A. ' " SEC-RA ‘ Maw“ String targem of ma: . v ‘ I“. 22:12: E? 32. 3'3. and “k" __‘ 53? 5392135 were measuru: tsazgies cf 0, 30, 6'7. 9' iata :ay be used in ‘- 0. Q ,_ ' ‘ 4. . «.J 4:52: 36.300 V19.~..5 C 'X b‘:. k. v K is”. .“I t...» . ‘ . {. ""‘ 2:5-‘Eerx caxculdt ¢s- .1: ms area of nuclear in v .‘CI fand cozpeti'iv AA :30 nwi“‘ ' . Y‘I - .. Vf‘! w. 3M do not procee ma, extensive infcma: .. .ne experimental neutr 3.3-: assisting interes :.i§isn A a 5 1 kCuStmct’ am “3.. 4...” Mb, of all r8a ianCtiCns’ at 19 . ‘é'LS C 3M Al) “0 C ’55‘. 3!“ ABSTRACT NEUTRON YIELDS FROM PROTON BOMBARDMENT OF THICK TARGETS Stopping targets of natural C, Al, Cu, Ag, Ta and Pb were bombarded by 22, 30, and 40 MeV protons, and the resulting neutron energy spectra were measured by the time-of—flight technique at labor— atory angles of O, 30, 60, 90, 120, and 150 degrees. The data may be used in practical experimental situations where thick target neutron yields are needed, for example, in shielding or neutron background calculations. The data also provide useful infor- mation in the area of nuclear reaction mechanisms, specifically, the magnitudes of and competition between compound nuclear reactions and reactions which do not proceed via compound nucleus formation. Also, extensive information is provided on the design and construct- ion of the experimental neutron time-of—flight facility used, with a View toward assisting interested physicists to operate such a facility, or to design, construct, and operate their own facility. Analysis of the data indicates that non-compound processes increase in importance rapidly with increasing bombarding energy, until at 40 MeV approximately 20% of all reactions resulting in neutron emission are non-compound reactions, at least in the heavy elements (A>60) . For the light elements C and A1, no clear distinction between the two types of processes could be made. :I ' Us ‘..ie L ‘ . uvivo E: the heavier elazents ”omgcund ; u‘-. 1; O... 337539235 33! GEUIYCfl 87‘. :‘re spectra can be e , In a.» n 4.3. .U.» . *"'Ye::1j: under dex'e 7",...o: ’2 these mejels h ~-—‘~-.x.g ”W162: and the-ct". buy». A . ‘ i 9-. .. ‘ ‘3”... . For the heavier elements it was found that the statistical fermi— gas model of the compound nucleus adequately describes the neutron energy spectra for neutron energies less than ~6 MeV. At higher neutron energies the spectra can be explained qualitatively by pre-equilibrium models, currently under development. It appears that further refinements in these models will yield better quantitative agreement between experiment and theory, although current agreement is not unreasonable . NEUTRON YIELDS FROM PROTON BOMBARDMENT OF THICK TARGETS by Thomas Marshall Amos, Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1972 - I 1 ' ’0 q, 3-221: .:.-:e to man. "a we'a‘n A "Q’ En’- a: ..;: Even-ale. “-5 .0; 1.5252123 E3 {7.8 co..,. I‘ a'~:~nnq Rfi" r 7 ......C33\,r b-8st J 3:12;: personal center: 'n-o-o'n'] p“v\~.¢~‘- . L.$.C.u.ay ak fink." .C‘ l- ‘-‘ Liifi Deerir‘g in tai-zi: My 7: . ° a.-. ..g.ang 1:: data r1 :‘rtzelr assistance 1 ...:r;::‘ag the cyclotr; “:4“? Hr. Rental fierce J'CLC also like to t , as“? b‘ ACKNOWLEDGEMENTS I would like to thank my thesis advisor, Professor Aaron Galonsky, flu his guidance. His encouragement, advice, and assistance were hflispensible to the completion of this work. To Professor Robert J. Sprafka and his wife, Sally, I give thanks fln'their personal concern and advice during the course of this work. I gratefully acknowledge the assistance of Dr. R. K. Jolly and lhu Robert Doering in taking the data, and the assistance of Mary Kay Zigrang in data reduction and analysis. For their assistance in construction of the experimental apparatus muiin running the cyclotron, I thank the cyclotron technical staff, empecially Mr. Norval Mercer and his machine shop staff. I would also like to thank the National Science Foundation and Khmigan State University for their financial support. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS............ LISTOFFIGURES LISTOFTABLES............. Chapter I. INTRODUCTION . . II. THE EVAPORATION THEORY OF COMPOUND NUCLEUS DECAY . . . A. Basic Statistical Arguments . . . . . . . . . . B. The Fermi Gas Model Of The Nucleus . . . . . . . . LU; APPLICATION OF THE STATISTICAL-FERMI—GAS MODEL TO THE PRESENT EXPERIMENTAL PROBLEM . . . . . . . . . . . A. The Inelastic Collision Probability And Assumptions Concerning Compound Nucleus Formation . . . . . B. Procedure Used In Calculating Absolute Thick Target Neutron Spectra And Yields . . . . . . . . . . . IV. 'THE EXPERIMENT . . . . . . . . . . . . . . . . . . . . A. Measurement 0f Neutron Energy Spectra By The Time-Of-Flight Technique . . . . . . . . . 1. General Comments On The Time-Of- -Flight Technique . . . . . . . . . . . Experimental Design And Procedure . . . . The Detector . . . . . . . . . . . . . . . The Time-Of-Flight Electronics . . . . . . Pulse Shape Discrimination . . . . . . . a. Application To Neutron Time-Of— -Flight b. Basis Of The Pulse Shape Effect . . . . c. Electronics . . . . . . . . . . . . . B. Beam Line . . . . . . . . . . . . . . . . . . C. Targets And Target Chamber . . . . . . . . . . D. Charge Collection And Integration . . . . . . . . E. Data Acquisition . . . . . . . . . . . . . . . . . UIJ-‘WN iii Page ii vii 12 12 13 20 20 20 25 28 31 34 34 35 36 44 47 SO 51 F Data Reduction . 1. Conversaon C Energy Spa (I C) "1 ' 1 m ‘ (‘3 r1 ’4 r‘) J b: I Absolute Neutron Distributions I. Estiaate Of Exre '. 2.13.1. ANALYSIS . l. Extraction 0f 3:2; Parameters . . 3. Extraction Of No Processes w AIA‘ ca.,.q ‘ “ "“Il \TW‘S UV. vuk. "-I.\ ' . ' :TW 9-, ~_:' -\ IN I I O . . . . . 5131'“? ..... A. . . . . . . Page F. Data Reduction . . . . . . . 51 1. Conversion Of Time-Of— —F1ight Spectra To Energy Spectra . .-. . . . . . . . . . . . 51 2. Calculation of Detector Efficiency . . . . - - - 54 a. Statement Of The Problem . . . . . . 54 b. Measurement Of Detector Threshold And Light Resolution . . . . . . . . . . . 55 c. Measurement Of Detector Response Function . . . . . . . . . . . . . . . . . 65 G. Corrections . . . . . . . . . . . . . . . . . 69 1. Absorption And Inscattering . . . . . . . . . . 69 2. Deadtime Correction . . . . . . . . . . . . . 72 H. Absolute Neutron Yield Spectra, Angular Distributions And Total Yields . . . . . . . . . . 75 I. Estimate Of Experimental Uncertainties . . . . . . . 101 V. DATA ANALYSIS . . . . . . . . . . . . . . . . . . . . . 103 A. Extraction 0f Nuclear Level Density and Radius Parameters . . . . . . . . . . . . . . . 103 B. Extraction Of Neutron Yields From Non-Compound Processes . . . . . . . . . . . . . . . . . . . . 110 VI. CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . 127 REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . 130 HPENDIX O O O O O C O O O O O O I O O 0 O O O O O 0 O O O O O 133 iv Ll C s ; Seutroo Evaporation De; ;. irzloied Vie-t of Detec I. Cretal'. Resolution as . .. kerlap Effect . . . 3 Sieatic of Detect: . .. beef-Flight Electra '. hise Shape Discrimina :. Pulse Shape Discrizlna 1 . Q i _(.- . goo-Dimensional Pulse . ire-of-Flight Spectru n: , - . “anatlon 3m "' . ..ne Layout Ta." ' F e. timber Assenbl - .,~,.:al Neutron and Ca 5 J in u a}, "u. JJE» . “v e‘ \1! v "the 56.12:: v “Ed .‘seutron De: no and ”CO Compton ’« CU: m. S7CO Compton unannel Analvze . .::ee-Dineosional Puls LIST OF FIGURES Figures Page 1. Neutron Evaporation Decay Chain . . . . . . . . . . . . . 18 2. Exploded View of Detector . . . . . . . . . . . . . . . . 22 3. Overall Resolution as a Function of Neutron Energy . . . 24 4. Overlap Effect . . . . . . . . . . . . . . . . . . . . . 26 5. Schematic of Detector . . . . . . . . . . . . . . . . . . 30 6. Time-of-Flight Electronics . . . . . . . . . . . . . . . 32 7. Pulse Shape Discrimination Electronics . . . . . . . . . 38 8. Pulse Shape Discriminator Cross-Over Time Spectrum . . . 41 9. Two-Dimensional Pulse Shape Discrimination Display . . . 42 IO. Three—Dimensional Pulse Shape Discrimination Display . . 43 ll. Time-of-Flight Spectrum Measured with Pulse Shape Discrimination . . . . . . . . . . . . . . . . . . . 45 lZ.BeamL1neLayout.................... 46 13. TargetChamberAssembly................. 49 14. Typical Neutron and Gamma—Ray Time-of-Flight Spectra . . 52 15. Calculated Neutron Detection Efficiencies . . . . . . . . 56 16a. 60Co and 57C0 Compton Recoil Spectra . . . . . . . . . . 57 16b. 6000 and 57Co Compton Recoil Spectra . . . . . . . . . . 58 17. Single Channel Analyzer Calibration Curve . . . . . . . . 6O 18. Single Channel Analyzer Calibration Curve . . . . . . . . 61 19. 60Co Compton Recoil Spectrum Showing Detector Light Resolution . . . . . . . . . . . . . . . . . . . . . . 63 20. Detector Light Resolution Curve . . . . . . . . . . . . . 64 was I.” miss Recoil Energy a: 1 -- ! '.?r::co Recoil Energy a: . ielazive Neutron Energy 1 Zetettor Response Cum .. .2rzet Ger-’8!“ F0\ or C: 5 Saxon Yield Spectra :. Satan Angular Distri T iatro: Total Yields [.1 I-marisoo Between Eva Data. The Solid Cur : :x::acted Nuclear Leve inaction of Mass Nu: r :xtracted Nuclear Radi U- ' ass tuber . .. .‘1::erentia1 Neutron 1 Ev: vm ' .aptration Spectra , 1 12' s diamond Neutron . OR-Cotpound Ne .cal and Exper Figures 21a. Proton Recoil Energy and Pulse Height Spectra 21b. Proton Recoil Energy and Pulse Height Spectra 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. Relative Neutron Energy Spectrum Detector Response Curve . . . . . . . . . . Target Geometry for Corrections . . . . . . . . . Neutron Yield Spectra . . . . . . . . . . . . . . . . . Neutron Angular Distributions Neutron Total Yields . . . . . Comparison Between Evaporation Theory and Experimental Data. The Solid Curves Represent the Data. Extracted Nuclear Level Density Parameters as a Function of Mass Number , , , , , . . . . . . . . . . Extracted Nuclear Radius Parameters as a Function of Mass Number . . . . . . . . . . . . . . . . . . . . Differential Neutron Energy Spectra with Extrapolated Evaporation Spectra . . . . . . . . . . . . Non-Compound Neutron Angular Distributions . . . . . . Total Non—Compound Neutron Yields . . . . . . . . . . . Probability for Collision Resulting in Pre-Equilibrium Neutron Emission . . . . . . . . . . . . . . . . . . Theoretical and Experimental Angular-Integrated Neutron Energy Spectra . . . . . . . . . . . . . . . . . . Angular Integrated Neutron Energy Spectra . . . . . . . vi Page 66 66 68 70 73 76 94 100 104 106 108 112 114 115 120 122 124 [.7 w I 1:, ' n’. . .‘ -. .. .-..s.rp:.on and lnscatte \ 2.?!e‘.’ Neutrons at .\' 32 E; = 30 He? LI ST OF TABLES Table Page 1. Gamma-Ray Sources, Their Decay Energies, and Compton Edge Energies . , . . . . . . . . 62 2. Absorption and Inscattering Corrections for 2.0 MeV Neutrons at Neutron Angle of 120° at Ep = 30 MeV vii Nuclear reactions at a: u -“v characterized 3‘ . s'n. .. fi'b. n :;:'s or "compound such I 1". 223.5 izterval between t‘: settitleus and the eter :a::i:agnita:'e to the t Lise-:3, and the outg“; 7.11:: 3f the available e “12:5, on the other har 22.7.1 has elapsed (10‘1' I‘.’ LILZECt particle and Li: .. I? .m a compound nuc 1e .is'tar' .. . ecec..ally, on the u I. acting this dynamic e 25¢a~ Nee of the details d :u‘ I. 5‘: ¢ . ”k 'tonservation laws 335 fro. ‘ ' .n tots equilibr 'h‘“ it is able 3&5 ‘ '4 Lamas “a? Onlv V" w ' ‘Nfii ’b a ..e.r occurrence w E I . INTRODUCTION Nuclear reactions at moderate proton bombarding energies (<100 MeV) are usually characterized as either "direct", or "non-compound" reactions or "compound nuclear" reactions. In purely direct reactions, the time interval between the impact of the incident proton upon the target nucleus and the emergence of an outgoing particle is close in order of magnitude to the transit time of a nucleon across the nucleus (10‘22 sec), and the outgoing particle generally carries away a large fraction of the available excitation energy. In strictly compound nuclear reactions, on the other hand, particle emission occurs after a much longer interval has elapsed (10'16 sec); this interval is sufficiently long that the incident particle and target nucleus may be considered to amalgamate and form a "compound nucleus" in which the available excitation energy is shared equally, on the average, among all nucleons present (Bo 36). In reaching this dynamic equilibrium, the compound nucleus loses all knowledge of the details cf its formation and is required only to obey general conservation laws. The compound nucleus decays when fluctu— ations from this equilibrium concentrate enough energy on a particular Particle that it is able to escape from the nucleus, at high excitation energies taking away only a small fraction of the total available energy. The two types of reactions have distinctive characteristics which manifest their occurrence. Outgoing particles resulting from non-compound reactions are in general high energy particles, and their angular distri- butions are forward peaked in the center of mass system. Non-compound I‘eaction cross sections also exhibit reasonably smooth behavior as a function iterating energy. Cot; 11:125. have isotropic a $3.12: their cross sec 22:517.; energy. 2:22:35 nuclear reactf sages :i the order of n; .-- Dyna! r 5" V #- .2:...:..1\. Etc), Unered (1: 22:2 significant at e: 5572:, no particular eno' :r;:.y :ease to occur, a: 4...-.. t13n on the . ' "I;- .. 4):: b catariing enere 1.. - L, :parmw . ‘05 h experine". \ o m -..:a::vel_v for a give“. M... range." C .. , ‘ 0- complete en s.- ‘.‘3...‘ «£— possible enerr 'u. 19d, new insi i; ..... 2. . ‘0. If“. e Present ‘I. “I a ~o' . eke.qu as {,1 22,1: . abolie d‘Scu l3 3: . {Celgld’ i“; ‘_h of bombarding energy. Compound nuclear reactions result in low energy particles, have isotropic angular distributions in the center of mass system, and their cross sections fluctuate rapidly as a function of bombarding energy. Compound nuclear reactions are dominant at proton bombarding energies of the order of nucleon binding energies (typically somewhat lemsthan 10 MeV), whereas non-compound reactions are usually considered tolnmome significant at energies greater than roughly 20 MeV. There is, lumever, no particular energy at which compound nuclear reactions abnmmly cease to occur, and there has been available only scant experi— mmnml information on the actual competition between the two processes atldgher bombarding energies. Any thorough experimental attempt to determine this competition qumndtatively for a given reaction at a given bombarding energy entails Immsurament of complete energy spectra of the outgoing particles, from fluemaximum.possible energy down to zero; the energy spectra should be taken over a wide range of angles. In such a case, the distinguishing features of compound and non-compound reactions may then be employed as Snides to determining the magnitudes of the contributions of the two different processes to the experimental results. If the bombarding energy is varied, new insight into the energy dependence of nuclear reaction processes may be gained. Although they present formidable experimental difficulties, reactions 1nVolving neutrons as the emitted particle are quite significant with regard to the above discussion, since the dominant process for decay (XE most compound nuclei is neutron emission. Charged particle Elmission is strongly inhibited by the Coulomb barrier, and for this min I" A Tsi'fil “N, v . an: the contribution tron tnaiority of cases. 2:12 Previous measurements c member of targets he :25 total yields cal?- :-:si':".e to draw convincin: 12555. Recently, 3365 j attained neutron enere' 229:3 in the proton bone-a 2;:esent measurements we .;:t':oc’:arc'ing energies. This paper reports the 1112322, 30, and 40 .‘ie 315:2 bombarded, and the iiét't of six angles per 1 .,. 4 1 a! L'.