Neutron Physics Background

Abstract

This chapter introduces fundamental properties of the neutron. It covers reactions induced by neutrons, nuclear fission, slowing down of neutrons in infinite media, diffusion theory, the few-group approximation, point kinetics, and fission product poisoning. It emphasizes the nuclear physics bases of reactor design and its relationship to reactor engineering problems.

Problems

• Problem 1.1 If atomic mass unit is designated by u, where 1 u is exactly one-twelfth of the mass of the ¹²C atom, equal to 1.661 × 10⁻²⁷ kg, then calculate the energy equivalent to a conventional mass equal to 1 u.

• Problem 1.2 Calculate the energy as Problem 1.1 using MeV as units.

• Problem 1.3  

  • (a) Calculate the mass defect and the binding energy for a nucleus of an isotope of tin ¹²⁰Sn (atomic mass M = 119.9022 u) and for an isotope of uranium ²³⁵U (atomic mass M = 235.0439). Assume the measured mass of the atom is M; the mass defect ΔM is given by

    $$ \Delta M=Z\cdot \left({m}_{\mathrm{p}}+{m}_{\mathrm{e}}\right)+\left(A-Z\right)\cdot {m}_{\mathrm{n}}-M $$

    • $Z\cdot {m}_{\mathrm{p}}$ = total mass of proton

    • $Z\cdot {m}_{\mathrm{e}}$ = total mass of electron

    • $\left(A-Z\right)\cdot {m}_{\mathrm{n}}$ = total mass of neutrons

  • (b) Assume the total binding energy for uranium is approximately the same as tin; what would be the total energy that will be released after fission of a single U²³⁵ nucleus?

• Problem 1.4 Calculate the mass defect for lithium-7. The mass of lithium-7 is 7.016003 amu. Assuming that:

  • m _p = mass of a proton (1.007277 amu)

  • m _n = mass of neutron (1.008665 amu)

  • m _e = mass of an electron (0.000548597 amu)

• Problem 1.5 Consider that 1 amu is equivalent to 931.5 MeV of energy; the binding energy can be calculated using the following relationship:

  $$ \mathrm{Binding}\ \mathrm{e}\mathrm{nergy} = \Delta m\left(\frac{931.5\;\mathrm{M}\mathrm{e}\mathrm{V}}{1\;\mathrm{amu}}\right) $$

  Then calculate the mass defect and binding energy for uranium235. One uranium235 atom has a mass of 235.043924 amu.

• Problem 1.6 Calculate the decay constant, mean life, and half-life of a radioactive isotope which radioactivity after 100 days is reduced 1.07 times.

• Problem 1.7 A block of aluminum has a density of 2.699 g/cm³. If the gram atomic weight of aluminum is 26.9815 g, then calculate the atom density of aluminum.

• Problem 1.8 Since the activity and the number of atom are always proportional, they may be used interchangeably to describe any given radionuclide population. Therefore, the following is true.

  $$ A={A}_0{\mathrm{e}}^{-\lambda t} $$

  where

  • A = activity present at time t

  • A ₀ = activity initially present

  • λ = decay constant (time⁻¹)

  • t = time

  Assuming a sample of material contains 20 μg of californium-252 and this element has a half-life of 2.638 years; then calculate:

  • (a) The number of californium-252 atoms initially present

  • (b) The activity of californium-252 in curies, assuming the relationship between the activity, number of atoms, and decay constant is shown in $A=\lambda N$, where A is the activity of nuclide (disintegrations/s), λ-decay constant of the nuclide (1/s), and finally N the number of atoms of the nuclide in the sample

  • (c) The number of californium-252 atoms that will remain in 12 years

  • (d) The time it will take for the activity to reach 0.001 curies

• Problem 1.9 Plot the radioactive decay curve for nitrogen-16 over a period of 100 s. The initial activity is 142 curies and the half-life of nitrogen-16 is 7.13 s. Plot the curve on both linear rectangular coordinates and a semilog scale.

• Problem 1.10 Find the macroscopic thermal neutron absorption cross section for iron, which has a density of 7.86 g/cm. The microscopic cross section for absorption of iron is 2.56 barns, and the gram atomic weight is 55.847 g.

• Problem 1.11 An alloy is composed of 95 % aluminum and 5 % silicon (by weight). The density of the alloy is 2.66 g/cm. Properties of aluminum and silicon are shown below.

  Element	Gram atomic weight	σ a(barns)	σ s(barns)
  Aluminum	26.9815	0.23	1.49
  Silicon	28.0855	0.16	2.20

  • 1. Calculate the atom densities for the aluminum and silicon.

  • 2. Determine the absorption and scattering macroscopic cross sections for thermal neutrons.

  • 3. Calculate the mean free paths for absorption and scattering.

• Problem 1.12 What is the value of σ _f for uranium-235 for thermal neutrons at 500 °F? Uranium-235 has σ _f of 583 barns at 68 °F.

• Problem 1.13 If a one cubic centimeter section of a reactor has a macroscopic fission cross section of 0.1 cm⁻¹, and if the thermal neutron flux is 10¹³ neutrons/cm² s, what is the fission rate in that cubic centimeter?

• Problem 1.14 A reactor operating at a flux level of 3 × 10¹³ neutrons/cm² s contains 10²⁰ atoms of uranium-235 per cm³. The reaction rate is 1.29 × 10¹² fission/cm³. Calculate Σ _f and σ _f.

• Problem 1.15 The microscopic cross section for the capture of thermal neutrons by hydrogen is 0.33 barn and for oxygen 2 × 10⁻⁴ barn. Calculate the macroscopic capture cross section of the water molecule for thermal neutrons.

• Problem 1.16 Calculate the minimum energy that a neutron with energy 1 MeV can be reduced to after collision with:

  • (a) Nucleus of hydrogen

  • (b) Nucleus of carbon