Photo-neutron reaction cross-section for 93Nb in the end-point bremsstrahlung energies of 12–16 and 45–70 MeV

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Nuclear Physics A ••• (••••) •••–•••

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www.elsevier.com/locate/nuclphysa

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93 Nb

Photo-neutron reaction cross-section for in the end-point bremsstrahlung energies of 12–16 and 45–70 MeV

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H. Naik , G.N. Kim , R. Schwengner , K. Kim , M. Zaman , M. Tartari b , M. Sahid b , S.C. Yang b , R. John c , R. Massavczyh c , A. Junghans c , S.G. Shin d , Y. Gey d , A. Wagner c , M.W. Lee e , A. Goswami a , M.-H. Cho d

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a Radiochemistry Division, Bhabha Atomic Research Centre, Mumbai 400085, India

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b Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea

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c Institut of Radiation Physics, Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany d Division of Advanced Nuclear Engineering, Pohang University of Science and Technology,

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Pohang 790-784, Republic of Korea

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e Research Center, Dongnam Institute of Radiological and Medical Science, Busan 619-953, Republic of Korea

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Received 9 July 2013; received in revised form 31 July 2013; accepted 2 August 2013

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Abstract The photo-neutron cross-sections of 93 Nb at the end-point bremsstrahlung energies of 12, 14 and 16 MeV as well as 45, 50, 55, 60 and 70 MeV have been determined by the activation and the off-line γ -ray spectrometric techniques using the 20 MeV electron linac (ELBE) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany, and 100 MeV electron linac at Pohang Accelerator Laboratory (PAL), Pohang, Korea. The 93 Nb(γ , xn, x = 1–4) reaction cross-sections as a function of photon energy were also calculated using computer code TALYS 1.4. The flux-weighted average values were obtained from the experimental and the theoretical (TALYS) values based on mono-energetic photons. The experimental values of present work are in good agreement with the flux-weighted theoretical values of TALYS 1.4 but are slightly higher than the flux-weighted experimental data of mono-energetic photons. It was also found that the theoretical and the experimental values of present work and literature data for the 93 Nb(γ , xn) reaction cross-sections increase from the threshold values to a certain energy, where other reaction channels

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* Corresponding author. Tel.: +82 53 950 5320; fax: +82 53 939 3972.

E-mail address: [email protected] (G.N. Kim). 0375-9474/$ – see front matter © 2013 Published by Elsevier B.V. http://dx.doi.org/10.1016/j.nuclphysa.2013.08.003

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opens. However, the increase of 93 Nb(γ , n) and 93 Nb(γ , 2n) reaction cross-sections are sharper compared to 93 Nb(γ , 3n) and 93 Nb(γ , 4n) reaction cross-sections. The sharp increase of 93 Nb(γ , n) and 93 Nb(γ , 2n) reaction cross-sections from the threshold value up to 17–22 MeV is due to the Giant Dipole Resonance (GDR) effect besides the role of excitation energy. After a certain values, the individual 93 Nb(γ , xn) reaction cross-sections decrease with increase of bremsstrahlung energy due to opening of other reaction channels. © 2013 Published by Elsevier B.V.

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Keywords: 93 Nb(γ , xn, x = 1–4) reaction cross-sections; 197 Au(γ , n)196 Au and 27 Al(γ , 2pn)24 Na reactions flux

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monitor; End-point bremsstrahlung energy of 12–16 and 45–70 MeV; Activation and off-line γ -ray spectrometric technique; TALYS calculation

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1. Introduction

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Nuclear data on reaction cross-sections of various materials are important for the study of the nuclear structure and reactions mechanisms. In particular, photon- and neutron-induced crosssections of various materials in the wide range of energies are important for different applications such as the design of radiation shielding, the calculation of absorbed dose in the human body during radiotherapy, in the physics and technology of fusion and fission reactors, nuclear waste transmutation, and astrophysical nucleosynthesis [1]. Besides these, the medium-energy photon and neutron-induced reaction cross-sections of the structural materials (e.g. Fe, Ni, Cr) and cladding materials (Zr, Nb) are of more interest for their applications in different types of reactors. This is because the safety and reliability of different types of reactors depend on the cladding performance. The cladding tube is subjected to various thermal and multi-axial stress conditions inside the reactor [2]. The presence of Nb in Zr–Nb alloys improves the thermal and multi-axial stress as well as the long-term corrosion resistance and mechanical properties [3–5]. Because a niobium has a low thermal neutron cross-section and it can be alloyed with zirconium for using in the cladding of nuclear fuel rods, and thus it can be extended fuel cycles with higher burn-ups. Recently, several Nb modified Zr alloys (such as Zirlo) have been developed for use in cladding applications [6]. A Zr–1%Nb alloy has been used as primary cladding in the countries of the former USSR and in Canada. A Zr–2.5 wt% Nb alloy has been used to replace Zircaloy-2 as the cladding in Candu-PHW reactors. Thus the photon and neutron-induced reaction cross-sections of the structural materials (e.g. Fe, Ni, Cr, etc.) and cladding materials (Zr, Nb) are of interest for their applications in different types of conventional reactors. Besides the conventional reactors, an accelerator driven sub-critical system (ADSs) [7–10] is of recent interest for the transmutation of the long-lived fission products and incineration of the long-lived minor actinides. In ADSs, the high-energy (GeV) proton from the accelerator strikes a heavy element like W, Pb–Bi, Th, and U, which yields a large number of neutrons by spallation reaction. The spallation target becomes a source of neutrons, which drives a self-sustaining fission chain in a sub-critical core. In the spallation processes, along with high-energy neutrons, high-energy photons are also produced, which can cause fission and different types of nuclear reactions of the long-lived minor actinides, spallation target as well as of the structural and cladding materials. Among the different types of nuclear reactions, photo-neutron emission is one of the exit channels. The photo-neutron can add to the neutron flux resulting from spallation, which can cause an increase of the total neutron flux. Thus, it is very much important to measure both the neutron- and photon-induced reaction cross-sections of structural materials (e.g. Fe, Ni, Cr, etc.) and cladding materials (Zr, Nb) for their application in ADSs and conventional reactors.

