Interaction between matter and radiation: an introduction

Transcript

1 Itacto btw matt ad adato: a toducto Ovvw o th basc pocsss Classcal lctomagtc wavs matt bsopto (classcal ad quatum) Scattg (classcal ad quatum) Basc lmts to ollows lctus Rlatvstc cts

2 Ma tactos Tasmtttd Photos Photo absopto: xctato wth o wth msso o lctos Photo scattg: lastc Thompso (Magtc) lastc Compto (Rama) Rsoat (lastc ad lastc)

3 Idct cts: dcay pocsss MTTR Matt s xctd by th adato It loos gy though dcay pocsss

4 xpmtal tchqus bsopto Photomsso Scattg: lastc Scattg: Dacto, SXS Ilastc Scattg: Compto, IXS Rsoat scattg: RIXS Imagg Fluoscc Yld ug spctoscopy

5 Th coss scto σ I I ( ) S σ S σ I σ I S ba -4 cm σ has o gomtcal mag: t s a masu o th tacto It s calld coss scto

6 Th coss scto σ II ρ s th dsty o th objcts σ tot σρ S x x I I σ tot S σρ x di I σρ dx I(x) I ρx σ µx

7 Scattg coss scto bsopto Photos a movd om th bam σ abs. Scattg Photos a scattd to a dt dcto σ scatt. Total coss scto σ σ abs. σ scatt.

8 Dtal Coss Scto dσ/ σ/dω dω Outcomg photos θ di I σρ dx Icomg Photos d N& N& scattd comg φ photos photos dσ d d Ω Ω ρdx ( ) dω dσ dσ ( θ, φ ) dω σ scatt dσ( θ, φ ) d dω Ω

9 Doubl Dtal Coss Scto d σ/dωd Icomg photos o gy θ dω Outcomg photos o gy ± d/ d N& vts dωd N& photos ρdx [ ] d σ dωd

10 Ba -4 cm Total coss scto σ o atoms

11 bsopto coss scto σ o atoms

12 bsopto coss scto σ o atoms

13 Coss Sctos: Classcal dto dn& N& sc. dσ dω dω ρdx ( ) di dω I dσ dω ρdx ( ) θ dω Dtal coss scto: t s th dtal pow scattd dω omalzd to th comg pow ad to th scattg objcts

14 Matt Itacto Radato I Classcal dscpto Radato: lctomagtc wavs dscbd by Maxwll quatos Matt: Macoscopc optcal costats Dp: mcoscopc dscpto o th matt as a smbl o classcal oscllato

15 Classcal ppoach Radato: lctomagtc wav composd o ad B Matt: Optcal costat Racto dx: ( () bsopto coct: µ() ( ) Itacto: Lotz oc F q v B Masumt: gvs ( () ad µ() Mcoscopc modl o th chag moto ( () ad µ()

16 Rlcto ad acto s th dx o acto Sll law o acto cos(θ) cos(φ) I I R ccodg to Nwto s ~ to /v v c/ Vacuum θ θ Mdum # φ R θ π/ I I R I T

17 bsopto coct d Ι Ι I(x) I -µ x x I I -µd µ d l I I ρ σ tot

18 B B µ t t ε Pla Wav vacuum t B s th wavvcto; t gvs th dcto o th popagato th wavlgth o th adato µ ε B t π π c ν c Th adato movs wth a spd qual to c c µ ε

19 Pla Wav vacuum B B -t -t ssocatd to th adato th s a gy dsty w qual to: w ε B ε µ µ B w ε Th tsty I o th bam s: I wc c ε

20 v µ ε µε µ µ ε Pla Wav matt t ε c µ ε B c B t t s th wavvcto π Dspso lato: π µε v v π πc/ /

21 .M. Wavs matt (ε µ ) / acto dx v µµε o ε c µε c No magtc mdum: µ Gally: ε > > c v < c I th matt th lght s slow tha th vacuum I th matt th wavlgth s shot tha th vacuum π

