Z, N and A

Z counts protons and identifies the element; N counts neutrons; A = Z + N is the mass number. Move right to add neutrons and up to add protons. A is a count, not a measured atomic mass in u.

Mass excess ME

ME = (m_atom − A u)c², using a neutral atom in its ground state. It is the difference from the integer-mass reference, expressed as energy; a negative value is not a negative mass. The neutral ¹²C atom defines 12 u, so its mass excess is zero. keV and MeV differ by a factor of 1,000.

Binding energy B and B/A

The atomic-mass convention used here is B = Z ME(¹H) + N ME(n) − ME(Z,N). B/A is the average per nucleon. This combination includes the small electronic-binding differences of neutral atoms; interpreting it as a precision nuclear binding energy needs those corrections.

Mass filters

Measured/extrapolated selects the mass-quality flag; # marks a value estimated from systematics. δm < 1, 10 or 100 keV means the quoted mass standard uncertainty is below that threshold and the mass is not extrapolated. Unknown uncertainty and missing mass are separate filters. An uncertainty of zero must never be inferred from an empty field.

Other filters

Stable, known half-life, confirmed isomers, magic Z/N, odd/even A, proton-rich N < Z and N≈Z select different properties. Even/odd refers to the integer proton and neutron counts. Available Δ⁽³⁾/Δ⁽⁵⁾ requires all neighbours in the respective calculation. Low Q requires a positive β⁻ or electron-capture energy below 1 MeV. An extrapolated excitation-energy flag is independent of the ground-state mass flag.

States, half-life and spin

An isomer is a metastable nuclear state, not a different element. The searchable state list preserves source designations, higher states and excitation energies Eₓ above the ground state. Other levels and analogue states require the advanced state filter. T½ is the half-life; Jπ is spin and parity. Models here predict ground-state masses, not isomer excitation energies.

Separation energies and drip lines

Sₙ is the energy to remove one neutron; S₂ₙ removes two. Proton quantities Sₚ and S₂ₚ are analogous. Negative separation energy means that emission is energetically possible; it does not specify its lifetime. A line marks the last bound entry under the displayed table convention, not a directly measured continuous boundary. A model table edge may limit the line.

Decay Q-values

Q is the available decay energy. With neutral atomic masses, Q(β⁻) = ME(parent) − ME(daughter), Q(EC) has the same mass-difference form, and Q(α) subtracts the daughter and ⁴He mass excess. Positron emission additionally needs 2mₑc² = approximately 1.022 MeV; positive Q(EC) alone does not guarantee β⁺ emission.

Shell gaps δ₂ₙ and δ₂ₚ

δ₂ₙ(Z,N) = S₂ₙ(Z,N) − S₂ₙ(Z,N+2); use Z in place of N for the proton form. A sharp change can indicate a shell closure. Magic-number guide lines mark 2, 8, 20, 28, 50, 82 and 126; these guides are not a claim that every shell remains equally strong far from stability.

Pairing indicators Δ⁽³⁾ and Δ⁽⁵⁾

These are odd–even mass-staggering indicators, not directly measured microscopic gaps. At fixed Z, Δₙ⁽³⁾ = (−1)ᴺ[ME(N+1) − 2ME(N) + ME(N−1)]/2. The mass-excess five-point convention is Δₙ⁽⁵⁾ = −(−1)ᴺ[ME(N+2) − 4ME(N+1) + 6ME(N) − 4ME(N−1) + ME(N−2)]/8. Proton forms use Z. Missing neighbours produce missing results.

Proton–neutron indicator δVpn

For even Z and even N, δVpn = [B(Z,N) − B(Z,N−2) − B(Z−2,N) + B(Z−2,N−2)]/4. It estimates an average interaction through binding-energy differences. Odd/even combinations use different finite-difference stencils; a curve is not a direct isolated two-particle potential.

Wigner indicator W

This chart defines W(Z,N) = δVpn(Z,N) − [δVpn(Z,N+2) + δVpn(Z,N−2)]/2, at fixed Z. It compares the local value to neighbours two neutrons away and can highlight structure near N = Z. It has energy units; it is neither the number of protons nor a universal standalone measurement of Wigner energy. Its value depends on this stencil and available masses.

Mass models, residual and β₂

FRDM1992 was published in 1995; FRDM2012 in 2016. HFB-17 and HFB-D1M are distinct models. ME(AME) − ME(model) is positive when the evaluated mass excess is larger. β₂ is a dimensionless quadrupole deformation parameter: its sign distinguishes prolate/oblate within the model convention. Model error bars are unavailable here, not zero; a global RMS error is not a per-nucleus uncertainty.

Chain plots and uncertainties

An isotopic chain fixes Z; an isotonic chain fixes N; an isobaric chain fixes A. Range controls select chains and horizontal coordinates. Error bars show quoted standard uncertainties; shared occurrences of the same mass cancel before propagation. Remaining distinct masses use a diagonal covariance approximation because the full AME covariance is unavailable. A connecting line guides the eye; gaps are missing data, not zero.

Process paths, colours and saved figures

r denotes rapid neutron capture; rp denotes rapid proton capture. The orange and green paths are illustrative paths, not a reaction-network calculation for every temperature or density. EC means electron capture; β⁺ means positron decay. Adjust overlay width before PNG/PDF saving; PDF contains the same high-resolution image. CSV keeps numeric precision. Website branding is omitted from figures.

AME2020 / NUBASE2020 · δVpn · Δ⁽⁵⁾ · FRDM2012