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Sufficient reaction cross-sections of 93 Nb induced by neutron [11] and limited data on monoenergetic photon [12] are available in literature. However, in the conventional reactors and ADSs, the photon energy available is in the form of bremsstrahlung radiation. The (γ , n) and (γ , 2n) reaction cross-sections of 93 Nb available in literature [12] are in the GDR region for monoenergetic photons based on the neutron counting technique. For the end-point bremsstrahlung energies, the only data on 93 Nb(γ , n) reaction cross-section based on the off-line γ -ray spectrometric technique is available at 10–12.5 MeV [13] and 32 MeV [14] but not at higher energies. Similarly, there is no data available on the (γ , 3n) and (γ , 4n) reaction cross-sections of 93 Nb. In view of this, in the present work, the 93 Nb(γ , xn; x = 1–4) reaction cross-sections are determined at the end-point bremsstrahlung energies of 12–16 and 45–70 MeV using an activation and off-line γ -ray spectrometric technique. The 93 Nb(γ , xn) reaction cross-sections induced by mono-energetic photon were also calculated theoretically using the TALYS 1.4 code [15]. Then the flux-weighted average 93 Nb(γ , xn) reaction cross-sections for the different end-point energies were obtained from the experimental and theoretical (TALYS) data of mono-energetic photons and are compared with present data to examine the role of excitation energy.

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2. Experimental procedure

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Different sets of experiments were performed by using the 20-MeV electron linac (ELBE) at Helmholtz-Zentrum Dresden-Rossendorf (HZDR), Dresden, Germany and the 100-MeV electron linac at Pohang accelerator laboratory (PAL), Pohang, Korea. In the 20 MeV electron linac at HZDR, three different irradiations were done at the bremsstrahlung end-point energies of 12, 14, and 16 MeV to measure the cross-sections of the 93 Nb(γ , n)92 Nb reaction. For each irradiation, a stack of Nb–Au sample was made. The size of the high purity (99.999%) Nb metal foil was 0.9 cm × 0.9 cm with thickness of 0.05 mm and weighing 32.6 to 35.5 mg. On the other hand, the size of the Au metal foil was 0.8 cm × 0.6 cm with thickness 0.1 mm and weighing 83.2 to 101.6 mg. The 197 Au(γ , n)196 Au reaction was used as the photon flux monitor. All samples were wrapped individually with 0.025 mm thick superpure aluminum foil. The three different set of samples were kept inside separate capsules made of polypropylene. They are loaded on a sample holder and then sent one at a time to the place of irradiation using pneumatic carrier rabbit facility [16,17]. The bremsstrahlung radiation was generated by impinging the electron beam on a solid graphite beam dump [16,17]. The area directly behind the electron beam dump was used as a site for high flux (∼109 to 1010 photons cm−2 s−1 ) irradiations. Then individual samples irradiations were done for 8.5 to 10.5 hours with the end-point bremsstrahlung energies of 12, 14 and 16 MeV, respectively. During the experiments, the electron linac was operated with a pulse repetition rate (PRR) of 13 MHz, a pulse width of 10 picoseconds and an average beam current of 550 µA. The electron beam current was very much stable during the irradiation time of 8.5–10.5 h. Thus it produces constant photon flux throughout the irradiation. After the irradiation, the samples were brought back to the detector by using the same automated pneumatic rabbit carrier facility. Then, the γ -ray counting of the irradiated targets of Nb and Au along with an aluminum catcher was done by using energy and efficiency-calibrated 90% HPGe detector coupled to a PC based 16K channel analyzer. The resolution of the detector system was 2.0 keV at 1332.0 keV of 60 Co. The sample was kept at a suitable distance from the detector to minimize the loss of counts. At the same time the dead time of the detector system was kept below 10% to avoid the coincidence effects. The energy- and efficiency-calibration of

