Luiz Leal Oak Ridge National Laboratory. of Massachusetts Institute. of Technology (MIT)

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1 LzLl OkRdgNlLby LsPsdhNl Egg Dp f h MsshssIs f Thlgy(MIT) Csy f Lz Ll, Ok Rdg Nl Lby. Usd wh pss.

2 NI T Idpd Tsp Eq f Φ(E,,Ωˆ ) Ωˆ. Φ + Σ Φ = dωˆ ' de'σ s (E' E, Ωˆ ' Ω)Φ(E', ',Ωˆ ) + S 4 π 0 Σ Msplsss Σs Mspsgsss Hwhsqs d? () Ms by f flgh h, s, ; (b) Evldsglphyssdls; () Gd sglphyssds ( PCh! ) Hw s l physs ppld g h ss ss?

3 N +g I??? Illhgshlwys: S CATTERINGdREACTION R g p 1 d : H g h l s f g y ; s dd R g s l v d : ) R s D g (slvd d f R g ds f d l y p d s ; ls h f d 3 : C h l g s p b l h gy ll l s; b dg gy f s h

4 Th ss ss sh s (, fss), (, g) ffd ly by h f h g s (Dppl bdg ffs). I h f h sg ssshhlgs sd: () Kgy f h d s s pbl h bdg gy f h h g ( ll, sld, lqd). ATOMSARENOTFREE!!! (b) N wvlgh s f h d f h spg lls f ysls; () Sg f vs l h s ll f ysl f (h,h); (d) NyGAINlsgy;

5 Bppx Ad Fpsdpl Csd h s: Sg by sgl splssls ψ( ) hdssfyhq: + V () ψ( )=Eψ() µ

6 O [ + k ] ψ ( ) = F( ) Wh: k µe = d F( ) µ V ( ) ψ () = Th d wv dsbs f pl vlghz d.i sgv s ψ () = kz

7 Wlskwh [ + k ] kz = 0 Sggsdhwk: Dsh [ + ] kz = 0 k Thf,h qsbslvds [ wh + k ]ψ ( µ F( ) = V ( )ψ() ) Rllhψ( )= F( s ) sldd F( )

8 G sf ψ0( Sl [ ψ0( ) ' hd + k ] ψ ψ () 0 sgvs 0 ) dps k = 4π Th sl f g ()=δ( ') ψ s () gvl τ ' ' k ' ψ () = s 4π ' s bd by F( ')dτ τ

9 ψ s ( ) N sl V ( ) Bfp µ = π ψ( ) >> τ k ' V (')ψ( ')dτ 4π ' f ll vl s h kwqs. dg fh hf ' '. ˆ 1/ ' 1 wh ' '. ˆ

10 ˆ = Sggsdhwk: Shwh ' Thf ψ s ( ) '. ˆ ( ψ µ s ) = k '. ˆ k V ( π ') ψ ( ') dτ τ Dfg f (θ) µ = π bs, k '. τ ˆ V (')ψ( ')dτ

11 H k ψs( ) = f (θ) Wkw hh dfflsgss s s gv s σ(θ) σ(θ) d σ = dedω = f (θ) µ = k '. ˆ V ( ')ψ( π ')dτ Th fs Kw!!! τ ψ( ) d V ( ) sll

12 BAppx A ssp: ψ( ) Th pl wv f pl g s pld by h wv f,hs, ψ( ) kz = k. ˆ = z h d Rl: Id pl s wkly sd h pl g, σ(θ) µ = k '.( ˆ z ˆ ) V ( π ') dτ τ

13 F F V ( ) P s xpssf d V p ( p w ) l svylw. w h h l h v d f g y A ssps: ( ) Th p sp l = 0 l h llysy, s h p p l s d, ; h s w p v, g l l s ( T b h ) S p h l g s p g g π = s d l b yfs V ( ) µ δ Wh sh s ( ) glgh ssllkw!!

14 Tdsdhpddby F l sxghsg f s by sgl ls wh sp ffsdd. Rllh: ( k ψ ) = kz + f (θ) > f R Lw gy, s k µe = h k 0 H l ψ() = + l f (θ) k 0 k 0 > R > R, pls

15 Thsglgh sdfds = l f (θ) k 0 > R Ip f h sg lgh F=R h l sfw hv Rψ(R) = R = R[1 ψ ( R) ( ) ψ(r) = 0 d =R ] pbl sph

16 (b) ψ(r) <1 > 0 d < R Rlspldgbdss ()ψ( R) >1 < 0 Nbdss!!

17 Th dffl sg ss s whhfpsdplsh µ σ(θ) = π f k 0( lwgys) σ(θ) = Th lsgssss σ s σ s = 4 π σ s = 4π (θ) dω k.( ˆ z ˆ ) π τ µ δ( ) dτ

18 Th dv s f sss h h dshv vy lw gy. I s ls ssd h h ls f ss M s bd; hf, h sg lghs lld f. If h s wh ll f ss M whh h ls f ssm sldd,..,ls bd h ll, h Shödg q f h sys ll wll ld h ss bw h ( ) d h ll(m ). Thss: () SysdM + V ( ) ψ( )=Eψ() µ wh M µ = + M

19 (b) SysdM + V ( ) ( ψ ) =Eψ( ) µ' wh M' µ' = + M' Th Shödg q f h sys d M b w s µ' µ ' ψ( ) + V ()ψ( ) = Eψ( ) µ µ µ W s ffv pl f h sys M s µ ' ) V ( ) = ff µ V (

20 As w hv s, h B ppx gh wh h F psdpl h sg lgh wh hffvpls µ = bd π bd = + M M V ()dτ ff τ µ π V ()dτ τ

21 bd Thlbw d f s bd = + M f M Dfg A s h bw h ls ss M d h ss, A=M/whv bd A +1 = f A S h lw gybd sgssss bd σ s = 4π bd

22 Th l bw h bd d bd sgssss bd σ s = A + 1 σ A As xpl, f A=1(hydg) σ bd s = 4σ f f Sggsdhwk: bd () Whh s sd σ s σ f s? (b) Ifbh,hw?

23 MIT OpCsW hp://w..d.106 N Is d Appls Spg 010 F f b g hs ls Ts f Us, vs: hp://w..d/s.

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