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absorption ammonia molecule angle 9 angular distribution angular momentum anti-neutrino apparatus Assume B-field beam of spin Bose particle butadiene Calculate center of mass Chapter 13 Consider cyclotron resonance decays detector deuterons direction distance electron volts emission energy levels equal excited extra electron fermion ferromagnet figure filter which passes finding the particle frequency Hamiltonian matrix elements helium hole incident and target incident beam incoming particle intensity interference pattern magnetic field meson neutrino neutron scattering nucleus number of atoms number of photons particle enters particle has spin particle of mass passes only particles problem radiation region rotated saturation magnetization scattering scattering amplitude Schrodinger equation screen slits solid angle spacing spin 1/2 particles spin one particles spin one-half particles spin zero spins aligned splitter and restorer stationary Stern-Gerlach apparatuses Stern-Gerlach filter Suppose target neutrons uniform magnetic field unpolarized protons velocity voltage wave function wavelength x-z plane z-axis