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the detector system was done by counting the γ -ray energies of standard sources such as 133 Ba, 137 Cs, 22 Na and 60 Co. In the case of 100 MeV electron linac at PAL, five different irradiations were done at bremsstrahlung end-point energies of 45, 50, 55, 60 and 70 MeV to measure the (γ , n), (γ , 3n) and (γ , 4n) reactions cross-sections of 93 Nb. The bremsstrahlung was generated when a pulsed electron beam hit a thin tungsten (W) metal foil with a size of 10.0 cm × 10.0 cm and a thickness of 0.1 mm [18]. The W target was placed on a suitable stand at 18.0 cm from the exit window of electron beam. The Nb metal foil as mentioned before with area of 1.0 cm × 1.0 cm and weight of 40.6 to 41.5 mg was wrapped with a 0.025 mm thick Al foil with purity more than 99.99%. Similarly, Au metal foil of same size was also wrapped with 0.025 mm thick Al foil. The Al wrapper is necessary to stop reaction products recoiling out from the target during irradiation and to avoid radioactive contamination to the surrounding. Then a stack of Nb–Au sample was made, which was additionally wrapped with one more Al foil. The 197 Au(γ , n)196 Au reaction was used as the photon flux monitor for the 93 Nb(γ , n) reaction. On the other hand, the 27 Al(γ , 2pn)24 Na reaction of the Al wrapper a was used to determine the photon flux for the (γ , 3n) and (γ , 4n) reactions of 93 Nb. The use of different detectors for various reactions is based on their threshold values. The target stack assembly was fixed on a stand at a proper height behind the 0.1 mm thick W metal foil [18]. The sample was placed at 12 cm from the W target and was positioned at zero degree with respect to the direction of the electron beam. Different sets of target for Nb–Au stack were made for different irradiation. The target assembly was irradiated for 0.5–3 h with bremsstrahlung produced by bombarding the 45–70 MeV electrons on the tungsten metal foil. The current of the electron beam during irradiation was 10–35 mA at 3.75 Hz with a beam width of 1.5 µs. The electron beam current was very much stable during the irradiation time of 0.5–3 h. Thus it produces constant photon flux throughout the irradiation. However, during the irradiation some electrons also produce or pass through the thin tungsten along with the bremsstrahlung. Within the Weizsacker–Williams approximation [19,20] the electron–nucleus interaction occurs through a spectrum of virtual photons, while the bremsstrahlung is composed of real photons. Thus, the photo-nuclear reaction at the high energy electron beam is due to the spectrum of bremsstrahlung and virtual photons. After the irradiation, the irradiated target was cooled for 30 min. Then the cooled irradiated targets of Nb and Au along with individual Al wrapper were taken out from the irradiated assembly and were mounted separately on different Perspex (acrylic glass, 1.5 mm thick) plate [18]. The γ -ray counting of the reaction products from 93 Nb, 197 Au and 27 Al were done by using an energy- and efficiency-calibrated HPGe detector coupled to a PC based 4K-channel analyzer. The resolution of the detector system had a full width at half-maximum (FWHM) of 1.8 keV at the 1332.5 keV peak of 60 Co. The standard source used for the energy and the efficiency calibration was 152 Eu, having γ -rays in the energy range of 121.8–1408.0 keV. The detector efficiency was 20% at 1332.5 keV relative to a 300 diameter × 300 length NaI(Tl) detector. The dead time of the detector system during counting was always kept less than 10% by placing the sample at a suitable distance to avoid pileup and coincidence-summing effects. The γ -ray counting of the reaction products from the irradiated samples of 93 Nb, 197 Au and 27 Al were done by placing the samples in the shelf, which was 5 cm away from the detector. The γ -ray counting of the sample was done in live time mode and was followed as a function of time for at least three half-lives. Typical γ -ray spectrum of the irradiated 197 Au and 93 Nb samples along with 27 Al wrapper from the irradiation of the end-point bremsstrahlung energies of 16 MeV from ELBE and 55 MeV from PAL electron linac are given in Fig. 1 and Fig. 2, respectively.

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Fig. 1. Typical γ -ray spectrum of an irradiated gold foil with bremsstrahlung energy of 16 MeV.

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Fig. 2. Typical γ -ray spectrum of an irradiated 93 Nb along with 27 Al wrapper with bremsstrahlung energy of 55 MeV showing the γ -lines of 92 Nbm , 90 Nbm,g , 89 Nbm , 24 Na, and 22 Na.

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Table 1 Nuclear spectroscopic data of the radio-nuclides from the 197 Au(γ , n)196 Au, 27 Al(γ , 2pn)24 Na, 93 Nb(γ , n)92 Nb, 93 Nb(γ , 2n)91 Nb, 93 Nb(γ , 3n)90 Nb, and 93 Nb(γ , 4n)89 Nb reactions.

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196 Au

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24 Na

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91m Nb

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90m Nb

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γ -ray abundance (%)

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3. Data analysis

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3.1. Calculation of photon flux

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The net peak area (Anet ) corresponding to the photo-peak was calculated by summing the counts under the full energy peak and subtracting the linear Compton background. In the case of the 12–16 MeV bremsstrahlung irradiation, the photon flux was determined based on the activity of 332.98, 355.7 and 426.0 keV γ -lines of 196 Au from the 197 Au(γ , n) reaction. On the other hand, in the case of the 45–70 MeV bremsstrahlung irradiation, the photon flux was determined based on the activity of 332.98, 355.7 and 426.0 keV γ -lines of 196 Au from the 197 Au(γ , n) reaction as well as the activity of 1368.6 keV γ -line of 24 Na from the 27 Al(γ , 2pn) reaction. The photo-peak activities (Anet ) for 332.98, 355.7, 426.0, and 1368.6 keV γ -lines of 196 Au and 24 Na is related to the photon flux (ϕ) by the equation,   Nσ ϕIγ ε(1 − e−λt )(e−λT )(1 − e−λCL ) CL Anet = (1) LT λ where, N is the number of target atoms and σ  the average activation cross-section of the 197 Au(γ , n)196 Au or 27 Al(γ , 2pn)24 Na reactions, ϕ is the bremsstrahlung flux, I the branching γ intensity of the analyzed γ -rays, ε the detection efficiency of the activated product, λ is the decay constant (= ln 2/T1/2 ) for the isotope of interest, t, T , CL, and LT are the irradiation time, cooling time, clock time and counting time, respectively. In the above equation, the peak area has been corrected for dead time by multiplying by CL/LT factor. The γ -ray energies and the decay

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Table 2 Flux conversion ratios used to obtain the photon flux for different reactions of 93 Nb from the total flux based on the 197 Au(γ , n)196 Au and 27 Al(γ , 2pn)24 Na reactions flux monitors.

