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. Hama dani ,T.A.Younis ,S. A. Ebrahiem Departme nt of Physics , College of Education I bn Al-Haitham , Unive rsity of Baghda Abstract The cross section evaluation for (α,n) reaction was calculated according to the available International At omic Energy Agency (IAEA) and other exp erimental p ublished 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 M eV). The average weighted cross sections for all available exp erimental and theoretical(JENDL) data and for all the considered isotop es was calculated . The cross section of the element is then calculated according to the cross sections of the isotop es of that element taking into account their abundance . A mathematical representative equation for each of the element and their isotop es 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 y ield for (M o) for the first time ,which are very imp ortant in nuclear technology . Introduction When two charged nuclei , overcoming their coulomb repulsion , a rearrangement of the constituents of the nucleus may occur . Thus t he nuclear reaction takes p lace when an initial st ate involving nucleons is converted into different final st ate involving nucleons similar to the rearrangement of atoms in reacting molecules during a chemical reaction . Nuclear reactions are usually p roduced by bombarding a target nucleus with a nuclear p rojectile, in most cases a nucleon (neutron or p roton ) or a light nucleus such as a deuteron or an α-particle ….. etc [1]. If a target nucleus X is bombarded by a p article a , and result in a nucleus Y with emitt ed particle b , this is written as (2) : bYaX  ------ ( 1) To short en the notation a reaction of ty p e ( 1 ) is designated by : YbaX ),( ------- (2) In some cases b and Y have comp arable masses ( sp allation or fission ) , or are identical . In most cases in which more than two p roducts app ears , it is p ossible to describe the p rocess as a rap id sequence of two – p roduct 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 st ate with the emission of γ-rays [3] . The ory For bombarding energies below 100 M eV, nuclear reactions usually p roduce two p roducts [1]. They are of the ty p e : bYaX  ------- (4) Where X = t arget (at rest in the lab. Sy st em) a = bombarding p article Y = heavy reaction p roduct b = light reaction product Since the number of p rotons and neutrons remain unchanged in a reaction , all masses can be writt en 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 rep resents 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 p ositive , the reaction is said to be exo-ergic p rocess , if Q is negative , it is endo- ergic p rocess [1] . A reaction cannot take p lace unless p articles b and y emerge with p ositive kinetic energies , that is , 0 yb TT --------- (8) 0 aTQ -------- (9) In figure (1) the lab. sy st em Tx= 0 , Pa = (2maTa) 1/2 and a = (2T a/ma) 1/2 ,while in the C.M . sy st em: Pc.m . = Pa + Px ------ (10) and Vc.m . = Pa / (ma+ mx) ------ (11) Qo = M ac 2 + Mxc 2 – M bc 2 – My c 2 = T b + Ty – Ta ------ (12) Where Qo is the Q-value of the reaction with the product nucleus Y (in the ground st ate) . On t he other hand, many reactions leave Y in excited st ates, in that case: Q = M ac 2 + Mxc 2 – M bc 2 – My * c 2 = T b + Ty - Ta ------ (13) Then for ; Q>0 Mac 2 + M xc 2 > M bc 2 + My * c 2 ; Tb + Ty – Ta >0 ----- (14) and for ; Q<0 Mac 2 + M xc 2 < M bc 2 + My c 2 ; Tb + Ty – Ta <0 ---- (15) So the Q < 0 p rocess cannot occur sp ontaneously , 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 p article , Yn , for an id eal , thin , and uniform target and monoener getic 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 t arget which is not infinitesimally thin , the beam loses energy as it p asses 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 