Gamma Emission, Isomers and Internal Conversion

Introduction

Alpha and beta decay change the identity of a nucleus, but they very often leave the daughter in an excited state. The nucleus then sheds its surplus energy without changing Z or A. Usually it emits a gamma photon; sometimes it hands the energy to one of its own atomic electrons instead. A few excited states live long enough to be separated and used — the most famous being technetium-99m, which is injected into tens of millions of patients each year for diagnostic imaging.

Core explanation

Discrete nuclear levels. Like atoms, nuclei have quantised energy levels, but the spacings are thousands to millions of times larger: typically tens of keV to several MeV. A transition between two levels releases a photon of energy E γ ≈ E upper − E lower. Because the levels are sharp, gamma spectra consist of sharp lines that act as fingerprints of the emitting nuclide — cobalt-60, for example, is recognised by its lines at 1.17 and 1.33 MeV.

Gamma emission changes nothing but energy. The notation is ᴬX → ᴬX + γ. Mass number and atomic number are unchanged; only the nuclear energy (and a tiny amount of recoil) is involved.

Selection rules and multipolarity. A photon carries away angular momentum, at least 1ħ. Transitions are classified as electric (E) or magnetic (M) with multipole order L: E1, M1, E2, M2, E3 and so on. The lowest allowed L dominates. Transition rates fall steeply as L increases and as the energy decreases. An E1 transition of 1 MeV may occur in about 10⁻¹⁵ s, whereas a low-energy E3 or M4 transition can take minutes, hours or even years.

Nuclear isomers. When a state can only decay by a low-energy, high-multipolarity transition — typically because it has a very different spin from the levels below it (a "spin trap") — it becomes metastable. Such isomers are marked m: ⁹⁹ᵐTc (half-life 6.01 h), ¹³⁷ᵐBa (2.55 min). The shell model of the previous pages explains why isomers cluster just below magic numbers, where high-spin and low-spin orbitals lie close together.

Internal conversion (IC). Instead of emitting a photon, the nucleus can transfer the transition energy directly to an atomic electron, usually from the K or L shell, through the electromagnetic interaction. The ejected electron has a sharp energy:

E e = E transition − E binding (of that shell)

The vacancy it leaves is then filled, producing characteristic X-rays and Auger electrons. IC competes with gamma emission and is favoured for low transition energies, high multipolarity and heavy atoms (large Z, where inner electrons overlap strongly with the nucleus). Transitions between two spin-0 states (E0) cannot emit a single photon at all; they proceed by IC or, above 1.022 MeV, by pair emission.

Formulae

E γ ≈ E i − E f; recoil energy E R = E γ²/(2Mc²); conversion-electron energy E e = E γ − E B; total decay constant λ = λ γ(1 + α), where α = Nₑ/N γ is the internal conversion coefficient.

Step-by-step reasoning

To predict how an excited level de-excites:

1. Identify the spins and parities of the initial and final states. 2. Find the lowest allowed multipole order L and whether it is E or M. 3. Judge the rate: low L and high energy give prompt emission; high L and low energy give an isomer. 4. Consider Z and energy: a heavy nucleus and a low energy favour internal conversion. 5. Expect X-rays and Auger electrons whenever conversion occurs.

Visual explanation

Draw a nuclear level diagram: horizontal lines labelled with energy and spin. Arrows downward represent gamma transitions; a wavy side-arrow from one arrow to a K-shell electron represents internal conversion. The isomeric level sits as a thick line with a long half-life written beside it, and the only exit arrow from it is short and marked with a high multipolarity.

Real-world analogy

A nuclear isomer is like a ball resting on a ledge part-way down a staircase. It is higher than the floor, but the only way down is a narrow, awkward gap. It stays put for a long time, not because it lacks energy, but because the route down is hard to take.