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σ  of 197 Au(γ , n)196 Au (mb)

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93 Nb(γ , 4n)/27 Al(γ , 2pn),

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0.116

0.158

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0.820

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0.942

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2.482

2.269

2.012

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1.227

1.187

1.158

1.129

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0.481

0.580

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0.698

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data for the residual nuclide such as branching ratio, half-lives are taken from Refs. [21,22] and are given in Table 1. In the case of 14–16 bremsstrahlung irradiation, the average cross-section (σ ) for 197 Au(γ , n)196 Au reaction was calculated using the following relation.  σϕ σ  =  (2) ϕ

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The photon flux distribution for bremsstrahlung end-point energies of 12, 14 and 16 MeV were calculated by using the GEANT4 code [23]. The photon flux (ϕ) distribution with respect to photon energy (E) is presented in Fig. 3. Photo nuclear cross-sections (σ ) of 197 Au(γ , n)196 Au reaction have been reported by many groups [24–27]. For our calculation, we have used the crosssection of reaction of 197 Au(γ , n)196 Au from Ref. [28] by using mono-energetic photons, which is shown in Fig. 4 along with the value theoretically calculated values of the TALYS 1.4 [15] computer code. A short description of TALYS 1.4 computer code is given in the next section. For the end-point bremsstrahlung energies of the present work, the flux-weighted average 197 Au(γ , n)196 Au reaction cross-section (σ ) was obtained from the literature data [28] of mono-energetic photons as well as from the theoretical values of TALYS 1.4 [15] (Fig. 4). The flux-weighted average cross-sections for the 197 Au(γ , n)196 reaction from the literature and theoretical data are shown in Table 2. Then, the photon flux for the 197 Au(γ , n)196 Au reaction was calculated using Eq. (1) by rearranging the terms. The threshold for the 197 Au(γ , n)196 Au and 93 Nb(γ , n)92 Nb reactions are 8.073 MeV and 8.832 MeV, respectively. Thus the photon flux obtained from the 197 Au(γ , n)196 Au reaction has to be modified for the 93 Nb(γ , n)92 Nb reaction based on threshold value to bremsstrahlung end-point energy. In case of end-point bremsstrahlung energies of 12, 14 and 16 MeV, the weighted average flux obtained from the 197 Au(γ , n)196 Au reaction is multiplied by factors 0.699, 0.789 and 0.820, respectively. These factors are the flux ratio for 93 Nb(γ , n)92 Nb reaction from 8.825 MeV to 12, 14 and 16 MeV divided by the 197 Au(γ , n)196 Au reaction from 8.07 MeV to 12, 14 and 16 MeV, respectively. The different ratio used for the conversion of the photon flux for the 93 Nb(γ , n)92 Nb reaction to the total flux of 197 Au(γ , n)196 Au reaction based on the threshold values for the end-point bremsstrahlung energies of 12, 14 and 16 MeV are given in the Table 2.

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Fig. 3. Plot of bremsstrahlung spectrum for end-pint energies of 12, 14, 16, 45, 50, 55, 60, and 70 MeV calculated by using the GEANT4 code.

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Fig. 4. Cross-sections of 197 Au (γ , n)196 Au reaction as a function of gamma energy obtained by the existing experimental data [28] using the mono-energetic photons and the calculated values from the TALYS.

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In the case of bremsstrahlung irradiations of 45–70 MeV, the photon flux distribution were also calculated by using the GEANT4 code [23]. The photon flux (ϕ) distribution with respect to photon energy (E) is presented in Fig. 3. The integrated photon flux ϕ during individual irradiation was obtained from the number of observed activity (Anet ) of the 332.98, 355.7, 426.0 and 1368.6 keV γ -lines of 196 Au and 24 Na produced from the 197 Au(γ , n) and 27 Al(γ , 2pn) reactions, respectively. For the 197 Au(γ , n)196 Au reaction, the average cross-section (σ ) for 197 Au(γ , n)196 Au reaction was calculated in the aforementioned way from the σ value of TALYS [15] for mono-energetic photons. This is because the flux-weighted reaction cross-section ((σR ) from Ref. [28] can be obtained only up to the end-point bremsstrahlung energy of 24 MeV. On the other hand, 27 Al(γ , 2pn)24 Na reaction, the σR  value in the range of 0.045–0.2 mb corresponding to the bremsstrahlung energy range of 45–70 MeV is available in Ref. [29] and

