8.2 Problems
443
8.67 Natural Cobalt is irradiated in a reactor with a thermal neutron flux density of
3 × 10
12 n cm
−2 s
−1 . How long an irradiation will be required to reach 20%
of the maximum activity? Given T 1/2 = 5.3 years
8.68 In a scattering experiment an aluminum foil of thickness 10 μm is placed in
a beam of intensity 8 × 10
12 particles per second. The differential scattering
cross-section is known to be of the form
dσ
dΩ
= A + B cos
2
θ
where A, B are constants, θ is scattering angle and Ω is the solid angle.
With a detector of area 0.01 m
2 placed at a distance of 6 m from the foil, it is
found that the mean counting rate is 50 s
−1 when θ is 30
◦ and 40 s
−1 when θ
is 60
◦ . Find the values of A and B. The mass number of aluminum is 27 and
its density is 2.7 g/cm
2 .
8.69 A thin target of
48 Ca with 1.3×10
19 nuclei per cm
2 is bombarded with a 10 nA
beam of α particles. A detector, subtending a solid angle of 2×10
−3 steradians,
records 15 protons per second. If the angular distribution is measured to be
isotropic, determine the total cross section for the
48 Ca(α, p) reaction.
[University of Cambridge, Tripos 2004]
8.2.12 Nuclear Reactions via Compound Nucleus
8.70 Cadmium has a resonance for neutrons of energy 0.178 eV and the peak value
of the total cross-section is about 7,000 b. Estimate the contribution of scattering to this resonance.
[Osmania University 1964]
8.71 A nucleus has a neutron resonance at 65 eV and no other resonances nearby.
For this resonance, Γ n = 4.2 eV, Γ γ = 1.3 eV and Γ α = 2.7 eV, and all
other partial widths are negligible. Find the cross-section for (n, γ ) and (n, α)
reactions at 70 eV.
[Osmania University]
8.72 Neutrons incident on a heavy nucleus with spin J N = 0 show a resonance at an
incident energy E R = 250 eV in the total cross-section with a peak magnitude
of 1,300 barns, the observed width of the peak being Γ = 20 eV. Find the
elastic partial width of the resonance.
[University of Bristol 1970]
8.2.13 Direct Reactions
8.73 The reaction d +
14 N → α +
12 C has been used to test the principle of detailed
balance which relates the cross-section σ ab for a reaction a + x → b + y, to
the cross-section for the inverse reaction and has the form
(2S a + 1) (2S x + 1) P a
2
σ ab = (2S b + 1) (2S y + 1) P b
2
σ ba
443
8.67 Natural Cobalt is irradiated in a reactor with a thermal neutron flux density of
3 × 10
12 n cm
−2 s
−1 . How long an irradiation will be required to reach 20%
of the maximum activity? Given T 1/2 = 5.3 years
8.68 In a scattering experiment an aluminum foil of thickness 10 μm is placed in
a beam of intensity 8 × 10
12 particles per second. The differential scattering
cross-section is known to be of the form
dσ
dΩ
= A + B cos
2
θ
where A, B are constants, θ is scattering angle and Ω is the solid angle.
With a detector of area 0.01 m
2 placed at a distance of 6 m from the foil, it is
found that the mean counting rate is 50 s
−1 when θ is 30
◦ and 40 s
−1 when θ
is 60
◦ . Find the values of A and B. The mass number of aluminum is 27 and
its density is 2.7 g/cm
2 .
8.69 A thin target of
48 Ca with 1.3×10
19 nuclei per cm
2 is bombarded with a 10 nA
beam of α particles. A detector, subtending a solid angle of 2×10
−3 steradians,
records 15 protons per second. If the angular distribution is measured to be
isotropic, determine the total cross section for the
48 Ca(α, p) reaction.
[University of Cambridge, Tripos 2004]
8.2.12 Nuclear Reactions via Compound Nucleus
8.70 Cadmium has a resonance for neutrons of energy 0.178 eV and the peak value
of the total cross-section is about 7,000 b. Estimate the contribution of scattering to this resonance.
[Osmania University 1964]
8.71 A nucleus has a neutron resonance at 65 eV and no other resonances nearby.
For this resonance, Γ n = 4.2 eV, Γ γ = 1.3 eV and Γ α = 2.7 eV, and all
other partial widths are negligible. Find the cross-section for (n, γ ) and (n, α)
reactions at 70 eV.
[Osmania University]
8.72 Neutrons incident on a heavy nucleus with spin J N = 0 show a resonance at an
incident energy E R = 250 eV in the total cross-section with a peak magnitude
of 1,300 barns, the observed width of the peak being Γ = 20 eV. Find the
elastic partial width of the resonance.
[University of Bristol 1970]
8.2.13 Direct Reactions
8.73 The reaction d +
14 N → α +
12 C has been used to test the principle of detailed
balance which relates the cross-section σ ab for a reaction a + x → b + y, to
the cross-section for the inverse reaction and has the form
(2S a + 1) (2S x + 1) P a
2
σ ab = (2S b + 1) (2S y + 1) P b
2
σ ba