22 Og o th dlctc ucto (qualtatv) Th lctc ld o th adato caus a moto o th mcoscopc chags lctos ad ucl movs oppost dctos gvg s to luctuatg mcoscopc lctc dpols Dpols gat addtoal lctc lds that adds to th adato os Th dlctc ucto dscb th lato btw th.m. ld ad th ducd dpols: t s a complx quatty Ral pat ampltud lato Imagay pat phas lato

23 Complx dlctc ucto ε ε ε ε (ε ε ) ε ε ε s complx β ( ) ε ε ε ε β -ε ( ε ε ) ε

24 Complx wavvcto π π s complx c ( ) c β c ( ) ( β) c c

25 Wav-dampg: bsopto coct c ( β) ( t) ( t) - Stadad pla wav as vacuum wth / Itsty I I() - - I I µ x β c mpltud ducto bsopto coct µ µ β ε c c

26 Kams-Kog Rlato Th al ad magay pats o th dlctc ucto dpd o o th oth ε π ( ) ε ( ) d ε π ( ) ε ( ) d Causalty: th dpol momt P(t) at tm t s dtmd oly by th valus o th lctc ld at tm t t

27 Mcoscopc modl Th matt s composd o postv ad gatv chags t qulbum th postv ad gatv chags do ot gv s to ay dpol momt /- - - Oscllatg gatv chag Dampd oscllato d dt v γ v d dt v m t

28 Iducd dpol momt t m dt d dt d γ I statoay codto ( ) t t m γ ( ) γ m t (t) ( ) t γ m Z Z (t) p(t)

29 P(t) Np Dlctc ucto N umb o atoms p ut volum NZ m γ ( ) P εχ ε χ t χ NZ ε m γ ( ) ε χ NZ ε m γ ( )

30 Ral ad magay pat o th dlctc ucto ( ) γ m Z ε χ ε N ( ) ( ) γ m Z ε ε N ( ) ( ) γ γ m Z ε ε N

31 ε Gal bhavo o th al pat o th dlctc ucto ε () NZ ε m NZ ε m ( ) ( γ ) ε 6, NZ m ( >> ) ε 4, Ral pat,, -, -4, -6,

32 Bhavo o th al pat abov Ral pat 6, 4,,, β ε < ε -, -4, ε ε c c γ -6, ( t ) -t - Th s o popagato to th matt o gy xchag s calld xtcto lgth

33 Bhavo o th al pat at hgh gy ε NZ ε m ( >> ) Ral pat,,5,,5, -,5 -, -,5 -, ε ( >> ) <

34 Racto dx at hgh gy NZ NZ ε m ε m δ δ NZ 5 6 ε m

35 Total Rlcto Vacuum θ θ cosθcosφ Mdum < φ Th ctcal agl θ c s dd by cosφ cosθ c θ c δ θ δ w c 3

36 Us o Total Rlcto Vacuum Mdum < θ θ θ δ w c 3 X-ay Mos Suac Dacto RFLXFS

37 Total Rlcto: vasct wav

38 RFLXFS: vasct wav T o T Tx x T z α c α Λ ptato lgth Λ α c α α c & (u) Ud total lcto codto th X-ay bam s cod a lay o w ts o om th suac Suac sstvty

39 Total Rlcto: vasct wav z Somwhat couttutvly, th ampltud o th vasct wav ca actually b gat tha th cdt o.

40 Bhavo o th magay pat ε NZ ε m ( ) ( γ ) γ,,,, 8, 8, Ral pat Imagay pat 6, 4, Ral pat Imagay pat 6, 4,,,,, -, -, -4, -4, -6, -6, ε ( >> ) NZ ε m γ 3 β NZ ε m γ 3

41 bsopto coct µ I() β ε c c - -µ x I I Ral pat Imagay pat,, 8, 6, 4,,, -, -4, -6,

42 Matt Itacto Radato II Sm-Classcal appoach Radato: lctomagtc wavs dscbd by Maxwll quatos Matt: Quatum systm obyg Schodg quato (oscllatos, )

43 Smclasscal appoach Radato: classcal lctomagtc ld dscbd by th pottal vcto Matt: Quatum systm

44 Smclasscal appoach: th adato ot B gadv t c j c t c t V c V µ ρ j c V µ ρ t c O vcto s ough to dscb.m. adato Vcto pottal (,t)

