IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 Evaluation of The Nuclear Data on(α,n)Reaction for Natural Molybdenum H.M.T. Hamadani ,T.A.Younis ,S. A. Ebrahiem Department of Physics , College of Education Ibn Al-Haitham , University of Baghda Abstract The cross section evaluation for (α,n) reaction was calculated according to the available International Atomic Energy Agency (IAEA) and other experimental published data . These cross section are the most recent data , while the well known international libraries like ENDF , JENDL , JEFF , etc. We considered an energy range from threshold to 25 M eV in interval (1 MeV). The average weighted cross sections for all available experimental and theoretical(JENDL) data and for all the considered isotopes was calculated . The cross section of the element is then calculated according to the cross sections of the isotopes of that element taking into account their abundance . A mathematical representative equation for each of the element and their isotopes are "formulated" they represent the variation of the cross section with energy . The evaluated (α,n) cross sections which was used to calculate the neutron yield for (Mo) for the first time ,which are very important in nuclear technology . Introduction When two charged nuclei , overcoming their coulomb repulsion , a rearrangement of the constituents of the nucleus may occur . Thus the nuclear reaction takes place when an initial state involving nucleons is converted into different final state involving nucleons similar to the rearrangement of atoms in reacting molecules during a chemical reaction . Nuclear reactions are usually produced by bombarding a target nucleus with a nuclear projectile, in most cases a nucleon (neutron or proton ) or a light nucleus such as a deuteron or an α-particle ….. etc [1]. If a target nucleus X is bombarded by a particle a , and result in a nucleus Y with emitted particle b , this is written as (2) : bYaX  ------ ( 1) To shorten the notation a reaction of type ( 1 ) is designated by : YbaX ),( ------- (2) In some cases b and Y have comparable masses ( spallation or fission ) , or are identical . In most cases in which more than two products appears , it is possible to describe the process as a rapid sequence of two – product reactions [2] 11 YbXa  221 YbY  332 YbY  ------(3) IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 The excited product nucleus usually decays very quickly to the ground state with the emission of γ-rays [3] . Theory For bombarding energies below 100 MeV, nuclear reactions usually produce two products [1]. They are of the type : bYaX  ------- (4) Where X = target (at rest in the lab. System) a = bombarding particle Y = heavy reaction product b = light reaction product Since the number of protons and neutrons remain unchanged in a reaction , all masses can be written as atomic masses if electron binding energy differences (of a few eV) are ignored . Conservation of energy , therefore gives for the above reaction: yybbxaa TcMTcMcMTcM  2222 ------- (5) Where T represents the laboratory kinetic energy of each particle . The Q– value of the reaction is defined as the difference between the final and initial kinetic energies: ayb TTTQ  -------- (6) Or 2][ cMMMMQ ybxa  -------(7) If Q is positive , the reaction is said to be exo-ergic process , if Q is negative , it is endo- ergic process [1] . A reaction cannot take place unless particles b and y emerge with positive kinetic energies , that is , 0 yb TT --------- (8) 0 aTQ -------- (9) In figure (1) the lab. system Tx= 0 , Pa = (2maTa) 1/2 and a = (2Ta/ma) 1/2 ,while in the C.M. system: Pc.m. = Pa + Px ------ (10) and Vc.m . = Pa / (ma+ mx) ------ (11) Qo = M ac 2 + Mxc 2 – M bc 2 – Myc2 = Tb + Ty – Ta ------ (12) Where Qo is the Q-value of the reaction with the product nucleus Y (in the ground state) . On the other hand, many reactions leave Y