UNCLASSIFIED ORNL WW . . . . ' VW EL 788 ...W JR ..ORNV-pon 88 Dit?," to sc incl:01 in 200 5 520 Syru.Sim 0:: Pistection Against kidatics 1:. 9:20?, Catlinu, nr.2.2, October 1.2-1., 1964 UTIER TEC 30 1965 PARTICLES EMI'ITED IN THE FORWARD DIRECTION FROM HIGH-ENERGY NUCLEON-NUCLEUS KNOCK-ON REACTIONS* CONF-720-6 H. W. Bertini Oak Ridge National Laboratory Onk Ridge, Tennessee " e ridge, Tennessee : AGTER COPY , Energy and angular distributions of emitted secondaries from nucleon- nucl.eus reactions can be obtained from an available intranuclear cascade cal- culation. The main assumption in this calculation is that high energy (~ 100 MeV) nucleon-nucleus reactions occur via a series of individual par- ticle-particle reactions within the nucleus where the differential cross sections used in determining the scattering angles in the particle-particle reactions are the free-particle differential scattering cross sections. Examples of the shapes of the curves for the n-p and p-p free-particle differential cross sections plotted vs the laboratory scattering angle for 40- and 160-MeV neutron-proton and proton-proton reactions are illustrated in Figs. 1 and 2.? It should be noted that all the curves peak at zero degrees in the laboratory system. On this basis alone one would expect the angular distribution of the particles knocked out of the nucleus in parti- cle-particle reactions to be peaked at zero degrees, too. However, plots of these distributions (Figs. 3-6) indicate that the distributions decrease for small forward angles as the angle approaches zero. The decrease is attributable to the effect of the exclusion principle on the collisions which occur inside the nucleus. To illustrate, consider a simple nonrelativistic scattering reaction where the struck particle is at rest. When the masses of the two particles *Research sponsored by the National Aeronautics and Space Administration (NASA Order R-104). under Union Carbide Corporation's Contract with the U. S. Atomic Energy Commission. -2- are equal, the energy of the incident particle after scattering T is related to its initial energy T, by the expression T = To cose, where 0 is the angle of scattering. The scattering angle determines the energy of the scattered particle and hence the energy transferred to the struck particle. When 0 is small, the energy transferred to the struck particle is small. This is true even when the struck particle is moving. Now consider the assumption that attempts to approximate the exclusion principle in the intranuclear cascade calculation. Figure 7 is a schematic energy diagram of a single proton-neutron reaction occurring inside the nucleus. The primes refer to quantities after scattering, while the T's represent kinetic energies inside the nucleus. The assumption is that the energies of both particles after scattering must be greater than the Fermi energy, i.e., that In. To > If , in order to be an "allowed" reaction. Otherwise, the reaction is mot per- mitted to take place. Therefore, when the scattering angle is small, the energy transfer is small, and the only nucleons in the Fermi sea available for "allowed" reactions are those near the top of the sea, while reactions with all the other nucleons are "forbidden." This reduction in the nucleons available for small-angle scattering reactions reduces the nucleon-nucleus reaction cross section for particles emitted at small forward angles. Although only small energy transfers have been mentioned, the argument also holds for large energy transfer; that is, if the incident proton trans- fers energy to the struck neutron such that the neutron has the same energy that the proton had, the neutron will go off in exactly the same direction as the incident proton (equivalent to charge exchange scattering at zero charge exchange scattering angle) but the proton will assume the energy that the neutron had. Since the proton energy will then be below the Fermi energy, this reaction will be forbidden. From the expression T = T, cos? , one can see that the higher the incident energy the smaller this effect will be, because although the fractional change in energy will be the same for a given scattering angle the magnitude of the energy transfer will be larger, and hence more nucleons inside the nucleus will be available for "allowed" reactions. The effect is visible in Figs. 4 and 6. The point of this paper then is to illustrate a potential pitfall for those doing shielding calculations. One must be careful in making simplify- ing assumptions with respect to the angular distribution of high energy secondary particles. In the same vein on Figs. 7 and 8 are illustrated the fraction of high energy particles emitted between zero and a where o varies in steps of 5° for the same reactions as before. In order to include 50% of the fast particles one must use angular intervals from 0 to 25° or 0 to 45° depending 3 - - . * - - , - : on the case. The calculation predicts that less than 1% of the fast particles will be emitted in the first 5° cone. 3 - - . * - , 1- -50 References 1. H. W. Bertini, Phys. Rev. 131, 1801 (1963). 