45 Smclasscal appoach: th adato ( t ) B c t ot gadv B c ( t ) ( t )

46 Smclasscal appoach: th matt Matt: Quatum systm Th systm s chaactzd by ts Hamltoa H ad by ts guctos ad gy gvalus obtad by solvg th Schodg quato Ĥ Ε p m V Ε

47 Itacto Hamltoa c - p p t Ĥ Ĥ mc p mc Ĥ V mc p mc m p V c - p m Ĥ

48 Ptubato Hamltoa Ĥ Ĥ t Ĥ mc Ĥ t p mc La Quadatc ( t ) Tm dpdt tms

49 Fm Gold ul Th ptubato du to th.m. ld duc tastos om th goud stat to xctd stats wth a pobablty p ut tm gv by Γ π h M δ( ) π h M g( ) M ) H t. ) H t. ± ) H h t. ε

50 bsopto g( ) M π Γ h ± t. t. t. ε H H H M h ) ) ) t mc p mc Ĥ ( ) ) - - ( p ê m c π w δ h h ( ) ) - - ( p ê m π w δ h h

51 bsopto Coct I µ x I µ I di dx I di w Ndx h πc 4π hα µ h m α ( ) ê p δ( - - ) h c 37

52 bsopto Coct:dpol appoxmato 4π hα µ h m ( ) ê p δ( - - ) 4πhα µ h m ( ) ê p δ( - - ) Optcal tastos: 5 Å always vald

53 I th cas o X-ay, th wavlgth s w Å,.. o th sam od as th xtsos o th atomc obtals I gal th co stats spatal xtso ducs as /Z wth casg th Z umb o th atom wth spct to th hydog obtals th gy o th absopto dgs cass as Z ad th wavlgth o th adato dd to xct a co lvl dcass as /Z Tho o hgh Z lmts, dvatos om th dpol appoxmatos must b xpctd ad must b ta to accout.

54 bsopto Coct: lctc dpol m p m & ( ) m h h H H [ ] ( ) ê δ( - - ) µ 4πh α h µ 4π h α ( ê ) ( ) D ( ) Dsty o stats D

55 Scattg lctc ld gatd by a oscllatg pot lctc chag q Th chag s oscllatg ud th acto o th lctc ld o th comg adato z t P (t) θ x o θ y 4πε q c ( t ) s θ Th lctc ld s th pla (OzP)

56 Scattg by a lcto (>> ) v d dt m -t v -t (t) m jt θ 4 πε mc ( t ) s θ θ dω P o

57 Dtal coss scto Dtal coss scto ( omalzd dtal scattd pow) dσ dω o θ I dw dω P dω ε I dw c dw ds c ( 4π) I θ ε dw dω cds ε mc 4 πε cds ε s θ mc c θdω dω s lcto classcal adus θ

58 lcto classcal adus dσ dω 4 πε mc s θ s θ s calld th lcto classcal adus.88-5 m 4 πε mc mc I Gauss systm

59 Total scattg coss scto: polazd adato θ o dω La Polazato Ω θ Ω σ σ d s d d lcto / m 6.7 x 8 d s d s s d s Ω π θ θ π θ θ π θ θ σ π π Thomso coss scto

60 Scattg Pla θ z θ o π/ θ s Th pla omd by th dcto o th comg ad comg adato s calld s scattg agl It s th pla omd by ad Th agl θ s s calld th scattg agl (Somtms th scattg agl s dcatd wth θ s

61 Icomg Radato polazd ppdcula to th Scattg Pla z π/ π/ θ s Icomg adato polazd ppdcula to th scattg pla π s θπ/ sθ Scattg adato ppdcula to th scattg pla ( ê ê ) sθ dσ dω s θ ( ê ê )

62 z Icomg adato polazd th Scattg Pla θ Icomg adato polazd th scattg pla π s It s also ppdcula to x θ s y Scattg adato s polazd th scattg pla θ θ s π ( ê ê ) ( ) cos θ s θ s dσ dω ( ê ê )

63 dn ρ dv Chag dstbutos: Scattg Facto. O θ 4 πε P mc ( t ) ( ) ê ( t ) ê d θ 4 πε mc ( ( ) t ) ( ê ê ) ρ dv

64 . O Scattg Facto IV d θ Sgl xchagd wavvcto ( ) q ρ dv θ d θ Sgl ρ dv (q) q Sgl s calld th scattg acto s th Fou Tasom o th chag dsty (.u.)

