Gamma Decay

What actually happens

A nucleus is a quantum system with discrete energy levels, just like the electron shells of an atom but with energy gaps a million times larger. When a nucleus is left in an excited state — typically as the daughter of an alpha or beta decay, or after absorbing a neutron — it carries surplus internal energy. Gamma decay is how it gets rid of that energy: it emits a single photon whose energy equals the spacing between the starting level and the final level.

The defining feature is that nothing material leaves the nucleus. In alpha decay two protons and two neutrons depart; in beta decay a neutron converts to a proton (or vice versa) and a charged lepton is ejected. Gamma decay emits only light. So the atomic number Z and the mass number A are both untouched — the nucleus is exactly the same isotope before and after, just lower in energy. The asterisk in the notation marks the excited state:

A
 Z X*  →   A
          Z X  +  γ

This is true de-excitation, not transmutation. The energy released appears as the photon's energy plus a negligible kick to the recoiling nucleus.

Energetics and the recoil correction

If the initial nuclear level sits at energy E_i and the final level at E_f, the transition energy is ΔE = E_i − E_f. Almost all of this goes into the photon, but momentum conservation forces the nucleus to recoil, taking a tiny slice. For a nucleus of mass M, the recoil energy is:

E_recoil = E_γ² / (2 M c²)

E_γ ≈ ΔE − E_recoil  ≈  ΔE · (1 − E_γ / (2 M c²))

For a 1 MeV gamma from a mass-100 nucleus, Mc² ≈ 93,000 MeV, so E_recoil ≈ 5 eV — about five parts per million. Usually negligible, but not always: in the Mössbauer effect the nucleus is locked in a crystal lattice, the whole crystal recoils as one, M becomes astronomically large, E_recoil → 0, and the gamma is emitted with extraordinary energy precision (linewidths of nano-eV). That recoil-free emission is what makes gamma rays a precision ruler.

Decay mode	Emitted	Z change	A change	Penetration
Alpha	⁴He nucleus (2p + 2n)	−2	−4	Stopped by paper
Beta minus	electron + antineutrino	+1	0	Few mm of aluminium
Beta plus	positron + neutrino	−1	0	Few mm of aluminium
Gamma	photon (no rest mass)	0	0	cm of lead

A worked example: cobalt-60

Cobalt-60 is the textbook gamma source. It first undergoes beta-minus decay to nickel-60, but the beta almost never reaches the ground state — over 99% of decays land in an excited level of Ni-60 at 2.506 MeV. That excited nickel nucleus then cascades down through a 1.332 MeV level to the ground state, emitting two photons in quick succession:

60
27 Co  →  60
          28 Ni*  +  e⁻  +  ν̄        (β⁻, t½ = 5.27 yr)

60
28 Ni* (2.506 MeV)  →  Ni* (1.332 MeV)  +  γ₁ (1.173 MeV)
Ni* (1.332 MeV)     →  Ni  (ground)    +  γ₂ (1.332 MeV)

Those two sharp lines at 1.17 and 1.33 MeV are Co-60's fingerprint. Note the timescales differ wildly: the beta decay has a 5.27-year half-life set by the weak interaction, while the two gamma transitions happen within about a picosecond of each other. The slow step gates the fast step — Co-60 sources keep glowing with gammas for years because the bottleneck is the beta decay that keeps feeding the excited nickel.

Selection rules and multipolarity

Gamma decay is governed by electromagnetic selection rules. The photon carries away angular momentum and parity, so a transition between an initial state of spin/parity Jᵢᵖ and a final state Jꜰᵖ is only allowed for photon multipole orders L satisfying the triangle rule |Jᵢ − Jꜰ| ≤ L ≤ Jᵢ + Jꜰ, with L ≥ 1 (a photon cannot carry zero angular momentum, so 0 → 0 transitions are forbidden as single-photon emission and proceed by internal conversion instead). Each L corresponds to an electric (EL) or magnetic (ML) multipole, and the emission rate falls steeply as L rises.

