A beam of neutrons (mass m) traveling with nonrelativistic speed v impinges on the system shown in Fig. 1.7, with beam-s

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A Beam Of Neutrons Mass M Traveling With Nonrelativistic Speed V Impinges On The System Shown In Fig 1 7 With Beam S 1 (68.47 KiB) Viewed 32 times

A beam of neutrons (mass m) traveling with nonrelativistic speed v impinges on the system shown in Fig. 1.7, with beam-splitting mirrors at corners B and D, mirrors at A and C, and a neutron detector at E. The corners all make right angles, and neither the mirrors nor the beam-splitters affect the neutron spin. The beams separated at Brejoin coherently at D. and the detector E reports the neutron intensity I. Atomic and Molecular Physics 33 E H incident neutrons B 7777 Region of magnetic field Fig. 1.7 (a) In this part of the problem, assume the system to be in a vertical plane so gravity points down parallel to AB and DC). Given that detector intensity was to with the system in a horizontal plane, derive an expression for the intensity I, for the vertical configuration. (b) For this part of the problem, suppose the system lies in a horizontal plane. A uniform magnetic field, pointing out of the plate, acts in the dotted region indicated which encompasses a portion of the leg BC. The incident neutrons are polarized with spin pointing along BA as shown. The neutrons which pass through the magnetic field region will have their spins pressed by an amount depending on the field strength. Suppose the spin expectation value presses through an angle 8 as shown. Let (6) be the intensity at the detector E. Derive I@) as a function of 6. given that I(0 =0) = 1.