Real-world example

Technetium-99m emits a 140.5 keV gamma ray and has a 6.01 h half-life. The photon energy penetrates tissue yet is easily collimated and detected by gamma cameras; the half-life is long enough for preparation and imaging but short enough to limit dose; and the decay emits no alpha or high-energy beta particles. Its ground state, ⁹⁹Tc (half-life about 2.1 × 10⁵ years), contributes almost no activity.

Why?

Why does a larger angular-momentum change slow a transition so dramatically? The photon must carry away that angular momentum, and a wave with wavelength much larger than the nucleus couples very weakly to high multipoles. Each extra unit of L reduces the rate by a factor of roughly (kR)², where kR is often about 10⁻³ to 10⁻², so rates fall by factors of 10⁴ to 10⁶ per step.

Common misconception

"Internal conversion is a photoelectric effect: the nucleus emits a gamma ray which then knocks out an electron." This is wrong. No real photon is produced; the energy is transferred directly. The evidence is that E0 transitions, which forbid single-photon emission, still convert.

Worked example

Question: ¹³⁷ᵐBa de-excites by a 661.7 keV transition. The K-shell binding energy of barium is 37.4 keV. Calculate the energy of the K-conversion electrons and state what else is emitted.

Reasoning: E e = E transition − E K = 661.7 − 37.4 = 624.3 keV. The K vacancy is filled by an outer electron, emitting barium K X-rays (about 32 keV) or Auger electrons.

Answer: About 624 keV; barium X-rays and Auger electrons also appear.

Quick check

1. Why does a sample of technetium-99m still contain technetium atoms after its gamma emission, rather than a different element? Answer: Gamma emission changes only the nuclear energy state; Z and A are unchanged, so ⁹⁹ᵐTc simply becomes ground-state ⁹⁹Tc.

Exam focus

Be ready to write equations for isomeric transitions, to calculate conversion-electron energies from binding energies, and to explain which factors (low energy, high multipolarity, high Z) favour internal conversion over gamma emission. Always state that A and Z are unchanged.

Advanced insight

Gamma photon energies are not exactly E i − E f because the nucleus recoils with energy E γ²/(2Mc²), about 0.1 eV for ⁹⁹ᵐTc. Since natural linewidths are often far smaller, emitted photons cannot be reabsorbed by an identical free nucleus. Rudolf Mössbauer showed that nuclei bound in a crystal can emit and absorb recoil-free; the 14.4 keV line of iron-57 underpins Mössbauer spectroscopy, which probes oxidation and spin states of iron in minerals and proteins.

Summary

Excited nuclei de-excite by gamma emission or internal conversion, leaving Z and A unchanged. Transition rates depend strongly on energy and multipolarity; spin traps produce metastable isomers such as ⁹⁹ᵐTc and ¹³⁷ᵐBa. Internal conversion ejects an atomic electron with energy E transition − E binding, followed by X-rays and Auger electrons, and is favoured at low energy, high multipolarity and high Z.

Practice questions

1. Write the equation for the isomeric transition of technetium-99m. Answer: ⁹⁹ᵐTc → ⁹⁹Tc + γ (140.5 keV); A = 99 and Z = 43 are unchanged. 2. The L-shell binding energy of barium is about 6 keV. Estimate the L-conversion electron energy for the 661.7 keV transition in ¹³⁷ᵐBa. Answer: About 661.7 − 6 ≈ 656 keV. 3. Give two conditions that make internal conversion more likely than gamma emission. Answer: Any two of: low transition energy, high multipolarity, high atomic number, or an E0 (0 → 0) transition. 4. Explain why ¹³⁷Cs is identified by a 662 keV gamma line even though caesium-137 itself is a beta emitter. Answer: Most ¹³⁷Cs beta decays populate ¹³⁷ᵐBa, whose 661.7 keV isomeric transition produces the gamma line that is measured. 5. Why is an isomer usually found where levels of very different spin lie close in energy? Answer: The only available transition then needs a large angular-momentum change at low energy, which is extremely slow, so the state becomes long-lived.