DSpace at VNU: Thermal neutron cross-section and resonance integral of the Mo-98(n,gamma)Mo-99 reaction

Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 Contents lists available at ScienceDirect Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb Thermal neutron cross-section and resonance integral of the 98Mo(n,c)99Mo reaction Nguyen Van Do a, Pham Duc Khue a, Kim Tien Thanh a, Bui Van Loat b, Md.S Rahman c, Kyung Sook Kim c, Guinyun Kim c,*, Youngdo Oh d, Hee-Seok Lee d, Moo-Hyun Cho d, In Soo Ko d, Won Namkung d a Institute of Physics, Vietnam Academy of Science and Technology, 10 Dao Tan, Hanoi, Viet Nam College of Natural Sciences, Hanoi National University, 334 Nguyen Trai, Hanoi, Viet Nam c Department of Physics, Kyungpook National University, Daegu 702-701, Republic of Korea d Pohang Accelerator Laboratory, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea b a r t i c l e i n f o Article history: Received 28 May 2008 Received in revised form 26 November 2008 Available online 11 December 2008 PACS: 25.40.Lw 25.40.Ny 25.70.Ef Keywords: Thermal neutron cross-section Resonance integral 98 Mo(n,c)99Mo 197 Au(n,c)198Au 65 MeV electron linac Pulsed neutron facility Activation method a b s t r a c t We measured the thermal neutron cross-section and the resonance integral of the 98Mo(n,c)99 Mo reaction by the activation method using a 197Au(n,c)198 Au monitor reaction as a single comparator The highpurity natural Mo and Au metallic foils with and without a cadmium shield case of 0.5 mm thickness were irradiated in a neutron field of the Pohang neutron facility The induced activities in the activated foils were measured with a calibrated p-type high-purity Ge detector The necessary correction factors for the c-ray attenuation (Fg), the thermal neutron self-shielding (Gth) and the resonance neutron self-shielding (Gepi) effects, and the epithermal neutron spectrum shape factor (a) were taken into account In addition, for the 99Mo activity measurements, the correction for true coincidence summing effects was also taken into account The thermal neutron cross-section for the 98Mo(n,c)99Mo reaction has been determined to be 0.136 ± 0.007 barn, relative to the reference value of 98.65 ± 0.09 barn for the 197Au(n,c)198 Au reaction The present result is, in general, in good agreement with most of the experimental data and the recently evaluated values of ENDF/B-VII.0, JENDL-3.3, and JEF-2.2 by 5.1% (1r) By assuming the cadmium cut-off energy of 0.55 eV, the resonance integral for the 98Mo(n,c)99Mo reaction is 7.02 ± 0.62 barn, which is determined relative to the reference values of 1550 ± 28 barn for the 197Au(n,c)198Au reaction The present resonance integral value is in general good agreement with the previously reported data by 8.8% (1r) Ó 2008 Elsevier B.V All rights reserved Introduction Molybdenum (Mo) is a silvery-white, hard but softer transition metal Molybdenum and molybdenum containing alloys are important structural materials for accelerator-driven systems, fusion reactors and many other fields It is also very useful as a refractory and corrosion resistant material in accelerator applications [1] In addition, the radioactive 99Mo with half-life, t1/2 = 2.7489 days is widely used in medicine The daughter technetium radionuclide 99mTc (called metastable technetium) formed by bÀ decay from 99Mo, (99Mo(bÀ)99mTc with t1/2 = 6.01 h) is used in about 90% of the nuclear medicine examinations worldwide [2] The parent radionuclide 99Mo can be produced in principle in various ways Currently, the dominant route is the neutron fission of natural or isotopically enriched 235U through the reaction 235 U(n,f)99Mo, while the activation of a natural or isotopically en* Corresponding author Tel.: +82 53 950 5326; fax: +82 53 939 3972 E-mail address: gnkim@knu.ac.kr (G Kim) 0168-583X/$ - see front matter Ó 2008 Elsevier B.V All rights reserved doi:10.1016/j.nimb.2008.12.003 riched Mo by the proton induced reaction 100Mo(p,pn)99Mo and by the neutron capture reaction 98Mo(n,c)99Mo From 235U fission