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67, 3332 (1991) and J. N. , Phys. Rev Lett. 83, 4686 (1999)). In 1992, the GALLEX experiment, using a Gallium target in the Gran Sasso, also confirmed the solar neutrino deficit (P. , Phys. Lett. B285, 376 (1992)). R. , Phys. Rev. Lett. B. Smy, Mod. Phys. Lett. A 17, 2163 (2002)). The 2002 Nobel prize for physics was awarded to Raymond Davis Jr. and Masatoshi Koshiba, who are the pioneers of this chapter of neutrino physics. ). The atomic nucleus has a spin sn (sn = 3/2 for 87 Rb, sn = 7/2 for 133 Cs), which carries a magnetic moment µn .
Consider a neutron whose motion in space is x = vt, y = 0, z = 0. ˆ What is the Hamiltonian H(t) describing the coupling of the neutron magnetic moment with the fields B 0 and B 1 ? 48 4 Spectroscopic Measurement on a Neutron Beam Setting ω0 = −γB0 and ω1 = −γB1 , write the matrix representation of ˆ H(t) in the basis {|+ , |− }. 2. Treating B 1 as a perturbation, calculate, in first order time-dependent perturbation theory, the probability of finding the neutron in the state |+ at time t = +∞ (far from the interaction zone) if it was in the state |− at t = −∞.
5, the position of the central peak depends directly on the velocity. A dispersion in v will lead to a corresponding dispersion of the position of the peak we want to measure. The first method is highly preferable. A, v = h/(Mn λn ) 128 m/s. 7. 6 × 10−7 . 4 m. Actually, one can improve the accuracy considerably by analysing the shape of the peak. e. an angular frequency 20 times smaller than above). L. F. Ramsey, W. M. F. D. D. Miller, and P. Perrin, Phys. Rev. D 20, 2139 (1979). 5 Analysis of a Stern–Gerlach Experiment We analyze a Stern–Gerlach experiment, both experimentally and from the theoretical point of view.