important for the medical use of nuclear diagnostics reduces by 5–30% at the energies above 12 MeV, compared with JENDL-4.0.

Keywords :

• evaluation
• neutron nuclear data
• cross-section
• spectrum
• fission product
• Technetium-99
• radioactive waste
• Molybdenum-99
• nuclear diagnostics
• Maxwellian-averaged capture cross-section

1. Introduction

Technetium-99 is a radioactive fission product with a large cumulative fission yield of about 6% [1] in fission reactors. For long half-life of its ground-state (T _1/2 = 2.11 × 10⁵ years), it is regarded as one of the interesting targets for the nuclear transmutation by neutron capture reaction because the transmuted ¹⁰⁰Tcwith short half-life of 15.46 s soon β -decays into stable ¹⁰⁰Ru.

A metastable isomer of ⁹⁹Tc with T _1/2 = 6.015 h, ^99m Tc, is excited to the nuclear level with excitation energy E_x  = 142.68 keV, and it is of great interest to themedical use of nuclear diagnostics. However, its half-life is too short to carry ^99m Tc far from production sites, and to inject it into patients. From the viewpoint of transportation, radioactive ⁹⁹Mo is a useful nuclide since ^99m Tc is the daughter nuclide of ⁹⁹Mo with T _1/2 = 65.94 h. Molybdenum-99 has been generated by the fission reaction on highly enriched uranium at nuclear reactors. Furthermore, the production of ⁹⁹Mo by capture reactions on ⁹⁸Mo with reactor neutrons is now planned in the Japan Materials Testing Reactor of Japan Atomic Energy Agency (JAEA). In contrast to the production methods related with nuclear reactors, it is considered that ⁹⁹Mo can be created by ⁹⁹Tc(n, p) reaction with fast neutrons from accelerators [2], using ⁹⁹Tc extracted from radioactive waste in fission reactors as target material.

In JENDL, significant revision of nuclear data for ⁹⁹Tc was made for the development of JENDL-3.3 [3]. Hence, the revision in the update to JENDL-4.0 [1] was limited to a change in the neutron width of a negative resonance. The γ-ray production data were not included in the course of those revisions. After the release of JENDL-3.3, capture γ-ray spectra and capture cross-sections were simultaneously measured by anti-Compton NaI(Tl) spectrometer at Tokyo Institute of Technology [4]. Thus, it is now possible to make a reliable evaluation of the γ-ray production data. It should be noted that the ⁹⁹Tc data in ENDF/B-VII.0 [5,6] and JEFF-3.1.1 [7] were recently updated with the inclusion of γ-ray production data.

The objective of this work is to update the nuclear data (cross-sections, angular distributions, and energy spectra) of ⁹⁹Tc by taking account of information previously not available. In particular, important is the evaluation of capture cross-section in the keV to MeV region for the nuclear transmutation by accelerator driven system (ADS). The revision of ⁹⁹Tc(n, p) reaction cross-section is also requisite by means of recent experimental data, in order to accurately estimate the produced amount of ⁹⁹Mo by fast neutrons. Section 2 explains evaluation method and tools. The calculated results are presented and compared with evaluated and available experimental data in Section 3. The conclusion of this evaluation is described in Section 4.

2. Evaluation method

In this evaluation all reactions, which emit neutrons, protons, deuterons, tritons, ³He, α-particles and γ-rays, were considered if the reaction channels were opened up to 20 MeV. The calculation of neutron-induced reaction cross-sections was done by theoretical nuclear reaction calculation code, CCONE [8]. Although the upper energy of the resolved resonance region was 6 keV in JENDL-4.0, the energy range of the incident neutron was considered from 1 keV to 20 MeV in this work. The lower energy limit presently assumed will be replaced by an up-to-date upper limit of resolved resonance region, when the results of this work are compiled into an ENDF-formatted file [9]. The theoretical models used to calculate the reaction cross-sections were almost the same as those in the previous evaluation of neutron nuclear data for Zn [10] and Cs [11] isotopes. However, since there were a few modifications for the present work, the current setup is described in this section.