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thus was used in Eq. (1) to obtain the photon flux (ϕ). The threshold value for the 27 Al(γ , 2pn)24 Na reaction is 31.073 MeV. On the other hand, the threshold value for the (γ , n), (γ , 2n), (γ , 3n) and (γ , 4n) for 93 Nb are 8.83, 16.72, 28.77, 38.85 MeV, respectively. Thus the photon flux obtained from the 197 Au(γ , n)196 Au and 27 Al(γ , n)24 Na reactions have to be modified for the (γ , n), (γ , 2n), (γ , 3n) and (γ , 4n) reactions of 93 Nb based on the threshold values to bremsstrahlung end-point energy. In case of 93 Nb(γ , n) reaction, the photon flux from 197 Au(γ , n)196 Au reaction was used. This is to keep similarity between the end-point bremsstrahlung energies of 12–16 and 45–70 MeV for 93 Nb(γ , n) reaction. On the other hand, for the (γ , 2n), (γ , 3n) and (γ , 4n) reactions of 93 Nb, for the end-point bremsstrahlung energies of 45, 50, 55, 60 and 70 MeV, the weighted average flux obtained from the 27 Al(γ , 2pn)24 Na reaction is multiplied by different factors based on the ratio of threshold value to the end-point bremsstrahlung energy for (γ , 2n), (γ , 3n) and (γ , 4n) reactions of 93 Nb as mentioned before for the (γ , n) reaction. The different ratios used for the conversion of the photon flux for the (γ , n), (γ , 3n) and (γ , 4n) reactions of 93 Nb to the total flux of 197 Au(γ , n)196 Au and 27 Al(γ , 2pn)24 Na reactions based on the threshold values for the end-point bremsstrahlung energies of 45, 50, 55, 60 and 70 MeV are given in Table 2.

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3 4 5 6 7 8 9 10 11 12 13 14 15 16

18 19

The radio-nuclide produced from (γ , n)(γ , 2n)(γ , 3n) and (γ , 4n) reactions of 93 Nb are having m- and g-states with different half-life and γ -rays energies. The nuclear spectroscopic data for the reaction products of 93 Nb(γ , xn) reactions from Refs. [21,22] are shown in Table 1. The net peak area (Anet ) corresponding to the photo-peak for different reaction products were calculated by summing the counts under the full energy peak and subtracting the linear Compton background. From the net photo-peak area (Anet ) of the radio-nuclides of interest, the (γ , n), (γ , 3n) and (γ , 4n) reactions cross-sections of 93 Nb were obtained using the following equation

27 28

2

17

3.2. Calculation of 93 Nb(γ , xn, x = 1–4) reaction cross-sections

19 20

1

σ=

NϕIγ

Anet ( CL LT )λ −λt ε(1 − e )(e−λT )(1 − e−λCL )

20 21 22 23 24 25 26 27

(3)

All the terms in Eq. (3) have the similar meaning as in Eq. (1). As can be seen from Table 1, in the case of 93 Nb(γ , n) reaction, it is possible to measure the reaction cross-section of only m-state due to its suitable half-life of 10.15 d with high intensity γ -lines. However, it is not possible to measure the reaction cross-section of the g-state because of the quite long half-life of 3.5 × 107 years. Thus from the 93 Nb(γ , n)92m Nb reaction cross-section, the total 93 Nb (γ , n)92 Nb reaction cross-section was obtained by dividing the value with 0.5 [14]. This is based on the assumption of 55.2% contribution of the 92m Nb to the total 93 Nb(γ , n)92 Nb reaction cross-section at end-point bremsstrahlung energy of 32 MeV [14]. Since the contribution (isomeric yield ratio) at higher or lower energies to 32 MeV is not known, we have assumed throughout the value of 0.5. This assumption may underestimate the cross-sections below the end-point bremsstrahlung energy of 32 MeV and overestimate at higher energies. In the case of 93 Nb(γ , 2n) reaction, the product 91m Nb has a half-life of 60.86 d with very low intensity γ -lines, whereas the 91g Nb has a half-life of 680 y. Besides this, there is no literature data available on the isomeric yield ratio for 91 Nb. Thus it is not possible to obtain the 93 Nb(γ , 2n) reaction cross-section with off-line γ -ray spectrometric technique. For 93 Nb(γ , 3n) reaction, the product 90m Nb is very short-lived and decays to 90g Nb by internal transition with 100% branching intensity. The 90g Nb has a suitable half-life of 14.6 h and having γ -ray lines with good intensities. Thus the 93 Nb(γ , 3n) reaction cross-section was obtained without any assumption. For 93 Nb(γ , 4n) reaction, the metastable

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Table 3 Experimentally determined cross-section of the (γ , n), (γ , 3n) and (γ , 4n) reaction cross-sections of 93 Nb reaction at bremsstrahlung end point energies of 10–16 and 32–70 MeV from present work and flux-weighted values from literature [12] and TALYS [15]. Reactions

6

Bremsstrahlung energy (MeV)

[Ref.]

Experimental Metastable-state

7 8

93 Nb(γ , n)92m Nb

10

9

12

10 11

12.5

12 13

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14

16

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32

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93 Nb(γ , 3n)90 Nb

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Average reaction cross-section (σ ) (mb)

93 Nb(γ , 4n)89 Nb

45 50 55 60 70 45 50 55 60 70 45 50 55 60 70

[13] [12] This work [12] [13] [12] This work [12] This work [12] [14] [14] This work This work This work This work This work This work This work This work This work This work This work This work This work This work This work

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Total

Total

7

4.923 ± 0.120

–

11.263

8

8.726 ± 0.196

–

9.137 ± 0.079

–

14.607 ± 1.307

–

20.371 ± 1.645

–

29.900 ± 1.900

–

23.939 ± 1.891 22.598 ± 1.413 20.371 ± 1.483 18.530 ± 1.155 17.372 ± 1.772 – – – – – 0.032 ± 0.005 0.071 ± 0.005 0.094 ± 0.004 0.103 ± 0.008 0.094 ± 0.003

– – – – – – – – – – 0.131 ± 0.024 0.367 ± 0.043 0.560 ± 0.051 0.680 ± 0.076 0.721 ± 0.043