‘ . “as“ . .u lziiiélds, f,_._ . .RyEIISOn of the da' :15; n‘ 375 3: '¢' .etmc quantitativ 137$ , . . It and direct PTOCeS :3 aflfiiri is. on) the data ...:.or experiments. ” 5.3.3419" mes used to meat 1 reason the contribution from charged particles of all types is small for the great majority of cases. Previous measurements of neutron yields from proton bombardment of a large number of targets have been made (Ta 57), but these were measure— ments of total yields only. With such integral information it is not possible to draw convincing conclusions regarding compound and non-compound processes. Recently, Wood et_al_(Wo 6S) and Verbinski and Burrus (Ve 71) have obtained neutron energy spectra and angular distributions from thin targets in the proton bombarding energy range from 8 to 21 MeV; but until the present measurements were made, such data had not been taken at higher bombarding energies. This paper reports the results of a systematic survey of neutron prod— uction by 22, 30, and 40 MeV protons. Six targets, C, Al, Cu, Ag, Ta, and Pb were bombarded, and the neutron yields measured as time-of-flight spectra at each of six angles per target, for neutron energies above 0.5 MeV. The data are presented as absolute neutron energy spectra, and additionally as energy-integrated angular distributions, and energy- and angle-integrated total yields. Comparison of the data to predictions of the statistical-fermi-gas nmdel of the compound nucleus, adapted to the present experimental case, gives specific quantitative information concerning the competition between cxmpound and direct processes, both of which were observed in the experiment. In addition, the data are valuable in various practical applications; design of accelerator shielding, estimation of neutron background in accelerator experiments, calculation of efficiency corrections for solid state devices used to measure proton spectra in the energy range 22-40 MeV, esrimation of dose rates when neutron beams produced by accelerators wed in ercineering and tuations in h"? ' s1 " .p ‘ 2.4.1 5‘ e covered by tht‘ au- ' its: - “A r . are used in engineering and biological irradiations, and, in fact, in almost all situations in which neutron production by protons in the energy range covered by the experiment is an important consideration. .iuic Statistical A! 8113‘ uncut nuclei the fir: pasted from each other, a we order of several nun. nelcf toe nucleus has no‘ uprcperties of these . 31:13: energies, say, gre. neurones inadequate be. 3&3:th energies is too The very concept of th: “Emily behaves in lgn. melon free path of . 315m surprising sinc ”*3 356 Strongest of the i 22; Puticles. A conseqt l '4’ Md Compound nucleus s13 cetailed analysis (E «3:2: with its neighbors '1 W a compound nucler. v.11; - eis snared by the ( V I “3:. v . 11.1 "a" some add: even a sizeable fr‘. . long time and man‘- l‘n . - \n be C°“C€Utratec‘ II. THE EVAPORATION THEORY OF COMPOUND NUCLEUS DECAY A. Basic Statistical Arguments In most nuclei the first few lowest excited energy levels are separated from each other, and the ground state, by energies typically on the order of several hundred keV. The independent-particle shell model of the nucleus has met with great success in predicting the de- tailed properties of these low-lying levels. However, at higher ex— citation energies, say, greater than 15 MeV, the independent particle model becomes inadequate because the number of levels of closely neighboring energies is too great, particularly in heavy nuclei. The very concept of the formation of a compound nucleus, which subsequently behaves in ignorance of its mode of formation, implies that the mean free path of a nucleon inside the nucleus is very short; this is not surprising since the nucleon-nucleon force is known to be among the strongest of the known types of interactions between funda- mental particles. A consequence of this is that individual nucleons in an excited compound nucleus share their energy in a manner which so far defies detailed analysis (Ev 55), the interaction of a particular rumleon with its neighbors being a highly fluctuating function of time. When a compound nucleus is formed, the energy of the incident particle is shared by the collective motion of all the nucleons; each nucleon will have some additional energy, but no one particle is likely to have even a sizeable fraction of the incident energy (Mo 53). It may take a long time and many collisions before a sizeable amount of energy can be concentrated upon a single nucleon with the result that 5 mum. cooling the m ,1;an not in genera we: the direction nor mention vhich rem :xeeis by repetition of site residual nucleus IE5 another particle, 11 mufficient to ”boil 'iita such benavior ti negrofitably be viewed :2: than as confi~urat intact tatistical tee The above qualitativ inaction of the atati twill be set forth e tithe development of is» . a,‘ Patted, stro’ltly 31.1.? ' ' dtn one “Other Law was “9 Man: to :33 av erage propertie. I the c o“Potmd nu< :uedetau ‘ 0f it 8 f 1‘ or i k. as last as“: ‘ t. ‘9 <3 9 4. reaction “a P Mr. “a is (El 52) it escapes, cooling the nucleus by "evaporation". The particle which escapes will not in general be the incident particle, and will have neither the direction nor the energy of the incident particle. A reaction which results in evaporation of more than one particle proceeds by repetition of this process: the first particle is evaporated, and the residual nucleus is another excited compound nucleus which evapo- rates another particle, and so on, until the remaining excitation energy is insufficient to ”boil off" another particle. With such behavior dominating the picture, the nuclear levels may more profitably be viewed as quantized states of the nucleus as a whole, rather than as configurations of distinguishable nucleons, so that the methods of statistical mechanics and thermodynamics may be applied. The above qualitative discussion sketches the rationale behind the introduction of the statistical model. It contains several assumptions which will be set forth explicity here, and which should be kept in mind during the development of the model. First, nuclear matter consists of closely packed, strongly interacting particles which interchange energy rapidly with one another. Second, the results obtained from such con- siderations are meant to apply not to a single well defined state, but to the average properties of many states of closely neighboring energies. Finally, the compound nucleus behaves in a manner which is independent of the details of its formation. If this last assumption is valid, the cross section of a compound nuclear reaction X(a,b)Y, proceeding as X + a + (2* + b + Y* can be written as (Bl 52) we: (a) is the cross se c .':::artitle a striking nu 23:51:34 ezission of 'o, if :2 meet. ignition (II-l) can :1 are: and 5 denote all ’ :2: entrance and exit c 30"! ECG) can be ex; Q’s is the decay rat 3:! of I he nucleus. give Ere - 31m extends 0,48: 8] Tue ‘. rec.proc1ty thec "at: on of C Via any :- »38 0 this eXPIESg o(a,b) - oc(a)Gc(b) (II—l) ‘where oc(a) is the cross section for the formation of compound nucleus C by particle a striking nucleus X. Gc(b) is the probability that C decays by emission of b, leaving Y as the residual nucleus; it is a pure number. Equation (II-1) can be rewritten as ch ,8) = Och )Gc(3) (II-2) wherezx and 8 denote all the quantum numbers of the reaction partners in the entrance and exit channel, respectively. Now, Gc(8) can be expressed as Gc(8) ' r8 ‘1‘— (II-3) where F8 is the decay rate of C into channel 8, and F is the total decay rate of the nucleus, given by r-ZFB B (II—4) where sum extends over all channels into which C can decay. The reciprocity theorem (We 37) relates the cross sections for formation of C via any two channels a and 8: OJ!) _ ocw) 2 2 rs 1:: FBXB (11’5) Use of this expression in (II-3) gives mashefore. the 5“ he ninetic ene r32" are. is tne excitati 1m pOSSible V3 2325 is left in its 15L is large enou met. The measured 25 :oatinuous when t 2:le experimental re aility that particle 13W. GMT), is t - 2 GC(8) kBoc(8) Xk$0c(v) Y (II-6) ‘where as before, the sum extends over all open channels and k - (X)-l. The kinetic energy available to channel 8 is T = T -U (II-7) where U is the excitation energy of the residual nucleus, and Tmax is the maximum possible value of T, which will occur if the residual nucleus is left in its ground state (U - 0). If U is large enough many levels of the residual nucleus may be excited. The measured energy spectrum of the emitted particles be- comes continuous when the separation of these levels is less than the overall experimental resolution, or when the levels overlap. The pro- bability that particle b will be emitted with kinetic energy between T and T + dT, Gb(T), is then Gb(T)dT . ZGC(B)dT (II-8) ‘where here the sum extends over all channels 5 which are open in the energy interval dT about T. The number of terms in this sum is the number of states in the residual nucleus with excitation energies between U and U-dT, where U and T are related by (II-7). This number is written as w(U)dT, and the quantity u(U) is called the "level density”. Substitution of (II-6) into (II-8) gives the relative intensity . “-«ion of the emitted :szrzzt. P(1‘)dI '- are: :as been replaced b iaszixof I, that is, e rs 2c get an idea of the s ...: the quantity £5 i is either constant «its this quantity in I: this expansion is as Film . {the factors duQ t ‘ 0 . ‘\ "513;? ‘ and the Want 1 t V we dineng [On Of - 3.“. 'k‘b. “flute“ Q rigid“ at “31 uncleuS I distribution of the emitted particles P(T)dT - const. x T0c(8)w(Tmax-T)dT (II-9) 2 where k3 has been replaced by T. w(Tmax-T) is a rapidly decreasing function of T, that is, a rapidly increasing function of U (Be 38). To get an idea of the shape of P(T), it is only necessary to con- sider the quantity S 8 1nkw(T -T) (II-10) max where k is either constant or a very slowly varying function of T (Pr 62). Expanding this quantity in a Taylor series about U - Tmax gives (We 37) 8(Tmax-T) - S(Tmax)-Tld§’ +... (II—ll) dU U = T max If this expansion is used to approximate “(Tmax-T) in (II-9), this gives P(T)dT - const. x Toc(r)exp(:ZJdT (II-12) T where the factors due to k and S(Tmax) have been absorbed into the constant and the quantity r is given by l. r O-IO- C’. U! (II-13) 1 has the dimension of an energy and can be interpreted as a nuclear ”temperature" inasmuch as S - lnkw(U) can be considered as the entropy of the residual nucleus. Then (II-13) is simply the well known thermo— dynamic relation between temperature and entropy. Ear neutrons CCU) is ‘ ’57:“ energies (51 52) 5‘ zzsaises the behavior of selfish emission spec: itererature t. It has a tzzresoect to Ina: if 3;; :ezzezreted as the team imrzicie. not as the 1 assiso. has the shape of the Irelatioo between I and “3‘59?“‘15 Upon the assumed in the next 5 -. .ze :emi Gas riodel 01 :f i 9 he .n.ernal energv . «.eerature, and, if t L”? - series 1&2? . ' ‘mperatures , 5 ‘; e' I‘ .88 v - “Weenies (3e :33? ,steu to vanish - ~ c .5, 4., se: " 1* ‘v‘ari 0‘35 terms depe .~;.h 1. 10 For neutrons Oc(T) is a slowly varying function of T, except at very low energies (B1 52) so that the product Texp(-T/r) principally determines the behavior of P(T). The energy distribution P(T) is the "Maxwellian" emission spectrum of molecules evaporated from a surface of temperature T. It has a maximum at T - I, which should be small with respect to Tmax if approximation II—ll is to be valid. I should be interpreted as the temperature of the residual nucleus after emission of a particle, Egt_as the temperature of the compound nucleus before emission. Thus the shape of the spectrum is given by equation lI-12 provided the relation between T and r (or U and I, see 11-7) is known. This relation depends upon the adoption of a particular nuclear model, which is described in the next section. B. The Fermi Gas Model Of The Nucleus The internal energy of almost every system is an increasing function of temperature, and, if the temperature is low, can be written as a power series U 3 Co + clr + c212 +.... (II-14) At high temperatures, equipartition is reached and U a I, but the third law of thermodynamics (Nernst Heat Theorem) requires the heat capacity of any system to vanish at r = 0 (Ze 43) so that the above series must start, for low temperature, with at least the quadratic term. The coefficients of the various terms depend upon the particular model chosen for the system. ‘or excitation energie as i an be considered :mdius it (in 53). The K en: order in r, by (Fe . waif is tne energy of ' :Lie is) ereiis the nucleon mas S: the internal ener: «Lemmy, “Y be writs '4?" defi hes the Parana: | T. . ..iS important to r :3" th i. d ‘rou . ‘ Eh II 79 U 311v ' . ‘ Incependent Var; ~ ech - a is speCified 11 For excitation energies below roughly 50 MeV, a nucleus of mass number A may be considered a degenerate gas of A nucleons confined with- in a radius R (Mo 53). The internal energy of such a gas is given, to second order in r, by (Fe 50, Ki S8, Bo 69) _ AEf + 3n2 5 8 U U- ITJI> f (II—15) where Ef is the energy of the highest filled level at r - 0, and is given by (Fe 50) E - §E_(3n2A) f 2M (II—l6) where M is the nucleon mass. So the internal energy of the nucleon gas, measured from the zero point energy, may be written as u - 312 (II—l7) which defines the parameter a, and determines the form of the level density, through (II-7), for this model. It is important to note that, since I is a function of the kinetic energy T through II-7, the expression II—12 can be written with T as the only independent variable, provided that the level density parameter a is specified. 111. APPLE“: I0 t The inelastic Collisio pond hucleus Fomatio '32 arooability thdt _ slain: in traversing a t ‘4“ ~., r": 10 is the incident 1 Laos is the total 1 in approximate exprt .2. :ocgound nucleus for. r.» 'r - Ne ' ' v is the Coulono I ma. mes men the ouant‘ .‘u s ‘u‘ .5 derived basical is A {Alias a well def 15’ o I I, '1 III. APPLICATION OF THE STATISTICAL-PERMI-GAS MODEL TO THE PRESENT EXPERIMENTAL PROBLEM A, The Inelastic Collision Probability And Assumptions Concerning Com- pound Nucleus Formation The probability that a particle will undergo an inelastic nuclear collision in traversing a thickness x of material is I_ 8 l-exp(-nox) 10 (111-1) where I0 is the incident particle flux, n is the number of nuclei per 3 cm , and o is the total reaction cross section for the reaction. An approximate expression has been derived for the cross section for compound nucleus formation by a charged particle of energy B (B1 52) o - n(R+x)2(1-\_I_g ) E R+x (III-2) where V is the Coulomb potential at radius R+X. The cross section vanishes when the quantity in brackets becomes negative. This expres— sion is derived basically from the assumption that a nucleus of mass number A has a well defined spherical surface of radius R given by a - roA1/3 (111-3) where ro is the nuclear radius parameter. The quantity X appears since the position of the incident particle is undefined within that length; for 40 MeV protons X=.6f. (III-2) is based upon very simple semiclassical arguments and might 12 twisted t0 81“ only or: gavel, for the range 01 gain“: the reaction cro :55 sections are conpilat .,s?, and are taken fro: sages. It should be no: sszrcagly dependent upon L'se of (111-2) in (11] 222:: particle which str item system, that is 7725i: fora compound nucl. “WE Energies used 1 mlmud, but detail firsmlisequences with t ‘ rrocEdure .. Lsed I so Yields n Calc Jae prObIEH is to Ca. iii-,3 . en a thick (StOpp- “Ended ‘. D] pr°t0ns o 1 Parts: l 13 be expected to give only order of magnitude estimates, but it agrees quite well, for the range of incident energies covered by this experi- ment, with the reaction cross sections given by Janni (Ja 66); Janni's cross sections are compilations of experimental data for energies below 40 MeV, and are taken from Monte Carlo calculations (Be 63) for higher energies. It should be noted that the value of o and therefore of NIC is strongly dependent upon the value of ro used, because of III-3. Use of (III-2) in (III-l) is based upon the assumption that every incident particle which strikes the surface of a target nucleus forms a compound system, that is, all the flux lost from the incident beam goes to form compound nuclei. Because direct reactions do occur at the bombarding energies used in the experiment, this assumption is not strictly valid, but detailed discussion of this point awaits comparison of its consequences with the experimental data. B. Procedure Used In Calculating Absolute Thick Target Neutron Spectra And Yields The problem is to calculate absolutely the number of neutrons pro- duced when a thick (stapping) target of nuclei of charge 2 and mass A is bombarded by protons of initial energy E1. It may be divided into two parts: formation of compound nuclei, and their subsequent decay. A given target of thickness t is divided into, say, n equal slices. Then the energy loss of the protons in the first slice, AEl’ is calcu— lated using formulae referenced by Williamson 33_ 3;, (W1 62), so that the average bombarding energy for the first slice is given by El - E1 - gasl (III-4) "“l s timid, and employing gzzspztnd nuclei, as di- .2: flux is assrmeé, so - ' new | ’ ‘ C n I..."