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1 nuclear states 1 nuclear stability 2 1
2 nuclear chart 3 nuclear reactions Important concepts: projectile (A) target (B) residual nuclei (C+D) q-value of a reaction Notations for the reaction B(A,C)D A+B C+D 4 2
3 forces present in reactions nuclear (strong) weak electromagnetic gravitational 5 Coulomb effects in reactions Astrophysical S-factor Sommerfeld parameter 6 3
4 reaction rates and the Gamow peak 7 history of the universe 8 4
5 primordial nucleosynthesis Q-value for p(n,g)d 2.26 MeV T(universe to cool down to E=2.26)=7 min slightly less than T(free neutron decay) 9 CNO cycles and red giants 10 5
6 reactions in light stars 11 solar neutrino puzzle and nuclear reactions status in the nineties: measured solar neutrino flux << predicted flux 12 6
7 triple-alpha reaction α α 12 C α 13 heavier elements 14 7
8 medium mass elements and red giants 15 heavy elements and the s-process 16 8
9 heavy elements: elemental abundancies 17 heavy elements: how and where? Question 3 How were the heavy elements made? Where did they come from? 18 9
10 heavy element: r-process in the chart 19 how do we measure reactions rates? 14 C(n,γ) 15 C has impact on: neutron-induced CNO cycle heaviest element in non-homogenous bigbang abundancies from the r-process in supernovae 20 10
11 indirect methods: nuclear reactions direct measurement 14 C(n,γ) 15 C transfer reaction Coulomb dissociation 14 C(d,p) 15 C n low relative energy 15 C γ 208 Pb 14 C 21 breakup reactions and (n,γ) 208 Pb( 15 C, 14 C+n) 208 Pb@68 MeV/u Nakamura Reifarth 14 C(n,γ) 15 C Nakamura et al, NPA722(2003)301c 22 Reifarth et al, PRC77, (2008) 11
12 open problem for nuclear-astrophysics 7 Be(p,γ) 8 B Direct measurement S 17 (0)=22.1(0.6 exp)(0.6 th) ev b Coulomb dissociation S 17 (0)=20.6(0.8 stat)(1.2 sys) ev b ANC method transfer S 17 (0)=17.3(1.8) ev b ANC method breakup S 17 (0)=17.4(1.5) ev b 23 [Junghans et al, PRC 2003] open problem in nuclear structure [Jenny Lee et al, PRL 2009] 24 12
13 classification of reactions Direct reactions transfer momentum is small compared to initial momentum typically peripheral short timescale (10-22 s) E>10 MeV mostly one step final states keep memory of initial states Resonance reactions reactions that go through a resonance (peak in the cross section) intermediate step in the reaction longer time scale Compound reactions longer timescale many steps in the reaction all nucleons share the beam energy loss of memory from the initial state low energy reactions 25 direct reactions 26 13
14 direct reactions 27 many body structure 28 14
15 why do reactions? elastic traditionally used to extract optical potentials, rms radii, density distributions. [Lapoux et al, PRC 66 (02) ] 29 why do reactions? inelastic traditionally used to extract electromagnetic transitions or nuclear deformations 30 [Summers et al, PLB 650 (2007) 124] 15
16 why do reactions? transfer dσ/dω (mb/sr) example: 84 Se(d,p) 85 Se ground state 1 st E x = 462 kev l = 2 DWBA l = 0 DWBA traditionally used to extract spin,parity and spectroscopic factors θ c.m. (deg.) g.s. SF = 0.33 ± 0.09 (d 5/2 ) 1 st SF = 0.30 ± 0.08 (s 1/2 ) [J. Thomas et al, PRC 76, (2007)] 31 why do reactions? transfer 11 Li(p,t) 9 Li@ 3 A MeV measured both ground state and excited state 9 Li [Tanihata et al, PRL 100, (2008)] traditionally used to study two nucleon correlations and pairing 32 16
17 why do reactions? breakup 14 Be n+n+ 12 Be two nucleon correlation function Pb C [Marques et al, PRC 64 (2001) ] 23 O(Pb,Pb) 22 O+n+g [Nociforo et al, PLB 605 (2005) 79] 23 O γ 208 Pb n γ 22 O 23 O + γ n + 22 O 33 resonant reaction a + A C* Breit-Wigner shape σ scatt π = 2 k Γ ( 2l + 1) ( ) 2 2 E E + Γ 4 R 2 Γ = FWHM E R = resonant energy 34 17
18 compound reactions the decay of the compound state does not depend on the initial state. 35 classification of reactions 36 18
19 classification of reactions 37 selectivity of the reaction to resonances 38 19
20 evaporation of residues low energy» Maxwell distribution, with peak determined by the degree of excitation of the compound nucleus Some nucleons end up having enough energy to evaporate 39 energy distribution: compound vs direct pure compound nucleus formation can be seen at backward angles The more forward you go, the more pronounced direct components will appear 40 20
21 angular distribution: compound vs direct Direct reactions (ID): Forward peaked (large b) Compound reactions (NC): Distribution is generally isotropic (except for heavy ion collision where DL large) 41 kinematic of reactions energy in the relative motion 42 21
22 kinematics of the reaction apply laws of conservation conservation of mass conservation of energy consevation of momentum 43 basic concepts 44 22
23 equations of motion laboratory Center of mass 45 cross section The number of particle entering a detector depends on: solid angular size of detector number of scattering centers in the target flux of the incident beam the cross sectional area for the reaction to occur 46 23
24 cross section Definition of cross section: the area within which a projectile and a target will interact and give rise to a specific product. Units 1b (barn) = 10 fm x 10 fm 47 cross section in c.m. and lab Total cross section: the same in center of mass and laboratory Angular distribution of the cross section: 48 24
Semi-Classical perturbation theory Coulomb only First-order most used
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