many long-lived radioactive wastes with total activity much more exceeding the activity of 99Mo are formed [3] The proton induced nuclear reactions on natural molybdenum containing 92,94,95,96,97,98,100 Mo isotopic composition can also form many radioactive products with high-activities [4] For the 98Mo(n, c)99Mo reaction, practically waste is not created and the saturated activity of the 98Mo(n,c)99Mo reaction can be increased by increasing the neutron flux [5] The knowledge of the thermal neutron cross-section and the resonance integral for the 98Mo(n,c)99Mo reaction would become important because the neutron activation cross-section data are used in the production of 99Mo and may also used in other studies related to the interaction of neutrons with matter We found in literature a number of experimental and evaluated data on the thermal neutron capture cross-sections and the resonance integrals for the 98Mo(n,c)99Mo reaction However, most of the reported experimental data have been measured before 1990 The 463 N Van Do et al / Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 measured thermal neutron cross-sections for the 98Mo(n,c)99Mo reaction are varied from 0.12 barn [6] to 0.18 barn [7] This fact shows that, there are still large discrepancies among the experimental results The measured resonance integrals for the 98Mo(n,c)99Mo reaction are varied from 4.72 barn [8] to 8.2 barn [9] The difference between the lowest and the highest values of the resonance integral found in literature is 73.73% Obviously, there are still large discrepancies among the experimental results for the 98 Mo(n,c)99Mo reaction, especially among the resonance integral values Therefore, it is necessary to measure more new data for better comparison and evaluation We measured the thermal neutron capture cross-section and the resonance integral of the 98Mo(n,c)99Mo reaction by using the activation method at the Pohang Neutron Facility (PNF) based on the 65-MeV electron linac The thermal neutron cross-section and the resonance integral for the 98Mo(n,c)99Mo reaction were determined relative to the reference values of r0,Au = 98.65 ± 0.09 barn and I0,Au = 1550 ± 28 barn for the 197Au(n,c)198Au reaction In order to improve the accuracy of the experimental results, the correction factors for gamma-ray attenuation (Fg), thermal neutron self-shielding (Gth), and resonance neutron self-shielding (Gepi) effects, and the epithermal neutron spectrum alpha shape factor (a) were taken into account In addition, the true coincidence summing corrections were also taken into account in the 99Mo activity measurements The present results are compared with the experimental data and the evaluated values Experimental procedure 2.1 Neutron source The PNF based on an electron linac was proposed in 1997 [10] for nuclear data production in Korea and was constructed at the Pohang Accelerator Laboratory (PAL) on December 1998 [11] The characteristics of the PNF are described elsewhere [12–16], so only a general description is given here It consists of an electron linac, a photo-neutron target, and a 12-m long time-of-flight (TOF) path The photo-neutron target was composed of ten Ta plates with a diameter of 4.9 cm and an effective thickness of 7.4 cm There was a 0.15 cm water gap between Ta plates in order to cool the target effectively The housing of the target was made of titanium The photo-neutron target was located in the center of a cylindrical water moderator The water moderator made by an aluminum cylinder with a thickness of 0.5 cm, a diameter of 30 cm and a height of 30 cm The distributions of neutrons with and without water moderator were described elsewhere [17,18] The photo-neutrons produced in the giant dipole resonance region consist of a large portion of evaporated neutrons and a small fraction of directly emitted neutrons which dominated at high energies The neutrons produced in the Ta target without water moderator have a Maxwellian energy distribution with a nuclear temperature of 0.45 MeV The estimated neutron yield