Semi-empirical mass formula

In nuclear physics, the semi-empirical mass formula (SEMF; sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons.

Version

v1 · 2026-09-28 · History

Domain-specific #

11961

Domain group

Natural Sciences

Origin domain

Physics

Subdomains

Nuclear Physics, Liquid Drop Model → Physics

Core Idea

Semi-empirical mass formula is treated here as the recurring natural science, engineering, and health identity summarized by this source-grounded definition: In nuclear physics, the semi-empirical mass formula (SEMF; sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. In nuclear physics, the semi-empirical mass formula (SEMF; sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the.

Scope of Application

• Formula. ) shown as a function of the neutron number N and atomic number Z as given by the semi-empirical mass formula.

• Asymmetry term. For example, in the shell model, a proton and a neutron with overlapping wavefunctions will have a greater strong interaction between them and stronger binding energy.

• Asymmetry term. It should be dependent on the absolute difference |N - Z| , and the form (N - Z)^2 is simple and differentiable, which is important for certain applications of the formula.

• Pairing term. The pairs have overlapping wave functions and sit very close together with a bond stronger than any other configuration.

• The dependence on mass number is commonly parametrized . The Fermi-ball calculation we have used above, based on the liquid-drop model but neglecting interactions, will give an A^{-1} dependence, as in the asymmetry term.

Clarity

A clear use of Semi-empirical mass formula names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In nuclear physics, the semi-empirical mass formula (SEMF; sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from.

Manages Complexity

Semi-empirical mass formula compresses multiple natural science, engineering, and health details into a stable diagnostic relation. The source shows both the central mechanism—it treats the nucleus as a drop of incompressible fluid of very high density, held together by the nuclear force (a residual effect of the strong force): there is a similarity to the structure of a spherical liquid drop.—and the practical consequence—the value of.

Abstract Reasoning

1. Type the carrier. Identify the natural science, engineering, and health entities to which the claim applies.
2. State the relation. Use the source-grounded identity: In nuclear physics, the semi-empirical mass formula (SEMF; sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons. 3.

Knowledge Transfer

Within the home domain. Knowledge about Semi-empirical mass formula transfers literally when a new case preserves the same carrier type, relation, and recognition test. ) shown as a function of the neutron number N and atomic number Z as given by the semi-empirical mass formula. For example, in the shell model, a proton and a neutron with overlapping wavefunctions will have a greater strong interaction between them and stronger binding energy. Beyond the home domain. No canonical parent is asserted for Semi-empirical mass formula.

Neighborhood in Abstraction Space

Semi-empirical mass formula sits in a moderately populated region (59^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Physical Quantities, Operators & Formulas (33 abstractions)

Nearest neighbors

• Hydrostatic equilibrium — 0.86
• Antiparticle — 0.86
• Stokes's law — 0.85
• Rutherford model — 0.85
• Bethe–Feynman formula — 0.85

Computed from structural-signature embeddings · 2026-10-08