- uuv's'. o is excitation energy tA:iEl +Hp ‘ A+l iii" :1. f; t; is .ne proton sass f".o‘ ‘ ' .-....,.i+r) is the mass 5:5.cu.ated using the 2.": Mn. ‘5..:: 3 article is it,“ 1’ u, o" .kr ESults of this . m .H ~13: is Valid. For .- ‘Z‘de {me (Le 52) . 772— ~ timer of “Quito: '1‘. 5: ‘ “ Wand “11C leus :7- ' ; Man Iron heaVier . nae 3 Compqu 33:» 293 and p are res“ 14 Then the inelastic collision probability is calculated using (III-1) with x = t/n, and employing the assumption that all flux loss goes to form compound nuclei, as discussed in the previous section. Unit in— cident flux is assumed, so that the final result will be in units of neutrons/proton. The excitation energy available in the initial compound nucleus is given by ,3 UA= A Ei+M A+l p + M(Z,A) - M(Z+1,A+l) (III—S) where Mp is the proton mass, M(Z,A) is the mass of the target nucleus, and M(Z+1,A+1) is the mass of the compound nucleus; the mass differences are calculated using the mass excesses calculated by Garvey e£_al, (Ga 69). III-5 is based upon the assumption that all the energy of the incident particle is given to the compound nucleus; for the beam energies used, the results of this experiment indicate to what extent this assumption is valid. For very high incident energies (>100 MeV) it cannot be true (Le 52). The number of neutrons emitted is calculated under the assumption that the compound nucleus emits only neutrons or protons, neglecting competition from heavier particles, and gamma rays. Formation of com- posites inside a compound nucleus is relatively rare, and, except for deuterons and tritons, the Coulomb barrier strongly inhibits emission. So, if Pu and P1) are respectively the probabilities for neutron and pro- ton emission, then Pn + Pp = 1. PD and Pp can then be calculated if their ratio is known. This ratio is given by (Le 50, Le 52) El . is» ‘1 :a ~>qu ~KV“ a: I: i 15 P PED: (R /R )llaexp(2(aR )1/2-2(aR )1/2) III-7 n p n p P where R = U —S , III-Ba n A n R = — — . _ P UA Sp 0 7VC, III 8b “1 and UA = 52 III—8c e J The factor 5:15 the level density parameter a as previously discussed, and e takeseon values typically between 8.5 and 20, depending on the nucleus under consideration. III-7 is an expression for the ratio of the level densities of the two possible residual nuclei which are left with excitation energies Rn and RP; Rn and'Rp are the effective energies available for the emission of neutrons and protons from nucleus A excited to energy UA’ and become U for the next evaporation, when A the outgoing particle energies are accounted for. Sn and S are the neutron and proton separation energies, as calculated from the mass excess tables of Garvey et al.; VC is the Coulomb barrier, and the factor 0.7 allows for some barrier penetration; r is the temperature of the residual nucleus. 5(3) ‘ 3Pr 23o neutrons are If only one neutrc Ci: the initial 1‘ t'... . ‘ “9 Pro: .. 5-333 . it 13 as, let‘s: fl 1’ Strong} ~53 terrier t; 3 4 32:13:} ener'éie 1337a l6 N(U) - 3PnPnnPnnn + 2(PnPnnPnnp + PnPinnpn + PpPpannn) If two neutrons are possible, N(U) I ZPnPnn + PnPnp + PpPpn (III-9b) If only one neutron is possible, N(U) - Pn (III-9c) P1 k(U) is the probability that particle k is emitted from a compound 1 nucleus following emission of i in the first stage and j in the second when the initial excitation energy is U. If the probability for proton emission is less than .05 at any stage, it is neglected, and that stage is considered to decay totally by neutron emission. From III-7 it is easy to see that the Coulomb barrier strongly inhibits proton emission. Apart from this effect of the barrier, the evaporation sequence is governed largely by the sepa- ration energies with the consequence that it tends roughly to follow the valley of stability, or tends toward it. Only for light nuclei, where the barrier is low, and for neutron—deficient nuclei, is the proton emission expected to be important. The emission of particles is followed until the excitation energy of the residual nucleus is insufficient to permit further neutron or proton emission; the remaining energy is assumed to be lost by gamma- ray decay, and is not considered further. A diagram of a part of the gnupchhain for whit? fizgxe I. It is worth '. :rlizated by the fact t'r- Li“. but their excitati: ;:'.‘:i:': they are reached. its lizited decay chair: romance for the pro: sizzlation becomes quire chifications of the ‘Prél, are not included Izevery isportant in s .is'ise, "thermal" exnan tease such an effect ha "’ on ...r :5 PM of excitati tssib‘ ' ‘ .e in this experime r a neutron is emit "’ to have the for- ?!) ‘i‘h “me Process 4%. !k ' “18 Inc ldEn t Wm M" e ‘2‘. (Ikcence of r 98 ‘ naas in» l7 evaporation chain for which the calculation is performed is presented in Figure 1. It is worth pointing out here that the calculation is complicated by the fact that some nuclei in the chain have the same (Z,A), but their excitation energies depend upon the specific manner in which they are reached. Fortunately this difficulty is surmountable with a limited decay chain (<6 particles emitted), resulting only in inconvenience for the programmer; for longer decay chains the calculation becomes quite cumbersome. Modifications of the level density due to angular momentum effects (Pr 62) are not included in the calculation since they are thought not to be very important in single-nucleon-induced reactions (Be 63). Likewise, "thermal" expansion of the nuclear radius is neglected, because such an effect has been estimated to be small, on the order of 12 for 48 MeV of excitation (B0 62), the highest excitation energy possible in this experiment. If a neutron is emitted at a given stage, the energy spectrum is assumed to have the form P(T)dT = N T exp /2a(TMAx-T) dT (III-10) where the normalization factor N is the absolute probability for reach- ing that stage. In this way, the absolute energy spectrum is con— structed for comparison with the experimental data. The whole process is repeated for successive slices of the target, until the incident proton energy is below 0.7 of the Coulomb barrier. The dependence of results of the calculation upon the number of slices, n, was investigated; the results were independent of n for n: 10, so ten l8 n-<.n-N m-<.N-N N-<.N-N m-<.N-N m-<._-N N-<._-N _-<._-N mango moose cowumuomm>m couusoz m-<.N-N m-<..-N N-<._-N .H ouswfim _-<.N _J'.... _ .‘AIL‘Y “a v ’ “ steamer used in tne The absolute total ne :eezted at the end of ti std results. A list in. ".212: :ne thick tarzet yi- 19 was the number used in the calculation. The absolute total neutron yield, and its energy Spectrum, are presented at the end of the calculation for comparison with the experi- mental results. A listing of the computer program DECAY, which calcu— lated the thick target yields is given in the Appendix. geassrenent of iieuti’OI .‘ersnique 1. seneral Cont-eats Ire tine-of-flignt (. traverse a known film fratsese velocities, t . T13 :etbnd is well suit-g noes proton beats of nar Leger constant interval 31:: such a bean, t1.- 126: by the occurrence ‘I‘naneutron is detect 12% first that produced 's’éinot occur at exact: it“? maF’Pen at some I ”’33“; the main requ. Z’étant interval relat If prompt gm ray ciifitected at time t c 7"”. “at ”a5 on target; 8.; ‘ar: the same Speed no "‘39Utron is then 9: IV. THE EXPERIMENT A. Measurement 0f Neutron Energy Spectra By The Time-Of—Flight Technique 1. General Comments On The Time-Of-Flight Technique The time-of—flight (TOP) method measures the times taken by neutrons to traverse a known fixed distance, and so determines their velocities; #1 from these velocities, the energies of the neutrons can be calculated. This method is well suited for use with the MSU cyclotron, which pro- duces proton beams of narrow (<0.5 nsec) bursts separated by a much longer constant interval (~50 nsec). . "s With such a beam, the flight time of a neutron is an interval deter- mined by the occurrence of two signals: one signal occurs at time t when a neutron is detected; the other signal fixes the time at which the burst that produced the neutron was on target. This second signal need not occur at exactly the same instant as the neutron was produced, but may happen at some known time to after (or before) the neutron was produced; the main requirement is that this signal be displaced by a constant interval relative to each beam burst. If prompt gamma rays produced by nuclear reactions in the target are detected at time to, this establishes the time at which a given beam burst was on target; gammas are convenient for this purpose since they have the same speed no matter what their energies are. The flight time of a neutron is then given by tn - L/c + (t-to) (IV-la) 20 Ennis the speed of 1: 1:11:35 and $313385. 0! ' f 3311 between the proc. :s:, and tne arrival of iot‘nt and to are me; mail, It, and time intc: LES; i.e., tne seconn tt mine: as 3:: isocnronous cyclotr be derived from the t he relativistic ex. Eerev I ' ' . n J!“ and ‘1 times to the classica; Tne detector for a Swine organic scint :lier (P11) tube; a typ‘i #:32ng neutrons are c. that - _ .ney induce in t, ht§ftn T. tuCQ no attempt n" i “‘1 approximate exl :2 Dame? . trage IESOIU: “if: t _ g he “Erlvat; 21 where c is the speed of light, and L is the distance traversed by both neutrons and gammas, or “flight path“; the quantity L/c is the time interval between the production of a gamma ray or neutron by a beam burst, and the arrival of that gamma ray at the detector. Both t and to are measured relative to a fixed standard "clock'' signal, tc, and time intervals are the experimentally measured quanti- ties; i.e., the second term on the right-hand side (IV-la) can be rewritten as t-to a (t-tc) - (to-tc) (Iv—1b) If an isochronous cyclotron produces the incident beam, the tc signal can be derived from the rf accelerating voltage on the dees. The relativistic expression for the kinetic energy of a neutron is Tn - an2(y-l) (Iv—1c) 2 where vn 8 L/tn and y - (l-vi/c )‘3; for low energy neutrons, this reduces to the classical expression .,,2z _. 1n qflnb /cn (IV 1d) The detector for a neutron TUF system usually consists of a fast- rise-time organic scintillator optically coupled to a fast photo-multi- plier (PM) tube; a typical system is shown in exploded View in Figure 2. Although neutrons are detected by means of the charged particle recoils which they induce in the scintillator, it is only important that the detector give a signal which accurately fixes the time at which a recoil occurred; no attempt need be made to relate the recoil energy directly to the energy of the incident neutrons. An approximate expression which shows the factors contributing to the percentage resolution of a time of flight system can be obtained by taking the derivative of the logarithm of both sides of (IV-1d): 22 uouuouun mo 3ma> vmvoaaxm .N shaman tire: is the flight ti: , I. . a” '3 do! ‘4: h‘ .115 Lee O‘Lrta A A :::i:ns :roa both rm. '1: ”he uncertainty in 1 0 25255 of the scinti . . .'; .H := 1 u“ _ N.: :i: - e differenCe i .. vL t e SYSten ~ “all IESOlutIO Tr t ._ can t ‘~"F;S’ .9. a Smal ~=rz~ . 23 fi‘zfln‘“ 291. tn L (IV-23) where tn is the flight time of a neutron of kinetic energy Tn on flight path L; Athis the overall time resolution of the system including con- tributions from both finite beam pulse width and electronics effects. AL is the uncertainty in the flight path due primarily to the finite thickness of the scintillator; it actually makes its contribution to r] the resolution of the system through the finite transit times of neutrons and photons between the front and rear edges of the scintil- lator. The contribution to the percentage resolution of the system is given by ” 2A£fi = (1‘n8)(2AL) (IV—2b) tn L ‘where B= vn/c, and n is the index of refraction of the scintillator; this time difference is clearly less than the second term of (IV—2a) for all B>0, reflecting the fact that (IV-2a) overestimates the reso— lution of the system. Adding these contributions in quadrature gives the overall resolution of the system: ATn = 2 Atn 2 + (l—n8)2 AL 2 1/2 (IV—2c) Tn tn L The first term of (IV—2c) is most important for high energy neutrons, i.e., small t; the second term is most important for low energy neutrons, since their transit time across the scintillator thick- ness is long, and they may interact at any point along their path. A 0.. n c 00m: v.0 u o/V EU AVG. I J. l JAN - - ill- it! rub U AJAW- . 24 . a fill...- I mwumcm couusmz mo coauocam m we cowusaommm Hamum>o .m wuswflm $2): a» me ow mm on mm ON 9 o. m o — — q _ q 4 _ q a A. i -N L: Sdquci .m Ll EN 1»... I. N u U .26» .m “/u m@ m... u c L. ommc v.0 u a _ so on. u ._ am so 8.. u .5 :22: illustratim Far 3 given 1 teteasure‘i is 11‘ age at 503 p01] 1.2 time 35 d0 5‘ _-;5 is called '0‘ -_-;;'.se:l, because -::i:s:ance, the bursts are tier, flight tin. :5 :easu-red un is u- :es:.u:ion would ‘I: 4. ‘gwm. ~ ..a-35ra:Ed D... .ne relative *r‘:.13&3t is det 222-;- . ”dental lini £05 I "101]. I?" ; “H 43:..ded to r tUElr e“! a i “at if tfin .x‘;i:t , 25 graph illustrating this effect is shown in Figure 3. For a given flight path, the range of neutron energies which can be measured is limited by the pulse repetition rate of the accelerator, since at some point faster neutrons will arrive at the detector at the same time as do slower neutrons produced by the preceeding beam burst. This is called ”overlap”, and it causes the time spectrum to become confused, because one time then corresponds to two or more energies. For instance, the MSU cyclotron produces a beam of 40 MeV protons, in which bursts are spaced 54 nsec apart. With a flight path of 1.5 meter, flight times of neutrons in the energy range 3.5 ~40 MeV may be measured uniquely. If the flight path were shortened to 0.5 meter, the minimum energy detectable without overlap is 0.5 MeV, but the resolution would be worse by a factor of three. The overlap effect is illustrated by Figure 4. The relative importance of energy range and resolution in a given experiment is determined by the type of information desired and other experimental limitations which will be discussed in the following section. 2. Experimental design And Procedure The measurement of neutron yields undertaken in this eXperiment was intended to include, as far as possible, all neutrons produced, whatever their energies; preliminary theoretical calculations indi- cated that if the minimum neutron energy measured were 0.5 MeV, the essential features of the energy Spectrum would be adequately deter- mined. As noted in the previous section, the repetition rate of the “Va .. . % ‘3‘ 26 noowmm amauo>o .a muswwm 335 NEE. PIG...“— ONN 0m. 0.! 00. 00 ON (swam) Hin mam m.— \ x l esLerator, and the er. angst path "“15“ C' ,3 resolution and r hotner limitation :erespozse of the Cat :i;'.astit scintillator regent" energies (50 t :erecoil energy rang. L‘eietector and elect: aerating conditions , seams give pulses 0 St: in the experiment “3325 range, so an e “515819 experiment Sections which were la 563m for neutrons :5: the Output PUlses Beating Rage of the like. 0.1: was tile“ meac an ,. 3;, ‘lth enernv r 6. . ‘ 83 dUe t O h] 0. ‘9 . ’ a t“ a: 238: 4 8‘28 great n "as 1e .