2.1. Optical model

Basically, the parameters of optical model potential (OMP) for particle emissions were taken from global OMPs of Koning and Delaroche [12] for neutron and proton, Lohr and Haeberli [13] for deuteron, Becchetti and Greenlees [14] for triton and ³He, and Mcfadden and Satchler [15] for α-particle, but different OMPs were also used for better evaluation as follows.

For neutron OMP of target ⁹⁹Tc the coupled-channels (CC) optical model based on the rigid rotator model in CCOM code [16] was employed to evaluate the total cross-section and to obtain the neutron transmission coefficient which was applied to statistical model calculation. In the CC calculation the 9/2⁺ ground-state was coupled with the 11/2⁺ (E_x  = 726.76 keV), 13/2⁺ (E_x  = 761.95 keV) and 15/2⁺ (E_x  = 1526.48 keV) levels. The value of deformation parameter was chosen to be 0.20, whose value is consistent with that of surrounding even–even nuclides derived by Raman et al. [17]

The functional forms of the OMP were taken from Kunieda et al. [18]. The OMP was composed of the realvolume, imaginary surface, imaginary volume, real spin-orbit and imaginary spin-orbit terms. The real volume V_R and imaginary surface W_D terms are given by the following forms:

where Z, N, and A are the numbers of proton, neutron, and nucleon in the target nucleus, respectively. E ^† is theincident neutron energy relative to the Fermi one. V_R ^(0–3), V_R ^DISP , W_D ^DISP , WID_D , C _viso , C _wiso , λ _R,D , R _R,D,V and a _R,D,V are the OMP parameters. Some of them were modified in order to obtain better agreement with measured total cross-sections [19]. The used parameter values are summarized in Table1 . The forms and parameter values of OMP for the other terms were the same as those provided in Kunieda et al.

Table 1. Values of neutron OMP parameters for real volume and imaginary surface terms for ⁹⁹Tc.

= −34.31 MeV

= 0.027

= 1.2 × 10^−4 MeV^−1

= 3.5 × 10^−7 MeV^−2

= 94.88 MeV

C viso  = 24.3 MeV

λR  = 6.51 × 10^−3 MeV^−1

= 11.17 MeV

WIDD = 11.90 MeV

C wiso  = 18.0 MeV

λD = 0.014 MeV^−1

R R,D,V  = 1.21 A ^1/3 fm

a R,D,V  = 0.669 fm

The resulting neutron total cross-section in the energy range from 10^–2 to 20 MeV is shown with theexperimental data of Foster and Glasgow [19] and evaluated data of JENDL-4.0, ENDF/B-VII.0, andJEFF-3.1.1 in Figure 1a . The large discrepancy is found among the present result and the evaluated data in the range of 10⁻² to 2 MeV where no experimental information has been obtained yet, and thus, efforts of measurement are expected to resolve this situation. Figure 1b enlarges the energy range of 1–20 MeV in Figure 1a for a detailed comparison. The result obtained with the adjusted OMP parameters better reproduces the measured cross-sections than JENDL-4.0.

Figure 1. Total cross-sections for ⁹⁹Tc in the energy ranges (a) from 10⁻² to 20 MeV and (b) from 1 to 20 MeV.

For proton and α-particle emission from Tc isotopes, the OMPs of Perey [20] and Mcfadden and Satchler [15], respectively, were adopted with modified diffuseness parameters of real volume potential, which were changed to 0.52 and 0.45 fm for the proton and α-particle OMPs, respectively. For neutron emissions from ^95,97,99Mo the local potentials of Koning and Delaroche [12] were applied.

2.2. Preequilibrium model

The contributions of the preequilibrium process to the reaction cross-section were calculated by applying the two-component exciton model [8]. The global parameterization [21] for the exciton model was adopted. In this prescription the neutron single-particle state density of ¹⁰⁰Tc was multiplied by a factor 1.07, which was determined from comparisons with measured cross-sections.

