The nuclear attractive force must turn into a repulsion at...

The nuclear attractive force must turn into a repulsion at very small distances to keep the nucleons from crowding too close together. What is the mass of an exchanged particle that will contribute to the repulsion at separations of $0.25 \mathrm{fm} ?$

Key Concepts

Yukawa Potential

The Yukawa potential is a model for describing the strong force between nucleons, which proposes that this force is mediated by the exchange of particles with mass. It shows that the force has an exponential decline with distance, with a characteristic range inversely proportional to the mass of the exchanged particle. This links the force's effective distance scale with the properties of the mediator, explaining why very short ranges require exchange of relatively heavy particles.

Compton Wavelength

The Compton wavelength of a particle, defined as ?/(mc), represents a fundamental quantum mechanical length scale associated with its mass. It is significant in determining the range of forces mediated by virtual particles. In the context of nuclear forces, the Compton wavelength indicates that heavier particles have shorter wavelengths, hence they can only contribute to interactions at very short distances.

Meson Exchange Mechanism

Meson exchange is the process in which nucleons interact by exchanging mesons, which are bosons responsible for mediating the strong force. This mechanism accounts for both the attractive and repulsive aspects of the nuclear force: lighter mesons mediate the longer-range attractive forces, while heavier mesons contribute to the short-range repulsion necessary to prevent nucleons from coming too close together.

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