érn HEM) .. U" tons 312‘~. ‘5." re 27 accelerator, and the effects of overlap, place a practical limit upon the flight path which can be used, and so effectively determine the energy resolution and range of energies measured. Another limitation is placed upon the experimental apparatus by the response of the detector to the recoiling protons. The response of plastic scintillator to protons has been investigated for a wide range of energies (Go 60, Ve 68) and found to be highly non-linear over the recoil energy range covered by this experiment. For instance, with the detector and electronics available, 40 MeV neutrons, under typical operating conditions, give output pulses up to 8 volts and 0.5 MeV neutrons give pulses of (0.020 volts. The hIM standard electronics used in the experiment are not able to process pulses over such a wide voltage range, so an energy spectrum could not be measured completely in a single experimental run. Each energy spectrum was measured in two sections which were later joined together to give the complete energy spectrum for neutrons above 0.5 MeV. The detector gain was raised so that the output pulses for 0.5 to 3.5 MeV neutrons were in the optimum Operating range of the electronics: the energy Spectrum of these neutrons was then measured with a flight path of 0.5 meter to eliminate overlap, with energy resolution of about 8% for 3.5 MeV neutrons. Large pulses due to higher energy neutrons were rejected. For measure- ment of energies greater than 3.5 MeV, the detector gain was lowered, the flight path was lengthened to 1.5 meter, and pulses due to low energy neutrons were rejected; the TOF spectra were measured with energy resolution of 4.7% for 40 MeV neutrons. 1. :he detector Ine detector used it :gliquid mounted on an marines: because it is 1:215 suitable for use . Tue scintillator us 12m chosen because i: aristics allow discrin; seats, and because its anon-s. anapsulation :att'ne scintillator c. ‘43:: degrade its perfo: “Aside diaensions 4.44 c e: provided by the ma" .2 anew for thermal e._. cmces of tne chaste T . .ne scintillator a .ms-Corning Svlgarl 312”” ‘ mes ooth mechanic . < lesu‘ race of the they l‘eresi L naet, the who l‘ l-.' Man; 9 My bubbles “ =‘-‘r:ace. lite r the p~ 4 “‘SClr‘. 3223315 of tne scinti‘I .A. ac... W. "lte Paint. 28 3. The uetector The detector used in this experiment was a chamber of scintillat- ing liquid mounted on an RCA 8575 PM tube; this PM was chosen for the experiment because it is a high-gain, high-resolution tube whose out- put is suitable for use with fast timing circuitry. The scintillator was glass~encapsulated NE213, a liquid plastic; it was chosen because its hydrogen content is high, because its charac- teristics allow discrimination between neutron- and gamma—ray-initiated events, and because its light output is suitable for fast timing appli- cations. Encapsulation in glass ensures, to the maximum degree possible, that the scintillator cannot become contaminated by any inpurity which might degrade its performance. The glass container was a cylinder with inside dimensions 4.44 cm diameter by 1.90 cm thick; a small chamber was provided by the manufacturer on the curved surface of the cylinder to allow for thermal expansion of the scintillating liquid. The walls and faces of the chamber were 0.16 cm thick. The scintillator and PM tube were coupled mechanically and optically with Dow-Corning Sylgard encapsulating resin. This rubbery substance provides both mechanical support and excellent optical contact between the surface of the chamber and the outer photocathode surface. Before the resin set, the whole assembly was placed under roughing vacuum to eliminate any bubbles from the region between the scintillator and the PM surface. After the PM-scintillator combination had been firmly joined, the outside of the scintillator was coated with Eastman-Kodak high reflec- tance white paint. This paint helps ensure that the light collection ggedetector will be 0? firezard. {ten the paint had c. 53;: electrical tape to .23:th leakage could 25:55; even destroyinz one emote chain. he detector was t': ‘24:. contained , in an :1 signed for an eon 537 itzear preazplifier : so: was then surroun .I;'.g.'. eagnetic perne -.:.:er1ng vitn PF. o: taste 3. me detector was :1“; i“ on an arc about .0 age ‘ “"3195 struck Ilia: . 1222 v . ce~ and tne detec 7 "3 Placed arou {‘1 {lined I to tedUCQ I‘:3F:ute‘ ..'.€ gain 0f “18" . u ‘0 its d‘lv 29 of the detector will be optimized and is superior to aluminum foil in this regard. When the paint had dried, the whole assembly was wrapped with black electrical tape to prevent leakage of light into the assembly. Such light leakage could create a severe noise problem in the detector, possibly even destroying the PM tube by inducing very heavy currents in the dynode chain. The detector was then mounted upon an ORTEC Model 271 PM base, which contained, in addition to a resistor bleeder chain Specially designed for an RCA 8575, a fast timing discriminator at the anode, and a linear preamplifier at the ninth dynode. The whole phototube-scintil— lator was then surrounded by a cylindrical shield of hetic, a material of high magnetic permeability, to prevent stray magnetic fields from interfering with PM operation. A diagram of this assembly is shown in Figure 5. The detector was then mounted on a wooden cart which could be moved on an are about the target position, so that neutrons from the target always struck normal to the face of the detector. Wooden holders were provided to enable placement of shadow bars between the target and the detector for background measurements. No extra Shield- ing was placed around or about the detector, and nearby material was minimized, to reduce any possible background due to neutron scattering or capture. The gain of the PM tube was adjusted by altering the high voltage supplied to its dynode resistor chain. When neutron energies between 0.5 and 3.5 MeV were being measured, the high voltage was —l700 volts; wad». Adormkqum v.04 gm \ swim in QJU.IW Uabmzqu: IUQZdIU ZO.WZ¢¢g I> 1> ..|1§»n. UQ» ((H‘rl. (IS- 2- ZAU. b Talc. v‘v il‘ ‘ .Ibl‘ >4 . .2 £255 1 . lrfiU FEQZ k: :2 * fix! .53.: \ll: .1 . HM - . \ \ . .1553: lwu \v .omvn‘k Iv) 1‘ ."\l‘ In; .8 we ..... a - a §«...»‘I y .n‘. z «(1:1 It»?! i v; g 32 umE mmkagu 024 004 or AL. mghwmhw 9.4 555 8.. SE 392”. .C. och t Echoing 930 $323 ><4mo r. 85 54... was 448 mg 020030242 mwhwimbum HH I'll-I 00x: k/ kxndu «Chum... mo twice Hard) :0. I (mmd Adhzwiiuaxw z. gist be minimize red at the same t is: this purpose; ail: losses and p Issaccurence of t Fever and bia SEC), which alsc 32. Since all t: uzotn P91 Operatj llxtmmtor. muc :resnold was set 1.1 below the Dir :e elecnromCs . i :1 experiment . " miter the Count zikrly set . r. .,. We lPUC out. fige t0 the data Sits-’2' , ‘5: use- t"“mpl {gilt signal . ‘ a 3:? an and a no 33 effect be minimized if a wide range of neutron energies is to be meas- ured at the same time with optimum resolution. The CFPHT is excellent for this purpose; it is located in the PM base to reduce possible cable losses and pickup of electronic noise from nearby equipment. The occurence of the event is marked by the output of the CFPHT. Power and bias are supplied to the CFPHT by a time-pickoff control (TPOC), which also provides additional logic shaping of the CFPHT out- put. Since all the pulses generated by lower energy neutrons are small at both PM operating voltages, and the CFPHT involves a zero-crossing discriminator, much care was taken to insure that the discriminator threshold was set above the discriminator noise level, that it was set ‘well below the minimum pulse-height level which governed the rest of the electronics, and that it remained there throughout the course of the experiment. To guard against bias drifts, a ratemeter was used to monitor the count rate of the CFPHT to insure that the bias remained properly set. The TPOC output signal passed through roughly 40 meters of RG-8 cable to the data acquisition area of the laboratory, through a nano— seconds cable delay, and was finally presented to the “start” input of a time—to-amplitude converter (TAC), an instrument which produces an output signal proportional to the interval between the arrivals of a start and a stOp signal. The TAC stop signal was derived from the cyclotron rf system in the following manner. A probe adjacent to a dee of the accelerator picked up the sinusoidal rf acceleration signal on the dees; this signal was subsequently attenuated and presented to a zero crossing .3 figmtor, which gettrough zero, f Tris "clock” 51 wires one output sie-of-tvo to all: ;:;:e:tical spect 2:23;; this effec rat is not quite su inuhinator for l in: into the 'stOp 332131? of operation :38 is)? SPQCIT d:r:second delay a El: and tnen to a mg‘t°‘dlsital c luster. 5- Pulse Sha; a. AWlic In the measure ”mated u a la 1:: ,. . an“ Vito the s 34 discriminator, which puts out a fast logic signal each time the input goes through zero, from positive to negative. This "clock" signal was then fed into a fast scale-of-two, which produces one output signal for every two input signals. Use of this scale-of—two to eliminate every other rf clock pulse causes two separate but identical spectra to be accumulated, and automatically calibrates the TAC; this effect is called "doubling". The output of the scale of two is not quite suitable for use by the TAC, so it was fed into a fast discriminator for logic shaping. The fast logic pulse produced then ‘went into the "at0p” input of the TAC, which was used in its linear region of operation (~852 of full scale). The TOF spectrum produced by the TAC was fed through a linear microsecond delay amplifier to satisfy gating and coincidence require- ment and then to a linear gate and pulse stretcher, which fed into an analog-to-digital converter (ADC) interfaced to an on—line digital computer. 5. Pulse Shape Discrimination a. Application To Neutron Time—Of-Flight In the measurement of neutron TOF spectra, difficulty may be encountered if a large flux of gamma rays is present. Gamma rays can interact with the scintillator by Compton scattering with the electrons in the scintillator, and if the flux is very high, may cause severe background and count rate problems and degrade the quality of the neu- tron measurement. The gamma rays have four principle sources: (1) prompt cascades sawing nuclear ‘ 2139 rats“; (3) :eili-E'S’ etc. Of 6 :t'ne tar89t° Ga: :tine vita the b' 35, relative to ‘ :3591:h°'e"er' i! inexact feature . are tiae-uncorrela tackground under t l'nus, to avoi mend subtraction Enron spectrum. was by simple p :ectrou energies :: tron ~ «5 and gamma-i an rejection ma 35 following nuclear reactions in the target; (2) proton bremsstrahlung in the target; (3) neutron capture by nuclei in the walls, floor, ceiling, etc. of the experimental area; (4) and induced radioactivity in the target. Gammas from (1) and (2) above are directly correlated in time with the beam bursts which produce them, and in fact fix the time, relative to the rf clock signal, at which a beam burst was on target; however, in certain experimental situations they may mask an important feature of the neutron spectrum. Gammas from (3) and (4) are time-uncorrelated with the beam and will provide a smooth, flat background under the whole TOF spectrum. Thus, to avoid loss of information and uncertainty due to back- ground subtraction, it is desirable to eliminate the gammas from the neutron Spectrum. Unfortunately it is generally not possible to reject gammas by simple pulse height selection since, as in the case of the neutron energies measured in this experiment, pulse heights from neu- trons- and gamma-induced recoils may cover almost the same range. Gamma rejection may be accomplished, however, by a method which depends on a difference between the shapes of pulses induced by the two dif- ferent particles. b. Basis Of The Pulse Shape Effect At energies below 100 MeV neutrons react with plastic scintil- lators via n-p elastic scattering, and by (n,p), (n41) and (n,n'3a) reactions with carbon; the energy of the recoiling charged particles from these reactions is deposited in the scintillator and some of this energy is eventually converted by molecular de-excitation into a light Gama r‘ 593' at: electronS 232:? in me 5' In paSSing :res as 103126 :.e energy. C33 :1: energy 105 iezsity is high as; unction 0 :Les of the SC zegending upon susequent deca Least two expon mats also dep Hith prope the conditions 136 incident pa nation (PSLJ) . c. Elect): 36 flash. Gamma rays, as previously noted, undergo Compton collisions with electrons in the scintillator, which recoil and deposit their energy in the scintillator. In passing thru the scintillator a recoiling charged particle pro— duces an ionized track whose specific ionization density depends upon the energy, charge, and mass of the particle. The light output per unit energy loss in an organic scintillator is less when the ionization density is high (Go 60), resulting in a non-linear scintillator response as a function of recoil energy (Wr 53, Bi 51). Furthermore, the mole- cules of the scintillator are excited to different modes of excitation depending upon the specific ionization of the recoil (Ow 58), and their subsequent decay by scintillation has been observed to consist of at least two exponential decays whose relative intensities and time con— stants also depended upon the incident particle (Sj 65). With proper care, this dependence of scintillator response upon the conditions of its initial excitation may be exploited to identify the incident particle. This technique is called pulse shape discrim- ination (PSD). The PSD electronics are described in the next section. c. Electronics A number of PSD techniques have been published (A1 61, Da 61, R0 64), all of which vary widely in resolution, complexity, and acceptable range of pulse heights. This experiment required the ability to distinguish easily between neutron- and gamma-ray-initi- ated events over a wide range of pulse heights. An adaptation of this technique first proposed by Roush et a1. (R0 64) was chosen as L he :25 ‘ulfilling c ‘ 2f the current :inat'a) is mid E522 AG) and 3(1'4 3::r, and 3"”: an 15(l.e., the rec :iffarentiated t3"; respect to the he; mauve amount of Ine time at u :f :32 CFP'dI‘, whic Second available f Lie .0? signal) wa magi) 132 meters 3228 the TPOC pul 23:12 was employed 1133 and another 1 £,E n, “anosecond ca 37 best fulfilling the requirements of the experiment. If the current pulse arriving at a given PM dynode (in this case the ninth) is initiated by scintillator light with two principal decay constants, the pulse may be expressed as a function of time as i(t) - A(E)exp(-at) + B(E)exp(-bt) (IV-3) where A(E) and 8(5) depend upon the energy E deposited in the scintil- lator, and a>b, and all four constants depend upon the exciting parti— cle (i.e., the recoiling particle). If the resulting voltage pulse is differentiated twice, the time at which the resultant crosses zero with respect to the beginning of the original signal depends sensitively on the relative amount of slow component present in the initial pulse (R0 64). The time at which a detector pulse began was marked by the output of the CFPHT, which, as shown in Figure 7, fed into the TPOC. A second available fast logic output of the TBUC (the other was used for the TOP signal) was then amplified by a fast logic amplifier and fed through 152 meters (500') of RG—8 cable. Amplification was necessary since the TPOC pulses were severely attenuated by cable losses; RG—8 cable was employed to minimize such losses. After a second amplifica- tion and another 152 m length of RG—8, followed by a switch-select- able nanosecond cable delay, the pulses were fed into the stop input of a TAC. The linear pulse height signal from the ninth dynode of the PM was amplified by a linear pre-amplifier and sent to a double-delay- line amplifier (UUL), where it was double-delay-line differentiated in order to extract the pulse shape information as described at the ‘ . 