65 θ q (q) Sgl Scattg Facto V s calld th scattg acto (q) q ρ dv Numb o lctos p ut volum Scattg ampltud to: Fou Tasom o th chag dsty ( lcto uts) Fo atoms, molculs, cystals dσ dω ( ê ê ) ( q) Phas Poblm

66 Scattg Facto o lctos Sgl quatum lcto: ρ (q) q ρ dv (q) q dv

67 Scattg vcto q θ q θ 4π s s θ q θθ q 4π s Θ s Θ

68 Ovvw θ 4πε mc ( ê ê ) ( t ) ( ê ê ) ( t ) θ d θ dσ dω Sgl ( ê ê ) ( ) ρ dv Sgl (q) dσ dω ( ) ê ê ( q) dν& dσ dn& dω scattd ds dω

69 omalous cocto lctos a ot but a boud v d dt γ v d dt m v m t v ( ) γ γ -t m γ ( ) γ

70 omalous cocto γ ( ) γ << t low qucy lcto do ot Cotbut to th scattg >> t hgh qucy th lcto bhavs l lctos

71 omalous cocto o atoms j j j j ( ) j j γ γ 4 Gmaum Z3 Gmaum tomc Scattg Facto gy

72 omalous cocto o atoms: ad o G 4 Gmaum Z gy (V)

73 omalous cocto o u γ j j j j j γ ( ) j Gold Z

74 KK & Optcal thom " mc N µ µ " ( )d π 5 tot 3mc " ( ) d π

75 omalous scattg to solv th phas poblm B sc. ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) q ( ) B B B B B B B B

76 Fdl law ( ) ( ) q B sc. B I(q) Wh ad B a al I(q)I(-q) ( ) ( ) ( ) ( ) ( ) ( ) B B B q * B * q B q B Fdl law

77 Fdl law Wh ad B a complx I(q) I(-q) ( ) ( ) ( ) ( ) ( ) ( ) B B B q * B * q B q B ( ) ( ) ( ) ( ) ( ) ( ) B B B q * B * q B q B ( ) { } ( ) { } B B q R R q ) I( I(q ) Φ Φ Φ B B B Φ

78 Scattg Th ull lastc ad lastc scattg coss scto I patcula: o th aomalous scattg o th soat scattg o addtoal scattg asg om th magtc tacto btw th lctomagtc ld ad th lctos Full quatum appoach s dd, whch: th matt s tatd as a quatum systm th lctomagtc ld as a sambl o photos

79 Scattg th smclasscal appoach - I Ĥ p mc mc Ψ h Ψ t Ψ h t Ψ h t cocto ĵ p v p m m c

80 Scattg th smclasscal appoach - II m m m mc p m t) (, j Ψ Ψ Ψ Ψ Cut assocatd wth a lcto: mc m v j t s ( ) ê ê d d Ω σ

81 lastc Scattg at hgh gy - I t l cocto h h h Ψ ± * * mc mc p m j Ψ Ψ Ψ Ψ Dos ot dpd o tm Dpd o tm cocto t Ψ h

82 . O lastc Scattg at hgh gy - II j mc d θ 4 πε mc ( ) ê ê ( t ) ( ) ρ dv σ ( ) ( ) ê ê q ( ) q jq d dω

83 Ilastc Scattg at hgh gy j m mc mc Ψ * Ψ m t * m ( )t m ( ) ± m j v mc dσ dω. ( ê ê ) dσ dω. ( ) ê ê m # q m

84 Ilastc Scattg at vy hgh gy dσ dω. ( ê ê ) m # m q m # m q m # q m m q q m # m m q (q) q dσ dω. ( ) ( ) ê ê (q)

85 Ilastc Scattg at vy hgh gy dσ dω. ( ê ê ) ( (q) ) dσ dω l. dσ dω. ( ) ê ê Th sum o th lastc ad lastc coss sctos s qual to th Classcal coss scto o a lcto

