Kisslinger Potential

Kisslinger Potential

The Kisslinger potential is a specific type of optical model potential used in nuclear physics to describe the interaction between a nucleon (such as a proton or neutron) and a target nucleus. It was introduced by Leonard S. Kisslinger in 1955, and incorporates important effects such as non-locality and spin-orbit coupling into the potential used to model nuclear scattering.

Overview

In nuclear scattering processes, the optical model represents the average interaction between the incoming particle and the nucleus. The Kisslinger potential refines this by introducing a non-local, energy-dependent, and spin-dependent term that improves agreement with experimental scattering data, particularly for intermediate energies (10–100 MeV).

Unlike simple local potentials, the Kisslinger form includes terms that depend on both the position and momentum of the particle, leading to a more accurate description of elastic and inelastic nucleon-nucleus scattering.

Mathematical Form

The Kisslinger potential is typically expressed as a non-local operator:

$V(\overrightarrow{r},{\overrightarrow{r}}^{\prime })=[V(r)+iW(r)]\delta (\overrightarrow{r}-{\overrightarrow{r}}^{\prime })+V_{\text{so}}(r,r^{\prime })(\overrightarrow{\sigma }\cdot \overrightarrow{L})$

Where:

• $V(r)$ is the real part of the potential.
• $W(r)$ is the imaginary (absorptive) part.
• $\overrightarrow{\sigma }$ is the Pauli spin vector.
• $\overrightarrow{L}$ is the orbital angular momentum operator.
• $\overrightarrow{\sigma }\cdot \overrightarrow{L}$ represents the spin-orbit coupling.
• The potential is non-local, meaning it depends on $\overrightarrow{r}$ and ${\overrightarrow{r}}^{\prime }$ independently.

Significance

The inclusion of non-local and spin-orbit terms in the Kisslinger potential allows for a better reproduction of angular distributions and differential cross-sections in nucleon scattering experiments. It also laid the foundation for more sophisticated optical potentials that are now standard in nuclear structure and reaction theory.

Applications

The Kisslinger potential is used in:

• Elastic and inelastic nucleon-nucleus scattering calculations.
• Analysis of nuclear reaction data.
• Extraction of nuclear densities and form factors.
• Studies of nuclear structure using scattering observables.

Legacy and Modern Use

While more modern global optical potentials such as the Koning–Delaroche potential have become widely used, the Kisslinger potential remains important historically and theoretically. It is often cited in the development of non-local optical models and remains a pedagogical example in theoretical nuclear physics.

References

• Kisslinger, L. S. (1955). "Theory of the Optical Model in Nuclear Scattering". Physical Review. 98 (3): 761–767. doi:10.1103/PhysRev.98.761

See also

• Optical model
• Nuclear scattering
• Spin–orbit interaction
• Nuclear potential

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