in excited states, in that case: Q = M ac 2 + Mxc 2 – M bc 2 – My *c2 = Tb + Ty - Ta ------ (13) Then for ; Q>0 Mac 2 + M xc 2 > M bc 2 + My *c2 ; Tb + Ty – Ta >0 ----- (14) and for ; Q<0 Mac 2 + M xc 2 < M bc 2 + Myc 2 ; Tb + Ty – Ta <0 ---- (15) So the Q < 0 process cannot occur spontaneously, which means that there is a threshold energy Ta(thr) given by [1]: Ta(thr) = Ethr = - Q (1 + Ma/M x) ------- (16) In general, the Q-value of reactions in terms of Ta, Tb, M a, M x, M b, M y, and angle ( )is given by IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 cos)( 2 )1()1( 2/1 bbaa yy a a y b b TMTM MM M T M M TQ  ------ (17) which is called the Q equation. The Yield of neutron detected per incident particle , Yn , for an ideal , thin , and uniform target and monoenergetic beam of energy Eb is given by [4] : )()()( bbn EEntY  -------- (18) Where : (nt) is the a real number density of target atoms  is the reaction cross section  is the neutron-detection efficiency For target which is not infinitesimally thin , the beam loses energy as it passes through the target , and the Yield is then given by :     b thr E E n E dX dE EdfEE Y )( )()(  ----------- (19) In which ( Ethr = Eb - ∆E ) Where : ∆E is the energy loss of the beam in the target f is the number of target atoms in each target molecule )( E dX dE  is the stopping power per target molecule . If the target is sufficiently thick, and there exists one atom per each molecule (i.e., f = 1) and taking the efficiency  (E`) = 1, then the resulting yield is called the thick-target yield which is given by [4] :  b thr E E b dXdE dEE EY )/( )( )(  ------ (20) Where ( Ethr ) is the reaction threshold energy. The sets of experimental data were compared in given energy intervals . First , averaged cross-section values were determined by taking the characteristics of the excitation function of the reaction in equation into account , namely the structural characteristics of their alpha particle energy dependence . The averaging was done over energy intervals of 0.5 MeV in general for alpha particle energies up to 25 MeV. Values for the weighted average cross-sections based on (n) measured values were determined for each energy interval using the expression for σ-bar[5] :     n i i n i ii w w 1 1   -------- (21) , where : 2)( 1 i iw   Is the weight given to the experimental value on the basis of the fractional standard deviation[5] IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010    n i i FSD w 1 1  -------- (22) Result and Discussion Cross Section of 92 Mo(α,n) 95 Ru Reaction : The reaction Q-value and threshold energy are (-9.0016 Mev,9.3936 Mev) respectively for the neutron emission reactions on ( 92Mo) by α-particle bombardment. The latest cross sections of 92Mo(α,n)95Ru reaction available in literature have been measured and declared by Denzler [6] , Esterlund [7] , Levkovskij [8] and Graf [9] . These data have been plotted , spline interpolated and recalculated in steps of (1 MeV) from threshold energy to (25 MeV) of the α-particle energy by using Matlab program . The weighted average cross sections and the corresponding error are calculated by using eq. (21) , (22) respectively . The evaluated cross sections from ref. [6] , [7] ,[8] and [9] are listed too in table (1) . Fig. (2) shows the corresponding cross sections with an empirical formula . Cross Section of 94Mo(α,n)97Ru Reaction : The reaction Q-value and threshold energy are (-7.94387 Mev, 8.28246 Mev) respectively for the neutron emission reactions on (94Mo) by α-particle bombardment. The cross sections of the 94Mo(α,n)95Ru reaction have been published as a function of α- energy by Levkovskij [8] and Graf [9] . These data have been plotted , sp line interpolated and recalculated in steps of (1MeV) from threshold energy to (25 MeV) of the α-particle energy by using Matlab program . The weighted average cross sections and the corresponding error are calculated by using eq. (21) , (22) respectively . The reproduced cross sections from ref.