3%.? r»: .V.. .: I‘vevfivt 38 D g E HIGH $ VOLTAGE O R ‘ 9"! '3 9 D N CFPHT V' E g e rx LINEAR DDL V PREAMP AMP POWER TPOC 41; J: n FAST LOGIC 5Top TAG mm A” START v- v- 500 FT. RG-B '_—‘E————-‘———————_ v v- GATE l DELAY AND DELAY .FL FAST LOGIC l AMP DELAY AMP ANP GEN. _L ' - l 41’ ENABLE J1 500 FT. RG-s l ”NEAR LINEAR GATE n n GATE v- I AND AND STR. STR_ NANOSECOND I CABLE DELAY I n n n I To me Jr TO TOF TO ADc SYSTEM Figure 7. Pulse Shape Discrimination Electronics fl; 4 fish '3- J1.” r4 gm of tnis sect 5;:7ed because it dc me: that double RC amtput pulse cross 3:12.15. differentia! Toe 3.31. has two T has sent directly :zsadelay amplifiel either: into a linea: '11-‘- 33! used to ext] “Li Single-Channel If I pulse fell T :aI'S-‘CA put out two I ‘iizazed that the pu, 93;: signal Which ma 23. the 9°81tive l me it '33 “Sed to '41:: levels determin we negatiVe pul 39 beginning of this section. Double delay line differentiation was employed because it does not cause baseline shift problems to the extent that double RC differentiation might, and because the result- ant output pulse crosses through zero faster than in the case of double RC differentiation (Mi 65). The DDL has two outputs, bipolar and unipolar. The unipolar out- put was sent directly to the data acquisition area where it was fed into a delay amplifier, to satisfy gating and coincidence requirements, and then into a linear gate and pulse stretcher. The bipolar pulse, which was used to extract the pulse shape information was fed into a timing single-channel analyzer (TSCA). If a pulse fell within a range determined by two discriminators, the TSCA put out two pulses: a positive, slow logic signal which indicated that the pulse was within the range, and a fast negative logic signal which marked the time at which the bipolar signal crossed zero. The positive logic pulse was sent to the data acquisition room, where it was used to enable the linear gates; thus the TSCA discrimi- nator levels determined which signals would be presented to the ADCs. ' The negative pulse from the TSCA was fed into the start input of the TAB. This pulse was used as a start, and the CFPHT signal was delayed about 2 microseconds because the CFPHT, as noted previously, was set below the TSCA lower level and so had a higher count rate; the dead time of a TAC is significantly reduced if the start rate is lower than the stop rate. Separate DDL—TSCA combinations were used for the measurement of low-energy and high-energy neutron spectra. The gains of the DDL's efferent. and edbn .-: scarces as (165:1 4-2.. . . . “if to F ’U output was i .zzastrezci'er whence it .. ,.~q . 5‘ ~.-‘ _ L. 2:."ng of W0 3“ 3:35 the neutron pus- 0‘. ..~n? I. :vt‘l“ . my; l5 SEEN-{n .;,. o'qql V mu. .he detectCY . .y 6““ .o nle'rl {Lap Ctr)? ... , u- ‘ . ’ ha a“! . :ztzizularly at low .:.. .. serge. The abi r-vv '-a.~ is. ami germs-raj; l'. 7;; "‘ Lss ezzect mav be . .'. u .s' zanear pulse hei. atensicnal nulti—L- M. to an on-line (ii: '4 it. ' ...1s experiment .h' m: .1 the CO‘DUIE' .mlayed on a str' be obtained. F1" s. ~5 ,ncte the ‘arry 0nmmouo ecumcflfiwuomfio onmnm omasm .m muswwm . o .- I "o. . \I O . a... a as. \\\\os\o\ \\§\\\\\\ . “ U Q o a o a \ THO"? 42 emanmflo coflumcfiefluomflo oomSm mmfism HmuowmcoEHolosp .o whomwm . ‘. .\\“ .0 0 000 0 0 . .0 ... 0.00.0. 0000.00......00.00..0......0.‘ n 00 0 00 0 o O 0 0 0 O 0 .I 0‘ O 0 O ‘ U .. . 0 0 0 . 0 0 . . 000 0 0 0. o . 00. . 000000 0 .0 O 0‘ o o O 0 . . \ o 0 . ..... ‘ O ” 000.000.000.00 ‘....Q . 0.........0....0000 0 O 0 fl 0 0 . 0 0 O 0 I. n 0 l0 0 00 0 0". 0 0 I 0. 00 .0 00 0 00 l . .G. . 000 . 000 0 0.0 00 0.. l ....0. ... . 00.0 0 . 0 0“ O I"..” 0 .. . .0 . . 0 I . .0 o . . .. . . . 0...... . . . 0 o. 0 0.00 .0 000. .0 .00 0000 o . .0. 000 0 0. 0 00 00000000.. 90000 I . .0 .0.‘ 00. 00 .0 0 0 0 .. 0 . 0 0 0.00 0 . . ... N . . . . .0. . 0 0 . 000... 0 ~u ....... ......... . . . . .. .« ..«....»«.» .«uumm «.«u 0. 00 Q . . .............00000' .0 0 0 00 0 .0 0 0 O. O: 0 0 0 O0... 0 o . . .. . . . ..000 .0 .0 00.0 0 0 . 0 0 00 0 00.0 00.. 00 0 0 0 O .000... 0... o 0 . C 00000.. 000000 . . .0 00 0000000...00 . 00 .000 000... 0.0.: . .0. .00 0000.0000~.0.: 0 ..0. .0. . 00 ...00.....:. .... .. . . 9.0:: n 0.00000 . c. 1” ......... ..-..0....0....000..0.0...0..000.000.000.......00....0000I00000000000 . .000 0.. 1 :vMMC. . 00 0. 000 000 G ..0 000....... .0...000:00 . 0 0 .00. ............0000 0006000200 0 0. 0. 0000.00.00...........00000..000...00 . 0 0.....000000....00..000000...0..0.0=0 . .000....0..0000......0..0000.00.00000.0.v0 .. .0... .0 .0.00000000...0..00.00000000.00000=00 c . . .o. 0......0000.....00.0.0.000.000.000000 .00000.0.0000000000.000000000000000000060 . . . 000..o..0000000000000000....000..00000 0 0 0.000 00000000000....00000000000e0 . 0 00.0.0.0000.000000000000000000e 00.............00000.0000000.- . .. .0..0.00.0.....00.000:000= . 0 0.. . 00.000000.u000 “00 0 0 000000000000000000 $00 0 o 000 0 000...000=000 . .00 . 000 0000:0000 0 0 000 C 0.... . 0 . 00 .0 . t ..... .. ... .......00.0..... ...0.....00 .000...00..0..0.....0 .00 0 0 0 0 0 - ...... .. o 000 0 V .000000 . 0 .0 0 00 .00... .00 0 0 . IIOQOIQUIO . .00. . 00. 0 . 0.00.0000000000.0..‘ ‘ .0 OK . 0 0. 0 . ‘ r I . v . . l... I0,000 43 01" lh‘ “ 4"": - ‘Q I. I -:'-..'."0.':':. l':'l ."'A:’l"i‘ifl." wag-u”. I. ."A .M ' 0 C Three-Dimensional Pulse Shape Discrimination Display Figure 10. E 1 co 5 .- -'. v' . .Q. 0 ‘ i233} la...‘ I I 00-11.! L'. (D (‘0. “-1 . Lu: .. ’ - 7" 0. “00A , _ (I) 0, {I 44 The ”bands” shown in Figure 9 are digital gates which set limits for determining which events will be accepted by the computer for further on-line analysis; they are determined empirically at experimental run time. Events which fall outside the bands are not considered further; these rejected events were an insignificant frac- tion of total number of events. Events which fall inside the bands may be used in two principal ways: (1) they may be accumulated as separate neutron and gamma-ray pulse height spectra; (2) they may be used to determine whether a given TOF pulse should be stored in a y-TOF spectrum or a neutron TOF spectrum. Option (2) was taken for this experiment. A figure of merit for the PSD system used in this work, the gamma- rejection ratio, is given by R - #y's in a peak in y_TOF spectrum #y's at same point in n TOF spectrum (IV—4) Gamma-rejection ratios typically on the order of 200:1 were easily achieved in most experimental situations, as illustrated by Figure 11, which shows typical TOF spectra for both neutrons and gammas. B. Beam Line The MSU Cyclotron was used to provide beams of protons at energies of 22, 30, and 40 MeV. The details of the beam transport system have been discussed in reference Ma 67. The beams were defined spatially by slits l, 3, and 4, shown in Figure 12. After being focussed at slit 3 by quadrupole magnets Q1 and Q2, (Q3 and Q4 were turned off except at 40 MeV where a little additional strength was required to -.=‘.__. .mm H I'.‘ i 4S 4H04 DOC: + JL + 000 +4Jl 4% El 5 $- 53 3.3 as? 0 - IOO_— g s U) - o f l- + + + ————+— 250 500 750 I000 Figure 11. Time-of—Flight Spectrum Measured with Pulse Shape Discrimination 46 uoomma mafia anon .NH shaman all: j\\\\h§\\ \Kflw\\\\\\\§§\\\\§ // 0.8 //fl .1 ’ \\\\\\ 47 focus the beam), the beam passed through slit 4 and was bent through +45° by steering magnet M3, then bent through -3l.5° by magnet M4 into the neutron TOF beam line. After going through an intermediate focus produced by Q7 and Q8, the beam was focussed on target by quadrupole triplet Q9-Q10. No energy analysis was performed upon the beam; experience with the cyclotron beam has shown that the energy resolution of the unans- lyzed beam is ~0.1%, or 40 keV at 40 MeV. Slits l, 3, and 4, in conjunction with the ion source of the cyclotron, were used principally to limit the beam current so that the count rate in the detector was kept at an acceptable level. The magnetic field strengths of all magnets were calculated for the beam energies used; fine adjustments were made empirically,based on remote visual observation of the beam spot on remotely controlled quartz and plastic scintillators in the beam line. Particular atten— tion was devoted to the size and placement of the beam spot at the target position. C. Targets and Target Chamber The targets used at a given energy in the experiment were discs 2.54 cm in diameter, with thickness equal to the range plus range straggling of the incident protons, as given by range-energy tables (Ja 66). The only exceptions were for carbon at 22 and 30 MeV, where targets made for 30 and 35 MeV respectively, were used; this should in no way affect the experimental results, or conclusions drawn from them. 4:05 - 48 The targets were fabricated from natural C, Al, Cu, Ag, Ta, and Pb. These elements were chosen because they span a wide range of nuclear masses. The target discs were press-fitted into thin rectan- gular aluminum frames 5.08 cm wide by .16 cm thick by 2.86 cm high, for mounting on a target ladder; the frames were made as thin as poss- ible to minimize any extraneous material around the targets. The target ladder was long enough to mount 6 targets plus a 2.54 cm by _ 2.54 cm Pilot B scintillator. ffi1j_ A diagram of the target chamber assembly is shown in Figure 13. i The chamber walls were .32 cm thick, and the entrance to the chamber % was through a narrow Opening 3.6 cm in diameter and 11 cm long to E 3 minimize the possibility of incorrect charge collection due to escape of electrons from the chamber. A 2.54 cm viewport was drilled into the side of the chamber to allow for visual observation of target height, target angle, and beam spot size and location on the scintillator; to provide vacuum integrity of the chamber, a piece of mylar .0125 cm thick by 25 cm2 was fastened over the viewport with epoxy resin. To allow convenient illumination of the chamber interior, a clear lucite blanking port was used to blank off the lower end of the chamber. Target position and target angle were changed by a drive unit mounted at the tap of the chamber; the drive unit was actuated remotely from a control panel in the data room. The targets and target holder were isolated electrically from the drive unit by a DBLRIN insulator, and electrically connected to the chamber walls by a long flexible spring. The chamber itself was 49 TARGET DRIVE SHAFT .q. . INCIDENT BEAM .t...., ..-.J e :3. co m TI AH m m s .c mm c. nu ~L_3q V'N ......................................... A Y on on Tom m RWW R. mo xv. mu a: .co pr. .un mm .VTE5 we no n~ \LUCITE PORT ILLUMINATION FOR Target Chamber Assembly Figure 13. 50 insulated from both the drive unit and adjoining beam pipe by UBLRIN insulators. Thus, the targets and target chamber performed as a Far— aday cup for charge collection purposes. D. Charge Collection and Integration The beam incident upon the targets was collected and integrated by an Blcor Model A310B Current Indicator and Integrator. This cur— rent integrator has been calibrated using an internal source and exter- nal sources and found to be accurate to within 1% for each current scale (Ku 67). Before each experimental run, the integrator was checked with its internal source, and with a precision battery and resistor, and found to be consistent with the previous measurements. The performance of the CFPHT and TSCA, as noted previously, were sensitive to count rate; in particular the TOP and PSD resolution were observed to deteriorate at CFPHT count rates above 10 kHz. This placed a practical limit on the incident beam intensity. For the measurement of 0.5-3.5 MeV neutrons, where the yields were largest, the beam had to be limited to currents on the order of 10710, 10-9, and 10"8 amp for 40, 30, and 22 MeV, respectively. For these low scales, particularly at 40 MeV, the current integrator was observed to be not very accurate at low currents and was sometimes observed, between runs, to be integrating spurious positive and negative currents; this effect was not observed to be greater than about 102, and did not always occur. Corrections made for this effect will be discussed in the section on data reduction. 51 B. Data Acquisition Data were taken under the computer code TOOTSIE (Ba 71), Operated in its LIGHT mode. In this mode the PSD and pulse-height signals from the electronics are initially displayed on a Tektronix 611 storage scape as a 128 channel by 128 channel two-dimensional plot, with x— axis - pulse height, y-axis - PSD signal. The data and display may be manipulated by both teletype commands and switch actuated signals. Digital gates, called ”bands”, were drawn around the groups of signals corresponding to gamma-rays and neutrons. Then the data- taking mode of the program was initiated; in this mode the TOP signals were stored in either one of two 1024 channel spectra depending upon whether the corresponding PSD-pulse height signals fell within one digital gate or the other. Thus separate neutron and gamma TOF spec- tra, as shown in Figure 11, were accumulated; events falling outside the bands were rejected, and, in this mode of Operation, none of the two-dimensional data were stored. The data were output from the computer on punched cards and as 1024 channel histogram plots. F. Data Reduction 1. Conversion of Time-Of—Flight Spectra to Energy Spectra A TOP spectrum can be converted into an energy spectrum by equa— tions IV-la and IV-lb if the time calibration of the system is known; the calibration of the TOP TAC is derivable from the location of the two y-ray peaks. Figure 14 shows a typical neutron TOF spectrum with its associated gamma spectrum. If n1 and n2 are the channel numbers 52 4 4 IO n n2 “.5; loco: e L * : 000 g ; 8 .8 .8 88.9 '00.- fig, 3 m - o S I- + + + _______+.__ 250 500 750 I000 Figure 14. Typical Neutron and Gamma—Ray Time—of~Flight Spectra .1 53 of the two gamma peaks, as indicated, then the expression for the total TOF corresponding to the 1th channel is given by ‘1 ”.E +.flgf1 (IV-5) c (nZ—nl)f where L is the flight path, c is the speed of light, and f is the fre- quency of the rf accelerating voltage; the time difference correspond- ing to the channel number difference nz-nl is equal to the period of the accelerator. Then the neutron velocity is vi - L/ti, and the neu— tron energy corresponding tO channel 1 is given by 3'. fl _'4.l'i'J-i#; C'ILIIIQ _ A ' (47 IL'. '- Tn(i) - MnGZm-viz/cz)‘l5 -1) (IV-6) I r1 ‘9‘. where Mn is the neutron mass; the energy width of channel 1 is given by AT(i) - T(i) - T(i—l) (IV-7) If the number of counts in channel 1 is N(i), then the neutron yield (in units of neutrons/proton/sr/MeV) is given by Y(i) a 2N(i)/AT(i)AOqc(T(i)) (IV-8) where q is the number of incident protons, A0 is the solid angle sub- tended by the detector, and s E(T(i)) is the detector efficiency for neutrons of energy T(i), and the factor of 2 appears since the TOF spectrum was doubled. The TOF spectra were converted to energy spectra using a digital computer. The TOF data were summed over a number of channels corre- sponding to the experimental resolution as measured by the full-width- 54 at half maximum (FWHM) of the y-ray peak; channel-by-channel conver- sion is not necessary since the flight times are only determined to within the FWHM. Summing in this manner also masks out unimportant statistical variations in the TOF spectra, and gives smooth energy Spec- tra without altering any essential features of the data. 2. Calculation of Detector Efficiency a. Statement Of the Problem The most important factor affecting the absolute normalization of the data, aside from the measured incident flux, is the efficiency of the neutron detector. This efficiency is a function Of neutron energy and also depends strongly upon the following factors: (1) the detector threshold; (2) the response of the detector to recoiling charged par- ticles of various energies; (3) the neutron cross-sections of the detector components. Cross sections (3) have been measured over the neutron energy range of interest and are tabulated in reference Ku 64. (l) and (2) depend upon the particular detector used and its associated electronics, and must be measured for each individual apparatus. The detector efficiencies in this experiment were calculated using a modified version of the computer program TUTEFF developed by Kurz (Kn 64). The accuracy of this calculation has been investigated exten— sively and compared with experimental efficiency measurements (We 62, Bo 62, hu 70) and found to be accurate within kurz's error estimate of 3102, even though it does not include edge- and end-effect corrections; rescattering contributions are included. The principal contributions to the uncertainty in the calculation, at neutron energies greater ~00. an '3.‘.. :- “00' LA. V‘ 0.- AL. :“JT ‘ '0‘. Ja‘ 0. ' , w ‘eC01 'U. was a... . &. 