Compound Nucleus Reactions

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Brandon Francis
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1 Compound Nucleus Reactions E CM a Q CN Direct CN decays Time. Energy. Two-step reaction. CN forgets how it was formed. Decay of CN depends on statistical factors that are functions of E x, J. Low energy projectile, medium or heavy target. 1

2 Compound Nucleus Reactions 2

3 Compound Nucleus Reactions Consider p + 63 Cu at E CM p = 20 MeV. Calculate E CM +[m( p 63 Cu) + m(p) m( 64 Zn)]c 2. Divide by 64 available energy per nucleon << 8 MeV. Multiple collisions long time statistical distribution of energy small chance for a nucleon to get enough energy Evaporation. Higher incident id energy more particles evaporate. See also Fig in Krane. 3

4 Direct Reactions Random collisions nearly isotropic angular distribution. Direct reaction component strong angular dependence. See also Fig in Krane. 4

5 Direct Reactions Peripheral collision with surface nucleon. 1 MeV incident nucleon D?? more likely to interact with the nucleus CN reaction. 20 MeV incident nucleon D?? peripheral collision Direct reaction. CN and Direct (D) processes can happen at the same incident particle energy. Distinguished by: D (10-22 s) CN ( s). [Consider a 20 MeV deuteron on A=50 target nucleus]. Angular distribution. 5

6 Direct Reactions (d,n) stripping (transfer) reactions can go through both processes. (d,p) stripping (transfer) reactions prefer D rather than CN; protons do not easily evaporate (Coulomb). [(p,d) is a pickup reaction]. What about (α,n) transfer reactions? HW 36 Show that for a (d,p) reaction taking place on the surface of a 90 Zr nucleus, and with 5 MeV deuterons, the angular momentum transfer can be approximated by l = 8sin(θ/2), where θ is the angle the outgoing proton makes with the incident id deuteron direction. (Derive a general formula first). J π ( 90 Zr )=0 + l gs Fig in Krane. J( 91 Zr) = l ± ½,π = (-1) l Optical model, DWBA, Shell model, Spectroscopic Factor. Nuclear and Radiation Physics, BAU, Second Semester, θ 0º 14.4º 29º 44º dσ dω meas = S dσ dω calc 6

7 Neutron-induced Reactions X(n,b)Y( σ 2 n D Y + b H II C C H I X + n E v Γ b b( (Q+E n n) Γ n (E n ) 2 v P n ln ( E ) n Probability to penetrate the potential barrier For thermal neutrons Γ b (Q) constant P o (E thermal ) = 1 Q >> E n P >o (E thermal )=0 Non-resonant σ E ) n n ( E ) 1 v 7

8 Neutron-induced Reactions 8

9 Nuclear and Radiation Physics, BAU, Second Semester,

10 Neutron-induced Reactions n-tof CERN 10

11 Nuclear and Radiation Physics, BAU, Second Semester,

12 Neutron-induced Reactions n_tof CERN 12

13 Neutron-induced Reactions 13

14 Charged Particle Reactions What is the Gamow Peak? Nuclear Radius 14

15 Charged Particle Reactions Electron Screening 15

16 Charged Particle Reactions e 2 = 1.44x10-12 kev.m Tunneling probability: P HW 37 e 2πη2 Gamow factor η = Z 1 Z 2 hv e Sommerfeld parameter 2 In numerical units: 2πη = 31.29Z1Z 2 E µ(u) µ ( ( kev CM ) 2L+ 1 For γ-ray emission: Multipolarity Γ L ( E γ ) = α LE γ Γ Dipole E γ ) = α E 3 ( 1 γ 16

17 Charged Particle Reactions σ (E) E e 2πη σ ( E) σ ( E) = πd 2 1 2πη E e 1 E S( E) Nuclear (or astrophysical) S-factor 17

18 Charged Particle Reactions E C =?? 18

Collective model. Large quadrupole moments nucleus as a collective

Collective model. Large quadrupole moments nucleus as a collective Collective model Large quadrupole moments nucleus as a collective body (Liquid drop model). Interactions between outer nucleons and closed shells cause permanent deformation. Single-particle state calculated