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

1

Collective modelAverageshape

Instantaneousshape

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

2

Collective model

φ),(θ Y(t)αRR(t) λμλ

λ

λ μλμavr

μ- λ,λμ

Instantaneouscoordinate

Symmetry

Amplitude Sphericalharmonics

r0A1/3

= 0monopole

= 1dipole

= 2quadrupole

= 3octupole

.

http://wwwnsg.nuclear.lu.se/basics/excitations.asp?runAnimation=beta10

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

3

Collective model

YαR

YαYαYα R

),(YαRR(t)

1010avr

1- 1,1- 1,10101111avr

1μ

1

1 μ1μavr

Both monopole and dipole excitations require high energy.

R(t) = Ravr +00 Y00

= 0monopole

= 1dipole

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

4

Collective model

= 2quadrupole

• Quantization of quadrupole vibration is called a quadrupole phonon. • A phonon carries two units of angular momentum.• This mode is dominant. For most even-even nuclei, a low lying state with Jπ=2+ exists.

2020avr

2- 2,2- 2,2,-12,-1202021212222avr

2μ

2

2 μ2μavr

YαR

YαYαYαYαYα R

),(YαRR(t)

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

5

Collective model

-2 -1 0 1 2

-2 -4 -3 -2 -1 0

-1 -3 -2 -1 0 +1

0 -2 -1 0 +1 +2

1 -1 0 +1 +2 +3

2 0 +1 +2 +3 +4

l = 4 = +4, +3, +2, +1, 0, -1, -2, -3, -4l = 2 = +2, +1, 0, -1, -2l = 0 = 0

Triplet0+, 2+, 4+

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

6

Collective model

Two-phonon triplet at twice the energy of the single phonon state.

HW 24HW 24Krane 5.10

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

7

Nuclear Reactions

X(a,b)Y• First in 1919 by Rutherford:

4He + 14N 17O + 1H14N(,p)17O

• Incident particle may: change direction, lose energy, completely be absorbed by the target……• Target may: transmute, recoil……• b = Capture reaction.• If B.E. permits fission (comparable masses).• Different exit channels a + X Y1 + b1

Y2 + b2

Y3 + b3 …….

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

8

Nuclear Reactions• Recoil nucleus Y could be unstable or emission.

• One should think about: Reaction dynamics and conservation laws i.e. conditions necessary for the reaction to be energetically possible. Reaction mechanism and theories which explain the reaction. Reaction cross section i.e. rate or probability.

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

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Nuclear ReactionsConservation Laws• Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??) …….

apa X

pY

pb

Y

bQTTcmcm iffi 22

+ve Q-value exoergic reaction. -ve Q-value endoergic reaction.

aYb TQTT +ve Q-value reaction possible if Ta 0. -ve Q-value reaction not possible if Ta 0. (Is Ta > |Q| sufficient?).

Conservation of momentum ……

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

10

Nuclear Reactions• Conservation of momentum.• We usually do not detect Y.Show that:

• The threshold energy (for Ta): (the condition occurs for = 0º).

• +ve Q-value reaction possible if Ta 0.• Coulomb barriers…….!!!• -ve Q-value reaction possible if Ta > TTh.

bY

aaYYbYabaabab mm

TmmQmmmTmmTmmT

])()[(coscos 2

HW 25HW 25

abY

bYTh mmm

mmQT

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

11

Nuclear Reactions

• The double valued situation occurs between TTh and the upper limit Ta

\.

• Double-valued in a forward cone.

aY

Ya mm

mQT

\

aba

aaYYbY

Tmm

TmmQmmm ])()[(cos max

2

HW 25HW 25 (continued)(continued)

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

12

Nuclear Reactions

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

13

Nuclear Reactions

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

14

Nuclear Reactions

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

15

Nuclear Reactions

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

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Nuclear Reactions

• If the reaction reaches excited states of Y

58Ni(,p)61Cu

Highest proton energy

exbexYaXex EQcmEcmcmcmQ 02222 )(

less proton energy

even less ….

See Figures 11.4 in Krane

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

17

Nuclear Reactions

Neutron scattering• Inelastic Q = -Eex (=-E*).• Elastic Q = 0.

HW 26HW 26Discuss the elastic and inelastic scattering of neutrons using the relations you derived in HW 25.