86 Complt scattg coss scto Th aomalous scattg,.. th dpdc o th Scattg acto o th qucy Th ull lastc ad lastc scattg coss scto Th addtoal scattg asg om th magtc tacto btw th lctomagtc ld ad th lctos Full quatum appoach s dd, whch: th matt s tatd as a quatum systm th lctomagtc ld as a sambl o photos

87 Th lctomagtc ld ad ts quatum stats π h ( ),,, L3, c a a,...,,, m m,,...,, Ô,,...,,,,,...,, â,,,...,,,...,, â,,...,,,

88 Itactos quatum appoach V m m m m p H mc mc mc mc p mc mc mc mc H V m m m m c p - H mc mc mc mc H p mc mc H ( ) p a a L c π mc mc mc mc - p mc mc mc mc H,,, 3, h ( ) ( ) ( ) ( ) ( ) -,,,, -,,,,,,, 3 3 a a a a a a a a L c π L c π mc mc mc mc mc mc mc mc H h h,

89 Fm Gold Rul Th ptubato ducs tastos btw tal ad Fal stats wth a popablty w Γ π h M M ) H π δ( ) M g( ) h ) H ) H t. t. ε t. m l....,... photos

90 Scattg - I Scattg volvs two photos: o s movd om th tal stat Th scod s catd th al stat l. l....,...,...,,... -,..., oto,... oto Such tastos a du to:. tms th st od (Thompso ad Compto scattg ). tms p th scod od (omalous ad soat scattg)

91 lastc ad lastc scattg I od ptubato thoy o th tm ~ photos photos photos photos l. l. l. l. photos photos photos photos l. l. l. l.,...,,...,,..., -,...,...,...,...,...,...,...,...,...,...,...,...,...,,...,... { ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) } a a a a a a a a V c π V c π mc mc mc mc...o...o...o...o ;... ;... ;... ;... H...,...,...,..., ;... ;... ;... ;... M,, -,,,, -,,,,,,,,,, o o o o o o o o o o o o h h...,, o

92 Scattg - III { ( ) ( ) ( ) ( ) } a a a a V c π V c π mc mc mc mc M,, -,,,,,, o o o o o o h h,, o { ( ) ( ) ( ) ( ) } ( ) ( ) -q,, -q,,,, -,,,,,, V c π V c π V c π mc mc mc mc a a a a V c π V c π mc mc mc mc M h h h h h /mc cm

93 Scattg - IV Coss scto d σ dω d Γ c V w Dsty o stats π M c V h g(g(g(g() dn V g() 3 3 d hc ( π) ( ),, dω -q dσ ddω Σ ( ) -q ê ê,,

94 Scattg Coss Scto (o latvstc) d σ dωd Σ ( ) -q,,

95 lastc scattg d σ dωd Σ ( ) -q,, lastc scattg Fal lctoc stat qual to th tal o dσ dω ( ) -q ê ê,,

96 Ilastc Scattg at vy hgh gy dσ dω. ( ) q ê ê m m# m # m q m # q m m q q m # m m q (q) q dσ dω. ( ) ( ) ê ê (q)

97 Ilastc Scattg at vy hgh gy dσ dω. ( ê ê ) ( (q) ) dσ dω l. dσ dω. ( ) ê ê Th sum o th lastc ad lastc coss sctos s qual to th Classcal coss scto o a lcto

98 H mc Cotbuto du to p p - mc π c V h a a ( ),,,, p l.... M..., l. ) H...,... -,..., ) H ) H t. ε t. oto,... oto t. M ) H ) H t. ε t. a l. a......,... l.,...,,...,... ( l l ) h a ( l l ) h a

99 lastc coss scto - - ε ε p p ε ε p p m dω h h - / ε ε p p m dω dσ Γ h t th soac

