W. Udo Schröder, 2005 Gamma Decay 1

W. Udo Schröder, 2005 Gamma Decay 2 Photons Photons: generated by moving charge distributions. Distributions can have intrinsic angular momentum (spin) Rotations: move charge distributions and direction of spin Vector field rotating about z axis Rotating vector field (magnitude + direction) Analogous for S x, S y Intrinsic spin=1 system Have to couple S with orbital L  J

W. Udo Schröder, 2005 Gamma Decay 3 Electromagnetic Multipole Radiation Helmholtz Eq. commutes with angular momentum operator  construct orthogonal solutions with well defined angular momentum  vector potential: Following Greiner & Maruhn (“Nuclear Models”), Jelley (“Fundamentals of Nuclear Physics”)

W. Udo Schröder, 2005 Gamma Decay 4 Interaction with Radiation Field Expressed plane elm wave (= Wf of photon) in terms of multi-pole components, each of well defined (“good”) angular momentum Initial and final nuclear WF V is cancelled through photon state density

W. Udo Schröder, 2005 Gamma Decay 5 Electric and Magnetic Multipole ME EE EE     Transition Transition/Selection Rules

W. Udo Schröder, 2005 Gamma Decay 6 Long Wave Length Limit Basically true for all  spectroscopy: Continuity Equ.

W. Udo Schröder, 2005 Gamma Decay 7 Transition Rate V cancelled by normalization

W. Udo Schröder, 2005 Gamma Decay 8 Reduced Transition MEs Reduced ME unpolarized proj +target: Average over M i, sum over M f Integrate over angle

W. Udo Schröder, 2005 Gamma Decay 9

W. Udo Schröder, 2005 Gamma Decay 10 Weisskopf’s Estimates of s.p. Transition Probability Consider single nucleon in circular orbit (extreme SM) and long wave (kR « 1)  particle wave function Weisskopf Estimates

W. Udo Schröder, 2005 Gamma Decay 11 Weisskopf’s Eℓ Estimates T 1/2 for solid lines have been corrected for internal conversion. Experimental E1: Factor slower than s.p. WE  Configurations more complicated than s.p. model, time required for rearrangement Experimental E2: Factor 10 2 faster than s.p. WE  Collective states, more than 1 nucleon. Experimental Eℓ (ℓ>2): App. correctly predicted.

W. Udo Schröder, 2005 Gamma Decay 12 Weisskopf’s Eℓ Estimates T 1/2 for solid lines have been corrected for internal conversion. Experimental Mℓ: Several order weaker than Eℓ transitions.

W. Udo Schröder, 2005 Gamma Decay 13 Special B Values for Rotational Bands K-selection rules for rot bands: K=|K i -K f |≤ 1. K-forbiddenness: =K-1

W. Udo Schröder, 2005 Gamma Decay 14 Summary: WE sp Estimates/W.u. Weisskopf Units (W.u.)

W. Udo Schröder, 2005 Gamma Decay 15 Collectively Enhanced Transition Rates 0 MeV 0.32 E2

W. Udo Schröder, 2005 Gamma Decay 16 Isospin Selection Rules Reason: n/p rearrangements  multipole charge distributions photon interacts only with 1 nucleon (t = 1/2)  T = 0, 1 Example E1 transitions: Enhanced (collective) E2, E3 transitions T = 0 Collective (rot or vib) WF does not change in transition.

W. Udo Schröder, 2005 Gamma Decay 17 Gamma Decay of Isobaric Analog States For same T, wfs for protons and neutrons are similar  “Mirror Nuclei” 19 Ne and 19 F W.u.

W. Udo Schröder, 2005 Gamma Decay 18 Isospin Selection Rules for Gamma Decay E1 M1

W. Udo Schröder, 2005 Gamma Decay 19 E2 Gamma Transitions rotational band vibrational band Collectively enhanced E2

W. Udo Schröder, 2005 Gamma Decay 20 E2 Transition Rates 40 Ca Inter-and Intraband E2 Transitions (W.u.) E2 often collectively enhanced Strong E2 transitions within bands Weaker between different bands because of different intrinsic structure of band heads some band mixing

W. Udo Schröder, 2005 Gamma Decay 21 Electric Transition Strengths in Odd-n Nuclei SM: No E transitions in odd-A (odd-n) nuclei, since e(n)=0 E1  effective charges for n, p due to c.m. motion E2  core polarization  mixing of states

W. Udo Schröder, 2005 Gamma Decay 22 Examples of Magnetic Transitions