0R,- '1 ”u . “~a C M . n“ 'F' 55 than 10 MeV, arise from uncertainties in the measured cross sections for neutron-carbon reactions. In general, however, the accuracy Of the calculation has been well verified. Two calculated efficiency curves used in the experiment are shown in Figure 15. 6. Measurement of Detector Threshold and Light Resolution For a given detector size, the two most important parameters for calculation of the efficiency are the lower level pulse height thres- hold, and the light resolution at that threshold; they are particu- larly important for neutrons which cause pulses which just barely exceed the threshold. TOTEFF requires that the detector threshold be known in terms of “equivalent electron energy”, i.e., that the response of the detector to recoiling electrons Of various energies be measured. The measure- ment was performed by using gamma-ray sources Of known energies which emit only one or two well separated gamma rays: such sources yield pulse height spectra, in the detector which are characteristic of recoiling electrons with well defined compton edge energies. A typi— cal pulse height spectrum for 60Co is shown in Figure 163, with the Compton energy for the 1.33 MeV gamma ray indicated; the Compton Spec- trum of 5700 with the 41 keV compton edge and 123.5 keV full energy peak indicated is shown in Figure 16b. The maximum energy E of the recoiling electrons is related to the gamma-ray energy by (Ev 55) E = EYK/(l + K) (IV-9a) where R a ZEY/Mec2 (IV—9b) More 1. I ‘t'IItl‘ 'II‘III'III‘ .20 .l5 NEUTRON DETECTION EFFICIENCY .05 Figure 15. 56 DETECTOR THICKNESS = |.9| cm DETECTOR RADIUS = 2.22 cm UPPER CURVE: THRESHOLD 0.06 MeV : E8 FRACTIONAL RESOLUTION = 0.l8 LOWER CURVE: THRESHOLD = 0.85 MeV = Ee FRACTIONAL RESOLUTION = 0.06 l l l l 1 J I2 I6 20 24 28 32 En (MeV) Calculated Neutron Detection Efficiencies 36 57 000. Dow muuomam HHoomm acuaaoo oon was 0000 mum—>52 szz22 2 EN -wz z. Zamhomam q FIG-m1 mmJDa 008 l l .moH muawwh 3 O n N II& 80.0. S Iflu 3 no 3 nquom “H” V N N 3 _| nXX%Om 58 Con mmmEDZ Oom mpuomam Hwoomm scuaeoo ovum mam ouoo muzquo 0mm 2 1ng 85cm :6 >2 one — m_N-mz Z_ Eamkomam HIQMI ~65 53:50 >8. :VIIIY meD& 00; “.s‘. .DOH musmam OO- 1 .0. qu 1 No_ m MN l 0D / flu ”H V I no_ N MN fl: fil 1 VO— g no— .u " ‘I it; 3‘; II» |‘ 59 Me being the electron mass and c the Speed of light. The two TSCA-DBL amplifier combinations used in the experiment were calibrated as follows. The Compton recoil spectra were accumulated using a Nuclear Data NDl6O multi—channel analyzer; the zero level of the analyzer had been previously set using a precision pulser. The TSCA dial was moved until no events below the Compton edge were accepted; the resulting curves of TSCA dial setting vs electron energy are shown in Figures 17 and 18. A number of gamma sources were used to cover the widest pos— sible range of electron energies: S7Co, 203Hg, 22Na, l37Cs, 6000, 208T1, and 120* in a Pu-Be neutron source; use of the last source required PSD. These sources, their gamma ray energies and correspond— ing Compton edge energies are listed in Table 1. The light resolution as a function of electron energy was mea- sured as the energy difference between two points on the Compton edge spectrum; as illustrated in Figure 19, these points were taken to be the energies at which the Compton curve passed through 75% and 25% of its maximum value. Measured in such a way, the light resolution cor— responds closely to the full width at e’l/2 of a Gaussian resolution function centered at the Compton energy. It is proportional to E: and its magnitude depends on the light collection efficiency of the scintillator, the efficiency of the PM photocathode, and the design characteristics of the PM; the fractional (percentage) resolution of the system is then preportional to 32%. The fractional light reso- lution measured for the experimental system is shown in Figure 20 as a function of recoil electron energy. 60 m>uso sowumunfiamo umuxamc< Hmscmnu mamawm 39: >omwzm zombow4m CON. 000. 00m 00m 00¢ OON _ q —, - dI .4 - q . . . came Emuzm .15“: 83 8 mkz_oa ZO_._.0mw2w Zomhomqm w m N _ 4 T a an... 88 .33 be 9.2.01 20..rusu cowusHommm unmfiq ocuomumo .ou muswfim $2): >0mmzm Zomkomqw 0_ 0.. I ..0 .0.0 .q.... . _...~.1. . _.qfi.... . . — _ —p—h_P_ h — Pb—b-.__ h NOIln'IOSBU % 00. 65 c. Measurement of Detector Response Function Apart from the threshold and light resolution the detector effi- ciency depends upon the response of the scintillator to charged par- ticle recoils, especially recoiling protons. This response function, or ”light curve”,relates the scintillator light output for a recoiling proton of a given energy to the energy of an electron which causes the same pulse height. The following simplified example shows how the efficiency depends upon the light curve. If monoenergetic neutrons are incident upon the detector, and their energy is below the threshold for reactions with carbon (~7 MeV), then only n-p collisions will produce detectable events. The fraction of neutrons colliding with protons in a thickness x of scintillator is N - l - exp(-nonp(En)x) (IV-10) The energy spectrum of the recoiling protons is shown in Figure 21a. Then the number of events per pulse height interval, as shown in Figure 21b is given by dN . dN dEp dL dEp dL (IV-11) where L is the light output in electron energy units and, as shown in Figure 21a, dN/dEp is constant. The efficiency is then given by ME“) L05“) e-IggdL-gy. I601,“ dL dE 3'1; ' IV-12 th. p th. ( ) 1.). 66 m_ muuomom uxmflmm wmasm pom zwumsm HHoomm cohoum .LHN shaman 6:2: m>_._.<..mm. exam... wmuan. o_ m o o Cd. '19 ('IVAHBLNI .LHDIBH ssm/ssswnu) NP muuommm unwfimm mmasm 6cm mmumcm HHoomm noboum gas: am if: 26 c . aumHQM .NN muswwm $62. cu m: 0. .2 N. 0. 0 .V N _ A - _ A d 0 O 000. 000m 3 m Eamkwmmm owmamu=0 success“ Houoouon .mm ouswwm A>0_2V #DQFDO #10: NO. .O_ 00. _-O_ N-O_ ....d. 4 1.... . 1 . —...... q « 1qq.qq . . _...a. . q . .0— r 11111111 J IITITI I Co_ I 1 d3 - 1 W: I 1 a n . M P h _o_ ezmzamaxm :ms.-. - 8 5:2 20E n H.256 Eo: .. ” m._xmz_mmm> m 4:».p . _ _:__p_ p _ 7:». r _ r —:.~.b _ p ru.bp__ _ O_ N 71 used were those for 15 MeV neutrons. For each target, the neutrons were assumed to originate at that point at which the full range inelastic collision probability of the incident protons is half of its original value (Ja 66); then, since the target thicknesses were known, the amount of material traversed by the neutrons for a given detector angle can be calculated (see Figure 24a). This quantity is vital to the calculation of the removal cor- rection. For the high energy neutron spectrum, the removal correction due to non-elastic reactions in the target was calculated, using the non- elastic cross sections tabulated in hu 58. Since the elastic scatter- ing angular distribution is strongly forward peaked at higher neutron energies (Ga 70), almost any neutron whicn is elastically scattered away from the detector will be compensated for by a neutron of the same energy which is scattered into the detector (the scattering angles are very small, typically less than 10°), so no correction for either re- moval or inscattering by this process is necessary. Non-elastic reactions by high energy neutrons may lead to an iso- tropic evaporation neutron spectrum which would result in some small raising of the low energy end of the measured spectrum. It was esti- mated, on the basis of the measured energy spectrum, corrected only for the detector efficiency, that the number per unit solid angle of high energy neutrons was equal to 102 of the number of low energy neutrons. A given target was divided into 3 regions of scattering material as shown in Figure 24b, and the solid angles of each region were calculated; then the percentage correction for a given region is given by 72 c - n (do? AQ x (IV-15) d3! where n is the number of target nuclei per cm3, dg_is the cross section for (n,n') reactions, assumed to be equal to thediotal non-elastic cross section divided by 40, A9 is the solid angle of a given region, and x is an average distance to escape from that region. The removal of low energy enutrons by non-elastic scattering was calculated and the correction applied to the data; this correction is I {’1 ICE!- small, because the non-elastic cross sections are small for low energy neutrons (flu 58). The contribution of elastic scattering to the re- moval of low energy neutrons was also calculated since the elastic l I" ail-P'mk‘. angular distributions are not so strongly forward peaked as at higher energies, and no ”exact" compensation occurs. The elastic inscattering correction for low energy neutrons was calculated by using equation IV-15 above, assuming the elastic scat- tering cross sections at low energy are isotropic and dividing the target into three regions as shown in Figure 24b. The total correction was then applied separately to each high- and low-energy spectrum. The removal correction for the 40 MeV Pb target spectrum at 30°, is 2.2% for the high energy part of the spec- trum and 4.25% for the low energy part; the total inscattering cor- rection to the low energy Pb spectra at 40 MeV is 8.8%. A represent- ative list of these corrections is given in Table 2. 2. Deadtime Correction The deadtime of the ADCs was monitored during each run using the ”channel zero” option of the data-taking code TOOTSIE. A logic pulse 73 mcofiuoouuou Hmuumomufio 6am nouumomcH How mhuosomu .nqm muswwm b d4 923.. Emma; mGOfluomuuoo you muumsomo uowuma .mqm ouswfim o O O) I \ Pb Ta Ag Cu A1 Z Inscatter Z Absorption 6.1 12.6 5.6 15.4 11.7 22.1 8.0 9.8 9.8 12.5 19.3 22.2 74 Table 2. Absorption and Inscattering Corrections for 2.0 MeV Neutrons At Neutron Angle of 120° at Ep 8 30 MeV 75 generated by a random frequency pulser and presented to the channel zero input was counted only if the ADCs are free to accept an event. So the fractional livetime of the ADCs is the ratio of the pulses counted to those presented. The beam currents used in the experiment were generally steady, so that no problem arose because of the source of channel zero pulses not being directly correlated with the beam (La 71). The percentage deadtime corrections were included when the TOF spectra were converted to energy spectra. These corrections generally T1 fell in the range from 52 to 152, depending upon the beam current used and the yield from a given target. H. Absolute Neutron Yield Spectra, Angular Distributions and Total Yields The data converted from TOF spectra to energy spectra as pre- viously described, with all corrections included, are presented in Figure 25 as absolute neutron yield spectra at each of six production angles. These yield spectra were then integrated over energy to obtain the angular distributions of all neutrons shown in Figure 26. The angular distributions were then integrated over angle to give, for each target and bombarding energy, the absolute total yields plotted in Figure 27. These total neutron yields are presented in Figure 27, together with the total thick target yields obtained by Tai et a1. (TA 57) at 18 and 32 MeV. The Tai experiment was performed by neutron activation of a manganese sulfate bath. When the great difference between the two techniques is considered, the agreement of the results of the two experiments is excellent, with regard to 76 n-s. . muuomam mama» souusoz .mu musmfim 96.2. >0mmzm 20Ebmz o... mm om mm om n. 3 m o or mm on nm 9w 9 - 1 a 4 a q q q - CID“ - q q 5 q 4 o-o. .. >2). mm 62 . >62 mm o u a“ 6 . $22 on: .. . >22 on. c o o c ..... ’03... o 0 0 >22 ow as >22 ow . .12 /M.m../j.a omo om . owe o ma / m6 92 6.... NM /8S/N0108d /SN08103N Figure 25. '77 (continued) “"1“ 1 11111111 1 'TI'TTTTVfi'T. l‘mvyv1 I Innpr' * 8 [I] C) D_ g L O E 0) o ' ST 1. . 1 «0". “n""f:",a”’ mutuLé {4111111 1 Jnllljj v 'r =r v v e 9. 2 s '9. PB 80 DEG 40 MeV v 1: A9IN /HS/N010Hd /SN08 10" 10" o-w o 1 17711111 1 WWTTT'1“—| 30 MeV 22 MeV . ......... ......... 1......“ J, 10" to“ 10" 30 MeV 22 MeV '2 I. .LRBN 10" 15 80 ES 30 35 LIO 10 (MeV) HO NEUTRON ENERGY 15 20 25 10 1. i .15 -T‘ [I 'l...‘"~:_ n . TW.IC 78 (continued) Figure 25. $6.2. >ommzm ZOmHDwz o... mm om mm cm W. o. m o 0.... mm om mm cm W. o. w o . . 41 . . .1 . a-o. . . .. . .1 . . a-o. >65. 0m >22 0m . 6-0. 6-2 >22 mm ..2 >62 mm ....2 w s n m: . ... .r.. 010“ . 010" n >65. 0e ..., >22 0v . W o . o oo. ....n 6.. ...f. I ..... .. ...-o. ".2 T ......... ..a a. v ... .. ... U ..a/ ' ..../ m .. . ...» F /’0 ’10" /. ’10" m umo om. own om. F «to. «-2 . mm. mm. Wu » p _ c c .r a u-o. r _ p1» . e c _ ”-9. AalN /8S/ NOlOHd /SN08103N 79 (continued) Figure 25. t1 ’1“ >0mmzm zomkamz ..2m222. or mm 8 mm 9.... m. a. m a q . a d a 4 J I Can.— w P >22 mm o-o. n >65. on m. K.... m. 4.6. fl ..- >m.>. 0e ... ...-S . 2-9. owe om a H .-.. P F P L h P F ”lad 0.... Wm 8 Wm Om mu 3 >22 om >62 mm >22 ow . ..--I mumeu A. .-o. “-2. n-a. 2-9. .-s. ”-2 ABW /8S/N0108d/SN08103N 80 (continued) Figure 25. $22. 5mmzm nm cu m— a. n e - ..-... >62 mm K-°fl Vb. /.N. ...... omo om mp ZOE-DMZ or mm cm mm cm W. o. m o . . . . . . . -e. >22 0m o-o. >05. mm “IO“ 6.... . . . .3]. >2 ow / 92 1...,- ..-... mun ow . ck -.. _ p _ _ p _ r we. AaIN /HS/N0108d /SN08103N 81 (continued) Figure 25 . mail 11:2 .I I .12 $22. >0mm2m 207.....sz or mm 0m mm Ow fin 2 n O or WM 8 mm 0m 2 m . . J I4 4 4 la a - Tod - 4 a 4 4 I. . >05. 0m >62 on. ..2 . >22 mm >22 NN K.9. .. . . . . . .....r 9.9. .-. s. . m 2 >22 CV ..a. .21 >02 0.? ..... a... ...a .2 "00‘ . ... ....... /9 . w M w /. ...-9. /.... owe om. . omo 9m. . E .- .-2 ¢ .- F P h b 1- L L ”90% b b P L b P 9-9. 9-9. k.9. M...: 9-9. 2-9. n.9. , wood AGW/HS/N0108d /SN08103N 82 (continued) Figure 25. $2): or mm om mm cm W" a" n a q a 4 a a q a ‘Ouau cued .. >22 mm N.2 \4w22 ow .1, vs 00...}... ’oo~ owe om mmHmHm Gian P F b F b L- b ”.a~ >ommzm ZOmsz or am om nm am an o“ m a . d 4‘ 11¢ 4 Lfi \Al, I4 JISLw Hm hwm ..-QH -m 1n. hwm >22 mm #2 3gw<4 nymw >22 ov: wmo o it» P F » ~ AGW / HS/NOLOad /SNOH.L03N 83 (continued) Figure 25 . 9E): >omwzm ZOEbmz om mm cm W" 3 n a... .' % . 2 . . O . , m M1111 1 IIIIIII | llllllll I llllllll I IIIIIIII l LO 7 12 d‘ d q d d d $3 .. >m2 mm o “ch 0:2 >22 ow . vs ...2 Duo 00 ac >22 Om >22 oc . owe om , ..3 2,. 2.. 'g a AalN/HS/NOLOHd/SNOHJIIBN T 2 0) f3 , aco— 84 (continued) Figure 25 . $222 2. mm on no 8 n. 2 m a u . q 4 J J J J - CID“ ..2 >22 Om . . 2...: mm . k.... .. #2. >22 O¢ .2 ".3 “NV" #52 owe 02 em ..2 >omwzm ZOEbmz on no 8 n. S n a J J J J 4 J 019‘ . .-3 >22 Om . .. >22 mm . ~-od . . . v.3 >02 ow . a u x ...... ....w .. ”no“ 2. owe omH em ..2 P p L h h P ”0°“ A9W /BS/ NOLOHd/SNOHLOHN 85 (continued) Figure 25. or 3222 mm 8 mm 8 m2 2 n o d d 4 4 J 4 d WWWTTW’T'Y' . 0-3 . >22 mm . . . K.2: >22 on m...: >22 ow. . ...,. ”-2 ..../ / as Owe cm 3 Q ”-2 b L b b L b b ”lad 0: mm >ommzm ZOEbmz 8 mm 8 m2. 2 uuvr—[rerT-r—r—pmh—I—t—jmm 2‘ ..>22 mm >22 90.. >220¢..I 80 m C) 'd I Q Cd K.2 $2 1.1-; .1..._J.m..n.1...L_._lu11Jl-1-.1 21111111 .1_1__I 0 NW / HS/ NOiOHd / SNOHJJ) 3N 86 (continued) Figure 25 . o V2 32>: >ommzm 20¢:be Snug ru— 3 * d 4 >32 Om 0mm. cm 1 1 >22 mm or mm on mm am 9 3 n o a... an - J d J .4 J 4| 4 , .16“ d >22 on ..s >22 mm #3 Vb“ o. 00...! >22 0v .,.. ..z “-2 .2 we» owe em :0 ..-... Ibl If p p p n L ”lad L A9W/ 88/ NOiOHd / SNOHJIEN 87 (continued) Figure 25. O 3' 32>: >omwzm ZOEbMZ pnvvww 1 —rn711-r‘r*‘1nrrrr1—T-jI [1111111 fl ["1111 1 T ["1111 T T THY—rrrTT cm mm cm W" 3 m a J J . J J J I 010“ >22 on .-22 u-a2 u-o_ «-02 2.92 owe omH :0 «-92 "-22 am mu om 1- Jq J 22w22 hum” >22 ow . mm 3 >22 mm ...... owe omH 30 J Q .. a-a2 .-92 MW fl: 2-22 mmw HO O m ?b~z/ d w m. “-2 N / ob HO / run: w a A Glam «.3 88 (continued) Figure 25 . S2): .13 >22 On «-22 92 >22 .o.¢. . . vs 73 owe om >ommzw zomhsmz or mm cm mm cm mu 3 d .1 d - 4 d ?2 m sgw<2 Aumw «.92 mmw . >ms. mm Wm *2 B w . . . . ..... .1... Il- >22 ow H vs m 3:. I/ .....t/ S / . H 2 W .. #b M wwo o 9 0 Fl :5 89 (continued) Figure 25 . $2): >0mmzm zomhamz 2. mm om mm cm W" 3 m o J J J J J J J , DID— ...: >02 Om >05— NN . k.3 v.2 . . ... ...... .../J. >32 0? .34/ u n-3 /C ...2 owe om 12¢ .-.: VS :2 no on ma om d u 1 1 >22 Om >029. owe om *9 t. '2. g 'I‘ d f AalN/HS/NOLOHd /SNOH.LOBN «-2 $2 $2): or mm on mm om ma ed M o J '4 J J J 4 d \\.. a-o~ “-9“ ..a. 90 ”tad ,.o~ owe omfi |:¢ (continued) use.