Subatomic Physics

10.5. Multipole Radiation 301
Figure 10.8: Determination of the half-life of a short-lived nuclear state, decaying by gamma
emission. The block diagram is shown at the left; a typical curve of coincidence counting rate
N(D), taken as a function of the delay time D, is given at the right.
The wave functions ψΛ and ψΣ have the same parity, and their product is even
under the parity operation. The vector x, however, is odd under parity, and the
integrand is therefore also odd; the integral consequently must vanish. Similarly, it
can be shown that dipole radiation cannot explain the 2 + → 0 + transition in 170Yb. The treatment given in the previous section must therefore be generalized if it is to
explain all electromagnetic radiation emitted by subatomic systems.
The approximation that leads to electric dipole radiation is introduced by keeping
only the first term in the expansion (10.61). Removal of this restriction is
straightforward but lengthy, and we shall quote only the final result. (9) The emitted
radiation can be characterized by its parity, ηP , and by its angular momentum
quantum number, j. For any given value of j, the photon can carry away even or
odd parity. It is customary to call one of these two an electric and the other a
magnetic transition. Parity and angular momentum are related by
electric radiation: ηP =(−1) j
magnetic radiation: ηP = −(−1) j .
(10.80)
9 Introductions to the theory of multipole radiation can be found in the following references: G.
Baym, Lectures on Quantum Mechanics, Benjamin, Reading, Mass., 1959, pp. 281, 376; Jackson,
Chapter 9; Blatt and Weisskopf, Chapter 12 and Appendix; S. A. Moszkowski, in Alpha-, Betaand
Gamma-Ray Spectroscopy, Vol. 2, (K. Siegbahn, ed.), North-Holland, Amsterdam, 1965,
Chapter 15; T. W. Donnely and J. D. Walecka, Ann. Rev. Nucl. Sci. 25, 329 (1975).