The particle pickup and knockout processes [22] were also included in this evaluation, in order to take into account an additional contribution to the cross-section of (n, α) reaction. The contribution of knockout process was enhanced by a factor of 5.1 to reproduce available experimental data [23,24] of the ⁹⁹Tc(n, α) reaction cross-section.

The γ-ray emission channel from preequilibrium process was taken into consideration to simulate the direct and semi-direct capture reactions [25].

2.3. Statistical model

The statistical model in the CCONE code was based on the Hauser-Feshbach formalism [26] with width fluctuation correction [27].

2.3.1. Nuclear level density

The data of discrete levels (excitation energy, spin-parity and γ-branching ratios) were taken from Reference Input Parameter Library, RIPL-3 [28]. The nuclear level density was adopted from the formulation by Gilbert and Cameron [29]. This prescription assumed the constant temperature model for lower excitation energies and the Fermi gas model for higher excitation energies, in order to describe the level density above the highest energy E_c of the adopted discrete levels. The level density in the constant temperature model ρ_T is expressed by

where T is the nuclear temperature, U is the excitation energy corrected by the paring energy Δ. The parameters T and E ₀ were fixed when the constant temperature model matched smoothly with the Fermi gas model at an excitation energy E_m , and with the discrete levels. The pairing energy and the level density parameter a in the Fermi gas model were taken from Mengoni and Nakajima [30]. The latter has an energy dependence characterized by an asymptotic value a*. In this work the parameter a* was adjusted so as to get better agreement with an average level spacing of s-wave neutron resonances which was derived from experiments. If there were no experimental data available, a systematics for a* was employed from Mengoni and Nakajima. The shell correction energy E_sh was calculated as the difference between experimental mass [31] and the mass derived from empirical formula [32]. Table 2 summarizes the values of parameters used for the present level density formulation.

Table 2. Parameter values in the level density formula.

Nucleus	a* (1/MeV)	Δ (MeV)	E sh (MeV)	T (MeV)	E 0 (MeV)	Em (MeV)	Ec (MeV)
^100Tc	13.416	0.000	3.026	0.656	–1.965	4.467	0.711
^99Tc	12.177	1.206	2.480	0.842	–2.089	7.844	1.329
^98Tc	12.575	0.000	1.596	0.798	–2.610	5.916	0.714
^97Tc	11.968	1.218	0.908	0.954	–2.588	9.301	1.393
^99Mo	13.000	1.206	3.378	0.720	–1.426	6.548	1.405
^98Mo	12.500	2.424	2.453	0.768	–0.152	8.019	2.768
^97Mo	12.700	1.218	1.700	0.760	–1.082	6.610	1.848
^97Nb	11.968	1.218	2.742	0.595	0.404	4.170	2.113
^96Nb	12.000	0.000	1.864	0.535	–0.249	2.047	1.368
^95Nb	11.759	1.231	1.724	0.754	–0.545	5.985	1.710

2.3.2. Gamma-ray strength function

The standard Lorentzian form was adopted for γ-ray strength function of E1 radiation. The parameters for electric giant dipole resonance (GDR) were determined so as to reproduce measured capture γ-ray spectrum [4] for ⁹⁹Tc. It was found that additional small E1 resonances around 6 and 1 MeV were needed to explain the shape of spectra. The former resonance may be called pygmy one. One of the reasons for introduction of the latter correction might be attributed to the insufficient knowledge of nuclear level for¹⁰⁰Tc. The parameters determined for GDR and additional small resonances were listed in Table 3 . The parameters for GDR and so-called pygmy resonance were also applied to other Tc isotopes. The strength functions for the M1 and E2 radiations were adopted from the prescriptions by Kopecky and Uhl [33]. The calculated capture cross-section was normalized to experimental data [4] by multiplying the γ-ray strength function by a factor 0.76. The resulting γ-ray strength function for s-wave resonances in units of 10⁻⁴ is 105.5, being consistent with the compiled ones of Mughabghab [34] (108 ± 8) and RIPL-3 (100 ± 14). The obtained result for capture cross-section will be shown in Section 3.1.

