The Wu Experiment

For a long time it was believed that parity symmetry (the interchange of left and right) held in every interaction. In 1956, the Chinese-American physicist Chien-Shiung Wu showed that it is in fact violated, specifically in the interaction ^{60}_ {27}Co\rightarrow^{60}_ {28}Ni+e^-+\bar{\nu}_e+2\gamma. T.D Lee and C.N. Yang had suggested to her that pseudo scalar quantities such as  \langle\sigma \cdot p_e\rangle, where \sigma – is the nuclear spin and p_e is the electron momentum – might actually not be invariant under parity conservation. No physicist had ever measured such a quantity, so C. S. Wu quickly devised a novel experiment to do so. In this problem we will follow a calculation of Wu to investigate why parity conservation implies that the expectation value of the chosen pseudo-scalar is 0

  1. The parity operator acts on a wave function as follows P\psi(x)=\psi(-x). Show for an odd or even wavefunction viz. (odd: \psi(-x)=-\psi(x), even: \psi(-x)=\psi(x)) that the probability the wave function is between -a and a is invariant under parity.
  2. Show that parity invariance implies that \langle\sigma \cdot p_e\rangle=0


The discovery of the parity violation in weak interactions and its recent developments
Chien-Shiung Wu
Published in: Lect.Notes Phys. 746 (2008), 43-70

Experimental Test of Parity Conservation in Beta Decay
C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hoppes, and R. P. Hudson
Phys. Rev. 105, 1413 – Published 15 February 1957