9.846 ± 0.240 7.159* 17.452 ± 0.392 12.797* 18.274 ± 0.158 13.965* 29.214 ± 2.614 22.776* 40.742 ± 3.290 37.810* 59.800 ± 3.800 54.200 47.878 ± 3.782 47.878 ± 2.826 45.196 ± 2.966 37.060 ± 2.310 34.744 ± 3.544 3.011 ± 0.351 2.903 ± 0.363 2.702 ± 0.382 2.546 ± 0.276 2.249 ± 0.329 0.163 ± 0.024 0.438 ± 0.043 0.654 ± 0.051 0.783 ± 0.076 0.815 ± 0.043

9

16.219 17.324 28.503

42 43 44 45 46 47

10 11 12 13 14

46.580

15 16

50.851 42.084 39.903 37.745 36.013 33.407 2.823 2.759 2.615 2.470 2.231 0.166 0.480 0.697 0.809 0.811

* Flux weight average cross-section calculated from Ref. [12].

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and ground state have suitable half-lives of 1.18 and 1.9 h and having γ -lines with good intensities. Thus the 93 Nb(γ , 4n) reactions cross-sections of metastable- and ground-state was obtained individually. From the individual cross-sections of metastable- and ground-states, total 93 Nb(γ , 4n) reaction cross-section was obtained without any assumption.

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4. Results and discussion

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Ground-state

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TALYS [15]

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The 93 Nb(γ , n)92m Nb reaction cross-section determined in the present work at the endpoint bremsstrahlung energies of 12, 14, 16, 45, 50, 55, 60 and 70 MeV are given in Table 3 along with the literature data at 10 MeV [13], 12.5 MeV [13] and 32 MeV [14]. In Table 2, the 93 Nb(γ , n)92m Nb reaction cross-section at the end-point bremsstrahlung energies of 10–16 and 45–70 MeV are based on the weighted average flux from the 197 Au(γ , n)196 Au reaction crosssection of mono-energetic photon from Ref. [28] or from TALYS [15]. On the other hand, the 93 Nb(γ , 3n)90 Nb and 93 Nb(γ , 4n)89m,g Nb reaction cross-sections at the end-point bremsstrahlung

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Fig. 5. Cross-sections of 93 Nb(γ , xn; x = 1–4) reaction as a function of gamma energy obtained by the existing experimental data [12] using the mono-energetic photons and the calculated values from the TALYS.

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energies of 45–70 MeV are based on the weighted average flux from the 27 Al(γ , 2pn)24 Na reaction cross-section. The uncertainties associated to the measured cross-sections come from the replicate measurements. The overall uncertainty is the quadratic sum of both statistical and systematic errors. The random error in the observed activity is primarily due to counting statistics, which is estimated to be 5–10%. This can be determined by accumulating the data for an optimum time period that depends on the half-life of the nuclides of interest. The systematic errors are due to uncertainties in photon flux estimation (∼2%), the irradiation time (∼0.5%), the detection efficiency calibration (∼3%), the half-life of the reaction products, and the γ -ray abundances (∼2%). Thus the total systematic error is about ∼4.15%. The overall uncertainty is found to be in between 6.5 and 10.8%, coming from the combination of a statistical error of 5–10% and a systematic error of 4.15%. The (γ , n), (γ , 3n) and (γ , 4n) reactions cross-sections of 93 Nb at the end-point bremsstrahlung energies of 45, 50, 55, 60 and 70 MeV were determined for the first time. Similarly, the 93 Nb(γ , n) reaction cross-section at the end-point bremsstrahlung energies of 12, 14 and 16 MeV are also determined for the first time. In literature, there are only three values at endpoint bremsstrahlung energies of 10 MeV [13], 12.5 MeV [13] and 32 MeV [14] based on the same activation and off-line γ -ray spectrometric technique. Besides this, one set of (γ , n) and (γ , 2n) reaction cross-sections of 93 Nb is available within 24 MeV based on the neutron counting method [12]. However, the literature data in Ref. [12], the (γ , n) and (γ , 2n) reaction crosssections of 93 Nb are for mono-energetic photons, which is shown in Fig. 5. In the case of (γ , 3n) and (γ , 4n) reaction cross-sections of 93 Nb, there is no data available in literature even based on the mono-energetic photons. Thus the (γ , n), (γ , 2n), (γ , 3n) and (γ , 4n) reaction cross-sections of 93 Nb as a function of photon energy were calculated theoretically using the TALYS code 1.4 [15]. The TALYS is a computer code basically used to calculate the nuclear reaction cross-sections that involve the projectiles like neutrons, photons, protons, deuterons, tritons, 3 He- and alphaparticles, in the energy range of 1 keV to 200 MeV and for target nuclides of mass 12 and heavier. In TALYS, the reactions cross-section to all open channels can be calculated. Several

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Fig. 6. Photon flux-weighted average cross-sections of 93 Nb(γ , xn; x = 1–4) reaction as a function of gamma energy obtained by this work using the bremsstrahlung photons, the existing experimental data [12–14] using the mono-energetic photons and the calculated values from the TALYS.