This is why isomers exist. If the only allowed transition requires a large change in spin — say ΔJ = 4 — it must proceed through a high multipole order, and the rate is suppressed by many orders of magnitude. The excited state then lives far longer than the typical picosecond. Technetium-99m is exactly this: its 142 keV state would need a fast M1 transition that is hindered, so it survives for hours.

Competing channels: internal conversion and pair production

Photon emission is not the only way a nucleus sheds excitation energy.

• Internal conversion. The nucleus transfers its energy directly to an inner-shell electron through their electromagnetic coupling, ejecting that electron with kinetic energy ΔE − B (the transition energy minus the electron's binding energy). The vacancy left behind fills with X-rays or Auger electrons. The internal conversion coefficient α = N_electrons / N_gammas rises sharply with atomic number Z (roughly as Z³) and falls with transition energy, so low-energy transitions in heavy elements often emit electrons more often than photons.
• Internal pair production. If the transition energy exceeds 2mₑc² = 1.022 MeV, the nucleus can de-excite by creating an electron–positron pair directly, without a real photon. This channel is small but measurable for high-energy transitions.

For a 0⁺ → 0⁺ transition — same spin zero, same parity — single-photon emission is strictly forbidden (a photon must carry L ≥ 1), so the nucleus is forced to use internal conversion or pair production. This is why some excited states show no gamma line at all.

Why gamma rays penetrate so deeply

An alpha or beta particle is charged and loses energy continuously by ionizing every atom it passes, so it has a definite, short range. A gamma ray is neutral and massless: it travels in a straight line until it suffers one of three discrete interactions, each with a small probability per unit length. Intensity therefore falls exponentially rather than stopping at a fixed depth:

I(x) = I₀ · e^(−μ x)

half-value layer:  HVL = ln 2 / μ

The linear attenuation coefficient μ depends on photon energy and on the absorber's density and atomic number. The three competing mechanisms are the photoelectric effect (dominant below ~0.5 MeV, scales like Z⁴⁻⁵), Compton scattering (dominant 0.5–5 MeV), and pair production (above 1.022 MeV, scales like Z²). Because the photoelectric and pair channels favor high Z, shielding uses dense, heavy elements like lead and tungsten.

Gamma energy	HVL in lead	HVL in water	Dominant interaction
100 keV	~0.1 mm	~4 cm	Photoelectric
500 keV	~4 mm	~7 cm	Compton
1 MeV	~8 mm	~10 cm	Compton
5 MeV	~15 mm	~23 cm	Compton + pair
10 MeV	~13 mm	~32 cm	Pair production

JavaScript — gamma decay calculations

// Nuclear recoil energy and the corrected gamma energy
// E_recoil = E_gamma^2 / (2 M c^2);  M c^2 ~ A * 931.5 MeV (mass-energy per nucleon)
function recoilEnergy(E_gamma_MeV, A) {
  const Mc2 = A * 931.494;          // nuclear rest energy in MeV
  const E_recoil = (E_gamma_MeV * E_gamma_MeV) / (2 * Mc2); // MeV
  return E_recoil * 1e6;            // convert to eV
}

console.log(`1 MeV gamma, A=100: recoil = ${recoilEnergy(1, 100).toFixed(2)} eV`); // ~5.4 eV
console.log(`1.33 MeV (Co-60->Ni-60): recoil = ${recoilEnergy(1.332, 60).toFixed(1)} eV`); // ~15.9 eV

// Photon energy -> wavelength and frequency
function photonProperties(E_MeV) {
  const E_J = E_MeV * 1.602e-13;    // MeV -> joules
  const h = 6.626e-34, c = 2.998e8;
  return {
    frequency_Hz: E_J / h,
    wavelength_pm: (h * c / E_J) * 1e12, // picometres
  };
}

const p = photonProperties(1.0);
console.log(`1 MeV gamma: f = ${p.frequency_Hz.toExponential(2)} Hz, lambda = ${p.wavelength_pm.toFixed(2)} pm`);
// f ~ 2.4e20 Hz, lambda ~ 1.24 pm — far shorter than an atom