— Figure 25. >0mmzm ZOmHDwz Ffrrrrv r '"HlII I or om mm om ma od m o 4 x4 4 d a 4‘ 4a-ofi A >22 om M92 1 L m ... N n MM .44 n .. \, (4 MWMW ¢ Any u .. N .. S Ma; xx Anv . y./ .. >22 oc . ”-2 m ...... L / .1. S no / W -on /.. .. M owe omfi Izm .mbH p— r h- 7— LULLLJ_1_ ~-o" 91 Figure 25. (continued) IIIIII I T [IIII] I I T IIIIIII T I 'IIIIIIT r TTTIITT I IIIIIIIW I [VIII] I I T g L 1 1n m 1- (‘D O LLJ ‘ m L) D > m r- O E ‘ (l8 m o V » .. g , J a .' 2 ° ' £3 1- .‘ 1n .- 8 2 * —~ .-" . N r- .. ° N 4 9. A 1' > .~' 5 g .9 P / g -4 m V ‘ .. ” 5 E 111 L 11111111 1 J1111l 1 11111111 _°_hn_r111 1 11111111 1 1111111 1 1 o >- .L J ‘1' 9 =r V3 w ~ ° a S? 9. 2 2 9. '9. '9. '2 '° Lu Z w 1:: FM” ' Fm'" ' l"""' ' I'm" ' pun”! '1:- Z 82 - . 43 .- D J Lu - (D 3 Z L) “J > Q g .. D a 0 q- “ . > : - ° '43 ‘2” ; > .‘: q; Jun r- 8 0.. 2 H ." N - . . N J2 ...... .. 4n «:1 mummy wanna.- »nmcu-p 10mm? nmmq. 1053:? w':‘v.'.~,7° 9. 9. 9. 2 9. 2 £2 ‘2 AGW / HS/ NOLOBd /SNO&:LLf13N 92 (continued) Figure 25 . 92>: >omwzm ZOEbwz or on ma 8 n— 2 n - a 4 4 1 q q q - 9°— .. >22 mm ..2 >22 8 ...2... .... .. 1.. . .... / 016‘ >22 0v . .. ../ ./ m u $2 ./\ .13 owe o0 U Uno- o|r mm a mm 8 4 4 , 92 0.2 h.2 . >22 om . Uno— >m§ O? . ....2 ...s wwo ow nuc— a-.. AGW/HS/NOiOad/SNOHLHBN 93 (continued) Figure 25. or 926 >0mwzw 20¢sz mm cm nm em n" S n o d 4 d d d 1 d , Clad >22 mm . . .-o. >22 on . ... ~-o. owe on; >32 0? . n.2 m-o~ nm em mm om mm 3 m o Inn, u fiWfl‘ c33- InnTIY T '"VYIII v rnvyt v I "[17 I Clan >22 om «-2 >22 ov C» “.2 / .4. h ”30‘ owe 93 ”My n-o_ , ~-°~ AalN /HS/NOJ.OHd/SNOHU13N 94 . 30 MeV 0. (fl I l 1 Illl? l ‘0 WV '5? J} U I'rl'l NEUTRONS/ PROTON/ SR LllllJJ -5 L L L l I 1 '0 O 30 60 90 IZO ISO l80 Figure 26. Neutron Angular Distributions .I V ‘ .r.f..73' -.na_'.'.'_x.r.-.t. l Figure 26. 95 (continued) 10'2— I I U I l I (I o (DIO's- 30 MeV (z: k; T o a . +— I é? . \ Nev (I) Z . O 0: f.— a :04 Z I III... l lllllll so so 90 :20 T50 Iéo NEUTRON ANGLE (deg) I l‘ ‘l \ I ll’ \ Fr, \l‘rwllnl‘ \ "HUI/n: III E ‘ U I ‘Z 96 Figure 26 . (continued) IO-2 U I t 1 I I \ I Z 4 E2 . E 22 MeV - \ q ‘é’ - J .05 D ’4- -‘ UJIO _ : Z : d I 1 P 1 IO'5 lllll 0 3'0 60 90 1'20 I30 l80 NEUTRON ANGLE (deg) 97 Figure 26 . (continued) IO'Z _. I I I I I I Cu ‘1 . 40 MeV 0: -3 S '0 30 MeV E ,9 : 00: q a. b\\22 MeV W \ . é’ - ' d E B IO'4 .- 1 '0-5 I J l l l 1 O 30 60 90 IZO ISO l80 NEUTRON ANGLE (deg) 98 Figure 26. (continued) '0-2 I I V l I Al 1UI1III llllll “3 IO'3 - - "g’ b 40 MeV : I. l o . E _ 30 MeV _ \ m I- u m l0 :- -: z : j I I I- -( IO'5 1 l l L l l 0 30 60 90 I20 I50 l80 NEUTRON ANGLE (deg) Figure 26. I0-3- 99 (continued) 40 MeV 3:) . \ I Z . g 30 MeV 3 E .I \ b d g m d I'- I: ! IO'5: I : 22 MeV : P I |()-€5 l I 1 1 1 LL 0 30 60 90 IZO ISO IBO NEUTRON ANGLE (deg) I}? F "at." |O° IO"I NEUTRONS/ PROTON IO'3 IO-4 l 1 J J J I 0 IO 20 3O 4O 50 60 Figure 27. I0"2 100 I I I I U r I I IIT'II I IU'IIU' U I C NEUTRON TOTAL YIELDS : Pb- D _ To- A 01- 0 AI - A 5' C3 - 0 1111111] 1 1 111111. 1 11111111 1 111111 E MeV P Neutron Total Yields. The 18 and 32 MeV data were taken from reference Ta 57. 101 both the absolute magnitude of the total yields and the behavior of these yields as a function of bombarding energy. 1. Estimate of Experimental Uncertainties One of the principle sources of uncertainty in the experimental results is the uncertainty in the calculation of the neutron detection efficiency of the scintillator. The error in the calculation has been estimated (Ku 64) to be about :_10Z. This estimate was based upon the known errors in the measured neutron cross sections used in the calculation. The calculation has been investigated experimentally by several groups (We 62, Ga 61, Hu 70) and found to be accurate to within the experimental errors, which are typically about i 152. This latter value, 1 152, was taken to be the error in the calculated efficiencies. Possible errors in the normalization of the data due to faulty charge integration were noted previously. The energy spectra of the low-energy neutrons (0.5 - 3.5 MeV) were compared carefully with the corresponding spectra of the higher energy neutrons, and examined for agreement in both slope and magnitude in the region where they overlapped. Except for minor effects due to finite pulse height resolution at threshold, the "low" and "high" energy data agreed very well in slope. In cases where the magnitudes of two spectra differed in the region of overlap, the low energy spectra were scaled to match the high energy spectra. Only for a few spectra were the scaling factors different from unity by more than 15%. 102 In addition, the total gamma-ray yields from each target (in counts/ucoul), which should be isotropic, were examined for deviations from isotropy as an indication of faulty charge integration. For cases in which the high- and low-energy neutron yields did not agree in magnitude, the gamma yields for the low energy runs differed from isotropy by roughly the same amount as the neutron yields, 15%, so this was taken to be indicative of the error in the data due to faulty charge integration. In any case, such adjustment of the normalization of the low energy data as described above is justifiable only if the results agree well with previous experimental data, as in Figure 27, and if analysis of the data yields reasonable values of extracted parameter r0, as discussed in section V. Except at detection threshold and the very highest neutron energies, where statistics are poor, the statistical error in the data is typically 1 42. So the data are estimated to be good to about i_20%. The fractional non-compound yields as obtained in the next section depend only upon the uncertainty in the efficiency calculation and certain assumptions made in their derivation, which will be discussed in section V, also. V. DATA ANALYSIS A. Extraction of Nuclear Level Density and Radius Parameters Perhaps the most distinguishing feature of the heavy (A > 60) element neutron energy spectra shown in Figure 25 is that each has two distinct components. The spectral shape of the low energy (< 7 MeV) neutrons, which have left their residual nuclei with relatively high excitation energies, is characteristic of an "evaporation" spectrum as predicted by the statistical fermi-gas model of the compound nucleus. The energy spectrum of neutrons with energies greater than 6 or 7 MeV, on the other hand, cannot be explained by such a model, and will be discussed in the next section. The statistical fermi-gas model of the nucleus as developed and applied in sections II and III was used to analyze the evaporation portions of the neutron energy spectra in an attempt to determine the nuclear level density parameter a, and nuclear radius paramenter r0. a chiefly affects the shape and slope of the evaporation neutron energy spectrum, while ro affects its normalization. All the spectra for a given target at a given bombarding energy were plotted on the same graph. The previously described program DECAY was run.with a number of values for a and r0, and the results of the calculations were plotted on the same graph for comparison with the data. A typical plot is shown in Figure 28 for the case of Ta at 40 MeV. The value of a which was considered to give the best fit to the data was a = A/lO MeV‘l. The other two 103 'Ilfi’f. 1%,... 104 I0'2 I . . . . E? o: ..I C) c"? A we” 4}. 0 2 (D < > 0) 2 . e Q °" ‘ WOO % IO'5 0; \o 60 I— ”On ° g x 0 ~94! l50° \ \ -6 IO %’ I20° \, 0: " 90° +— -7 -I 8 IO 0 (MeV ) Z x - 26 O - l8 IO'8 0 - l3 lo-Q 1 L 1 1 1 1 1 O 5 IO I5 20 25 30 35 4O NEUTRON ENERGY (MeV) Figure 28. CMparison Bemeen Evaporation Theory and Experimental Data. The Solid Curves Represent the Data. 105 sets of points correspond to the a values as indicated, which were considered just barely unacceptable; these values of a were considered to be indicative of the errors involved in using the model and in choosing the "best" fit. The targets thus analyzed were Cu, Ag, Ta, and Pb. All fits to the data were chosen by eye. In view of the integral nature of the data and the simple assumptions employed in the calculations it was not deemed appropriate to employ xz-type fitting techniques. Figure 29 shows the results of this method of analysis of the data; the error bars shown.were determined by the method described above. The upper line plotted in this graph corresponds to a - A/ll MeV‘l, which is obtained from the form of the model developed by Lang and LeCouteur (La 54). This model considers explicitly the competition between neutron and proton emission, and for this reason is more relevant to this experiment than some older models, which did not consider proton emission at all. In any case, the level density parameters obtained are in excellent qualitative agreement with both the simple and modified forms of the theory, and in reasonably good quantitative agreement with previous experimental values (Bo 62). The experimental values of a determined here for Pb reproduce -- at least at 22 and 30 MeV —- a previously Observed (Bo 62) and predicted (Ne 56) decrease in the level density attributed to shell closure (or near shell closure) in the Pb isotopes. 106 umnasz mmmz mo cofiuocam m mm mumumEMHmm hufimcon Ho>oa umoHoaz vouomuuxm .om ounwwm < mwm Dom mt Om_ mm 0mg mm 0.0 MN of >22 mm. D >ms_ Om... 4 >22 on. x - p n b - IbI h p P O 107 An apparent dependence of 3 upon bombarding energy is also indicated in the case of Pb. Such effects have been noted by other investigators (W0 65, Si 62, Al 64) using other incident particles, lower bombarding energies, and other targets, so it is perhaps not too surprising to see it in some of the cases considered here. Such an effect, however, disagrees with the basic assumptions of the model, unless one offers as a possible explanation that the shell effects in lead, which are prominent at low bombarding and excitation energies and do not conflict with the model, decrease in importance as the excitation energy increases. In any case, the errors made here in extracting the values of a from the data do not allow such a statement to be made definitively without further experimental corroboration. Similar statements might also be made about Cu, which is one proton removed from the Z = 28 closed proton shell, but, again, such conclusions should await further more detailed experimental results. The values of rO which gave the correct normalization for each target are shown plotted in Figure 30. The value of ro for the heavy targets is 1.2f. This value is somewhat low compared to values generally used for rO (1.3 - 1.6f) (Ta 58, Ha 62) in this sort of calculation. However this is consistent with the assumption that all of the flux lost from the incident beam goes into formation of compound nuclei which may subsequently decay only by neutron or proton emission. This assumption was necessitated by the unavailability of detailed information regarding the contributions of T" 108 3932 most mo coauocam a mo mumuoamumm madam umoaosz vouomuuxm .0m 3ng < mum—232 mmflz I mNN OON mt 09 mm. 00_ wk. Om mm 0 (squaI) OJ ... mN._ 109 all types of reactions and reaction mechanisms to total reaction cross sections. In fact it is hoped that this experiment may yield some information in this regard. While neutron evaporation was predominant in this experiment, other reaction.mechanisms certainly can and do contribute to the total reaction cross sections at the bombarding energies used, so that the above assumption would lead to a somewhat smaller value of ro than if these reactions were accounted for explicitly. A somewhat different approach will be employed in the next section to analyze the behavior of one of these other types of reactions. One case where the assumptions of the model are not valid is I i that of A1 at all bombarding energies used. The neutron energy spectra from this element do not have the shape characteristic of neutron evaporation, so one.might suspect a breakdown of the model, and that suspicion is readily confirmed when analysis of these data is attempted in a manner similar to that employed for the heavier elements. As shown in Figure 30, the values obtained for r in 0 this case are quite small compared to the values obtained for the (ather elements, which very likely indicates significant competition from other reactions and reaction mechanisms. In fact evaporation of protons, alphas and even heavier particles is much more likely in this situation than for the heavier elements, because the Coulomb barrier is not high enough to inhibit them very strongly. Furthermore, no suitable fit could be made to these energy spectra in order to obtain a value for the level density parameter. 110 None of this is unexpected, since Al is a light nucleus, and the lower limit for the validity of the statistical fermi-gas model is around A - 40 to A - 50 (Mo 53). Carbon is a similar case. The statistical fermi-gas model is certainly not applicable to such a light nucleus, and from the shapes of the neutron energy spectra themselves, it is evident that the treatment which gave very good results for the heavy 1.4 elements would give no meaningful results for carbon; thus, no fil TI attempt was made to analyze the carbon data in this fashion. B. Extraction of Neutron Yields from Non-Compound Processes r The relatively flat neutron energy spectra extending to very high neutron energies (see Figure 25) cannot be explained by the simple statistical theory used in section VA. Such spectral shapes are not characteristic of neutron evaporation from a highly excited compound nucleus, and have been observed in (p,n) reactions (Gr 71, Ve 69) and (p,p') reactions (Ra 71). They have been interpreted by some authors (Gr 66, Cl 71, Bl 72) as evidence of a process involving the emission of particles from the compound nucleus during the equilibration period while the incident energy is being distributed among all the nucleons. This pre-equilibrium statistical model of nuclear reactions as developed by the above authors is derived from detailed consideration of the reaction mechanism. The model is based upon a stepwise sequence of nucleon- nucleon interactions inside the nucleus which tend to create ever more complicated many-particledmany-hole configurations. 111 In this way, the incident energy is eventually distributed among all the nucleons, and statistical equilibrium is finally reached. Pre—equilibrium emission occurs because at each stage in the sequence, particularly the beginning stages, there is a reasonable probability that a nucleon will be emitted into the continuum rather than undergo a subsequent collision with another nucleon. Therefore, it was decided to extract the non-compound fiffl} contribution to the total neutron yield in another manner which ;- ”Lu relies basically upon certain features of the data. Differential neutron energy spectra were obtained for each target at each angle f . by subtracting a thick target spectrum from the corresponding K. J spectrum at the next highest bombarding energy; the only two such subtractions possible with three bombarding energies were to subtract the 22 MeV data from the 30 MeV data, and the 30 MeV data from the 40 MeV data. Then the evaporation spectrum was extrapolated to higher energies as shown in Figure 31, and subtracted from the experimental curve. These latter differences are then interpreted as the non-compound parts of the spectrum, as indicated in the figure. Above roughly 7 MeV the evaporation spectra are largely insignificant, and the values of the non-compound spectrum are equal to the experimental data points. This type of analysis was applied only to Cu, Ag, Ta, and Pb. In the case of Al, no satisfactory distinction could be made between evaporation and non-compound spectra, and C cannot be discussed in any terms meaningful to either of the models under consideration. 