Cross section measurements on zirconium isotopes for ~14 MeV neutrons and their theoretical calculat

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1.Introduction

Zirconium metal and its alloys are widely used in national defense, aerospace, atomic energy, and other fields owing to their excellent physical and chemical properties. Accurate nuclear reaction cross sections on zirconium isotopes around 14 MeV neutrons are crucial for the development of nuclear weapons, development and utilization of nuclear energy, application of nuclear technology, etc. Therefore, these cross sections of (n,2n), (n,α), (n,p), (n,d), and (n,γ) reactions on zirconium isotopes around 14 MeV neutrons have been studied by numerous researchers worldwide and can be found in the experimental nuclear reaction data (EXFOR) library [1]. However, the cross section of the ⁹⁴Zr(n,d*)^93m+gY [d*= d+(n+p), similarly hereinafter] reaction has been measured by only two groups at single neutron energies of 14.7 MeV or 14.1 MeV, and there is a large difference between the two values obtained, which are 2.43 ± 0.21 mb [2] and 0.8 ± 0.1 mb [3], respectively. For the ⁹⁶Zr(n,γ)⁹⁷Zr reaction, the cross section has been measured by more than 20 groups [1]; however, three of them were induced by neutrons through the D-T reaction [4-6], and there are significant differences in those data, the maximum difference between them being more than a factor of 30. Thus, it is necessary to measure them again and provide their excitation functions. In this work, the cross sections of the ⁹⁴Zr(n,d*)^93m+gY and ⁹⁶Zr(n,γ)⁹⁷Zr reactions have been measured in the neutron energy range of 13.5-14.8 MeV via the activation technique. At the same time, combined with the theoretical models of nuclear reactions, the computations of the excitation functions of the above-mentioned two nuclear reactions were conducted by adopting the nuclear theoretical model program system Talys-1.9 [7]. Their excitation curves were acquired in the neutron energy range from the threshold to 20 MeV. In addition, the cross sections of the ⁹⁶Zr(n,2n)⁹⁵Zr, ⁹⁰Zr(n,α)^87mSr, ⁹⁴Zr(n,α)⁹¹Sr, ⁹⁰Zr(n,p)^90mY, ⁹²Zr(n,p)⁹²Y, and ⁹⁴Zr(n,p)⁹⁴Y reactions of ~14 MeV neutrons were measured, and their excitation curves in the neutron energy range from the threshold to 20 MeV were acquired. The cross sections obtained are compared with earlier experiments by other researchers and with the theoretical results obtained by Talys-1.9.

reaction	abundance of target isotope (%)	product nuclides	T_1/2	E_γ/keV	I_γ (%)
⁹⁴Zr(n,d*)	17.38	^93m+gY	10.18 h	266.9	7.4
⁹⁶Zr(n,γ)	2.8	⁹⁷Zr	16.749 h	743.36	93.09
⁹⁶Zr(n,2n)	2.8	⁹⁵Zr	64.032 d	756.725	54.38
⁹⁰Zr(n,α)	51.45	^87mSr	2.815 h	388.531	82.19
⁹⁴Zr(n,α)	17.38	⁹¹Sr	9.65 h	1024.3	33.5
⁹⁰Zr(n,p)	51.45	^90mY	3.19 h	479.51	90.74
⁹²Zr(n,p)	17.15	⁹²Y	3.54 h	934.47	13.9
⁹⁴Zr(n,p)	17.38	⁹⁴Y	18.7 m	918.74	56
⁹³Nb(n,2n)	100	^92mNb	10.15 d	934.44	99.15