[8] and [9] are listed too in table (2) . Fig. (3) shows the corresponding cross sections with an empirical formula . Cross Section of 100Mo(α,n)103Ru Reaction : The reaction Q-value and threshold energy are (-4.57193 Mev,4.75509 Mev) respectively for the neutron emission reactions on (100Mo) by α-particle bombardment, and the cross sections of the 100Mo(α,n)103Ru reaction have been published as a function of α-energy by Graf [9] and Esterlund [7] . These data have been plotted , spline interpolated and recalculated in steps of (1 MeV) from threshold energy to (25 MeV) of the α-particle energy by using Matlab program . The weighted average cross sections and the corresponding error are calculated by using eq. (21) , (22) respectively . The reproduced cross sections from ref. [9] and [7] are listed too in table (3) . Fig. (4) shows the corresponding cross sections with an empirical formula . The Natural Molybdenum Natural Molybdenum Composed of (14.84%) of 92Mo , (9.25 %) of 94Mo , (15.92%) of 95Mo , (16.68%) of 96Mo , (9.55%) of 97Mo , (24.13%) of 98Mo , and (9.63%) of 100Mo . The threshold energies of 92 Mo(α,n) 95 Ru reaction , 94 Mo(α,n) 97 Ru reaction and 100Mo(α,n)103Ru reaction lies in the range of our work . The isotopes 95Mo , 96Mo , 97Mo and 98Mo does not reacte with α-particle , for this reason the cross section of natMo(α,n)Ru are calculated from the cross sections of 92Mo , 94Mo and 100Mo and the results are listed in table (4) in step of (1 MeV) . Fig. (5) shows the corresponding cross sections with an empirical formula. IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 The neutron yields of the following (α ,n ) reactions have been obtained using equation ( 21) ,and the results are plotted in fig. (6) Reference 1. Bowler , M.(1973) , " Nuclear physics " , Pergamon Press Ltd , Oxford . 2. Meyerhof , W. (1967) " Element of Nuclear physics " Mc Graw – Hill Book INC . 3. Smith , C . (1964) , " Nuclear physics 4. Norman , E. and Chupp, T. (1984) , phys. Rev. C 30 , 239 . 5. Audi , G. and Wapstra , (1995), A . " Nuclear physics " , A 595 , 4 , 409 . 6. Denzler , F. and Roesch , F. (1995), Excitation function of alpha-particle induced nuclear reactions on highly enriched Mo-92: comparative evaluation of production routes for Tc- 94m. J. Radiochimica Acta , 68,13 . 7. Esterlund , R. and Pate , B. (1965), Analysis of excitation functions via the compound statistical model. J. Nucl. Phy. , 69,401 . 8. Levkovskij , V. and Levkovskij , Act. (1991), Activation cross section unclides of average masses (A=40-100) by protons and alpha-particles with average energies (E=10-50 Mev). Cs. By Protons and Alphas , Moscow . 9. Graf , H. and Muenzel , H. (1974), Excitation Functions for alph-particle reactions with molybdenum isotopes., J. of Inorganic and Nuclear Chemistry , 36 , 3647 . Table (1) : The Cross Section of 92 Mo(α,n) 95 Ru Reaction as afunction of α-particle Eα(MeV) Cross Section (mb) Weighted average cross section(mb) error(mb) Denzler 15%[6] Esterlund 12%[7] Levkovskij 10%[8] Graf 10%[9] 9.0 ---- 0.55 34.4286 ---- 0.5624 0.066 10.0 ---- 3.01 62.2308 ---- 3.2088 0.3606 11.0 ---- 5.47 98.3846 ---- 5.8818 0.6549 12.0 36.6 21.1773 161.5 6 7.334 0.5803 13.0 75.2222 50.1318 193.8182 32 41.361 2.7136 15.0 286 163.1789 313 175.5 198.1799 11.61 16.0 327.4286 226.6667 366.2 302.2857 290.0498 16.6522 17.0 459.0667 278.3333 433 443 373.4472 21.5654 18.0 414.25 324.0588 486.9 532 421.6858 24.2863 19.0 626.6 365.8235 463.2 553 461.3275 26.4888 20.0 479.8 365.5 445.3333 574 448.0994 25.6441 21.0 498.3333 358 470 554 451.1607 25.8257 22.0 346.2857 312.2857 376.8 453.0909 367.9672 20.9695 23.0 327 261.2 290 352.1818 300.557 17.0776 24.0 296.0000 207.6923 250.0000 278.00 248.2944 14.1265 25.0 162.0000 164.6154 193.2857 210.50 183.7526 10.4315 IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 Table (2) : The Cross Section of 94Mo(α,n)95Ru Reaction as afunction of α-particle Eα(MeV) Cross Section (mb) Weighted average cross section(mb) error(mb) Levkovskij 10%[8] Graf 18%[9] 12 203.5 11 12.8053 1.9707 13 236 53.5 79.5498 8.9163 14 374 96 144.9056 15.6866 15 379.9091 283 345.2724 30.4541 16 391.2 470 405.0812 35.5076 17 507.25 686 533.0592 46.9203 18 528.6 702 554.4254 48.765 19 515.8 678 540.3828 47.5108 20 472.3333 654 497.5242 43.8364 21 401.8 583.4444 424.9937 37.5272 22 347.6 512.8889 368.1227 32.5306 23 258 442.3333 275.516 24.5436 24 247.6 370 262.4631 23.208 25 221.2857 295 232.1932 20.4259 Table (3) : The Cross Section of 100Mo(α,n)103Ru Reaction as afunction of α-particle Eα(MeV) Cross Section (mb) Weighted average cross section(mb) error(mb) Graf 10%[9] Esterlund 18%[7] 10.8 64 22.4256 34.2574 3.4142 11 66.0909 25.8412 39.1738 3.8038 12 76.5455 42.9189 59.8871 5.4375 13 87 56.124 73.8521 6.5923 14 88 68.5432 81.4393 7.1643 15 89 74.0185 84.3775 7.4007 16 82 65.7194 76.7161 6.7392 17 75 55.7701 68.1114 6.0083 18 64.4444 42.8749 55.583 4.9466 19 54.4706 33.8233 45.291 4.0595 20 46.8235 27.4323 37.6425 3.3976 21 39.75 22.7893 31.5364 2.8546 23 28.6957 ---- 28.6957 2.8696 24 26.087 ---- 26.087 2.6087 25 23.6364 ---- 23.6364 2.3636 Table (4) : The Cross Section of nat Mo(α,n)Ru Reaction Eα(MeV) Cross Section (mb) Mo-92 Mo-94 Mo-100 Mo-nat 9 0.5624 ---- ---- 0.0835 10 3.2088 ---- ---- 0.4762 11 5.8818 ---- 39.1738 4.6453 12 7.334 12.8053 59.8871 8.04 13 41.361 79.5498 73.8521 20.6083 14 75.6147 144.9056 81.4393 32.4676 15 198.1799 345.2724 84.3775 69.4731 16 290.0498 405.0812 76.7161 87.9012 17 373.4472 533.0592 68.1114 111.2867 18 421.6858 554.4254 55.583 119.2152 19 461.3275 540.3828 45.291 122.8079 20 448.0994 497.5242 37.6425 116.1439 21 451.1607 424.9937 31.5364 109.3011 22 367.9672 368.1227 26.2536 91.1859 23 300.557 275.516 28.6957 72.8513 24 248.2944 262.4631 26.087 63.6369 25 183.7526 232.1932 23.6364 51.0229 IHJPAS mb mb P` Pb mx P -P ma Pa ma mx my Py -P ̀ my (a) Laboratory system. (b) C.M. system. Fig. (1):The nuclear reaction observed in laboratory and center of mass coordinates Fig.(2): Cross Sections of 92Mo(α,n)95Ru Reaction    IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 Fig.(3): Cross Sections of 94Mo(α,n)95Ru Reaction Fig.(4):Cross Sections of 100Mo(α,n)103Ru Reaction IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3) 2010 Fig.(5): Cross Sections of natMo(α,n)Ru Reaction Fig.(6): Neutron Yield for nat Mo IHJPAS 2010) 3( 23مجلة ابن الهیثم للعلوم الصرفة والتطبیقیة المجلد الخاصة لعنصر) α,n(تقییم المعطیات النوویة لتفاعالت یومدالمولب سمیرة احمد ابراهیم ،تغرید عبدالجباریونس ،الحمداني دى مجید توفیقه د ، ابن الهیثم-كلیة التربیة ،قسم الفیزیاء جامعة بغدا الخالصه قد تم حسابها وفقا للمعلـن مـن سـجالت الوكالـة الدولیـة للطاقـة الذریـة وهـي ) α,n( ان قیمة المقاطع العرضیة لتفاعالت ، ENDFمثــل ،بینمـا تؤشـر ســجالت المكتبـات العالمیـة المشـهورة، ادر المقــاطع العرضـیة احـدث وادق مصـدر مـن مصـ JENDL ،JEFF الى ان بعض المقاطع العرضیة للنظائر التي تم تناولها قد تم اعدادها في زمن سابق. ــى تخــذأ ــة للمقــاطع العرضـــیة للمـــدى الطــاقي مـــن طاقـــة العتبــة والـ ــات المطلوبـ ة وبخ) MeV25(القیاسـ طـــوات طاقیـــ )1MeV ( ومن ثم ایجاد المعدل الموزون للمقاطع العرضیة لكل طاقة من طاقات جسیمات الفا السـاقطة وتـم جدولـة جمیـع .كافة البیانات المستحصلة النظائر للعناصـر باالعتمـاد علـى المقـاطع العرضـیة المحسـوبة لكـل نظیـر مـن العنصـر وعلـى وفــرة المقـاطع العرضـیة حسـبت المعادالت الریاضیة لكل نظیر قید الدراسة والتي تمثل تغیـر المقطـع العرضـي بداللـة واستبطت. نظائر في الطبیعة لهذه ا .الطاقة ـــــــیلة ال ــــ ــــ ــــ ـاب الحصــ ــــ ــــ ــــ ــــ ــــــتحدثة لحســـ ــــ ــــ ــــ ـــیة المســـ ــــ ــــ ــــ ــــ ـــاطع العرضــ ــــ ــــ ــــ ــــ ـــــذه المقـ ــــ ــــ ــــ ــــــتخدمت هــــ ــــ ــــ ــــ ـةاســ ــــ ــــ ــــ ــــ ــــ . نیوترونی IHJPAS IHJPAS IHJPAS