NE 255/J.Vujic Department of Nuclear Engineering University of California Berkeley, California Homework Set 1 Due Sep 16, 2008 1. Suppose that the neutron number density is given by n(z,E)exp(z)/E, and suppose that the absorption cross section is a(E)1/E. (a) Specify the units for n(z,E) and a(E). (b) How many neutrons are there with energies between 1 and 2 MeV in the cube with sides of 1 cm centered at the origin? (c) What is the rate at which these neutrons are being absorbed? 2. Consider a one-dimensional, monoenergetic, time-independent neutron transport equation in purely absorbing medium: (z,)za(z)(z,)Qext(z,), z[0,H], and [1,1]. (d) Assume the vacuum boundary conditions. List all assumptions that were made in order to derive this equation, starting from the general neutron transport equation with 7 independent variables. Solve this equation analytically for angular neutron flux if Qext(z,) is isotropic plane source located at z = 0. Determine thr scalar neutron flux for z[0,H]. 3. Consider the same problem as defined in Problem 1. Assume that Qext(z,) is uniformly distributed constant isotropic source. Solve this equation for the angular and scalar neutron flux: (a) Using the result from Problem 1 and presenting the uniformly distributed source as a sum of plane sources. (b) Using any other method. 4. For the given angular neutron number density n1n(r ,E,)0(1cos) 4E r A, and A is a unit area perpendicular to the z-axis, find at r : where (a) The angular neutron flux density, (b) the energy dependent scalar flux, (c) the energy independent scalar flux, (d) the rate at which neutrons exit through the area A, (e) the rate at which neutrons enter through the area A, (f) the net current through the area A. For each quantity specify the corresponding units. 本文来源：https://www.wddqw.com/doc/22aa5d946bec0975f465e2ef.html