reaction	the measured cross sections (in mb) at various neutron energies (in MeV) literature values E_n/MeV, σ/mb
⁹⁴Zr(n,d*)^93m+gY	1.15±0.06	1.19±0.06	1.93±0.09	2.17±0.10
⁹⁶Zr(n,γ)⁹⁷Zr	2.33±0.10	2.24±0.09	1.85±0.09	1.84±0.08
⁹⁶Zr(n,2n)⁹⁵Zr	1502±63	1520±66	1521±68	1577±70
⁹⁰Zr(n,α)^87mSr	2.9±0.2	3.1±0.2	3.6±0.2	3.6±0.2
⁹⁴Zr(n,α)⁹¹Sr	3.86±0.16	4.10±0.18	4.77±0.20	5.09±0.22
⁹⁰Zr(n,p)^90mY	9.8±0.4	10.1±0.5	11.4±0.5	11.1±0.5
⁹²Zr(n,p)⁹²Y	17.2±0.7	17.8±0.8	21.4±0.9	20.2±0.9
⁹⁴Zr(n,p)⁹⁴Y	5.2±0.3	6.5±0.3		7.3±0.4

4.Results and discussion

In our work, the errors stem mainly from the counting statistics (0.2%-5.7%), standard cross section (1.1%-1.5%), detector efficiency (2.0%), sample weight (0.1%), sample geometry (1.0%), γ-ray self-absorption (1.0%-1.5%), and the fluctuation of the neutron flux (1.0%), among others.
For the ⁹⁴Zr(n,d*)^93m+gY reaction, as shown in Table 2 and Fig. 2, the trend of the theoretical excitation curve obtained by the computer code system Talys-1.9 increases with increasing incident neutron energy around 14 MeV. In the neutron energy range of 13.5-14.8 MeV, the fitted line of our experimental values is in good agreement with the theoretical excitation curve obtained by Talys-1.9. These two existing experimental datasets [2, 3] are well distributed on both sides of the theoretical curve, although there is a significant difference between them, which is reliable. The theoretical excitation curve generally matches these experimental data (including our results) reasonably well.
For the ⁹⁶Zr(n,γ)⁹⁷Zr reaction, Table 2 and Fig. 3 show that the fitting line of our results in the neutron energy range of 13.5-14.8 MeV is consistent with the theoretical excitation curve obtained by Talys-1.9 within the experimental error. The result of Pepelnik et al. [4] is considerably lower than that of the fitting line of our experimental values and that of the theoretical excitation curve obtained by Talys-1.9 at the corresponding energy, which is dubious. The result of Perkin et al. [6] is significantly higher than that of the fitting line of our experimental values and that of theoretical excitation curve obtained by Talys-1.9 at the corresponding energy, which is likewise dubious. The result of Wagner and Warhanek [5] is close to that of the fitting line of our experimental values and that of theoretical excitation curve obtained by Talys-1.9 at the corresponding energy.
For the ⁹⁶Zr(n,2n)⁹⁵Zr reaction, shown in Table 2 and Fig. 4, our experimental cross sections around the neutron energy of 14 MeV are in agreement, within the experimental error, with those of the fitting lines of Filatenkov [13], Molla et al. [15], and Hanlin Lu et al. [16] at the same energies as well as the theoretical values of the excitation curve obtained by Talys-1.9 at the corresponding energies. The three experimental datasets of Hanlin Lu et al. [16] at neutron energies of 16.86, 17.63, and 17.69 MeV are significantly lower than the theoretical excitation curves obtained by Talys-1.9 at the corresponding energies, which is dubious. The fitted line of our cross sections around the neutron energy of 14 MeV is consistent with the theoretical excitation curve obtained by Talys-1.9 within experimental error.
The cross sections of the ⁹⁰Zr(n,α)^87mSr reaction are shown in Table 2 and Fig. 5. They show that the fitted line of our experimental cross sections is in agreement, within the experimental error, with the fitted line of the cross sections of Marcinkowski et al. [20], except for the two values at the neutron energies of 15.9 and 16.6 MeV as well as the theoretical excitation curve obtained by Talys-1.9. In contrast, the results of Filatenkov [13] and Semkova et al. [17] are overall higher. The results of Molla et al. [15] at neutron energies of 13.64 and 13.88 MeV are low, and at the neutron energies of 14.1, 14.58, 14.83 MeV, they are high.