per kW of beam power for electron energies above 50 MeV at the Ta target is about 1.9  1012 n/s [17], which is consistent with the calculated value based on Swanson’s formula, 1.2  1011 Z0.66, where Z is the atomic number of the target material [19] The total neutron yield per kW of beam power was also measured by using the multiple-foil technique and found (2.30 ± 0.28)  1012 n/s [18] The neutron energy spectrum with the water moderator is shifted to lower energy region because of the effect of moderation by water To maximize the thermal neutrons in this facility, we have to use water to a level of 3–5 cm above the Ta target surface [17] In this experiment the water level was cm above the target surface 2.2 Sample irradiation Natural Mo metallic foils, 12.7 mm in diameter and 0.1 mm in thickness, were used as the activation samples The Au and In metallic foils were used as the comparator reactions and the neutron flux monitors, respectively The characteristics of Mo, Au and In foils are given in Table In order to measure the thermal neutron cross-section and the resonance integral for the 98Mo(n,c)99Mo reaction by activation method relative to the 197Au(n,c)198Au reaction, the natural Mo and Au foils were irradiated with and without a Cd cover with a thickness of 0.5 mm The neutron fluxes exposed to each sample during the irradiation were determined from activities of the In monitors stacked alternatively between Mo and Au foils The Mo, Au and In foils were stacked on the sample holder as shown in Fig 1, where Mo(Cd) and Au(Cd) denote the activation foil covered with a 0.5-mm thick Cd The irradiation time was 150 yielding enough the activities to be measured in a c-ray counting system The thermal neutron flux at the center of the moderator surface was determined based on the activity of the 197Au(n,c)198Au reaction (t1/2 = 2.69517 d, Ec = 411.80 keV, Ic = 95.58% and r0 = 98.65 barn), and the obtained value was (5.85 ± 0.31)  108 n cmÀ2 sÀ1 kWÀ1 The neutron flux exposed to each sample was extrapolated from the measured activities of In foils irradiated simultaneously with the foil samples The cadmium ratio is defined by CR = (R/RCd), where R and RCd are reaction rates per atom for bare and Cd-covered isotope irradiation, respectively The obtained cadmium ratio for 197Au is 2.77 ± 0.04 and that for 98Mo is 1.21 ± 0.02, respectively The main nuclear data together with their uncertainties indicated in the bracket for the nuclear reactions considered such as 98Mo(n,c)99Mo, 197Au(n,c)198Au and 115In(n,c)116mIn are listed in Table based on the table of isotopes [20] 2.3 Measurement of activity The induced gamma activities emitted from the activation foils were measured by using a high-resolution c-ray spectrometer The c-ray spectrometer was a p-type coaxial CANBERRA high-purity germanium (HPGe)-detector with a diameter of 59.2 mm and a thickness of 30 mm The HPGe-detector was coupled to a computer-based multichannel analyzer with the associated electronics to determine the photopeak area of c-ray spectrum The spectrum analysis was done using the GENIE-2000 computer program The energy resolution of the detector was 1.80 keV full width at half maximum (FWHM) at the 1332.5-keV peak of 60Co The detection efficiency is 20% at 1332.5-keV relative to a 76.2-mm diameter  76.2-mm length NaI(Tl) detector The detection efficiency for the c-ray spectrometer was calibrated with a set of standard sources: 241Am (59.541 keV), 137Cs (661.657 keV), 54Mn (834.848 keV), 60Co (1173.237 keV and 1332.501 keV), and 133Ba (80.997 keV; 276.398 keV; 302.853 keV 356.017 and 383.815 keV) The Table Characteristics of Mo, Au and In foils Foil Diameter (mm) Thickness (mm) Weight (g) Purity (%) Au Au Mo Mo In 11 In 12 In 13 In 14 In 15 In 16 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 12.7 0.03 0.03 0.10 0.10 0.05 0.05 0.05 0.05 0.05 0.05 0.0731 ± 0.0004 0.0726 ± 0.0004 0.1284 ± 0.0006 0.1290 ± 0.0006 0.0470 ± 0.0004 0.0466 ± 0.0004 0.0471 ± 0.0004 0.0468 ± 0.0004 0.0472 ± 0.0004 0.0471 ± 0.0004 99.95 99.95 99.90 99.90 