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options are included for the choice of different parameters such as γ -strength functions, nuclear level densities and nuclear model parameters, etc. In the present work, we calculated photoninduced reaction cross-section on a 93 Nb target using the default option in the TALYS code [15]. All possible outgoing channels for the given photon energy were considered. However, the cross-sections for the (γ , n), (γ , 2n), (γ , 3n) and (γ , 4n) reactions were collected and plotted in Fig. 5 as a function of photon energy. This is to compare the theoretical (γ , n) and (γ , 2n) reaction cross-sections of 93 Nb with the available experimental data of literature [12]. It can be seen from Fig. 5 that, the theoretical (γ , n) and (γ , 2n) reaction cross-sections of 93 Nb as a function of photon energy calculated by using the TALYS 1.4 shows a similar structure of the available experimental data [12]. However, the total 93 Nb(γ , n)92 Nb reaction cross-section from TALYS 1.4 computer code has a slight left side shift from the threshold to 12 MeV and 18 to 24 MeV as compared to the available literature data [12]. On the other hand, 93 Nb(γ , 2n)91 Nb reaction cross-section from TALYS 1.4 around 16–20 MeV is slightly higher than the available literature data [12]. In order to compare with the present data, the flux weighted average (γ , n), (γ , 2n), (γ , 3n), and (γ , 4n) reaction cross-sections of 93 Nb were obtained from the literature data [12] and theoretical values obtained from TALYS code based on mono-energetic photon by using Eq. (2) and plotted in Fig. 6. The flux-weighted (γ , n), (γ , 3n), and (γ , 4n) reaction cross-sections of 93 Nb are also given in Table 3 to compare with the experimental data. It can be seen from the Table 3 that the experimentally obtained 93 Nb(γ , n)92 Nb reaction cross-section of the present work at the end-point bremsstrahlung energies of 10–16 MeV are slightly higher than the fluxweighted value of literature data [12] but are closer to the values of TALYS [15]. However, there is no literature data available to compare with the experimental data of 93 Nb(γ , n)92 Nb reaction cross-section at end-point bremsstrahlung energies of 45–70 MeV. The experimentally obtained 93 Nb(γ , n)92 Nb reaction cross-section at end-point bremsstrahlung energies of 45–70 MeV from the present work and literature data at 32 MeV are slightly higher than the flux-weighted TALYS value. This may be due to the use of isomeric ratio of 0.5 for 92 Nb throughout the end-point bremsstrahlung energies, which was mentioned in Section 3.2. In the case of (γ , 3n), and (γ , 4n)

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reaction cross-sections of 93 Nb, there is no literature data available to compare with the present experimental data. However, the experimentally determined (γ , 3n), and (γ , 4n) reaction crosssections of 93 Nb at the end-point bremsstrahlung energies of 45, 50, 55, 60 and 70 MeV of present work are in close agreement with the flux-weighted values of TALYS within uncertainty limits. Further, it can be seen from Fig. 6 that the experimental and theoretical 93 Nb(γ , n)92 Nb reaction cross-sections increase very sharply from the threshold value of 8.832 MeV to 16 MeV, i.e. where the (γ , 2n) channel opens up. Above 16 MeV, it increases very slowly up to 20 MeV and then remains constant up to 24 MeV, i.e. where the (γ , 2n) reaction channels remains constant, and thereafter slowly decreases up to end-point bremsstrahlung energies of 70 MeV. This is due to the opening of other reactions channels. Similarly, the experimental and theoretical 93 Nb(γ , 2n)91 Nb reaction cross-sections increase very sharply from the threshold value of 16.72 MeV to 20 MeV. However, within the end-point bremsstrahlung energies of 18–24 MeV, the flux-weighted experimental data based on mono-energetic photons [12] are lower than the theoretical values of TALYS [15]. Otherwise above 20 MeV, both the experimental and theoretical 93 Nb(γ , 2n)91 Nb reaction cross-sections increase very slowly up to 24 MeV and then remains constant up to 29 MeV, i.e. up to the opening of (γ , 3n) reaction channel, and thereafter slowly decreases up to end-point bremsstrahlung energies of 70 MeV. This is due to the opening of other reactions channels. The theoretical and experimental (γ , 3n), and (γ , 4n) reactions cross-sections of 93 Nb also shows similar trend (Fig. 6) as of (γ , n), and (γ , 2n) reaction channels. First it increases sharply from its respective threshold value to a particular values and remains constant to a certain extent, where other reaction channels starts increasing. Then it starts decreasing due to the contribution of excitation energy to the other reaction channels. The above observations indicate the role of excitation energy and its partition in to different reaction channels. Besides the above observations, it can be seen from Fig. 6 that the increase trend of cross-section from threshold value up to the excitation energy of the next channel is more pronounced for the (γ , n) and (γ , 2n) reactions compared to (γ , 3n) and (γ , 4n) reactions. This is because the increase trend of (γ , n) and (γ , 2n) reaction cross-sections lies within 10–25 MeV, where GDR effect plays its role besides excitation energy.

31 32

35 36 37 38 39 40 41 42 43 44 45 46 47

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

5. Conclusions

33 34

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(i) The 93 Nb(γ , n)92 Nb reaction cross-section at the end-point bremsstrahlung energies of 12, 14 and 16 MeV has been determined by using the activation and off-line γ -ray spectrometric technique. Similarly, the (γ , n), (γ , 3n), and (γ , 4n) reactions cross-sections of 93 Nb at the end-point bremsstrahlung energies of 45, 50, 55, 60 and 70 MeV were also determined using the same technique. (ii) The (γ , n), (γ , 2n), (γ , 3n), and (γ , 4n) reaction cross-sections of 93 Nb as a function of mono-energetic photon energy was theoretically calculated using the TALYS 1.4 code. The flux-weighted average (γ , n), (γ , 2n), (γ , 3n), and (γ , 4n) reaction cross-sections of 93 Nb at different end-point bremsstrahlung energies were then obtained from the theoretical values of TALYS and the experimental literature data based on mono-energetic photons. (iii) The experimentally determined (γ , n), (γ , 2n), (γ , 3n), and (γ , 4n) reactions crosssections of 93 Nb at end-point bremsstrahlung energies of 10–16 and 32–45 MeV are in close agreement with the flux-weighted values of TALYS and literature data based on mono-energetic photon.

