Stabilitätslinie

Stabilitätslinie, literally "line of stability," is a term used in several scientific disciplines to denote a boundary or locus in parameter space along which a system remains or becomes energetically favorable or dynamically stable. Its precise meaning depends on context.

In nuclear physics, the stabilitätslinie appears on a chart of nuclides with neutron number N on one axis and proton number Z on the other. It marks beta stability: nuclides on or near the line do not undergo beta decay, while those with fewer or more neutrons tend to decay toward it. The line defines the valley of stability, and heavy nuclei deviate due to changing binding energy and shell effects. Boundaries known as the neutron and proton drip lines lie beyond the stability line and mark the limits of bound nuclides.

In dynamical systems and control theory, the stabilitätslinie can refer to the stability boundary in parameter or state space that separates regions of stable from unstable behavior. As a parameter varies, crossing the line may correspond to a bifurcation or loss of stability of an equilibrium, determined by conditions on eigenvalues or Lyapunov functions.

In thermodynamics and materials science, the term is sometimes used to describe the boundary in phase diagrams that separates thermodynamically stable from unstable or metastable phases, under given temperature, pressure, and composition.

The term is primarily used in German-language literature; English uses lines of stability or stability boundaries. Each field defines the line according to its governing equations and experimentally observed stability criteria.