Experimental Determination of Cross Sections for (n,x) Nuclear Reactions

Transcription

1 WDS'07 Proceedings of Contributed Papers, Part III, , ISBN MATFYZPRESS Experimental Determination of Cross Sections for (n,x) Nuclear Reactions N. Dzysiuk and I. Kadenko Taras Shevchenko National University of Kyiv, Department of Nuclear Physics, Ukraine. Abstract. The neutron-activation method was used for obtaining new experimental data on cross sections both for 72 Ge(n,2n) 71 Ge nuclear reaction and for some other (n,x) reactions on zirconium and germanium isotopes. The neutron generator was used as a neutron source. The samples in a shape of foils of natural germanium and zirconium were irradiated by DT- neutrons. The following sources of uncertainties are taken into account: instability of neutron flux in time, real geometry of experiment, the effect of true coincident summing of gamma-rays during activation product spectrum measurements and the effect of self-absorption of gamma-rays in a sample. The obtained results could be useful to avoid ambiguity in values of cross sections for nuclear reactions specified and to indicate the necessity of additional experiments for reduction the cross section uncertainty. Monte Carlo simulations were used in calculations of correction factors. Introduction Precise determination of nuclear reaction cross sections and investigations of interaction between neutrons and atomic nuclei have taken prevalent place in modern neutron physics. Requirements of neutron cross sections with high accuracy depend on amount of nuclear data practical applications such as: astrophysics, transmutation of radioactive waste, radiation medicine and fusion technology studies as well. Notwithstanding the fact that in the world there are exists many bases of experimental and evaluated nuclear data, but they are still incomplete and essential discrepancy at the energy range about 14 MeV observed between results obtained by others authors [1]. Moreover a discrepancy between existing results leads to errors during interpolation of experimental data and has action upon the quality of estimated data. Neutron cross sections are important for development of fusion reactor technology in the view of activation, radiation-damage and mechanical stability of construction materials as well as radiation protection etc. Furthermore, measurements of nuclear reaction cross sections in this energy range are important for testing of nuclear reaction models. Germanium and zirconium elements were selected because of significant role in nuclear spectroscopy measurements and nuclear reactor building respectively. One of the considered reactions is 72 Ge(n,2n) 71 Ge was chosen due to lack of such information in experimental nuclear data base [2]. Experimental method Experimental measurements have been performed at the Nuclear Physics Department of Taras Shevchenko National University of Kyiv. Activation cross section measurements were curried out using a conventional, widely used scheme: irradiation cooling gamma-rays counting [3]. Germanium and zirconium samples of natural composition in the shape of foil were irradiated by D-T neutrons. The neutron generator NG-300/15 was used as a source of fast neutrons. It was made two series of experimental measurements. Cross sections of 92 Zr(n,p) 92 Y, 94 Zr(n,p) 94 Y nuclear reactions were measured in the first experiment and cross sections of 72 Ge(n,2n) 71 Ge, 70 Ge(n,p) 70 Ga for 14.5 MeV neutron energy were measured in second experiment. Neutrons with energy 14 MeV are generated by T(d, n) 4 He reaction. The maximum current of ions beam was 10 ma. For this purpose a molecular component of deuteron beam D + 2 has been used. A diaphragm, which gave an opportunity of getting beam diameter 10 mm, has been used to decrease disperse of neutron energy in ion-pipe that allows to use different parts of sample after every irradiated series. Location of deuteron beam axis was defined from distribution of neutron flux density on the target by method of foil activation. 188

