Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (α scatt.

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1 Nucler Rections Shpe, interction, nd excittion structures of nuclei scttering expt. cf. Experiment by Rutherford (α sctt.) scttered prticles detector solid ngle projectile trget trnsmitted prticles K. Muto (TIT)

2 nottion: A(,b)B rection b A B elstic scttering p(d,d)p nd n(d,d)n 3-body interction A gs A gs fundmentl interction between nd A K. Sekiguchi et l., PRC89( 14)064007

3 A(,b)B rection b A B elstic scttering inelstic scttering A gs A gs fundmentl interction between nd A A gs A* excittion spectrum of nucleus A E

4 A(,b)B rection b trnsfer rections trnsfer rection (below: n exmple of pick-up rection) 16 O 17 O 16 O 208 Pb gs 207 Pb level schem of 207 Pb A B trnsfer rection (below: n exmple of stripping rection) 17 O 16 O 17 O 208 Pb gs 209 Pb level schem of 209 Pb fusion rection A gs X (+A) interction between nd A structure of nd A

5 hypernucleus production rections (K -,π ) rection π 12 C (π +,K + ) 12 ΛC rection K - K - A gs A Λ (π +,K + ) rection K + π + π + O. Hshimoto nd H. Tmur, Prog. in Prt. nd Nucl. Phys. 57 ( 06)564 A gs A Λ excittion spectrum of hypernucleus A Λ

6 (e,e Κ + ) rection 12 C(e,e Κ + ) 12 ΛB e e - e - A gs A Λ K + S.N. Nkmur et l., PRL110( 13) T. Gogmi, Ph.D. Thesis (Tohoku U.) 2014 L. Tng et l., PRC90( 14)034320

7 Cross sections flux = the number of prticles crossing unit re per unit time incident bem event rte (the number of event per unit time per trget nucleus) : proportionl to the incident flux cross section

8 Cross sections event rte (the number of event per unit time per trget nucleus) : proportionl to the incident flux cross section differentil cross sections (ngulr distribution) units: 1 brn = cm 2 = 100 fm 2 (1 mb = 10-3 b = 0.1 fm 2 )

9 Cross sections (experiments) S t the trget thickness bem intensity: the number of trget nucleus: detection efficiency

10 Cross sections (theory) A(,b)B rection b A B center of mss frme b θ cm A trnsition B

11 Cross sections lbortory frme b A B θ lb center of mss frme b trnsformtion A energy nd momentum conservtions B θ cm

12 Born pproximtion V(r) θ trnsition rte for elstic scttering: perturbtion

13 Born pproximtion V(r) θ momentum trnsfer incident flux: θ

14 Electron scttering e - e - Form fctor * reltivistic correction:

15 cf. electron scttering off unstble nuclei (SCRIT) K. Tsukd et l., PRL118, (2017)

16 proton rdius puzzle mu-on electron

17 Distorted Wve Born pproximtion (DWBA) perturbtion distorted wves perturbtion V(r) θ inelstic scttering trnsfer rections

18 Opticl model Rection processes Elstic sctt. Inelstic sctt. Trnsfer rection Compound nucleus formtion (fusion) Opticl potentil Loss of incident flux (bsorption) (note) Guss s theorem r

19 Woods-Sxon + volume &surfce imginry prts H. Skguchi et l., PRC26 (1982) 944

20 Appendix: DWBA in ocen coustics Fishfinder (bckwrd) scttering of (ultr-)sonic wves due to fish etc. one cn know the number of fish N T if one knows the differentil cross sections

21 J. Accoust. Soc. Am. 125 ( 09) 73 Modeling of squid DWBA: locl wve number inside squid!

22 Krill ( オキアミ ) mesurement DWBA K. Akmtsu nd M. Furusw, ICES J. of Mrine Science 63 ( 06) 36

23 Impulse pproximtion exmple: A Z(K -,π - ) A ΛZ rection π - high energy single scttering pproximtion K - n Λ kinemticl fctor elementry process Plne wve impulse pproximtion (PWIA) Distorted wve impulse pproximtion (DWIA)

24 excittion energy (MeV) O. Hshimoto nd H. Tmur, Prog. in Prt. nd Nucl. Phys. 57 ( 06)564 T. Motob et l., PRC38( 88)1322

25 excittion energy (MeV) m n +m K = 1432 MeV m π +m Λ = MeV m π +m n = MeV m K +m Λ = MeV Q > 0 Q < 0 O. Hshimoto nd H. Tmur, Prog. in Prt. nd Nucl. Phys. 57 ( 06)564 1p 1/2 1p 3/2 T. Motob et l., PRC38( 88)1322 1s 1/2 n l=0 l=0 l=1 Λ 1p 1s

26 reltion between q nd l n K - Λ π - b (impct prmeter) l ~ kb (clssiclly) l ~ b(p -p) = bq

27 1p 1/2 1p 3/2 l=0 1p excittion energy (MeV) O. Hshimoto nd H. Tmur, Prog. in Prt. nd Nucl. Phys. 57 ( 06)564 T. Motob et l., PRC38( 88)1322 1s 1/2 n l=1 l=0 Λ l ~ b(p -p) = bq 1s

28 Absorption cross sections Rection processes Elstic sctt. Inelstic sctt. Trnsfer rection Compound nucleus formtion (fusion) Loss of incident flux (bsorption) rection cross sections totl scttering cross section - elstic cross section fusion inelstic trnsfer

29 Interction cross sections nd hlo nuclei 11 Li something else interction cross section σ I = cross section for the chnge of Z /o N in the incident nucleus trget nuclei trnsmission method N in N out d

30 Interction cross sections nd hlo nuclei 11 Li something else interction cross section σ I = cross section for the chnge of Z /o N in the incident nucleus trget nuclei Projectile Trget Slide: A. Ozw R I (P)

31 Discovery of hlo nuclei I. Tniht, T. Kobyshi, O. Hshimoto et l., PRL55( 85)2676; PLB206( 88)592

32 Rection cross sections b Gluber theory (opticl limit pproximtion:ola) stright-line trjectory (high energy scttering) dibtic pproximtion simplified tretment for multiple scttering:

33 Density distribution which explins the experimentl σ R M. Fukud et l., PLB268( 91)339

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (a scatt.

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (a scatt. Nucler Rections Shpe, interction, nd excittion structures of nuclei scttering expt. cf. Experiment by Rutherford ( sctt.) scttered prticles detector solid ngle projectile trget trnsmitted prticles http://www.th.phys.titech.c.jp/~muto/lectures/qmii11/qmii11_chp21.pdf

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