t he beam in the target f is the number of target atoms in each target molecule )( E dX dE  is the stopp ing p ower p er target molecule . If the target is sufficiently thick, and there exists one atom p er each molecule (i.e., f = 1) and taking the efficiency  (E`) = 1, then the resulting y ield is called the thick-target y ield which is given by [4] :  b th r E E b dXdE dEE EY )/( )( )(  ------ (20) Where ( Ethr ) is the reaction threshold ener gy . The sets of exp erimental data were comp ared in given ener gy 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 st ructural characteristics of their alp ha p article energy dependence . The averagin g was done over energy intervals of 0.5 M eV in general for alp ha particle energies up to 25 M eV. Valu es for the weighted average cross-sections based on (n) measured v alues wer e determined for each en ergy interval using the exp ression 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 exp erimental value on the basis of the fractional st andard 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 S ection of 92 Mo(α,n) 95 Ru Reaction : The reaction Q-value and threshold energy are (-9.0016 M ev,9.3936 M ev) resp ectively for the neutron emission reactions on ( 92 M o) by α-particle bombardment. The latest cross sections of 92 M o(α,n) 95 Ru reaction available in literature have been measured and declared by Denzler [6] , Esterlund [7] , Levkovskij [8] and Graf [9] . These data have been plott ed , sp line interpolated and recalculated in steps of (1 M eV) from threshold energy to (25 M eV) of the α-particle energy by using M atlab p rogram . The weighted average cross sections and the corresp onding error are calculated by using eq. (21) , (22) resp ectively . The evaluated cross sections from ref. [6] , [7] ,[8] and [9] are list ed too in table (1) . Fig. (2) shows t he corresp onding cross sections with an empirical formula . Cross S ection of 94 Mo(α,n) 97 Ru Reaction : The reaction Q-value and threshold energy are (-7.94387 M ev, 8.28246 M ev) resp ectively for the neutron emission reactions on ( 94 M o) by α-particle bombardment. The cross sections of the 94 M o(α,n) 95 Ru reaction have been p ublished as a function of α- energy by Levkovskij [8] and Graf [9] . These data have been p lott ed , sp line interp olated and recalculated in st eps of (1M eV) from threshold energy to (25 M eV) of the α-p article energy by using M atlab program . The weighted average cross sections and the corresp onding error are calculated by using eq. (21) , (22) resp ectively . The reproduced cross sections from ref.[8] and [9] are list ed too in table (2) . Fig. (3) shows t he corresp onding cross sections with an empirical formula . Cross S ection of 100 Mo(α,n) 103 Ru Reaction : The reaction Q-value and threshold energy are (-4.57193 M ev,4.75509 M ev) resp ectively for the neutron emission reactions on ( 100 M o) by α-particle bombardment, and the cross sections of the 100 M o(α,n) 103 Ru reaction have been p ublished as a function of α-energy by Graf [9] and Est erlund [7] . These data have been plott ed , sp line interpolated and recalculated in steps of (1 M eV) from threshold energy to (25 M eV) of the α-particle energy by using M atlab p rogram . The weighted average cross sections and the corresp onding error are calculated by using eq. (21) , (22) resp ectively . The rep roduced cross sections from ref. [9] and [7] are list ed too in table (3) . Fig. (4) shows t he corresp onding cross sections with an empirical formula . The Natural Molybdenum Natural M olybdenum Composed of (14.84%) of 92M o , (9.25 %) of 94M o , (15.92%) of 95 M o , (16.68%) of 96 M o , (9.55%) of 97 M o , (24.13%) of 98 M o , and (9.63%) of 100 M o . The threshold energies of 92 M o(α,n) 95 Ru reaction , 94 M o(α,n) 97 Ru reaction and 100 M o(α,n) 103 Ru reaction