2 The average neutron energy was determined experimentally using Zr/Nb ratio [4]. Because of cross section value strongly depends on neutron energy, as we know that in neutron generator neutron energy connected with deuteron energy. But when deuterons slow down through the thick tritium targets in most of neutron generators the mean interaction energy within the titanium is somewhat less than the incident energy. It is therefore not possible to determinate deuteron energy without precise knowledge of the tritium distribution in the target. Hence it is not appropriate to employ the kinematical equation directly. The samples were irradiated under 0, 120 and 150 degrees angles relative to deuteron flux 8 direction on 75 mm distance from Ti-T target. The average neutron flux density was (n/s). Magnitude of neutron flux density was kept constant with accuracy 5 %. The neutron flux on the samples was determined through the activation technique using the 27 Al(n,α) 24 Na reaction. Time of irradiation has been chosen in range of min. Instrumental spectrums have been measured by 3 HPGe detector with sensitive volume of 110 сm (Canberra). Detector was placed in 50 mm thick lead shielding. Energy resolution was determined as 2.1 KeV γ1332 KeV 60 Co and 1.2 KeV for γ122 KeV 152 Eu. Usage of 90 Zr(n,2n) 89(g m) Zr monitor gives essential advantage because inner monitors lead to decrease errors caused by incomplete knowledge of irradiation geometry, geometry of spectrums measurements and assumption of uniform volume distribution of activity. All experiments preliminary have been optimized: cooling time was minimized for detection of short-lived nuclei, time of irradiation was enough long for providing of high reaction yields. All cross sections have been determined by following equation: ( 1 m tirrad m tcooling m m tmes m ) ( 1 ) t x tcooling _ x x tmes _ x ( 1 x irrad ) ( 1 ) Sx εm e e e Nm nγ λ m x σ x = σ S ε e e e N n λ m x x γ x m where: m means monitor and x investigative respectively, - cross section of monitor nuclear reaction; σ x cross section of investigative nuclear reaction; t irrad time of irradiation, t mes _ х, t mes _ m time of measuring; t cooling _ х, t cooling _ m cooling time; Nx, N m number of nuclei in materials; n γ x, n γ m quantum yields for gamma-rays; ε x, ε m detector efficiency; Sx, S m ln( 2 ) peaks area; λx, λ m constant of radioactive decay ( λ = ). All cross section values were T obtained in relation to the standard reaction cross sections of 27 Al(n,α) 24 Na and 90 Zr(n,2n) 89(g m) Zr. Identification of activation products were implemented by variation of conditions of irradiations and measurements as well. In neutron generator hall the background neutrons were generated via nonelastic scattering of fast neutrons on the constructive materials and walls. For protecting from bakgraund neutrons investigated samples enclosed into indium and cadmium foils because they have big neutron radiation capture cross sections of thermal and resonance neutrons. True-coincidence summing and self-absorption For providing of high accuracy were obtained results it was imperative and very important to take into account some effects which lead to underestimations of cross sections values. Decay of a nucleus is described as a set of cascades of transitions, each cascade having its own probability of occurrence. The detector with high efficiency geometries is cause coincidence summing effects: two or more gamma-rays emitted from the same atom can interact with a detector within a very short time (up to 1 µs). As a result, the detector cannot distinguish between them and treats them as a single interaction, the energy transfer being the sum of the individual interactions. Such coun-trate independent coincidence summing effects can seriously affect a gamma-ray spectrum. Calculations of corrections are quite complicated task, because for this purpose it is necessary to know the total efficiency of detector when implement measuring of volume source. Therefore, the variation of the total efficiency over the source volume should be taken into account. The correction factor has been calculated by NucliseMaster+ code [5]. The input parameters for calculations were the information about nuclear 1/ 2 σ m m (1) 189

3 structure from estimated data base ENSDF and geometry of measurements. The first step is making imitation of all intranuclear and intratomic cascades, which accompanied by emission of correlated gamma-rays and X-rays. In the second step repeats all previous calculations excluding correlations between radiated particles. Thus correction factor equal to ratio of energy line areas were calculated in two mentioned cases. The effect of self-absorption leads to underestimations of measured results as well. The reason of this effect is finite dimensions of used samples instead of point geometry. The incident gamma-rays can interact with the material via one of three main mechanisms: photoelectric absorption, Compton scattering and pair production and in that way can be absorb there. Calculations of absorption µ ρ d corrections can be done according to the simple formula: K = (µ - attenuation absorption d e µρ 1 coeffisient; ρ-density; d-thickness), but this formula quite approximate because valid only for longdistant geometry measurements. The samples have been placed on the detector surface, so that is why, it was important to take into account gamma-rays which radiated under little angels to normal direction. A modeling approach has been used with Monte Carlo simulations. The correction factor equals to the ratio of detector efficiency in cases of point and volume radiation sources. The efficiency of point and volume sources (activated foils) was calculated by MCNP4C code [6]. The code follows the interaction history of each gamma-ray until their energy is dissipated, considering the secondary particles formed as a result photoelectric absorption, Compton scattering, or pair production interactions. In MCNP4C calculations the number of histories generated at each run was chosen so, that provided the statistical uncertainty associated to the full-energy absorption was less than 1%. Optimization of the detector geometry parameters has been done by minimisation of the relative deviation between calculated and experimental efficiency of calibration point sources ( calc exp ) 100 ε ε / ε exp (in %) for each locations and energy. For this calculations was used the semiconductor model of coaxial HPGe detector, which was built and tested by additional experimental efficiency measurements. Peculiarity of determination of cross section for nuclear reaction 72 Ge(n,2n) 71 Ge It should be emphasized that essential part of the present work is the investigation of 72 Ge(n,2n) 71 Ge nuclear reaction. The absence of information about this reaction has been aforementioned. This task is quite complicated, because the product of reaction is a nucleus 71 Ge which does not emit prompt gamma-rays at excited state but decays only by electron capture channel. The decay scheme of 71 Ge is presented in Figure 1. The half-life of 71 Ge is 11.4 days. The cross section was determined by detection of gallium X-ray with energy KeV. For determination of this cross section the time of irradiation was 120 min, with further cooling time of 7 days. During of cooling time the activities of others reaction products with half-time life less entirely decayed. The time of measurement of instrumental spectrum was chosen as 6 days. Spectrum was measured with Ge-planar detector (ORTEC). High energy resolution of this detector has provided to distinguish the X-Rays of germanium and gallium atoms during instrumental spectrums measurements. Figure 1. Decay scheme of 71 Ge. 190