99.99 99.99 99.99 99.99 99.99 99.99 464 N Van Do et al / Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 Fig Configuration of the neutron source based on the Ta target and water moderator system and the experimental arrangement of the activation samples The samples are arranged slightly off-center to minimize the photon background from the Ta target The numbers in this figure refer to dimension in cm Table Nuclear decay data and their uncertainties given in parenthesis used for the determination of the radioactivities [20] Reaction 98 Mo(n,c) Main resonance energy (eV) 99 Mo Main c-rays Half-life Isotopic abundance (%) Energy (keV) Intensity (%) 12.1 2.7489 d (6) 140.511 (1) 158.782 (15) 181.068 (8) 580.51 (7) 739.500 (17)a 777.921 (20) 4.52 (24) 0.0189 (8) 5.99 (11) 0.0032 (5) 12.13 (22) 4.26 (8) 24.13 (31) 197 Au(n,c)198Au 4.9 2.69517 d (21) 411.80205 (17)a 675.8836 (7) 95.58 0.084 (3) 100 115 In(n,c)116mIn 1.46 54.41 (17) 416.86 (3) 1097.3 (2) 1293.54 (15)a 27.7 (12) 56.2 (11) 84.4 (17) 95.7 (2) measured detection efficiencies were fitted by the following function: Data analysis a c-Rays used in calculations ln e ẳ X an lnE=E0 ịịn ; 1ị nẳ0 where e is the detection efficiency, an represents the fitted parameters, E is the energy of the photopeak, and E0 = keV The waiting and the measuring times were chosen based on the activity and the half-life of each radioactive isotope In order to minimize the uncertainties caused by random coincidence and pile-up effects, we have chosen the appropriate distance between the sample and the detector for each measurement Generally, the dead times were kept below 0.4% during the measurement The activated foil was attached on a plastic sample holder and can be set at a distance from to 105 mm from the radioactive source to the surface of the detector To measure the activities of the 98Mo(n,c)99Mo, 197Au(n,c)198Au and 115In(n,c)116mIn reactions, we have chosen the c-ray peaks with high intensity, well separated, and relatively low background The activity of the 99Mo was determined by using the c-ray of 739.50 keV (12.13%) The activity of the 198Au was determined using the 411.80 keV (95.58%) c-ray peak In case of the 116mIn, the activity was measured using the 1293.54 keV (84.4%) c-ray peak The measuring times were varied from several ten minutes to several hours depending on the statistics of the c-ray peaks A high-purity (>99.99%) Mo foil with a natural isotopic composition (92Mo 14.84%, 94Mo 9.25%, 95Mo 15.92%, 96Mo 16.68%, 97Mo 9.55%, 98Mo 24.13%, and 100Mo 9.63%) was used for measuring the thermal neutron cross-section and the resonance integral of the 98 Mo(n,c)99Mo reaction We thus considered the following possible competing reactions: (1) 100Mo(n,2n)99Mo caused by fast neutrons with threshold energy of about 8.37 MeV and (2) 100Mo(c,n)99Mo reaction caused by high-energy photons with threshold energy of about 8.29 MeV The fast neutron flux was also checked based on the well known 27Al(n,a)24Na reaction (t1/2 = 14.9590 h, Ec = 1368.633 keV (100%) and 2754.028 keV (99.94%) and crosssection r(n,a) = 725 lb) [21] According to the characteristics of neutron flux distribution on the present experimental configuration [17], the neutrons were well thermalized, and the activity contribution from the 100Mo(n,2n)99Mo reaction to the 98Mo(n,c)99Mo reaction can be neglected For the 100Mo(c,n)99Mo competing reaction, the activity can be calculated based on the integral cross-section and the photon flux exposed to the sample The integral crosssection of the 100Mo(c,n)99Mo reaction was taken from reference [22] The photon flux was determined by the activation method using the well known 197Au(c,n)196Au reaction The activity contribution from the photonuclear reaction of 100Mo(c,n)99Mo to the 98 Mo(n,c)99Mo reaction was estimated to be 0.11% N Van Do et al / Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 465 where Nobs is the net number of counts under the full-energy peak collected during the measuring time tc, no is the number of target nuclei, e is