lies in the range of our work . The isot op es 95 M o , 96 M o , 97 M o and 98 M o does not reacte with α-particle , for this reason t he cross section of nat M o(α,n)Ru are calculated from the cross sections of 92 M o , 94 M o and 100 M o and the results are list ed in table (4) in st ep of (1 M eV) . Fig. (5) shows the corresp onding cross sections with an emp irical formula. IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 The neutron y ields of the following (α ,n ) reactions have been obtained using equation ( 21) ,and the results are p lott ed in fig. (6) Re ference 1. Bowler , M .(1973) , " Nuclear phy sics " , Pergamon Press Ltd , Oxford . 2. M ey erhof , W. (1967) " Element of Nuclear p hy sics " M c Graw – Hill Book INC . 3. Smith , C . (1964) , " Nuclear p hysics 4. Norman , E. and Chupp , T. (1984) , p hy s. Rev. C 30 , 239 . 5. Audi , G. and Wap st ra , (1995), A . " Nuclear physics " , A 595 , 4 , 409 . 6. Denzler , F. and Roesch , F. (1995), Excitation function of alpha-particle induced nu clear reactions on hi ghly enriched M o-92: comparative evaluation of p roduction routes for Tc- 94m. J. Radiochimica Acta , 68,13 . 7. Esterlund , R. and Pate , B. (1965), Analysis of excitation functions via the comp ound st atistical model. J. Nucl. Phy . , 69,401 . 8. Levkovskij , V. and Levkovskij , Act. (1991), Activation cross section unclides of average masses (A=40-100) by p rotons and alp ha-p articles with average ener gies (E=10-50 M ev). Cs. By Prot ons and Alp has , Moscow . 9. Graf , H. and M uenzel , H. (1974), Excitation Functions for alph-p article reactions with moly bdenum isotop es., J. of Inorganic and Nuclear Chemistry , 36 , 3647 . Table (1) : The Cross Se ction of 92 Mo(α,n) 95 Ru Reaction as afunction of α-particle Eα(M eV) 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 28 6 163.1789 31 3 175.5 198.1799 11.61 16.0 327.4286 226.6667 366.2 30 2.2857 290.0498 16 .6522 17.0 459.0667 278.3333 43 3 443 373.4472 21 .5654 18.0 41 4.25 324.0588 486.9 532 421.6858 24 .2863 19.0 626.6 365.8235 463.2 553 461.3275 26 .4888 20.0 479.8 36 5.5 445.3333 574 448.0994 25 .6441 21.0 498.3333 35 8 47 0 554 451.1607 25 .8257 22.0 346.2857 312.2857 376.8 45 3.0909 367.9672 20 .9695 23.0 32 7 26 1.2 29 0 35 2.1818 300.557 17 .0776 24.0 296.0000 207.6923 250.0000 27 8.00 248.2944 14 .1265 25.0 162.0000 164.6154 193.2857 21 0.50 183.7526 10 .4315 IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Table (2) : The Cross Se ction of 94 Mo(α,n) 95 Ru 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 Se ction of 100 Mo(α,n) 103 Ru Reaction as afunction of α-particle Eα(MeV) Cross Section (mb) Weighted average cross s ection(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 Se ction 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) La boratory system. (b) C.M. system. Fig. (1):The nuclear reaction observed in l aboratory and cente r of mass coordinates Fig.(2): Cross Se ctions of 92 Mo(α,n) 95 Ru Reaction    IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Fig.(3): Cross Se ctions of 94 Mo(α,n) 95 Ru Reaction Fig.(4):Cross Se ctions of 100 Mo(α,n) 103 Ru Reaction IHJPAS IBN AL- HAITHAM J. FO R PURE & APPL. SC I. VO L.23 (3 ) 2010 Fig.(5): Cross Se ctions of nat Mo(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 جامعة بغداد ، ابن الهیثم-كلیة التربیة ،قسم الفیزیاء 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. M(القیاســـات المطلوبـــة للمقــاطع العرضـــیة للمـــدى الطــاقي مـــن طاقـــة العتبــة والـــى تخــذأ eV25 (طـــوات طاقیـــة وبخ )1M eV ( 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 ـــــاب الحصــ ــــ ــــ ــــ ــــــتحدثة لحســـ ــــ ــــ ــــ ـــیة المســـ ــــ ــــ ــــ ــــ ـــــــاطع العرضــ ــــ ــــ ــــ ـــــذه المقـ ــــ ــــ ــــ ــــــتخدمت هــــ ــــ ــــ ــــ ـــــةاســ ــــ ــــ ــــ . نیوترونیــــ IHJPAS IHJPAS IHJPAS