2. The cross sectionis reported by W. N. Hess (Revs. Mod. Phys. 30, 368 (1958)? in the center-of-mass system were lit by simple functions of the scattering angle and energy. The functions at 40 and 160 MeV were then converted to the laboratory system. This decrease was predicted long ago when intranuclear-cascade reactions were first postulated (R. Serber, Phys. Rev. 72, 1114 (1947)], but to the author's knowledge this has never been verified experimentally. -6- Figure Captions Fig. 1. The differential scattering cross section vs laboratory scatter- ing angle for 40 and 160 MeV proton-proton collisions. The differential scattering cross section vs laboratory scatter- ing angle for 40 and 160 MeV neutron-proton collisions. Fig. 2. Fig. 3. The differential cross section vs laboratory angle for emitted knock-on protons of all energies. Dashed line: knock-on protons with energy greater than 20 MeV. Fig. 4. The differential cruss section vs laboratory angle for emitted knock-or. neutrons for 50 MeV protons on cobalt. Solid line: knock-on neutrons of all energies. Dashed line: knock-on rieu- trons with energy greater than 20 MeV. Fig. 5. The differential cross section vs laboratory angle for emitted knock-on protons for 160 MeV protons on cobalt. Solid line: knock-on protons of all energies. Dashed line: knock-on protons with energy greater than 60 MeV. Fig. 6. The differential cross section vs laboratory angle for emitted knock-on neutrons for 1.60 MeV protons on cobalt. Solid line: knock-on neutrons of all energies. Dashed line: knock-on neutrons with energy greater than 60 MeV. Fig. 7. Schematic energy diagram of a proton-nucleus knock-on reaction . in which the proton collides with a neutron in the nucleus. V - yrt.. is the potential well of the nucleus and Tf is the Fermi energy of the nucleons in the nucleus. *-...kaina ometimes... - Man s -7- 0 Fig. 8. Fraction of knock-on protons emitted between oº and e. for 50 MeV protons on cobalt. The value of the fraction is plotted only over the last five degrees of the interval, i.e., as an example, the fraction of knock-on protons emitted in the angular interval 0° to 50° is plotted from 45 to 50° (0.65 for "knock-on" protons of all energies). Fraction of knock-on protons emitted between oº and eº for 160 MeV protons on cobalt. (See Fig. 8 for further explanation.) Fig. 9. UNCLASSIFIED ORNL-DWG 64-8455 40 MeV doidsl (mb/steradian) | 160 MeV 0 10 20 30 40 50 60 70 LABORATORY SCATTERING ANGLE (deg) 80 90 Proton-Proton Differential Scattering Cross Section (Laboratory System). UNCLASSIFIED ORNL-DWG 64-8456 40 MeV dold12 (mb/starodian) 160 MeV 0 10 20 30 40 50 60 70 LABORATORY SCATTERING ANGLE (deg) 80 90 Neutron-Proton Differential Scattering Cross Section (Laboratory System). UNCLASSIFIED ORNL-OWG 64-8458 doldS2 (mb/steradian) PROTONS OF ALL ENERGIES IL . PROTONS ENERGIES > 20 MeV form. I LILLE 0 20 40 140 160 180 60 80 100 120 LABORATORY ANGLE (deg) "Knock-on" Protons from 50-MeV Protons on Cobalt. UNCLASSIFIED ORNL-DWG 64-8459 4 : NEUTRONS OF ALL ENERGIES dold2 (mb/steradian) NEUTRONS WITH ENER- GIES > 20 MeVH L ula 0 20 40 60 80 100 120 LABORATORY ANGLE (deg) 140 160 "Knock-on" Neutrons from 50-MeV Protons on Cobalt. UNCLASSIFIED ORNL-DWG 64-8457 117 PROTONS OF ALL ENERGIES doldS2 (mb/steradian) TO PROTONS WITH ENERGIES > 60 MeV homom..!... conto . 20 40 12 .. . ........ ..... ..... .......... ....la 60 80 100 120 140 160 180 LABORATORY ANGLE (deg) "Knock-on" Protons froin 160-MeV Protons on Cobalt. UNCLASSIFIED ORNL-DWG 64-8460 NEUTRONS OF ALL ENERGIES dolds2 (mb/steradian) VIRI NEUTRONS WITH 1 ENERGIES>60 MeV to III.CAT T : 0 20 40 60 80 100 120 LABORATORY ANGLE (deg) 140 160 180 "Knock-on" Neutrons froin 160-MeV Protons on Cobalt. UNCLASSIFIED ORNL-DVIG 64-8468 INCIDNTPROTON SCATTERED I. TON SCAM!:D:D NEUMONT ENERGY ņ INITIAL NEUTROV -TV ORNL-DWG 64-8461 PROTONS WITH ENERGIES > 20 MeV i . PROTONS OF ALL ENERGIES FRACTION - - - - - - - - - - * -.. EX-MPLE OF ISOTROPIC _ EMISSION 0 10 20 100 110 120 30 40 50 60 70 80 90 O, LABORATORY ANGLE (deg) lu Fiacrion of All "Knook-on" Protons Emicicü Beiureen 0° and eº for 50-MeV Pacions en Cobcii. UMOL SSIFIED ORN DWG 64-8462 PROTONS WITH ENERGIES > 60 MeV --- .... PROTONS OF ALL ENERGIES FRACTION ...EXAMPLE OF ISOTROPIC EMISSION G - - 0 10 20 100 120 130 30 40 50 60 70 80 90 O, LABORATORY ANGLE (deg) Fraction of Ali "Knock-on" Protons Emirted Beiween oº and 6 for 160-MeV Protons on Cobalt. - NIL DATE FILMED 4 / 12 / 65 " 2 . W , .. - - - - ---- LEGAL NOTICE This report was prepared as an account of Government sponsored work. Neither the United States, nor the Commission, nor any person acting on behalf of the Commission: A. 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