the detector efficiency, Ic is the intensity of the c-ray, k is the decay constant, ti is the irradiation time, tw is the waiting time, s is the pulse width, and tcp is the cycle period 3.2 Resonance integral The resonance integral for the (n,c) reaction in an ideal 1/E epithermal neutron spectrum is defined by the following relation: I0 ẳ Z rEị E Ecd Fig Simplified decay scheme of 99 Mo Mo activity was determined by using the 99 Mo emits multiple c-rays, and some of them are in cascade (see Fig 2) [20] From Fig we can recognize that the net peak area of the 739.50 keV is increased due to the contribution of the sum peak formed by the true summing (also called cascade summing) of the 158.78 and 580.51 keV c-rays (summing-in) However, the c-ray of 739.50 keV is also in coincidence with the c-ray of 181.06 keV, and the true coincidence summing from these two c-ray peaks leads to decrease the net peak area of the 739.50 keV (summing-out) The true coincidence corrections for the 739.50 keV were calculated based on the measured total and absolute photopeak efficiency curves of the detector and the formulae for complex decay schemes given in references [23,24] When the measurement carried out at a distance of cm from the detector, the summing-in and the summing-out correction factors for the 739.50 keV c-ray peak were estimated to be 0.99 and 1.15, respectively 3.1 Thermal neutron cross-section The thermal neutron cross-section for the 98Mo(n,c)99Mo reaction, r0,Mo, has been determined relative to that for the 197Au (n,c)198Au standard reaction as follows [25]: RMo À F Mo;Cd RMo;Cd Gth;Au g Au   ; RAu À F Au;Cd RAu;Cd Gth;Mo g Mo ð2Þ where r0,Au is the thermal neutron cross-section of the 197Au (n,c)198Au reaction, Rx and Rx,Cd are reaction rates per atom for bare and Cd-covered x (Mo or Au) isotope irradiation, respectively The cadmium correction factor, Fx,cd accounts for the difference in count rate for Cd covered and bare samples, and Gth,x is the thermal neutron self-shielding factor for x samples The Westcott factor gx, correction for departure from 1/v cross-section behavior, for the 98Mo(n,c)99Mo reaction is 1.001 [26], and that for the 197Au(n,c)198Au reaction is 1.006 [27,28] The details of some other correction factors for the relevant nuclear reactions will be given in Section 3.3 After a bare and Cd-covered sample irradiations, the reaction rates RMo(Au) and RMo(Au),Cd for Mo and Au samples are determined by [18] RMoAuị or RMoAuị;Cd ẳ Z rEị 1eVịa E1ỵa ECd 99 c-ray peak of 739.50 keV The r0;Mo ẳ r0;Au 4ị where r(E) is the cross-section as a function of neutron energy E, and Ecd is the cadmium cut-off energy, which is usually defined as 0.55 eV However, the resonance integral defined in Eq (4) is not valid in a non-ideal, real epithermal neutron spectrum [29] The resonance integral, I0(a) for a 1/E1+a real epithermal neutron spectrum is defined as follows [29,30]: I0 aị ẳ In this work, the dE; Nobs k1 eÀktcp Þ ; no eIc ð1 À eÀks Þð1 À eÀkti ÞeÀktw ð1 À eÀktc Þ ð3Þ dE; ð5Þ where a is an epithermal neutron spectrum shaping factor, which is energy independent The relationship between I0 and I0(a) is given by [29]: I0 aị ẳ 1eVịa   I0 0:426g r0 0:426g r0 ; ỵ a a r ị 2a ỵ 1ịECd ị E 6ị where Er effective resonance energy (eV), as defined by Ryves [31,32], the term (I0 À 0.426gr0) represents the reduced resonance r integral, i.e with the 1/v tail subtracted The literature values of E are 5.65 eV for 197Au [33] and 241 eV for 98Mo [33], respectively The epithermal neutron spectrum shape factor, a at the sample irradiation position was experimentally determined by using the dual monitor method using the measured Cd ratios for the 197 Au(n,c)198Au and the 186W(n,c)187W reactions The half-life of the 187W is 23.72 h, and the main c-ray energies and intensities (%) of 187W used in the calculation are 479.53 keV (21.8%) and 685.77 keV (27.30%) After having the Cd ratios for the 197 Au(n,c)198Au and the 186W(n,c)187W reactions with the Cd cover thickness of 0.5 mm, the a-shape factor was derived from