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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

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4 Nov 2008Nuclear physics group meeting2 Some basics about the nucleus http://www.jlab.org/news/archive/2003/nucleons.html 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

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4 Nov 2008Nuclear physics group meeting3 Excitation of a nucleus Ground state excited state Single-particle excitation Collective excitation Pair-breaking A combination s 1/2 p 3/2 p 1/2 Cooper pair Broken pair

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4 Nov 2008Nuclear physics group meeting4 Gamma decay Transition between excited states or to the ground state by emitting a high-energetic photon ( ray) Gr. st. E1E1 E2E2 E 2 E 2 -E 1 E 1 E 1 -0 s 1/2 p 3/2 p 1/2

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4 Nov 2008Nuclear physics group meeting5 Types of radiation Electric dipole (E1), quadrupole (E2),... Magnetic dipole (M1), quadrupole (M2),... Single-particle (Weisskopf) estimates of transition rates ( energy in MeV): NB! Can deviate several orders of magnitude from observed rates! Smaller little overlap between initial and final Larger collective modes (more than one nucleon)

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4 Nov 2008Nuclear physics group meeting6 Selection rules Each photon carries a definite angular momentum L>0 Dipole: L=1, quadrupole: L=2,... E i, I i, i E f, I f, f L IfIf IiIi L I i = L+I f : |I i - I f | L I i + I f = no: even electric (E2, E4), odd magnetic (M1,M3) = yes: odd electric (E1,E3), even magnetic (M2,M4) Selection rules:

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4 Nov 2008Nuclear physics group meeting7 An example: partial decay scheme of 157 Gd

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4 Nov 2008Nuclear physics group meeting8 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: i f Transition operator

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4 Nov 2008Nuclear physics group meeting9 Average decay probability One state with energy E, lifetime t & width E= (Heisenberg: E t hbar/2) Connection with decay rate 1 : = /hbar Connection with lifetime: = 1/ t Average over several states: , 1 From Weisskopf and Wigner, 1930

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4 Nov 2008Nuclear physics group meeting10 Decay probability and -ray strength function Model-independent definition of the -strength 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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4 Nov 2008Nuclear physics group meeting11 How does the -ray strength function look like? Region for Oslo exp. neutrons protons p n n n+p

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