For the ⁹⁴Zr(n,α)⁹¹Sr reaction, shown in Table 2 and Fig. 6, the fitted line of our experimental cross sections in the neutron energy range of 13.5-14.8 MeV is in agreement, within the experimental error, with the fitted line of the cross sections of Filatenkov [13] except for the three values at the neutron energies of 13.56, 13.74, and 13.96 MeV and the fitted line of Marcinkowski et al. [20], as well as the theoretical excitation curve obtained by Talys-1.9. In contrast, the results of Molla et al. [15] and the values of Filatenkov [13] at the neutron energies of 13.56, 13.74, 13.96 MeV are higher.
For the ⁹⁰Zr(n,p)^90mY reaction, shown in Table 2 and Fig. 7, the results of Filatenkov [13], Molla et al. [15], Grallert et al. [19], Thiep et al. [22] are higher. In particular, the result of Sarkar and Bhoraskar [23] is significantly higher than all the other results, which is dubious. In contrast, the result of Osman and Habbani [18] is significantly lower than all the other results, which is also dubious. Our experimental cross sections are in agreement, within the experimental error, with those of the fitted line of the cross sections of Marcinkowski et al. [20] at the corresponding energies, as well as the theoretical values of the excitation curve obtained by Talys-1.9 at the corresponding energies.
For the ⁹²Zr(n,p)⁹²Y reaction, shown in Table 2 and Fig. 8, the fitted line of our experimental cross sections in the neutron energy range of 13.5-14.8 MeV is in agreement, within the experimental error, with the fitted lines of the cross sections of Filatenkov [13], Molla et al. [15] and Marcinkowski et al. [20]. The theoretical excitation curve obtained by Talys-1.9 generally matches these experimental data well.
For the ⁹⁴Zr(n,p)⁹⁴Y reaction, shown in Table 2 and Fig. 9, our experimental cross sections in the neutron energy range of 13.5-14.8 MeV are in agreement, within the experimental error, with those of the fitted line of the cross sections of Marcinkowski et al. [20] at corresponding energies. At the neutron energies of 13.5 and 14.1 MeV, our experimental values are in agreement, within the experimental error, with those of theoretical excitation curve obtained by Talys-1.9 at the corresponding energies. The cross sections of Molla et al. [15] and Begun et al. [24] are higher than that of the fitted line of our experimental values and that of theoretical excitation curve obtained by Talys-1.9 at the corresponding energy. The theoretical excitation curve matches these experimental data well in general.

5.Conclusion

The experimental cross sections of the ⁹⁴Zr(n,d*)^93m+gY, ⁹⁶Zr(n,γ)⁹⁷Zr, ⁹⁶Zr(n,2n)⁹⁵Zr, ⁹⁰Zr(n,α)^87mSr, ⁹⁴Zr(n,α)⁹¹Sr, ⁹⁰Zr(n,p)^90mY, ⁹²Zr(n,p)⁹²Y, and ⁹⁴Zr(n,p)⁹⁴Y reactions have been measured in the neutron energy range of 13.5-14.8 MeV via the activation technique. The excitation curves of the above-mentioned eight nuclear reactions within the incident neutron energy range from the threshold to 20 MeV were obtained by adopting the nuclear theoretical model program system Talys-1.9. Generally, our experimental results agree with some previous experimental values, as well as those of the theoretical excitation curve obtained by Talys-1.9 at the corresponding energies. The theoretical excitation curves match the experimental data well.
The results obtained in the present work are useful for strengthening the database, and the theoretical excitation curves are significant for the development and utilization of nuclear energy and the related applications.
We thank the crew of the K-400 Neutron Generator at Institute of Nuclear Physics and Chemistry China Academy of Engineering Physics for performing the irradiation experiments.

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