nuclear and radiation physics, bau, 1 st semester, 2006-2007 (saed dababneh). 1 nuclear reactions...

Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

1

Nuclear Reactions

Categorization of Nuclear Reactions• According to: bombarding particle, bombarding energy, target, reaction product, reaction mechanism.• Bombarding particle:

Charged particle reactions. [ (p,n) (p,) (,) heavy ion reactions ]. Neutron reactions. [ (n,) (n,p) ….. ]. Photonuclear reactions. [ (,n) (,p) … ]. Electron induced reactions………….

• Bombarding energy: Thermal. Epithermal. Slow. Fast. Low energy charged particles. High energy charged particles.

Neutrons.?


2

Nuclear Reactions• Targets:

Light nuclei (A < 40). Medium weight nuclei (40 < A < 150). Heavy nuclei (A > 150).

• Reaction products: Scattering. Elastic 14N(p,p)14N

Inelastic 14N(p,p/)14N* Radiative capture. Fission. Spallation. …..

• Reaction mechanism: Direct reactions. Compound nucleus reactions.

• More in what follows ….• What is a transfer reaction….?????

Stripping

Pickup

Reson

ant


3

Reaction Cross Section(s) (Introduction)

• Probability.• Projectile a will more probably hit target X if area is larger.• Classically: = (Ra + RX)2. Classical = ??? (in b) 1H + 1H, 1H + 238U, 238U + 238U • Quantum mechanically: = 2.

• Coulomb and centrifugal barriers energy dependence of .• Nature of force: Strong: 15N(p,)12C = 0.5 b at Ep = 2 MeV. Electromagnetic: 3He(,)7Be = 10-6 b at E = 2 MeV. Weak: p(p,e+)D = 10-20 b at Ep = 2 MeV.• Experimental challenges to measure low X-sections..

CMaXaXaaX

Xa

EEmm

mm

22


4


d,Ia

Detector for particle “b”

NI

dRd

a

b

“X“ t

arge

t Nuc

lei /

cm2

“a” particles / s

“b” particles / scm2

Typical nucleus (R=6 fm): geometrical R2 1 b.Typical : <b to >106 b.


5


Many different quantities are called “cross section”.

Krane Table 11.1

NI

r

d

d

drdR

a

b

4

),(4

),(

Angular distribution

“Differential” cross section(,) or ( )

or “cross section” …!!

Units … !

d

dddd

d

d

ddd

0

2

0

sin

sin

ddE

d

b

2

Doubly differential

Energy state in “Y”

dE

d

t for all “b” particles.


6

Coulomb Scattering

b

d

rmin

vovmin

• Elastic or inelastic.• Elastic Rutherford scattering.• At any distance:V = 0

Ta = ½mvo2

l = mvob

0

4

1 2

a

o

T

d

zZeV

r

zZemvmv

oo

22

212

21

4

1

No dependence on


7

Coulomb Scattering


8

Coulomb Scattering

bdbnxdf

bnxf

2)(

)( 2

n target nuclei / cm3 x target thickness (thin).nx target nuclei / cm2

b < b > db d

b

HW 27HW 27Show thatand hence 2

cot2

db

24

222

sin

1

4

1

4

)(

ao T

zZe

d

d

Rutherford cross section


9

Coulomb ScatteringStudy Fig. 11.10 (a,b,c,d)

in Krane

HW 28HW 28Show that the fraction of incident alpha particles scattered at backward angles from a 2 m gold foil is 7.48x10-5.

See also Fig. 11.11 in Krane.


10

Coulomb Scattering

• Elastic Rutherford scattering.• Inelastic Coulomb excitation.

See the corresponding alpha spectrum of Fig. 11.12 in Krane.


11

Nuclear Scattering• Elastic or inelastic.• Analogous to diffraction.• Alternating maxima and minima.• First maximum at

• Minimum not at zero (sharp edge of the nucleus??)• Clear for neutrons.• Protons? High energy, large angles. Why?• Inelastic Excited states, energy, X-section and spin-parity.

31

ARR

p

h

o

R


12

Compound Nucleus Reactions

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 Ex, J.• Low energy projectile, medium or heavy target.


13


a + X C* Y1 + b1 Y2 + b2 Y3 + b3 …..


14

Compound Nucleus Reactions• Consider p + 63Cu at Ep = 20 MeV.• Calculate Ep + [m(63Cu) + m(p) – m(64Zn)]c2.• 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 EvaporationEvaporation.• Higher incident energy more particles “evaporate”.



15


• Random collisions nearly isotropic angular distribution.• Direct reaction component strong angular dependence.



16

Direct Reactions• Peripheral collision with surface nucleon.• 1 MeV incident nucleon ?? more likely to interact with the nucleus CN reaction.• 20 MeV incident nucleon ?? peripheral collision Direct reaction.• CN and Direct (D) processes can happen at the same incident particle energy. Distinguished by:

D (10-22 s) CN (10-18-10-16 s).[Consider a 20 MeV deuteron on A=50 target nucleus].

Angular distribution.


17

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 (,n) transfer reactions?HW 29 HW 29 Show that for a (d,p) reaction taking place on the surface of a 90Zr nucleus, and with 5 MeV deuterons, the angular momentum transfer can be approximated by l = 8sin(/2), where is the angle the outgoing proton makes with the incident deuteron direction. (Derive a general formula first).

l 0 1 2 3

0º 14.4º 29º 44ºJ(90Zrgs) = 0+

J(91Zr) = l ± ½, = (-1)l

Optical model, DWBA, Shell model, Spectroscopic Factor.

calcmeas d

dS

d

d

nuclear and radiation physics, bau, 1 st semester, 2006-2007 (saed dababneh). 1 nuclear reactions...

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