Flytandedropmodellen

Flytandedropmodellen, or the liquid drop model, is a macroscopic approach to describing the atomic nucleus. It treats the nucleus as a drop of incompressible nuclear fluid with a surface that contributes to the total energy. The model emphasizes bulk properties and provides a simple framework for understanding nuclear binding and stability, without relying on detailed microscopic structure.

In its most common form, the binding energy B of a nucleus with mass number A and atomic number Z is approximated by the semi-empirical mass formula: B(A,Z) = a_v A − a_s A^(2/3) − a_c Z(Z−1)/A^(1/3) − a_a (N−Z)^2/A + δ(A). Here N = A − Z; a_v is the volume term, a_s the surface term, a_c the Coulomb term, a_a the asymmetry term, and δ(A) the pairing term (positive for even-even nuclei, negative for odd-odd, zero for odd A). The terms reflect, respectively, bulk binding, surface effects, electrostatic repulsion among protons, neutron–proton asymmetry, and pairing correlations between nucleons.

Historically, the model was developed in the 1930s as a macroscopic description of nuclear binding, culminating in the Bethe–Weizsäcker mass formula. It provides a baseline for understanding trends in binding energy and fission behavior, explaining why very heavy nuclei are unstable against splitting and why nuclei with certain numbers of protons and neutrons are more stable.

Limitations include the neglect of microscopic shell effects and deformation, which are important for precise predictions. Extensions, such as the finite-range droplet model and include shell corrections, improve accuracy and link the macroscopic picture to microscopic nuclear structure.