Neutron Slowing Down Distances and Times in Hydrogenous Materials. Erin Boyd May 10, 2005
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1 Neu Slwig Dw Disaces ad Times i Hydgeus Maeials i Byd May 0 005
2 Oulie Backgud / Lecue Maeial Neu Slwig Dw quai Flux behavi i hydgeus medium Femi eame f calculaig slwig dw disaces ad imes. Bief deivai f mea squae disace equied mdeae eu. Daa fm pape Aveage ime equied mdeae eu Daa fm pape Me Cal Simulai xplaai Oveview Wha was leaed? Refeeces
3 Neu Slwig Dw The pcess f educig he eegy f a eu fm he fas hemal eegy age. T deive he eu slwig dw equai fis begi wih he Neu Tasp quai. Ω + Ω Ω Ω Ω Ω + Ω Ω Ω f dd s s v dd f F 4 φ φ π ν φ By geig id f he spaial depedece f he flux we bai he slwig dw equai. + s F d S φ φ
4 Neu Slwig Dw c. The eegy asfe keel see i he eu slwig dw equai is: F α α α A-^ / A+^ 0 hewise Whee he fllwig assumpis ae made: i. elasic scaeig ii. age ucleus a es iii. ispic scaeig i CMCS This keel applies eu slwig dw because he eu lses eegy each ime i is scaeed by he ucleus.
5 Flux behavi i Hydgeus Mediums Begi wih slwig dw equai Le A meegeic pi suce a eglec abspi apply eegy asfe keel value. S S δ + + s s s S S c S c G d G cs G d S ; φ φ φ
6 Fudameal Quesi ad Issues Hw fa fm a pi suce des a eu f iiial eegy adm walk befe i eegy is mdeaed sme lwe eegy? > Femi addessed his pblem by esicig he eu mea fee pah λ a csa slwly vayig wih eegy. Hweve he eu scaeig c.x. f H is eihe csa slwly vayig i he eegy age 0. MeV < < 4 MeV.
7 Accuig f egy Depedece T deemie hw fa a eu wades befe i eaches a give lwe eegy he Femi eame is maipulaed such ha λ is w eegy depede. This mehd is valid as lg as he dmia eu scaeig mechaism is elasic ad he mea fee pah is kw.
8 Ne Displaceme The eu will avese a sequece f liea displacemes each emiaed by scaeig eve ha seds he eu ff i a ew dieci. Afe h pah he e displaceme R f he eu fm he igi is give by: R Image emved due cpyigh csideais. Please see: Ne Displaceme figue ake fm: Nellis W. J. Slwig-dw disaces ad imes f MeV eu i hydgeus maeials. Ameica Jual f Physics May 977.
9 Bief Deivai Magiude Squaed f he Ne Displaceme R is R. R k k R + k + k csθ k Whee θ k is he agle bewee he h ad he k h pahs. Neus scae wih adial disibui fuci e -/λ whee λ is he al mea fee pah. < > λ ad < > λ <csθ k > <csθ> k- µ k-
10 Deivai c. Thus if λ is csa he µ µ µ µ λ R Bu if λ vaies wih eegy he The mea squaed slwig dw disace is: + + k k R µ λ λ / R R ms
11 Daa: 4 MeV Neu Mdeaed i Hydge N 8 x 0 cm -3 Image emved due cpyigh csideais. Please see: Neu Mdeaed i Hydge able ake fm: Nellis W. J. Slwig-dw disaces ad imes f MeV eu i hydgeus maeials. Ameica Jual f Physics May 977.
12 Slwig Dw Time Aveage ime ave equied mdeae eu fm high lwe eegy is: υ ave λ Whee is he ime spe a each eegy. I he figue 4 MeV eus ae beig mdeaed f. Image emved due cpyigh csideais. Please see: Slwig Dw Time gaph ake fm: Nellis W. J. Slwigdw disaces ad imes f MeV eu i hydgeus maeials. Ameica Jual f Physics May 977.
13 Me Cal Simulai The sample pblem csiss f: MeV pi suce Neus emied wih dela fuci ime disibui Pi suce a he cee f he hydge sphee Hydge desiy N 8 x 0 cm -3 Hydge sphee has a ue adius f 50 cm Pah leghs ae chse admly fm a disibui weighed by al c.x. Scaeig agle ae chse admly fm a disibui weighed by he kw agula depedece f he c.x. Lcal eegy depsied i a cllisi is he calculaed based csevai f eegy ad mmeum. Flux allies wee placed a diffee adiuses i hydge sphee s e ca mi he mdeai. f was se be 40 ev
14 Oveview As eegy iceases he hydge c.x. deceases; hus he al mea fee pah is lage. --- Highe eegy eus peeae deepe ha lwe eegy eus. λ T N The highe he eu eegy he fase he eu lses eegy. / flux behavi is chaaceisic f he eu disibui duig slwig dw by elasic cllisis wih age. * Hydge is he ms efficie eu mdea sice i ca absb he lages faci f eu eegy pe elasic cllisi. σ T
15 Refeeces Nellis W.J. Slwig-dw disaces ad imes f MeV eu i hydgeus maeials. Ameica Jual f Physics Vl.45 N.5 May 977. J.R. Lamash Iduci Nuclea Reac They. 966 Neu Ieacis ad Applicais Lecue 9: Neu Slwig Dw.
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