112 - .1 1 .. .. _ : To *- O DEG. ‘tjzz__- EEpIg ESC)‘*"¥C) 11¢“! I0'4__ % I— E ‘\ 3‘» -5 l0 :- g -_- \§:Ep. =22«-30 ° I- :. MeV ' 0°: - \\ - a, .. ‘\ o (I) _ z O g3 . Flo-6:: B E 2 F " . : ,J—Ep<22MeV -7, l . '0 (IL—1*» 10 I 0 NEUTRON ENERGY (MeV) Figure 31. Differential Neutron Energy Spectra with Extrapolated Evaporation Spectra 1 11111111 1 1 I 111111 11l1111l 1 11114111 1 113 Subtracting the spectra in such a way presents the data in the most differential form possible. It has the advantage that the bombarding energy is then reasonably well defined for a relatively "thin" target, and facilitates comparison with theory. It is worthwhile to note here that for the heavier targets at 22 MeV, the minimum bombarding energy which can result in significant neutron production is about 14 or 15 MeV, where the incident 91 protons can no longer penetrate the Coulomb barrier. Hence the sza effective thickness of the targets, 7 or 8 MeV, compares favorably with the other two cases. Following subtraction, the differential non-compound Spectra ‘ “J ‘ were integrated over energy to obtain the total non-compound contribution at each angle for each bombarding energy range. These values were then plotted as the angular distributions shown in Figure 32. These angular distributions show a strong angular dependence, dropping off rapidly with increasing angle; this in itself is clear evidence of the non-compound nature of this part of the neutron spectrum. Figure 28 clearly shows the difference between the isotropic evaporation spectrum of neutrons with En < 6 MeV, and the marked angular variation of the energy spectrum of neutrons with higher energies. These angular distributions were then integrated over angle to get the total contributions of non-compound reactions to the total neutron yields; which are shown in Figure 33 expressed as percentages of the total neutron yields for each energy range. However, these percentages are not yet the fractions of reactions leading to F I0'3 1 I . . f . IO'3_ 1 r . . . E : I- -I E j I- -1 h- Cu -4 )- -I h- -1 P a: -4 E = soc-40 -¢_ _ EigIo E‘ p "'9" a §IO : : 5 ~ 35 - .. 5 "‘ ‘ +- F- -< a F -‘ g )- -I Q - -1 I- -1 \ \ (I) (I) 8 ~ 45 - . Ct I S -5 Ep:22~30mv S -5 I— d z +- -1 b d r .1 I- d - -1 n- .1 I- -1 I. j r- .1 IO-61 1 1 1 k 1 1 IO.6 L L 1 1 1 1 O 30 60 90 |20 I50 0 3O 60 120 ISO NEUTRON ANGLE (deg) 10-3? I I r f I T 10.3,. I I T I I I I - I A )- ‘1 I- -4 ’ To " * Pb ‘ p- d I- .1 L '1 I- -( = “4 M $10-4— 5” 3° ° W Ashe-4- Ep=so-4omv - \ t i'\ : 2 § : 1§ : - O I- 1 o l- : E )- -( E I- 03 f 1 \ ” 7 2 .U’ _ 8 § 22.-'30ij 5 S I11 I05: -. E I0'5_-.- 3 Z : : t - r- 4 I; 1 I- a r- A '- Ep<22 MeV -I I— «I IO'Gi 1 1. L [0.61 1 1 1 0306090I20I50 030609OI20ISO NEUTRON ANGLE (deg) Figure 32. Non-Compound Neutron Angular Distributions 115 NO. 00. co. no. mo. \IO. m0. evade» couusoz vaaooaooIcoz Hmuoh mum—232 mwSz kmemdh 08 on. 00. on o _ _ q _ W I 0 o 1 . >3. «N van .3 .o 3 w Io/// 1N9 d o a I 1 no. 3 . 0! >22 ontmu .am 3 I 10 I o O GIG I ..l. I 1 mo. 8 m 0 fl 1IIIlIlIIIIIIIIlllllllllllllllllllllllll 111FAH.MWW 0 a m >os. 3.30». m l I _ _ _ . mo. N .mm musmfim HOIHM SNOUJJBN JO NOllOVUJ 116 pre-equilibrium neutron emission occurring in each energy range; one more step is required to obtain these numbers, and the assumptions involved will introduce some model dependence into the analysis of the data in the manner described subsequently. Each compound nucleus which decays strictly by neutron evaporation will emit a number of neutrons; for Ta at 40 MeV, for example, four neutrons will be evaporated, with fewer emitted neurons at lower bombarding energies. This multiple evaporation must be accounted for in obtaining the probability for a nuclear reaction which results in pre-equilibrium neutron emission for each range of bombarding energy. The fractions of nonrcompound neutrons for each target in each bombarding energy range, as given in Figure 33, multiplied by the neutron evaporation multiplicity for the same case are the desired probability. Any calculation of evaporation.multiplicities, by whatever method, must be based upon some assumptions regarding the decay of the equilibrium compound nucleus. These multiplicities must be calculated somehow, and were in fact calculated by program DECAY as a necessary step in the cal— culation of the absolute neutron energy spectra used in the previous section. In so far as these multiplicities depend upon the assumptions upon which the calculations were based (and not just energetics), the probability values thus obtained also depend on those assumptions, the main one of which concerns the applicability of the statistical fermi-gas model to the experimental situation. 117 If this assumption is valid, the results of this procedure should also be valid, with only slight modifications which will be discussed shortly. Also, in order to obtain values for pre-equilibrium neutron emission which can be compared with Blann's calculations, some estimate of pre-equilibrium proton emission must be made. Pre—equilibrium proton emission affects the values of the neutron .! multiplicities used in determining the pre-equilibrium neutron :r1]h_! emission. Fortunately the dependence of this quantity on the pre-equilibrium proton emission is not too strong, as will be p _ shown in the following example. 5 Let the probability for pre-equilibrium proton emission, Pp, be some fraction of that for pre-equilibrium neutron emission, Pn BUCh tha t (V-l) Pp - xPn where x is a number between zero and unity. Pn is here the probability for a nuclear reaction resulting in pre—equilibrium neutron emission, which is obtained for a given case simply by multiplying the fraction of neutrons which are of pre-equilibrium origin as shown in Figure 33, by the appropriate neutron evaporation multiplicity; this evaporation.multiplicity must be corrected to account for the competition between pre-equilibrium and compound- nuclear processes, and a new Pn calculated. Then the total pre- equilibrium emission probability is Ptoc'Pn+Pp-Pn(1+x) (v—2) 118 So, if “0 is the evaporation.multiplicity obtained from program DECAY, which neglects pre-equilibrium emission, the new corrected multiplicity, M*, can be written as M* . Mo (1 - Ptot) + (Mo - 2.0) Pn + 1.5 Pp (v - 3) The first term accounts for the competition between pre-equilibrium and evaporation processes; the second term accounts for the reduction in the neutron multiplicity caused by removal of large amounts of energy by emitted pre-equilibrium particles. The number 2.0 inside the parentheses in the second term is a hypothetical value typical of the case of 30 to 40 MeV protons incident upon lead or tantalum; in cases such as copper at 22 MeV, where M6 was less than 2.0, 1.0 was used instead. The final term increases the multiplicity to account for pre-equilibrium proton emission, the factor 1.5 allows approximately for the fact that usually one, but seldom more than two neutrons can be evaporated following pre-equilibrium proton emission, at least at the excitation energies common in this experiment. Finally, if F is the fraction of neutrons which are of pre- equilibrium origin, as shown in Figure 33, and Pn is the probability of a collision resulting in pre-equilibrium neutron emission, then Pn - M* F (V “ 4) 119 The values of Pn obtained in this way are relatively insensitive to the value of x chosen in (V — 1); values of Pn were calculated for each spectrum with x - 0, .33, and 1.0, and in the case of Pb (40 - 30) the corresponding values of P are .235, .210, and .185. The higher and lower values of PD were taken to be indicative of the errors made in the assumptions upon which the calculations were based. The values of P thus obtained can then be compared with the theoretical values calculated by Blann's theory as shown in Figure 34, The theoretical values were obtained by integrating the calculated pre-equilibrium neutron energy spectrum over energy, and dividing the result by the total reaction cross-section which was also calculated at the same time. As Figure 34 shows, the agreement between experiment and theory is reasonable in the case of Ta, and not quite as good in the case of Cu. Any disagreement is likely explainable by a combination of the following: (1) an error, particularly in the case of Cu, in estimating the effects of pre-equilibrium proton emission on the neutron evaporation multiplicity; (2) at the lowest excitation energy, binding energy effects which cause large fluctions in the pre-equilibrium emission as a function of mass number (BI 72); (3) assumptions made in extracting the pre-equilibrium spectra from the experimental neutron energy spectra; and (4) need for modifications in the theory. In general, the agreement between the experiment and theory is rather good. 120 coemmHem couusmz aaaupfiawsomIoum a“ wowuHSmom sowmfiaaoo MOM hufiafipmpoum gas: >omm2w ZO_.—.<._._oxw O? on , ON 0. IUIUTI U I T U [1117' U IITTI IT - d Tfiqlfi - - fifiJ d d — d d - a J 1 11111,1 1 Nun: 1 1 11111 1 1 .Inz _1 NOISSIWB NOHLOBN WfllUBl'llflOB‘BHd NI ONIl‘lnSBU NOISIT'IOO 30 AlI'IIBVBOUd 1111 30-0 0 IX 0 3 1. em - aw dxm ESE new - . .sm egswam 121 It is also of value to compare the experimental pre- equilibrium spectral shapes with the theoretical spectral shapes predicted by Blann's calculations. It was mentioned at the beginning of this section that the pre-equilibrium statistical models in their current form cannot predict the angular variation of the pre-equilibrium spectrum. However, calculations have been developed (Bl 72) which do predict the shape of the total neutron spectrum, and these have been used in the analysis of other experimental data (Ve 71). The differential energy spectra were integrated over angle for each target and bombarding energy range to facilitate comparision with theory. The results of theory calculations for Ta and Cu are shown in Figure 35 along with the angular integrated experimental spectra. The theoretical and experimental curves appear to agree reasonably well with each other, apart from a slight difference in slope, which is not too severe. The experimental spectra are composites of many spectra generated over 10 MeV intervals of bombarding energy so it is to be expected that there would be some differences between the measured and calculated spectra. Given this limitation, the theory appears to be in very good qualitative agreement with the data and quite reasonable quantitative agreement as well. The angular integrated energy spectra for each target and bombarding energy range are shown in Figure 36. 122 7T 7T7 I If T I’ T 10"? ‘ TANTALUM 10'3 EXPERIMENT g: THEORY .— ........ ' 10'“I -’ " ..-“ 5 ,--... “MM-....-.“ E. = 35 MeV 5 , “““ \.. N..-“ I "w...“ E 10-5 TN.--“ ..‘a ‘ \ ‘s \. “5’ 26 MeV it 10‘s 5 I8 MeV E 10‘7 10'8 10'9 L 1 L L 1 1 1 0 S 10 15 20 25 30 35 NEUTRON ENERGY (MeV) Figure 35. Theoretical and Experimental Angular-Integrated Neutron Energy Spectra 123 Figure 35. (continued) we?“ T——""”r‘ """"‘T””‘”‘ r I r—»~-._.-..r \\ COPPER 10"3 \ EXPERIMENT . THEORY ————————— j 10'“ ........ - E ............................... Ep = 35 MeV I: I j: ............... ... j j Z . (13 10-5 3 , i’ O m d a d \ d a) 10"6 5 a o: ‘1 S . 11.1 _7 < Z 10 ‘i 10‘9 1. fi 10‘9 L 1 1 1 1 L 1 .I o 10 15 20 as 30 35 Ho NEUTRON ENERGY (MeV) 124 ANGULAR INTEGRATED SPECTRA 1 5 T T T l r [ 3 2 he 5' \3 Ep 30 w 40’MeV 10'3 ‘5 mm 0 c (IFUOJCD 1?; 2’ // 2 NEUTRONS/ PROTON/ MeV S 3 2 10'8 3 E 10" S 8 10‘8 5 3 2 10‘9 l 4 1 1 L 4 4 O S 10 IS 20 85 3O 35 Tm NEUTRON ENERGY (MeV) Figure 36. Angular Integrated Neutron Energy Spectra 125 Figure 36. (continued) ANGULAR INTEGRATED SPECTRA w-e “‘"‘T"‘" r' "r ‘ r'"‘ r ”r r“ 3 3i“ A' Ep = 22 ..._. 30 MeV m- g‘\ To / .0 CT 9 > $3 {W .5. E) m“ \\ 2 ‘ fix . g 10 C _s—'., § j 0: r ‘1 CL. : ' * (B :7; $ \ f 2 10 1 E .\ .3 I— \ 1 2) Egg IUF -§ 10 3 1 1 L -_.L.._...-.-.L___...L -.-..1..-____1__ ....1, 5 m 15 an as 30 35 no NEUTRON ENERGY (MeV) 10 Figure 36. NE UTRONS/ PROTON / MeV 10‘2 126 (continued) ANGULAR INTEGRATED SPECTRA 'l 10'3 T LI UNIT. 10‘” [IIITWr r IIIIInr . 10‘(5 I I IIIIIq 10'7 I I I [IIIII 10'9 r*IIIInq' I I I l l I :1 U EEF) ‘=: 2222 th§\/ 1 T l #1 1 IIIIIH 1 1,11111d I. 1 IIIIId l 1 IIIJId 1 l IIIII 1 A1 1 [1111' 1 1 1 1 1 5 10 15 20 25 30 NEUTRON ENERGY (MeV) :35 .C D VI. CONCLUSIONS Neutron yields from proton bombardment of thick targets were measured by the time-of—flight technique at proton energies of 22, 30, and 40 MeV. Time-of—flight spectra were measured for six natural targets -- C, Al, Cu, Ag, Ta, and Pb -- at laboratory angles of 0, 30, 60, 90, 120, and 150 degrees, covering the neutron energy range from 0.5 to 40 MeV. The data are of high quality; the overall experimental energy resolution, a function of the neutron energy, varied from 1:41 at 0.5 MeV to :_2.SZ at 40 MeV, and the statistical error was typically four to five percent; the overall experimental error is conservatively estimated to be about 20%, including a :_15% error in the calculation of the efficiency of the neutron detector. The statistical fermi-gas model of the nucleus as developed by LeCouteur appears to be able to describe adequately the neutron evaporation spectra measured in this experiment, at least for nuclei heavier than A = 50, even though emission of several particles is possible. Although determined at higher excitation energies, the values of ro and a obtained from the foregoing analysis of the evaporation spectra are in quite good quantitative agreement with previous experi- mental results, and in the case of the level density parameter, are qualitatively in excellent agreement with theory, even to the extent of reproducing shell closure effects in certain of the nuclei invest- igated. Apart from these shell effects, no pronounced variation of the level density parameter with bombarding (or excitation) energy was noted. 127 128 The pre-equilibrium model developed by Blann describes quite well on an absolute basis the measured energy spectra of pre- equilibrium neutrons, and also, therefore the frequency with which pre-equilibrium processes occur, particularly in the heavier nuclei investigated in this experiment. The results of this experiment substantiate in large measure theoretically predicted variations of pre-equilibrium neutron emission with both mass number and excitation energy. The probability of pre-equilibrium neutron emission determined by this experiment increases rapidly with excitation energy. For instance, the pre-equilibrium neutron emission from Ta increases by more than a factor of four between 22 and 40 MeV of bombarding energy. This is in rough agreement with theory, although detailed comparisons are difficult to make because the theoretical curve rises very steeply in this range of excitation energies. The shapes and magnitudes of the angular-integrated pre-equilibrium neutron spectra do not vary significantly with target mass number. This is true even for the case of 27Al, so that the pre—equilibrium spectra are very similar for the range of mass from 27 to 208, at least in the cases investigated here. In as much as this model is still being developed and refined, it appears likely that modifications to the theory can lead to better agreement between these experimental data and theory, and so to a better under— standing of the nuclear equilibration process. Much work is in progress to this end, and the results of this experiment very likely should be valuable in this effort. Further experiments with thin targets or a number of elements spanning the medium and heavy nuclei are highly desirable. 129 In view of the difficulty in distinguishing between the evaporation and pre-equilibrium neutron energy spectra in light nuclei (AKSO) further more detailed study of these nuclei along the line of this experiment may lead to improved criteria and methods for determining the two spectral components, not only for light nuclei but for heavy nuclei as well. The results of this experiment indicate a strong need for refinement of both the evaporation and pre-equilibrium theories fn-Wl as applied to light nuclei. This experiment is ahead of the development of pre-equilibrium : models in that the angular distributions of the pre-equilibrium neutrons have been measured and found to be forward peaked, whereas the theoretical models, at their current stage of development, are unable to describe the angular dependence of the data. Every effort has been made to present the data in as useful a format as possible, and it is hoped that they will be of value to physicists -- both experimental and theoretical -- to whom a knowledge of neutron emission from highly excited nuclei is of interest. Al Ba Be Be Bi Bl Bl Bo Bo B0 C1 Da Ev Fe Ga Ga Ge Go Gr 61 63 63 51 52 72 36 62 69 71 61 55 50 69 70 68 60 66 REFERENCES . Alexander and F. Goulding, Nucl. Instr. Meth. 13, 244 (1961). . 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