Table 3. Resonance parameters for E1 radiation.

	Er (MeV)	Γ r (MeV)	σ r (mb)
GDR	15.8	5	190
Pygmy	6	2	4
Correction	1	2.5	0.25

3. Evaluated results

In this section, the calculated reaction cross-sections, and γ-ray and neutron emission spectra are compared with measurements and major evaluated nuclear data libraries (JENDL-4.0, ENDF/B-VII.0, and JEFF-3.1.1).

3.1. Capture cross-section

Figure 2a represents the evaluated cross-section of capture reaction with the data of JENDL-4.0, ENDF/B-VII.0, JEFF-3.1.1 and experiments [4,35–39] in the energy range of 10⁻³ to 20 MeV. The present result, ENDF/B-VII.0 and JEFF-3.1.1 show good agreement with the recent data of Matsumoto et al. [4] and Kobayashi et al. [39] as shown in Figure 2b. In contrast, JENDL-4.0 reproduced the cross-section measured by Macklin [38], whose data are found to be smaller than the recent ones. At the higher energy of 14.7 MeV Qaim [35] reported the cross-section of 9 ± 2 mbarn. JENDL-4.0 gives large cross-sections above 10 MeV so as to explain his datum. However, Qaim noted that the large cross-section might result from the contamination of low energy neutrons. The present data, therefore, were evaluated without reference to that of Qaim, but with a small bump around 14 MeV which is caused by the direct and semi-direct capture reactions.

Figure 2. Cross-sections of capture reaction on ⁹⁹Tc in the energy ranges (a) from 10⁻³ to 20 MeV and (b) from 10⁻³ to 1 MeV.

The Maxwellian-averaged cross section (MACS) ofcapture reaction was calculated, combining the resolved resonance data of JENDL-4.0 at 6 keV as shown in Figure 3 , in which also given is the MACS derived from the capture cross-section in JENDL-4.0. It is found that the present result is consistent with the data of Gunsing et al. [40], who obtained the MACS based on a capture experiment in an unresolved resonance region. The calculated MACS is enhanced by 11% at 10 keV and 16% at 30 keV in comparison with that in JENDL-4.0 which is in fairly good agreement with previous data of Winters and Macklin[41]

Figure 3. Maxwellian-averaged cross sections of capture reaction on ⁹⁹Tc.

3.2. (n, p) Reaction cross-section

The cross-sections of ⁹⁹Tc(n, p) reaction are illustrated in Figure 4 . Recently, Reimer et al. [24] measured the cross-sections in a wide energy range of 8–20 MeV. The present result as well as ENDF/B-VII.0 and JEFF-3.1.1 reasonably reproduces their data. However, experimental data [23,24,35,42] at around 14 MeV provided somewhat larger cross-sections, compared with the present evaluation. JENDL-4.0 only gives cross-sections reasonable to explain the large ones. As a result, the produced amount of ⁹⁹Mo is by 5–30% smaller than that in the JENDL-4.0 in the energy range between 12 and 20 MeV, whose range isinterested in transmutation of ⁹⁹Tc in radioactive waste into medically useful ⁹⁹Mo by D-T neutrons.

Figure 4. Cross-sections of ⁹⁹Tc(n, p) reaction.

3.3. Other reaction cross-sections

The production cross-sections of metastable isomer (E_x  = 142.68 keV) by inelastic scattering are calculated and compared to JEFF-3.1.1 and experimental data [23,24,35,43,44] in Figure 5 . In order to explain the measured cross-sections, DWBA calculation to 142.68 keV-level using neutron local OMP [12] for ⁹⁹Tc was performed with angular momentum transfer L = 4 and normalization parameter β′ = 0.14. The calculated result is in good agreement with the measured data, although Reimer et al. [24] provided somewhat smaller cross-sections below 5 MeV with respect to the present evaluation and JEFF-3.1.1. It is found that the measured cross-section of Qaim [35] is large relative to those of Reimer et al.