the following equation [27,30,34]: ðCRà À 1ÞAu fQ 0:4264ịGgW Er;W ịa ỵ C a ẳ ; à ðCR À 1ÞW fðQ À 0:4264ÞGgAu ðEr;Au ịa ỵ C a 7ị I0 where CR* = CR/Fcd, C a ẳ 20:4264 aỵ1ịEaCd ; Q ẳ g r0 , G is the ratio of the epithermal neutron self-shielding factor Gepi to the thermal neutron self-shielding factor Gth given in Table for Au and W foils By using the nuclear data given in Table 3, the a-shape factor has been found to be 0.068 ± 0.005 The measured resonance integral I0(a) for the 98Mo(n,c)99Mo reaction has been determined relative to that for the 197 Au(n,c)198Au reaction as a standard by the following relation [25]: I0;Mo aị ẳ I0;Au ðaÞ Â g Mo r0;Mo CRAu À F Au;Cd Gepi;Au Gth;Mo    ; g Au r0;Au CRMo À F Mo;Cd Gth;Au Gepi;Mo ð8Þ where Gth,Mo(Au) and Gepi,Mo(Au) are the thermal and the epithermal neutron self-shielding factor for Mo (or Au) sample, respectively In the determination of the resonance integral from Eq (8), the thermal and the epithermal self-shielding factors, Gth and Gepi were calculated according to the Section 3.3 Then, the obtained I0,Mo(a) value was converted to I0,Mo by using Eq (6) 466 N Van Do et al / Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 Table Nuclear data used for a determination Nuclear reaction CR Er (eV) [33] Q0 [33] G Fcd [35] g [26,28] 197 2.77 ± 0.04 2.88 ± 0.05 5.65 20.5 15.7 13.7 0.302 ± 0.006 0.415 ± 0.008 1.009 1.101 1.006 1.002 186 198 Au(n,c) Au W(n,c)187W Table Correction factors used for the calculation of thermal neutron capture cross-section and resonance integral Nuclear reaction Er (eV) [33] Q0 [33] Gth Gepi FCd [35] g [26,28] 98 241 5.65 53.1 15.7 0.999 ± 0.006 0.989 ± 0.007 0.985 ± 0.013 0.299 ± 0.005 1.000 1.009 1.001 1.006 Mo(n,c)99Mo 197 Au(n,c) 198Au 3.3 Correction factors In order to improve the accuracy of the experimental results, the following correction factors such as the neutron self-shielding, the c-ray attenuation, the cadmium correction, and the g-factor were considered The thermal neutron self-shielding correction factor for thin slabs was calculated as follows [36]: Gth ẳ en ị ; n 9ị pffiffiffiffi where n ¼ 2= pR0 t, R0 is the macroscopic capture cross-section for thermal neutrons (En = 0.0253 eV), and t is the foil thickness The epithermal neutron self-shielding factor was calculated as follows [37]: Gepi ¼ 0:94 þ ðz=2:70Þ0:82 þ 0:06; ð10Þ P where a dimensionless variable z = tot(Eres)  1.5t  (Cc/C)1/2, which converts the dependence of Gepi on the dimension and physical and nuclear parameters into an unique curve [38] and P qN A tot Eres ị ẳ M rEres is the macroscopic cross-section at the resonance peak (Eres) (where q is the density; NA is the Avogadro’s number; M is the atomic weight; rEres is the microscopic cross-section at Eres), t is the foil thickness, and C is the total resonance width (C = Cc + Cn, where Cc and Cn are resonance widths for (n,c) and (n,n0 ) reactions) The correction factor for c-ray attenuation, Fg, in the activation foil at a given c-ray energy was approximated as follows [34]: Table Uncertainties for the thermal neutron cross-section and the resonance integral measurements Uncertainties due to Uncertainties (%) 197 Au 98 Mo Thermal neutron cross-section measurements Statistical error Geometry Detection efficiency Mass (foil weight) Half-life c-Ray intensity Summing correction g-Factor Thermal neutron self-shielding factor Reference thermal neutron cross-section Abundance 0.65 0.50 2.50 0.30 0.008 0.10 – 0.11 0.75 0.09 – 2.50 0.50 2.75 0.30 0.02 1.8 0.6 0.10 0.60 – 0.29 Total experimental uncertainty 2.76 4.27 Resonance integral measurements Epithermal neutron self-shielding factor Thermal neutron self-shielding factor Reference thermal neutron cross-section Reference resonance integral Cadmium ratio a-Shape factor g-Factor 1.70 0.70 0.01 1.81 1.50 4.45 0.11 1.35 0.50 4.61 – 2.18 50 0.10 Total experimental uncertainty 5.35 6.95 where l is the linear attenuation coefficient (cmÀ1), and t is the sample thickness in cm The cadmium correction factor for the 98Mo(n,c)99Mo and 197 Au(n,c)198Au reactions