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(iv) The experimental and theoretical (γ , n), (γ , 2n), (γ , 3n), and (γ , 4n) reactions crosssections of 93 Nb increases sharply from threshold value to a certain value. Then it remains constant up to certain energy where other reaction starts increasing. There after it decreases when the higher reaction channels remains constant. (iv) The increase trend of (γ , n) and (γ , 2n) reactions cross-sections of 93 Nb are more sharp within end-point bremsstrahlung of 25 MeV. This indicates for (γ , n) and (γ , 2n) reactions crosssections of 93 Nb within end-point bremsstrahlung energy of 25 MeV have more pronounced GDR effect besides the role of excitation energy.

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References

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The authors are thankful to the staff of electron linac ELBE at HZDR, Dresden, Germany, and that at PAL, Pohang, Korea, for providing the electron beam to carry out the experiments. This research was partly supported by the NRF through a grant provided by the Korean Ministry of Education, Science & Technology (MEST) (Project No. 122S-1-3-0436, Brain Pool Program), by the National Research Foundation of Korea (NRF) through a grant provided by the Korean Ministry of Education, Science & Technology (NRF-2010-0021375, NRF-2010-0018498), and by the Institutional Activity Program of Korea Atomic Energy Research Institute in 2013. One of the authors (H. Naik) thanks Dr. K.L. Ramakumar for supporting the program and for permitting him to visit CHEP, Korea, to carry out this experiment.

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[1] IAEA, Handbook on photonuclear data for applications cross-sections and spectra, IAEA-TECDOC-1178, 2000. Available online at: http://www-nds.iaea.org/publications/tecdocs/. [2] K.L. Murty, Appl. Mech. Rev. 46 (5) (1993) 194. [3] K.N. Choo, Y.H. Kang, S.I. Pyun, V.F. Urbanic, J. Nucl. Mater. 209 (1994) 226. [4] G. Sabol, G.R. Klip, M.G. Balfour, E. Roberts, in: Zirconium in Nuclear Industry, in: Eighth International Symposium (ASTM STP), vol. 1023, Philadelphia, 1989, p. 227. [5] G.P. Sabol, G. Schoenberger, M.G. Balfour, in: IAEA Tech. Comm. Meeting on Materials for Advanced WaterCooled Reactors, Plzen, Czech and Slovak Federal Republic, IAEA, 1991, p. 50. [6] P.S. Chowdhury, P. Mukherjee, N. Gayathri, M. Bhattacharya, A. Chatterjee, P. Barat, P.M.G. Nambissan, Bull. Mater. Sci. 34 (2011) 507. [7] F. Carminati, R. Klapisch, J.P. Revol, J.A. Rubia, C. Rubia, CERN/AT/93-49 (ET) (1993). [8] C. Rubia, J.A. Rubio, S. Buono, F. Carminati, N. Fietier, J. Galvez, C. Geles, Y. Kadi, R. Klapisch, P. Mandrilion, J.P. Revol, CERN/AT/95-44 (ET) (1995), CERN/AT/95-53 (ET) (1995), CERN/LHC/96-01 (LET) (1996), CERN/LHC/97-01 (EET) (1997). [9] C.D. Bowman, Annu. Rev. Nucl. Part. Sci. 48 (1998) 505. [10] S. Ganesan, Pram¯ana 68 (2007) 257. [11] IAEA-EXFOR, Experimental nuclear reaction data. Available online at http://www-nds.iaea.org/exfor. [12] A. Lepretre, H. Beil, R. Bergere, P. Carlos, A. Veyssiere, Nucl. Phys. A l75 (1971) 609. [13] R. Crasta, H. Naik, S.V. Suryanarayana, P.M. Prajapati, S. Ganesh, M. Kumar, N. Nathanial, V.T. Nimje, K.C. Mittal, A. Goswami, Radiochim. Acta (2013), in press. [14] A.K.Md.L. Rahman, K. Kato, H. Arima, N. Shigyo, K. Ishibashi, J. Hori, K. Nakajima, J. Nucl. Sci. Technol. 47 (2010) 618. [15] A.J. Koning, S. Hilaire, M.C. Duijvestijn, in: R.C. Haight, M.B. Chadwick, T. Kawano, P. Talou (Eds.), Proceedings of the International Conference on Nuclear Data for Science and Technology, ND 2004, Santa Fe, 2004, in: AIP Conf. Proc., vol. 769, 2005, p. 1154. [16] M. Erhard, A.R. Junghans, C. Nair, R. Schwengner, R. Beyer, J. Klug, K. Kosev, A. Wagner, Phys. Rev. C 81 (2010) 034319. [17] R. Schwengner, R. Beyer, F. Donau, E. Gosse, A. Hartmann, A.R. Junghans, S. Mallian, G. Rusev, K.D. Schilling, W. Schulze, A. Wagner, Nucl. Instrum. Methods A 555 (2005) 211.

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