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Introduction to Reactor Physics and Analysis

by: Donato Hoeger Jr.

Introduction to Reactor Physics and Analysis PHGN 590

Marketplace > Colorado School of Mines > Engineering Physics > PHGN 590 > Introduction to Reactor Physics and Analysis
Donato Hoeger Jr.
Colorado School of Mines
GPA 3.94


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This 15 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 44 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
PHGN598 Introduction to Nuclear Reactor Physics Summer 2006 Lesson 111 Agenda 1 Schroedinger equation for bound states 2 Solutions to the Schroedinger equation for spherical problems 3 Spectroscopic notation and multiplicity 4 Atomic shell model 5 Spin orbit force and the Nuclear shell model 41 39gt marv a bre a scw w Z M W3 L Dawkxm germ 9 Q JeWe ceozgzms 39 d ma an 675721 mM as acgrafx fmw af M 7 I MW 40008 Veh 2m Jx 3 4 41 W E 7 iiL 10 86 5 weave LS Pm a fI39I Jeanj Gay7444 alpaa my chl zcx Scjwea ma39 92 BOMSMQ fa oz Ia 07 Fm J 1 LJ V i E Bf Pa 45 50 Lpo Jh41239 VD 9 4 n 3mz1 En vi17 E My ZM L 39 m Introduction to the Shell Model Review of Atomic Shell Model Atoms nuclei and electrons interact Via Coulomb potential 2 V Z6 r Schroedinger equation 3dimensions 2 2 4 1 2 Z e r6 m V r ur9q E II 4 Separation of angular and radial dependence 935133 lwa s wre p Wvofsd Angular part is the spherical harmonic and is 39 the same for all spherically symmetric cases LQ LI39H 79 t is integer and e lt m4 6 r 2 e 1possible s w pm at A m 0 41 001 W 39 rI quot 0r U4 1371667 The radial part of the wavefunction for the atomic problem Rnl quotpolynomialquot X e39rar A a arcer 4 1 d a 7L E L V w 9 El I r a Gun 0 W26 turf39llng n m I A 1A Pomt gum 5 39E awn I 7 L quot ring q ampL I Lco Ai eY a 0 Bearat a fo 4 871 M IW 5 z I Solution Mayer and Jensen SpinOrbit Force Nuclear force strongly faVOrs spin and orbital angular momenta in parallel con guration 8 S 1 j 1 12 lower energy than 1 12 quotspinorbit splittingquot l Energy lpll2 2 1p 1 1 4 6 quot p32 wo spinorbit force with spinorbit force Nuclear Physics Fundamentals Lesson 33 Adding Angular Momentum in Quantum Mechanics Two sources of AM spin 3 and orbital l s O R For 3 12 only two possibilitites j I 12 or 39 j 1 12 Multiplicity is still 2 j 1 Example for pstate 11 we can have j 1 12 32 p32 2321 43 a j112 12 p12 2121 2 39 g IS39Z Jlll 31gt Spectroscopic notation quotLquotj A L Spect symbol Wspin multiplicity for L 2rd 0 39 s s 12 2 1 p p 32 4 p 12 2 2 d 52 6 1 32 4 3 f f 72 8 f 5 2 6 4 g g 92 10 5 g 8 Building atoms electrons are spin 12 fermions so they obey the Pauli exclusion principleonly one per state States Number TotalZ Closed atom Is 2 2 He 232p 26 8 Ne 3s3p 26 18 A 4s4p3d 2610 7 36 Kr 5s5p4d 26 10 54 Xe Closed shell atoms inert tightly bound electrons l Ionization Energy M W if f N 7 Evidence for Nuclear shell structure Neutron separation energies A W VAJ 2 8 20 so 82 gt N 4 Isotopic Abundances peaks when N or Z is a magic number quotMagic Numbersquot u 2 8 20 28 50 126 A Nucleon nucleon potential strong short ranged Nuclear density saturated constant Average mean field potential seen by one nucleon quot 9 I L V 06 density quot4 1 I 539 M Radial wavefunction given spherical bessel function j1kn1r f1 41 K 0 3quot where kl is the nth zero of theIth bessel function The allowed eigen energies are given by 1617111 V n1 5r 0 The resulting level ordering is E LL Sftc Multiplicity Total Nucleus C 4 1g 18 58 l 2P 6 39 40 3 1f 14 34 7 0 25 2 20 Ca 1 1d 10 18 7 l 1P 6 8 Q o ls 2 2 He Doesn t seem to work NaeMr 5441 ane 5 co tun 3d 4 m 4 m 4 u 2 6 39 112 L 2 3d5iz 6 2 li 392 10 3 132 124 26 3Plt f 3pm 4 2 52 5 2f 5 lt 272 8 1quot92 10 1h 39 2 sz 38 331 Zdl 1 42 32 2d lt quotT I 6 4 m 391 72391 8 1192 10 so 9 2quot12 2 2 Is 3 L 6 3 2P3 4 If 1quot12 8 28 23 h 4 2 ld lt 2 12 3quot 5 2 siri 6 l 2 8 lp lt pm lmz L quot 4 0 1quot 2 2 39 4 1 lt9 L06 What is the spectroscopic structure of 29Si 2 I AI f 2r 7 v u a L W quot03 04 c I 4 39 C 01447 lt2 40 f L Q 6 quotT 1 1 u I J v 3 Luigi 11755 3 N2 51 Qa pyongcar f gt 37 5 What is the spectroscopic structure of Cr V Angular momentum of nuclei near a closed shell Parade d neutron 52 17 O 39 7 J 52 16 O COI39C quotHolequot 39


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