Reminder: Spin precession

1
Reminder Spin precession

• Spin part of Hamiltonian
• Hspin -µB -? SB
• ? gq /2m (gyromagnetic ratio)
• Acts on spin space only, so really
• Hspin - ? Iwave fn ? SB
• So we ignore spatial wave function
• For B in z direction, Hspin - 2?0Sz
• ?0 ? B/2
• Time-independent Hamiltonian, so solution is

2
Matrix Representation

• If starting state is spin-left, i.e.
• a0 b0 1/v2,
• then we get precession with period 2?0

3
Neutron interferometry
ATOMINSTITUT Vienna

• Beam split by Bragg diffraction in vertical
  crystal planes
• Whole interferometer carved from a perfect
  crystal of silicon
• Separation between elements exact multiple of
  inter-atomic spacing.
• Only a dozen successfully made in 30 years!

Credit NIST, Boulder, Colorado
4
2p rotation (Warner et al 1975)

• g factor of neutron -3.83
• Precession frequency 2?0-geB/2mn
• de Broglie ? 0.1445 nm
• Effective l 2.7 cm allowing for leakage of B
  outside magnet.
• Time in field t l/v lmn?/h
• Angle precessed 2?0t -geB?l/h

• For 2p rotation we need B 3.4 mT 34 gauss
• Observed period 62 G
• 4p rotation needed to restore original state 2p
  rotation changes sign, as predicted by QM.