4 DZYSIUK AND KADENKO: CROSS SECTIONS FOR (n,x) NUCLEAR REACTIONS Results of measurements and calculations Six cross sections values were measured and presented in Table 1. The value of Ge( n, α ) m Zn cross section is good agreement with data from EXFOR [1]. Cross section of Ge( n, p) Ga reaction measured with higher precision. Comparison of experimentally obtained cross sections with calculations of excitation function for Ge( n,2 n) Ge reaction by code Talys -064 and data from two evaluated nuclear data bases Jendl-3.3 and Jeff-3.1/A is pointed in Figure 2. Talys is a computer code system for the analysis and prediction of nuclear reactions. It should be noticed that at 14 MeV energy is quite important to take into account the pre-equilibrium reactions thus for this in calculations of excitation function was used two-component exiton model [8]. Figure 3 shows the data comparison for nuclear reaction Ge( n, p) Ga, there pointed measured cross section value for neutron energy 14.5 MeV with data from database EXFOR. Between calculated solid and dash curves in Figure 3 observes some deviation in energy range 8 16 MeV. In this case Fermi gas model for level density calculations in compound stage of nuclear reaction with some distinctions (Ldmodel1 and Ldmodel2 [8]) was used. Conclusion Two new cross sections for 72 Ge(n,2n) 71 Ge nuclear reactions were measured. Effectiveness and correctness of using the neutron-activation method were confirmed by good agreement of obtained results with results of another research groups. Obtained results could be useful to avoid ambiguity in values of cross sections for nuclear reactions specified. Presented results can be used in the process of estimated data calculation and provide more correct cross section values for testing of nuclear reaction 70 Ge(n,p) 70 Ga 72 Ge(n,2n) 71 Ge models. 1Cross section, mb 0Talys-064 Jendl-3.3 % (Our results 2007) Jeff-3.1/A Neutron energy, MeV Cross Section, mb H.M. Hoang(1992)??? G.P. Vinitskaya(1967) C.S. Khurana(1965) E.B. Paul(1953) Our result(2007) Talys-0.64(Ldmodel1) Talys-0.64(Ldmodel2) 10Neutrun energy, MeV 12Figure 2. Comparison of our experimental data with Talys-0.64 calculations and data from evaluated databases for Ge( n,2 n) Ge Figure 3. Comparison of our experimental data with Talys-0.64 calculations and data from evaluated databases for Ge( n, p) Ga Table 1. Cross sections data Nuclear reaction Cross section, mb Neutron energy, MeV EXFOR Ge( n, α ) m Zn 3.67(0.61) (0.4) Ge( n, p) Ga 123(12) (65) Ge( n,2 n) Ge 768(66) Ge( n,2 n) Ge 892(51) Zr( np, ) Y 19.8(2.2) (12.5) Zr( np, ) Y 8.8 (0.6) (0.7) 191

5 Acknowledgments. The authors are grateful to the staff of neutron generator and especially to Dr. V. Maydanyuk for their help assistance during irradiation and measurements. References [1] Cross section information storage and retrieval system (EXFOR), National Nuclear Data Center (NNDC), Brookhaven National Laboratory, USA. (online) [2] Forrest R.A. Data requirements for neutron activation Part I : Cross sections, Fusion Engineering and Design, -2006, -V.81 pp [3] Begun S.V., Kadenko I.M., Maidanyuk V.K., Neplyuev V.M., Plujko V.A., Primenko G.I., Tarakanov V.K. Determination of the cross sections of (n, x) nuclear reactions on Y, La, Ta, Pb and Bi at the energy of neutrons about 14 MeV, Journal of Nuclear Science and Technology Suppl. 2, Vol. 1. pp [4] Agrawal H.M., Pepelnik R. Determination of the mean neutron energy using the Zr/Nb and the Ni method, Nuclear Instrum. and Meth. in Physics Research A366, [5] A. Berlizov, V. Danilenko, A. Kazimirov, S.Solovyova, Statistical modeling of true-coincidence corrections with using of estimated nuclear data in the calculations, Atom energy, 100, vol.5, 2006, pp (in Russian) [6] Briesmeister J.F. MCNP a general Monte Carlo N-particle transport code, Los Alamos National Laboratory Report, 1997, LA M. [7] Semkova V., Plompen A.J.M. Monte Carlo simulation of the efficiency of a large HPGe detector, Scientific report 2005, EUR EN [8] Koning A.J., Hilaire S. and M.C. Duijestijn Talys:Comprehensive nuclear reaction modeling Proceedings of the International Conference on Nuclear Data for Science and Technology-ND 2004, Sep 26- Oct.1,Santa Fe, USA 192