The collision frequency in the tunnelling model for the α decay of thorium.

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Chapter 7, Problem 17P

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The collision frequency in the tunnelling model for the α decay of thorium.

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PROBLEM 2: Consider neutrons slowing down by elastic scattering from 1.0 MeV to 0.025 eV in large spatially homogeneous regions. (a) Estimate the number of scattering events required for these neutrons to slow down in large regions of hydrogen (A = 1), iron (A = 56), and uranium (A = 238). (b) Suppose that in each neutron-nucleus collision, the probability that a neutron is captured is 0.001 (independent of energy). Estimate the probability that these neutrons in regions 238) will not be captured while of hydrogen (A 1), iron (A 56), and uranium (A slowing down from 1.0 MeV to 0.025 e V. Note: In practice, the probability that a neutron with energy E will be captured depends on E. This makes realistic calculations of the non-capture probability considerably more difficult.

A plot of neutron cross section versus energy for an even even nucleus shows resonance at energy 200 eV in the total cross-section with a peak cross-section of 1400 b. The width of the peak is 20 eV. Determine the partial width for scattering at this resonance.

Calculate the transmission probability of an particle of energy E= 5.0 MeV through a Coulomb barrier of a heavy nucleus that is approximated by a square barrier with V0 = 15 MeV and barrier width L = 1.3 x 10-14 m. Also, calculate the probability (a) by doubling the potential barrier height and (b) by using the original barrier height but doubling the barrier width. Compare all three probabilities.