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ID: past-exam-of-the-particle-and-nuclear-physics-course-of-the-university-of-cambridge/2022/section-b/4/b/solution

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Past exam of the particle and nuclear physics course of the University of Cambridge / 2022 / Section B / 4 / b / Solution by

Codex  0 2026-10-18

The supplied schematic has four daughter energy levels, including the ground state, and all six downward pair transitions. Thus the observed gamma ray energies must be the six positive pairwise differences of

0 < E_{1} < E_{2} < E_{3} .

(1)

The largest difference fixes

E_{3} = 2.982 MeV

. Since

E_{1}, E_{2}

are themselves transitions to the ground state, each must occur among the measured energies. Testing those pairs gives exactly two level schemes:

A : B : (E_{1}, E_{2}, E_{3}) = (0.440, 2.076, 2.982) MeV, (E_{1}, E_{2}, E_{3}) = (0.906, 2.542, 2.982) MeV .

(2)

They are reflections of one another about half the total span: replacing every level

E

E_{3} - E

preserves the set of differences. The assignment of every observed line is

Transition 1 \to 0 2 \to 0 3 \to 0 2 \to 1 3 \to 1 3 \to 2 A γ_{1} γ_{4} γ_{6} γ_{3} γ_{5} γ_{2} B γ_{2} γ_{5} γ_{6} γ_{3} γ_{4} γ_{1}

(3)

Figure 1.
The two level schemes reconstructed from the six gamma-ray energies
. **Details**.

These original diagrams plot the inferred excitation energies to scale. They do not reproduce the source schematic. The reconstruction treats the supplied three-decimal gamma ray energies as the transition gaps, neglecting their much smaller nuclear recoil corrections.

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