Figure 5. Cross-sections of inelastic scattering on ⁹⁹Tc. Production cross-sections of 142.68 keV-level in present and JEFF-3.1.1 data are compared with experimental ones [23,24,35,43,44].

Figure 5 also shows the calculated cross-sections ofinelastic scattering on ⁹⁹Tc along with the data of Qaim [35], JENDL-4.0, ENDF/B-VII.0 and JEFF-3.1.1. The cross-section reported by Qaim at 14.7 MeV was not directly based on his experiment, and was deduced from the nuclear structural similarity between ⁹⁹Tc-^99m Tc and ⁹³Nb-^93m Nb systems. The present evaluation gives smaller cross-section than the datum, while ENDF/B-VII.0 reasonably explains the derived value. In contrast, JENDL-4.0 has much larger cross-section above 12 MeV.

Figure 6 compares the calculated cross-sections of ⁹⁹Tc(n, 2n) reaction with JENDL-4.0, ENDF/B-VII.0, JEFF-3.1.1 and the result of Qaim [35]. JENDL-4.0 has a small cross-section at 14 MeV. This is due to the normalization to the cross-section presented by Qaim. It should be, however, noted that the (n, 2n) reaction cross-section of Qaim was based on some estimations. The cause of the small cross-section comes from the deduced large one of inelastic scattering. The present evaluation and JEFF-3.1.1 have similar excitation function and give almost same cross-section (1.52 barn) at 14 MeV.

Figure 6. Cross-sections of ⁹⁹Tc(n, 2n) reaction.

The cross-section obtained for ⁹⁹Tc(n, α) reaction is compared with measured ones [23,24,35,42–44] and evaluated data in Figure 7 , and it is consistent with the data measured by Reimer et al. [24] and Ikeda et al. [23]. The experiments by Qaim [35], Goldstein [43] and Filatenkov and Chuvaev [42] give relatively larger cross-sections in comparison with evaluated data. JEFF-3.1.1 has an excitation function which is different from the present result and other evaluations.

Figure 7. Cross-sections of ⁹⁹Tc(n, α) reaction.

Figure 8 represents the calculated cross-section of⁹⁹Tc(n, n′α) reaction together with measured ones [23,35,44] and evaluated data. The present result is consistent with the upper limit given by Golchert et al. [44] and with the data of Ikeda et al. [23]. The cross-sections in evaluated data are also almost reasonable, compared with the experimental data at around 14MeV. Including the cross-section in this evaluation, they, however, show a difference by 10 mbarn at 20MeV.

Figure 8. Cross-sections of ⁹⁹Tc(n, n′α) reaction.

3.4. Emission spectra

While the present evaluation considered the emission spectra of neutron, proton, deuteron, triton, ³He, α-particle and γ-ray, the evaluated results of capture γ-ray and neutron emission spectra are given in this section.

The calculated capture γ-ray spectra are compared in Figure 9 with the experimental values of Matsumoto et al. [4], who measured the spectra with incident neutron energies of 8-90 (average: 45), 190, 330 and 540 keV. The present result with supplemental two small E1 resonances listed in Table 3 reasonably reproduces the measured capture spectra. The spectra with 45 and 540 keV neutrons evaluated in ENDF/B-VII.0 and JEFF-3.1.1 are also plotted in Figure 9. ENDF/B-VII.0 shows almost flat spectra in the energy range from 0.5 to 3–4 MeV, and then, rapid decrease above 3–4 MeV. In JEFF-3.1.1 the spectra at lower emission energies are in agreement with the measurement. However, the deviation from the experimental values becomes large with increasing γ-ray energies. It should be noted that JENDL-4.0 does not contain the γ-ray production data.