are 1.000 and 1.009 [35], respectively The main correction factors used for the determination of thermal neutron capture cross-sections and resonance integrals for the 98 Mo(n,c)99Mo and 197Au(n,c)198Au are listed in Table We can see from Table that the main sources of the uncertainties for the thermal neutron cross-section measurement are due to the statistical error (2.5%), the detection efficiency (2.75%) and the c-ray intensity (1.8%) The main sources of the uncertainties for the resonance integral measurement are due to the reference thermal neutron cross-section (4.61%), the a-shape factor (4.5%), the cadmium ratio (2.18%), and the epithermal neutron self-shielding factor (1.35%) The total uncertainties for the thermal neutron crosssection and the resonance integral for the 98Mo(n,c)99Mo reaction of 5.1% and 8.8%, respectively, have been obtained by combining the uncertainties for Mo and Au listed in Table Results and discussion 4.1 Thermal neutron cross-section for The thermal neutron cross-section and the resonance integral for the 98Mo(n,c)99Mo reaction have been measured relative to the reference thermal neutron cross-section value of r0 = 98.65 ± 0.09 barn and the resonance integral value of I0 = 1550 ± 28 barn of the 197Au(n,c)198Au reaction The obtained results are the mean value from three replicate measurements The main sources of the uncertainties for the present results were estimated as given in Table The present result for the thermal neutron capture cross-section of the 98Mo(n,c)99Mo reaction is 0.136 ± 0.007 barn and is compared with the existing experimental and evaluated data in Table and in Fig As seen in Table and Fig 3, the previous experimental thermal neutron cross-sections of the 98Mo(n,c)99Mo reaction are varied from 0.12 barn [6] to 0.18 barn [7] Maximum deviation between two values is about 50% The present result, 0.136 ± 0.007 barn is Fg ¼ lt ; À eÀlÁt ð11Þ 98 Mo(n,c)99Mo reaction 467 N Van Do et al / Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 Table Thermal neutron capture cross-section for the 98 Mo(n,c)99Mo reaction Year Authors r0(barn) % Difference Monitor 2008 2006 2002 1994 1989 1988 1987 1984 1982 1979 1978 1977 1972 1969 1967 1961 1961 This work ENDF/B-VII.0 [39] JENDL-3.3 [26] JEF-2.2 [40] Babich and Anufriev [41] De Corte and Simonits [42] Gryntakis et al [43] Mughabghab [44] Wyrich and Poenitz [45] Kurosawa and Shimizu [46] Heft [47] Gleason [48] De Soete et al [9] Fabry and Jacquemin [6] Sims and Juhnke [49] Cabell [50] Dahlberg et al [7] 0.136 ± 0.007 0.1307 0.13 0.1291 0.14 ± 0.01 0.131 ± 0.002 0.13 ± 0.006 0.13 ± 0.006 0.1317 ± 0.0053 0.15 ± 0.03 0.144 ± 0.0053 0.145 ± 0.015 0.14 0.12 ± 0.005 0.137 ± 0.006 0.136 ± 0.003 0.18 ± 0.02 – À4.1 À4.6 À5.3 2.9 À3.8 À4.6 À4.6 À3.3 9.3 5.6 6.2 2.9 À13.3 0.7 0.0 24.4 Au – – – – Au – – Au Au Au, Sc, Co, U Au – Au 59 Co Au Au % Difference means that the percentage difference = 100  (1 – this work/literature value) in good agreement with the experimental results reported by Babich and Anufriev [41], De Corte and Simonits [42], Gryntakis et al [43], Wyrich and Poenitz [45], Sims and Juhnke [49], and Cabell [50] On the other hand, the measurements reported by Kurosawa and Shimizu [46], Heft [47], Gleason [48], Fabry and Jacquemin [6], and Dahlberg et al [7] differ by more than 5.1% from the present Fig Thermal neutron cross-sections of the Table Resonance integrals for the 98 98 result The evaluated values from ENDF/B-VII.0 [39], JENDL-3.3 [26], and JFF-2.2 [40] are agreed with the present result 4.2 Resonance integral for 98 Mo(n,c)99Mo reaction The present resonance integral value for the 98Mo(n,c)99Mo reaction given in Table has been found to be 7.02 ± 0.62 barn, Mo(n,c)99Mo reaction Fig Resonance integrals of the 98 Mo(n,c)99Mo reaction Mo(n,c)99Mo reaction Year Authors I0 (barn) Cd cut-off energy (eV) % Difference Monitor 2008 2002 1994 1994 1987 1984 1978 1977 1972 1972 1971 1969 1968 1967 1961 This work JENDL-3.3 [26] JEF-2.2 [40] ENDF/B-VI [40] Gryntakis et al [43] Mughabghab [44] Heft [47] Gleason [48] Stainnes [51] De Soete et al [9] De Corte et al [8] Koehler and Schneider [52] De Lange and Bigham [53] Sims and Juhnke [49] Cabell [50] 7.02 ± 0.62 6.553 6.954 6.81 7.3 ± 1.8 6.9 ± 0.3 7.42 ± 0.3 5.2 ± 0.2 7.1 ± 8.2 4.72 6.38 ± 0.15 6.3 ± 0.8 6.79 ± 0.042 6.69 ± 0.13 0.55 – – – – – 0.5 0.5 0.5 0.5 0.5 0.56 0.5 0.5 0.5 – Au – – – – – Au, Sc, Co, U Au Au – Au, Co, In Au In, Au Co Au % Difference means that the percentage difference = 100  (1 – this work/literature value) À7.1 À0.9 À3.1 3.8 À1.7 5.4 À35.0 1.1 14.4 À48.7 À10.0 À11.4 À3.4 À4.9 468 N Van Do et al / Nuclear Instruments and Methods in Physics Research B 267 (2009) 462–468 by assuming the cadmium cut-off energy as 0.55 eV and relative to the reference value of 1550 ± 28 barn of the 197Au(n,c)198Au reaction The Fig compares the present result with the existing experimental data and evaluated data As seen in Table and Fig 4, the existing resonance integrals for the 98Mo(n,c)99Mo reaction are in the range of 4.72 barn [8] to 8.2 barn [9] The present result, 7.02 ± 0.62 barn is in good agreement with the values obtained by Gryntakis [43], Heft [47], Stainnes [51], Sims and Juhnke [49], and Cabell [50] However, the present result differs from the data obtained by Koehler and Schneider [52], De Lange and Bigham [53], De Soete et al [9], Gleason [48], and De Corte et al [8] The evaluated resonance integral values of JEF-2.2 [40], ENDF/B-VI [40], and JENDL-3.3 [26] are lower than the present result by about 1–7% Conclusion The thermal neutron cross-section and the resonance integral for the 98Mo(n,c)99Mo reaction have been measured relative to the reference reaction 197Au(n,c)198Au by the activation method at the Pohang Neutron Facility The results obtained for the thermal neutron cross-section and the resonance integral of the 98 Mo(n,c)99Mo reaction are 0.136 ± 0.007 barn and 7.02 ± 0.62 barn, respectively The present results for the thermal neutron cross-section value and the resonance integral value are in good agreement with most of the existing experimental and the evaluated data within the limits of error as shown in Figs and Acknowledgments The authors would like to express their sincere thanks to the staff of the Pohang Accelerator Laboratory for excellent operation of the electron linac and their strong support This work was supported by the Korea Science and Engineering Foundation (KOSEF) through a Grant provided by the Korean Ministry of Education, Science and Technology (MEST) in 2007 and 2008 (Project No M2 07B090010810 and M2 08B090010810), by the Science Research Center project of the Center for High Energy Physics, Kyungpook National University, and by the Vietnam National Basic Research Program in Natural Science One of authors (Y.D.O) is supported by the Korea Research Foundation Grant (KRF-2006-353-C00014) References [1] M.S Uddin, M Hagiwara, F Tarkanyi, F Ditroi, M Baba, Appl Radiat Isot 60 (2004) 911 [2] P Froment et al., Nucl Instr and Meth A 493 (2002) 165 [3] J Bourges, C Madic, G Kochly, Nucl Technol 113 (2) (1996) 204 [4] V Krivan, Anal Chim Acta 79 (1975) 161 [5] A.I Ryabchikov, V.S Skuridin, E.V Nesterov, E.V Chibsov, V.M Golokov, Nucl Instr and Meth B 213 (2004) 364 [6] A Fabry, R Jacquemin, Progress Report, March 1969, p.195, Available from: Exfor Data Bank [7] R Dahlberg, K Jirlow, E Johansson, J Nucl Energy 14 (1961) 53 [8] F De Corte, A 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Gth,Mo(Au) and Gepi,Mo(Au) are the thermal and the epithermal neutron self-shielding factor for Mo (or Au) sample, respectively In the determination of the resonance integral from Eq (8), the thermal and. .. to measure the thermal neutron cross-section and the resonance integral for the 98Mo(n,c)99Mo reaction by activation method relative to the 197Au(n,c)198Au reaction, the natural Mo and Au foils... cross-section and the resonance integral of the 98Mo(n,c)99Mo reaction by using the activation method at the Pohang Neutron Facility (PNF) based on the 65-MeV electron linac The thermal neutron cross-section