Nuclear Reactions: Lecture on two-body description. Ismail Boztosun

Transcription

1 Nucea Reactions: Lectue on two-body desciption Isai Boztosun Feb 0 Wasaw boztosun@adeniz.edu.t

2 Contents Fundeantes: Types of nucea eactions Obsevabes Copound vs Diect eactions Coision theoy-eastic scatteing Lab vs CM oodinate systes Effective potentia Bon and DWBA eapes Optica ode Couped-channes ode-ineastic scatteing

3 Suggested boos G.R. Satche Intoduction to Nucea Reactions Ofod ni. Pess. I. Thopson & F. Nunes Nucea Reaction fo Astophysics Cabidge ni. Pess. C. Betuani & P. Danieewicz Intoduction to Nucea Reactions Tayo&Fancis L.S. Rodbeg & R.M. Thae Intoduction to Quantu Scatteing Theoy Acadeic Advanced Leve; G.R. Satche Diect Nucea Reactions Ofod ni. Pess N. Austen Diect Nucea Reactions Theoies Wiey N. K. Gendenning Diect Nucea Reactions Wod Scientific 3

4 Types of Nucea Reactions Scatteing vs Reaction - Eastic Scatteing aways pesent No enegy change XaaX a+a a+a Q=0 4 Mg C C 4 Mg - Ineastic Scatteing Enegy change Xaa*X* a+a a*+a* Q<0 4 Mg C C* 4 Mg* 3- Ineastic Reaction Enegy and nuceon change a+a b+b 4 N 4 Hep 7 O 4- Radiative Captue a+a B+gaa C 4 Hegaa 6 O 5- Photo Reaction gaa+a B+b 6 Ogaa 4 He C 6- Tansfe Reaction Xdp o Xpd C 6 He 4 He 4 C

5 Obsevabes Epeient: Angua distibution: E fied q vaiabe Ecitation function: q fied E vaiabe Theoy: Diect pobe: deteine coss-section fo the potentia Invese pobe : deteine the potentia V fo coss-section

6 Nucea Reactions: Copound Sa b vaues head-on Low enegy Two step: No eation to entance channe a+a C* ceation of CN C* b+b decay of CN Tiescae: s Isotopic/Syetic X- section ~q=90 0 Diect Lage b vaues peiphea High enegy One step a+a b+b Tiescae: 0 - s Fowad peaed-osciatoy X-section 6

7 7

8 Coss-section: a+a b+b Pobabiity of a eaction to occu b V q soid ange dw

9 Coision theoy: eastic scatteing Befoe coision Afte coision LAB CM

10 q ab q ab tan q ab sin qc cos q v c M v c E CM E ab

11 y CM R X

12 i i i i z y E V E V R X X X X M V 0 R M E V M R

13 Two body pobe: Schödinge Equation with effective potentia Two Body Pobe. Move fo LAB syste to CM.. Sepeate the CM otion 3. Find the educed ass = + 4. Define the tota Centa Potentia V 5. Sove the Sch. Eq. Fo this V. Reducing the inteaction of pojectie and taget nucei to inteaction of the educed ass with a potentia between the. = 3

14 Effective Potentia Nucea Potentias Phenoenoogica Micoscopic Doube Foding V R A 0 V R ep a 3 0 n F R d d R R Density of A Density of a NN inteaction +echange te ep 4 ep J00 E 4.5

15 Couob Baie vs Enegy R B ~ A /3 +A /3 V B =.44 Z Z /R B Beow the baie Vey few vaues R ati Nucea Astophysics Nea the baie Liited vaues patia wave epansion e: Optica CC CDCC DWBA etc. Fa above the baie Too any vaues no patia wave epansion e: Eiona Gaube sei-cassic theoies etc.

16 Two body pobe: Nueica Soution of Schödinge Equation Anaytic soution of the Schödinge equation is iited to few potentias: SW HO In genea thee is no anaytic soution nueica appoach Nueica soution : discetization N points with esh size h u 0=0 u h= o any constant u h is deteined nueicay fo u 0 and u h Nueov agoith u 3h u Nh fo age : atching to the asyptotic behaviou phase shift Bound states E<0: sae idea 6

17 Bon and Distoted Wave Bon Appoiation L whee L Mutipying by and integating a ove the space we get L d L i e is the fee patice soution V=0. sing Geen functions: G L 4 e G i d e i 4. d e e i i 4.

18 8 d e f i 4. q Scatteing Apitude and Coss-section If we use pane wave fo the d e e f i i BA.. 4 q scatteing apitude in Bon Appoiation is: d e f q iq BA 3 4 ; q Fo spheicay syetic potentia d q q d e iq sin 4 3

19 Distoted Wave Bon Appoiation 9 that such 0 ] [ d e i ] [ 4 * q q q f f f d f f DWBA 4 q q V H E 0 V E G H E V G VG G V d d d e V G V e d d e V de f i i i i q Incoing and outgoing waves

20 V R V 0e Eape: Gaussian Potentia 0 sin q f q V 4 d q sin q R 0 e 4 d q 0 f q V 3 V 0 R 3 e qr q q sin d dw Ce R q sin 0

21 Schödinge equation II: Patia wave ethods We ust sove: Fo bound states Discete Spectu Fo scatteing states Continuous Spectu

22 ] [ ig G S ig F Genea Soution: j F Besse functions G Neuann functions cos 0 q q q i C P e S i f f scatteing apitude R S ] [

23 Besse and Neuann functions Fo sa j!!!! n Fo age j sin / n cos / Eapes: sin j0 n0 cos 3

24 Phase Shift V attactive V epusive V=0 usin-/ =0 >0 V attactive V 0 usin-/+ <0 V epusive

25 Optica Mode Continuu Ecited States Feshbach s foais V Nüee Nucea V V V V V E E H V R iw Nucea Potentia: Cope Non-oca Enegy and ode space dependent Resonant

26 Mode: Genea Optica Mode Eastic Scatteing Couped-Channes Mode Eastic+Ineastic whee Defoation Rotatione R = R 0 [ + Y 0 q + Y 0 q 0 0 0

27 Optica Potentias Rea & Effective Rea Potentias Iaginay & Rea Potentias 6 He MeV Long Range Absoption

28 Resuts

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30 C- C

31 C- C MeV Singe- +

32 Thans 3