1. 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

2. 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

3. 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

4. 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

5. 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)

6. 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:

7. 4 Nov 2008Nuclear physics group meeting7 An example: partial decay scheme of 157 Gd

8. 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

9. 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

10. 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

11. 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