Introduction to Reactor Physics and Analysis
Introduction to Reactor Physics and Analysis PHGN 590
Colorado School of Mines
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This 17 page Class Notes was uploaded by Donato Hoeger Jr. on Monday October 5, 2015. The Class Notes belongs to PHGN 590 at Colorado School of Mines taught by Staff in Fall. Since its upload, it has received 10 views. For similar materials see /class/219611/phgn-590-colorado-school-of-mines in Engineering Physics at Colorado School of Mines.
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Date Created: 10/05/15
Interaction of Radiation with Matter I Energetic charged particles BetheBloch stopping formula H Gamma radiation photoelectric compton pair production 11 neutrons elastic scattering photocapture ssion action of energetic charged particles Inter with matter 3 j e 3 Atoms of target 6 material Dominant energyloss mechanism IONiZATION Stopping Power average kinetic energy lost per unit distance in the target material dEdx Systematics of Stopping Power V 096 Mug Bowler average kinetic energy lost per unit distance in the target material dEdx BetheBloch Quantum calculation dE 41thntZpe dX mecz I 1 2m 02 2 x 21n eB391 3 IOU3932 Ztnt number of electrons per unit volume a Zp 2 charge number Z of projectile 32 v2c2 1 11KEmpc22 mac2 electron rest energy 511 MeV O O mpc2 projectile rest energy IO average energy of the knockedout electron In a 6 E cV Stopping power example Use the BetheBloch formula to calculate the stopping power of air for 5 MeV alphas air IO 16 2t 09 eV dE39 J lMoVm hplhohln I win BetheBloch Energy Loss Formula The BetheBloch formula for the magnitude of the ionization energy loss dded P1 2 n 2 62 hc2 Mec2 LOQEZ H862 beta ZIon 1beta 2beta2 1 2 beta2 Mec2 4 922 hc2 n Pi zpz u H w beta Mecz where n is the atomic number density of the target Ztnne the electron number density in units of number per cubic angstrom Mec2 is the rest energy of the electron ZtZp is the target and projectile Z betavc hc 19733 evAngstrcrus and on is the mean electron excitation energy which is well approximated by 6 Zquot0t9 eV This gives the stopping power in units of eVAngstrom dividing by 100 gives MeVrnicrom The formula does not apply for very low speeds betaltltli beMwbkwhnuz 2 Convert to a function of kinetic energy with the following relativistic substitution rule The constants are taken from the Review of Particle Properties dsdxxldzdxlbetagtSqrt111xERE2 coastloc2gt51110 692gt1137hcgt19733 const81Ztgt14ngt04978ongt16149 conItAnztgt79ngt05907Iongt16799 conItAqZtgt47ngt05857Iongt16479 consthirCZtgt72ngt5377105Iongt1672 9 protonRlgt938327Zpgt1 ddeprotonddeKEconstlprotonconstsiz plotprotonPlotdzdxprotonlooKE11O1 electronRE gt511Zpgt1z dxdxaloctrondzdxxEconsteloctronconst81 plotoloctronPlotdzdxelectronlooK355 P10tLabo1gt39Stopping Power of electrons in 8139 AxesLabelgt39Energy Mev3939dzdx MeVmicron39 alphaREgt49315zngt2 dldxnlphaddeKxconstalphalconst81 plotalphnPlotddealphalooKE310 1de MeV 39 cron Atoppfgb Pager of electrons in Si 000044 000043 000042 000041 5 Energy Kev batheme 3 show I 9101319111 plotproton Plotubolo IIStopping Pm in 81 Howlmicron quot I AxeLabel In Its quot 39dxdx luvmicron 391 1de MeVmicron 0 2 r Stopping Power in Si MeVmicron 4 39 Energ Graphics Mean ion depth Max100 Max4 1 max40 3 damm lnllnlx Do hulaNI 01dx39dldxproton ngtln 1 Maud In 3 29629 N 01dldxproton ltlgt1 INI 01dldauloctron ngt1 NI 01dldxalphl JCSgt1 Int Olidlduloctron Klgt1 107181 776 932 bedwbkmhmuz 4 multiplying by 100 converts dVAnq gt IbVcn lthO39dldxxlconntlalphaconstairKEgt5 0992732 NtdldxxlIOOIconstprotonlconltAgxEgt1 00954981 hb8qrt1111938327 2 compareal0001 dxdxlZtgt47ngt585710 222pgt102gt113 lac2gt511betagtbbIongt1610 6479 00461308 00954981 S 14 STOPPING MeV mgcmz 05 TOTAL 0 2 1 0 E E l 1 Alum Dmuz ION 1 97910 Mun0 y 149 TARGET 9 rump 11x by 2321 2 3 4 ENERGY MeVamu ldbbr su14 Nullm 2 SNOI v mum n91 um m7 m 315 um Interaction of gamma radiation with matter Basically an electromagnetic interaction with the atomic electrons Three possibilities 6 39Y Photoelectrlc Y Y Compton Scattering e y 6 Pair Production Attenuation coef cient initial intensity surviving intensity IO It W M W W m v M M W It 10 5M 10 e up 9 c u linear attenuation coef cient cm1 p mass density gcm3 ulp mass attenuation coef cient cm2g Radiation shielding example What thickness of lead shielding is necessary to reduce an initial ux of 06 MeV 1 s by a factor of 1 million Use Figure 316 of Meyerhof 39 393 55 F 1 l I 4 at 047 18 1quot 036 a Z Wquot 22 am 7 g I Fig3 104 Interaction of neutrons with matter Since neutrons do not interact electromagnetically they do not interact with the atomic electrons and therefore will interact with the nuclei of the target material Possibilities 1 Elastic scattering bounces off A n n A nucleus with no excitation A J J Iquot q 2 Bounces off but leaves the target nucleus in an excited state A Inm t 1quot 3 Be absorbed by the nucleus emitting either a gamma or an alpha A 1364 4 Be absorbed by the nucleus causing it to undergo ssion A I L Elastic scattering of neutrons by target nuclei Billiardball kinematics f n n pn 6 n A O A 9 Initial Final pA Conservation of energy and momentum gt 2 9 2 2 PH Pn P 1 2mn 2mn 2m A gt a gt pn p 1 1 pA Energymomentum conservation gives Maximum recoil energy L L I max 1 21 s KEreco mg KEneutron For heavy target nuclei the neutron loses almost no energy For light target nuclei the neutron can lose a signi cant fraction of its energy for a proton target the neutron can loose all of its energy through an elastic collision quot m dim quot
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