ydinfunktio

Ydinfunktio is a term used in Finnish-language physics literature to refer to a function that describes properties of the atomic nucleus within quantum-mechanical models. In many contexts it denotes the nuclear wavefunction of a nucleon inside a nucleus, or its radial component, depending on the modelling approach.

In a common spherically symmetric setting, the nuclear wavefunction is written as a product of a radial part and angular part: psi_nlm(r, theta, phi) = R_nl(r) times Y_lm(theta, phi), where Y_lm are spherical harmonics and R_nl is the radial function. The radial function satisfies the radial Schrödinger equation with an effective potential that includes a central potential and, in many cases, a spin-orbit term. Boundary conditions require R_nl to behave like r^l near the origin and to decay at large r. The ydinfunktio is normalized so that the total probability over all space equals one.

In nuclear structure theory, ydinfunktio describes single-particle states within models such as the nuclear shell model or self-consistent mean-field theories. Potentials commonly used include the Woods-Saxon form or, for simple cases, harmonic oscillator potentials. Solutions yield energy levels and single-particle properties, which are then combined with many-body techniques to describe the full nucleus.

Computationally, ydinfunktio is obtained by numerical methods such as the shooting method, finite-difference discretization, or basis-set expansions, with attention to normalization and orthogonality. Applications include predicting binding energies, transition probabilities, and reaction cross sections; however, many-body correlations often require beyond-single-particle descriptions, limiting the accuracy of simple ydinfunktio models.