Figure 9. Capture γ-ray spectra on ⁹⁹Tc. The measured data represented by solid and open circles are taken from Matsumoto et al. [4]. The spectra at 45 and 540 keV in evaluated data of ENDF/B-VII.0 and JEFF-3.1.1 are included for comparison.

The calculated neutron emission spectrum at 14MeV is plotted with those of evaluated data in Figure 10 . There has been no experimental information yet. Hence, it is found that the present calculation shows a significant difference from the spectra of evaluated data. In JENDL-4.0, the spectrum has anunreasonable gap at 5 MeV, below which the contribution of neutrons emitted in (n, 2n) reaction is important. The main reason of this shape is that thecross-section of (n, 2n) reaction at 14 MeV was adjusted to a value of 1.23 barn, which is very small in comparison with the presently derived cross-section as seen in Figure 6. ENDF/B-VII.0 provides spectrum larger than the present evaluation in the energy range from 3 to 12.5 MeV. This result indicates that the contribution of neutrons emitted from the preequilibrium process is larger in the ENDF/B-VII.0 evaluation. JEFF-3.1.1 gives an emission spectrum similar to the present one below 5 MeV, while in 5-12.5 MeV the preequilibrium process shows a larger contribution than in the present evaluation. It should be noted that a pseudo resonance in continuum level is assumed both in ENDF/B-VII.0 and JEFF-3.1.1, but its presence and strength remain still uncertain.

Figure 10. Neutron emission spectra on ⁹⁹Tc with 14 MeV neutron.

4. Conclusion

The neutron nuclear data of ⁹⁹Tc were evaluated in the incident neutron energy range from 1 keV to 20 MeV, taking into account recently measured data. Theevaluation was performed by using the CC optical model code, CCOM, and nuclear reaction calculation code, CCONE. The optical model calculation with the adjusted OMP parameters reproduces the available experimental data of total cross-section. The statistical model calculations including the contributions of preequilibrium and direct processes were carried out to obtain the reaction cross-sections and spectra of neutron, proton, deuteron, triton, ³He, α-particle and γ-ray emissions.

The present evaluation made use of the measured data for cross-sections of inelastic scattering, capture, (n, 2n), (n, p), (n, α), and (n, n′α) reactions, and for γ-ray spectra. The calculated cross-sections reasonably explain the experimental values. In comparison with JENDL-4.0, the resulting capture cross-section is enhanced below 1 MeV. In particular, it is larger by over 10% below 200 keV. This result indicates that thetransmutation of ⁹⁹Tc into stable ¹⁰⁰Ru by ADS becomes efficient, relative to the estimation based on the data of JENDL-4.0. The reliable ⁹⁹Tc(n, p) reaction cross-section is required to estimate the produced amount of ⁹⁹Mo which β-decays into ^99m Tc, with T _1/2 = 65.94 h. The present calculation gives smaller cross-sections than those in JENDL-4.0. This result leads to the reduction in the production efficiency of ⁹⁹Mo if T(d, n) reaction is considered as neutron source.

The γ-ray emission spectra were evaluated by comparing the present calculation with the capture γ-ray spectra of Matsumoto et al. [4] measured in theincident energy range from 8–90 to 540 keV. The obtained results nicely reproduce the measurements. Itis found that the difference in neutron emission spectra between the calculated result and evaluated data at 14MeV is significant in the secondary energy range from 3 to 12.5 MeV. Hence, experimental work is needed to resolve the disagreement.

The presently evaluated nuclear data of ⁹⁹Tc including γ-ray emission spectra will be available withup-to-date resolved resonance parameters in the ENDF-6 format.

Acknowledgments

The author would like to thank Dr. T. Matsumoto of The National Institute of Advanced Industrial Science and Technology (AIST) for sending the measured capture γ-ray spectrum data. The author is also grateful to the members ofNuclear Data Center, JAEA, for valuable comments.