Nuclear Binding Energy Calculator mechanism

Model scope

The energy relation E_b=Δm c² is standard, but the mass convention is not. The instrument should explicitly branch between nuclear-mass input, using Z m_p+N m_n−M_nucleus, and atomic-mass input, using Z m_H+N m_n−M_atom. Because the current specification claims to accept atomic masses while prescribing only the nuclear-mass formula, it fails verification. The honest label should disclose the atomic-versus-nuclear mass convention, the isotope-table source/version, and the neglected electron-binding-energy correction.

• The stated mass-defect formula Δm=Z m_p+N m_n−M_nucleus is correct only when M_nucleus is a nuclear mass excluding electrons. The inputs explicitly allow measured atomic masses and isotope-table presets, which normally are atomic masses including Z electrons.
• For an atomic mass M_atom, the standard formula is Δm=Z m_H+N m_n−M_atom, where m_H is the neutral hydrogen-atom mass; equivalently, electron masses and electron binding-energy corrections must be handled explicitly.
• The specification does not state the formula for binding energy per nucleon; it should be BE/A, with A=Z+N.
• The specification does not define the mass unit or the exact isotope-table mass convention, so numerical results are ambiguous.

Units and conventions

• Test vectors use atomic masses in unified atomic mass units (u), with m_H=1.00782503223 u, m_n=1.00866491595 u, and 1 u c²=931.49410242 MeV.
• Atomic masses include the electrons associated with the Z protons; the corrected atomic-mass formula therefore uses neutral hydrogen-atom mass m_H rather than bare proton mass m_p.
• A=Z+N is dimensionless, mass defect is reported in u, total binding energy in MeV, and binding energy per nucleon in MeV/nucleon.
• Electron binding energies are neglected, as is standard for nuclear binding-energy calculations at this precision.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "Z": 1,
    "N": 0,
    "A": 1,
    "mass_type": "atomic",
    "measured_atomic_mass_u": 1.00782503223
  },
  "expected_outputs": {
    "mass_defect_u": 0,
    "binding_energy_MeV": 0,
    "binding_energy_per_nucleon_MeV": 0
  },
  "working": "Use Δm=Z m_H+N m_n−M_atom. Δm=(1)(1.00782503223)+(0)(1.00866491595)−1.00782503223=0 u. BE=0×931.49410242=0 MeV. BE/A=0/1=0 MeV/nucleon. This is the zero-binding edge case."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes a division-by-zero case at A=Z+N=0 and does not clearly define whether the supplied measured mass is atomic or nuclear. Applying the stated nuclear-mass formula directly to an atomic mass produces materially incorrect binding energies.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json