Transcript Gamma-ray strength functions

Gamma-ray strength
functions
Also called in the literature:
• radiative strength functions
• photon strength functions
Presentation OCL group meeting
Ann-Cecilie Larsen
Tuesday Nov 4, 2008
Some basics about
the nucleus
• Protons (p) and neutrons (n) in orbits
•
•
around the center of mass, kept
together by the strong force
Pairs of p and n in time-reversed orbits
 nucleon Cooper pairs with speed 
0.6c (unpaired nucleons:  0.2c)
Shell structure: some numbers of
protons and neutrons give very stable
nucleus
QuickTime™ and a
decompressor
are needed to see this picture.
http://www.jlab.org/news/archive/2003/nucleons.html
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Nuclear physics group meeting
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Excitation of a nucleus
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Ground state  excited state
Single-particle excitation
Collective excitation
Pair-breaking
A combination
Cooper pair
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p1/2
p3/2
s1/2
Broken pair
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Gamma decay
• Transition between excited states or to the
ground state by emitting a high-energetic
photon ( ray)
E2 E2-E1
p1/2
p3/2
s1/2
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E2
E1
E1 E1-0
Gr. st.
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Types of  radiation
• Electric dipole (E1), quadrupole (E2), ...
• Magnetic dipole (M1), quadrupole (M2), ...
• Single-particle (Weisskopf) estimates of
transition rates ( energy in MeV):
(E1)  1.0 1014 A 2 / 3 E 3 (s1)
(E2)  7.3 10 A
7
4 /3
5
1
E (s )
(M1)  5.6 1013 E 3 (s1)
(M2)  3.5 107 A 2 / 3 E 5 (s1 )
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NB! Can deviate several orders of
magnitude from observed rates!
Smaller  little overlap between initial and final
Larger  collective modes (more than one nucleon)
Nuclear physics group meeting
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Selection rules
• Each photon carries a definite angular
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momentum L>0
Dipole: L=1, quadrupole: L=2, ...
Ii = L+If:
L
Ei, Ii, i
L
If
Ii
Ef, If, f
Selection rules:
|Ii - If|  L  Ii + If
 = no: even electric (E2, E4), odd magnetic (M1,M3)
 = yes: odd electric (E1,E3), even magnetic (M2,M4)
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Nuclear physics group meeting
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An example:
partial decay scheme of 157Gd
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Nuclear physics group meeting
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What happens at high
excitation energy?
• Lots of levels, impossible to measure all
levels and their  transitions
• Measure average  decay properties
• Fermi’s Golden Rule:

2
2
f Hint i (E f )
i

f
Transition operator
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
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Average decay probability
• One state with energy E, lifetime t & width E=
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(Heisenberg: Et  hbar/2)
Connection with decay rate1: = /hbar
Connection with lifetime:  = 1/t
Average over several states: , 

1From
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Weisskopf and Wigner, 1930
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Decay probability and -ray
strength function
• Model-independent definition of the -strength
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function (dipole): f(E) = /(E3D) [MeV-3]
Connection with decay rate: =(fE3D)/hbar [s-1]
Neutron resonance spectrum
as a function of neutron energy
Resonance spacing D
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Nuclear physics group meeting
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How does the -ray strength
function look like?
n
n+p
protons
neutrons
n
p
Region for Oslo exp.
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Nuclear physics group meeting
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