Droppemodellen

Droppemodellen, known in English as the liquid drop model, is a macroscopic approach in nuclear physics that describes the atomic nucleus as a drop of incompressible nuclear fluid with surface tension and electric charge. It captures the bulk properties of nuclei, such as general trends in binding energy and stability, without invoking detailed quantum shell structure.

The binding energy is commonly expressed by a semi-empirical mass formula: B ≈ a_v A - a_s A^(2/3) - a_c Z(Z-1) A^(-1/3) - a_a (N−Z)^2 / A + δ(A,Z). Here A is the mass number, Z the proton number, and N = A−Z. The terms correspond to volume energy (a_v), surface energy (a_s), Coulomb repulsion (a_c), asymmetry energy (a_a), and pairing energy δ. The pairing term depends on whether the nucleus is even-even, odd-odd, or odd-A.

History and development: The model emerged in the 1930s with work by Carl von Weizsäcker and colleagues and was developed into the broader liquid drop picture used to describe nuclear masses and fission properties. It formed the macroscopic component of later macroscopic-microscopic models.

Applications and limitations: The model explains broad features such as the general scale of binding energies and why heavy nuclei tend to fission. It neglects quantum shell effects and detailed deformation, so accurate predictions require adding microscopic corrections in macroscopic-microscopic approaches.

Variants: Finite-range liquid drop models (FRLDM) introduce finite-range surface effects, and modern macroscopic-microscopic models combine the droplet terms with shell corrections to produce precise masses and fission barriers.