Threshold conditions used:
- Nucleus field: Eth = 2 me c² + \u005B(2 me c²)²\u005D / (2 M c²) = 2 me + 2 me² / M.
- Electron field (triplet): Eth = 4 me c².
Constants:
me c² = 0.51099895 MeV 1 u = 931.494102 MeV 1 MeV = 1.602e-13 J h = 6.626070e-34 J·s c = 299,792,458 m/sEnter inputs and compute to see results. For a quick check: Electron field gives about 2.044 MeV. For a proton target (A≈1), threshold is ~1.0226 MeV.
- For heavy nuclei, the recoil term 2 me2/M is very small; Eth ≈ 1.022 MeV.
- Triplet production requires ~2.044 MeV, independent of any A or M you enter.
- Mass number A is an integer; you can override with a precise custom M if needed.
The minimum photon energy required to create an electron–positron pair while conserving energy and momentum with a target that absorbs recoil.
That is 2 me c². A small extra term from nuclear recoil adds only a tiny amount, usually less than a keV for heavy nuclei.
Pair production in the field of an electron: γ + e⁻ → e⁻ + e⁻ + e⁺ with a threshold of 4 me c² ≈ 2.044 MeV.
Threshold depends primarily on target mass M. Cross sections scale strongly with Z, but the threshold energy is effectively constant aside from tiny recoil corrections.
me c² = 0.51099895 MeV, 1 u = 931.49410242 MeV, 1 MeV = 1.602176634×10⁻¹³ J, h and c are CODATA exact values.
They are precise for threshold kinematics. Effects like binding, screening, or nuclear excitation are negligible at threshold and are not included here.