// Exponential attenuation: intensity after thickness x
function attenuation(I0, mu_per_cm, x_cm) {
  return I0 * Math.exp(-mu_per_cm * x_cm);
}
function halfValueLayer(mu_per_cm) {
  return Math.LN2 / mu_per_cm; // cm
}

// Lead at 1 MeV: mu ~ 0.80 /cm
console.log(`Pb @1 MeV HVL = ${(halfValueLayer(0.80) * 10).toFixed(1)} mm`); // ~8.7 mm
console.log(`Through 5 cm Pb: ${(attenuation(1, 0.80, 5) * 100).toFixed(1)}% transmitted`); // ~1.8%

// Isomeric transition: surviving fraction of Tc-99m after t hours (t_half = 6.01 h)
function survivingFraction(t_hours, halfLife = 6.01) {
  return Math.pow(0.5, t_hours / halfLife);
}
console.log(`Tc-99m after 24 h: ${(survivingFraction(24) * 100).toFixed(1)}% left`); // ~6.3%

// Branching: internal conversion coefficient alpha = N_e / N_gamma
// gamma fraction = 1 / (1 + alpha)
function gammaYield(alpha) {
  return 1 / (1 + alpha);
}
console.log(`alpha=0.11 (Tc-99m 140 keV): gammas/decay = ${gammaYield(0.11).toFixed(3)}`); // ~0.901

Where gamma decay shows up

• Medical imaging. Technetium-99m emits a clean 140 keV gamma with a 6-hour half-life — energetic enough to escape the body, soft enough for gamma cameras, short enough to limit dose. It is used in tens of millions of scans per year.
• Cancer therapy. Cobalt-60's 1.17 and 1.33 MeV gammas drive teletherapy units and the Gamma Knife, and sterilize medical equipment and food.
• Gamma-ray spectroscopy. Each isotope's characteristic line energies identify unknown materials in nuclear forensics, environmental monitoring, and planetary science (orbiters map element abundances from natural gamma lines).
• Mössbauer spectroscopy. Recoil-free gamma emission and absorption resolves nano-eV shifts, probing chemical environments, magnetism, and even gravitational redshift (the Pound–Rebka experiment).
• Astrophysics. Nuclear gamma lines — like the 1.809 MeV line of aluminium-26 — trace recent nucleosynthesis across the galaxy; the 511 keV positron-annihilation line maps antimatter.
• Industrial radiography. Iridium-192 and cobalt-60 sources inspect welds and castings where X-ray machines cannot reach.

Common mistakes

• Thinking gamma decay transmutes the element. It does not. Z and A are unchanged; only the energy level drops. Gamma decay is de-excitation, not transmutation.
• Treating gamma decay as a primary decay. Gamma emission almost always follows another decay (or excitation) that leaves the nucleus excited. The gamma is the second act, not the first.
• Ignoring competing channels. Internal conversion and internal pair production can dominate, especially for low-energy transitions in heavy nuclei and for forbidden 0 → 0 transitions. Not every excited state emits a visible gamma line.
• Assuming gamma rays have a definite range. Unlike alphas and betas, gammas attenuate exponentially. There is no thickness that stops them completely — only a thickness that reduces them to a chosen fraction.
• Confusing gamma rays with X-rays by energy alone. They overlap in energy. The distinction is origin: gamma rays come from nuclear transitions, X-rays from atomic electron transitions or bremsstrahlung.
• Forgetting the recoil. For most purposes the recoil energy is negligible, but it is what defeats ordinary resonant absorption — and eliminating it (Mössbauer effect) is precisely what unlocks ultra-high-resolution gamma spectroscopy.