100 Total coss scto at hgh gy t hgh gy th cotbuto bcoms: πhc h q q p M V mc h ) ( ) ) dσ dω ( ) ( ) q h q q p ) ) ê ê π h M M p c V g( ) mc h

101 Magtc Itactos lctomagtc wav taspot both a lctc ad a magtc ld F Thomso scattg v F µ v H v gad ( µ H ) Is du to th vaato o th gy o th o uomty o th magtc ld o th adato

102 Magtc Itactos µ Magtc dpol oscllatos M Toqu v ( µ H ) Du to th vaato o th toqu assocatd wth th tm dpdac o th magtc ld o th adato

103 v F v F M T µ H Stgth o Magtc Itactos v gad F T gad π ( µ H ) F M ( ) ( v ) µ H gad µ H v h m H πh mc v h mc Compto v Oly magtc lctos a actv I I mag T.. 4 Z mag Z. 6 7

104 d Bgv Bul o NO(97) NO s a atomagtc cubc cystal (T Nl 5 C) N hav oly two lctos lcto sp a o-magtcally algd () pla Thy a at-omagtcally algd btw () plas

105 Hamltoa th latvstc appoxmato ( ) ( ) ( ), ad. ad. ad. ad. l. l. l. l. tot tot tot tot a a c p t s m c m m m ot ot ot ot s mc mc mc mc V m m m m c p H H H h h h

106 H Itacto tms th latvstc appoxmato mc ( ) H p mc ( ) H s 3 mc h ot Poducs scattg (II od P.T.) H m h c 4 s t I od scattg P.T. p b a c ( ) a b h mc

107 Rlatvstc appoxmato H mc ( ) H p mc ( ) H s 3 mc h ot H 4 m h m c s c t ( ) Γ π h ) H ) H 4 ) H ) H 3 ) H ε ) H 3 δ ( )

108 Cotbuto d H 4 allo scattg π c H q s 4 h mc V h ) H ) H ) H ) H M ) H ) H ε π c M -q V h t ( ),, ( * ) Out o phas Rducto acto Fou tasom o th sp dsty Polazato dpdac

109 Scattg om I od ptubato π c MI h V q ( * ) ( ) q * h mc s

110 Cotbuto o H ad H 3 M ) H ) H ) H ) H II 3 4 ) H ε ) H 3 H p mc ( ) H p... mc H s 3 mc h ot H s 3 mc h ( )... p s h ( )

111 Rsoat tm at hgh gy t som hous o a tdous calculato w gt: M {( ) ( ) ( ) ( )} * * * ê ê ê ê ê ê h mc πhc V q s Out o phas Rducto acto Fou tasom o th sp dsty Polazato dpdac

112 Total cotbuto at hgh gy om th I od tm (II od ptubato thoy) M h πhc mc V q q p ) h ( ) {( ) ( ) ( ) ( )} * * * ê ê ê ê ê ê ) q s

113 Total coss scto at hgh gy dσ dω π h M total c V g ( ) () ) ) { ( ) q q ) ) {() ) ) ( ) ( ) ( ) } * * * ê ê ê ê ê ê q q s h mc p h

114 j hq m hq q q p h Obtal momtum ( 4sθ ) ( ) q 4sθ q p ( 4sθ ) B ) ( 4sθ ) q j(q) c mc h B ) h q [ ] q M L q p h ( ) ( 4sθ ) q q M ( q) B mc hq L B m hq j q ) q p B ) q q j ( ) ( 4sθ ) q q M ( q) B ) L ( q) c ( ) [ ] q M q L

115 P L dσ dω P Total coss scto at hgh gy q p h q P S ( ) ( ) * ( ) ( ) ( ) * * ) ( ) ) h q p P q q ) ) mc L mc hq h ( ) M (q) q q PL q L PL L () ) ) () ) ) 4s θ B q s s mc M h S q P S ( )

116 dσ dω Total coss scto at hgh gy ) ( ) q M ( q) P L () ) ) 4s θ B h mc mc h { [ ] q P ( ) } L M q ρ(q) P L S S P S ) () ) ) ( ) * ê ( ) ( ) ( ) * * ê ê ê ê ê