Understanding Yukawa Potential  with LAMMPS

In 1932, while the Japanese physicist Hideki Yukawa was studying James Chadwick's atomic model, he noticed that physicists found it difficult to explain the outcomes of that model. The model states that positively charged protons and neutrons are packed inside a nucleus within a radius of 10^-14 meters. As electromagnetic forces impact the nucleus, they cause protons to repel each other; as a result, the nucleus could lose its existence. He took his initial inspiration from this constraint.

Later on, Heisenberg proposed a theory that elaborates on the "Platzwechsel" (migration) force between the neutrons and protons inside the nucleus, in which neutrons were made of composite particles. These were basically protons and electrons. In 1934, Fermi came up with an idea that was an improvised version of Heisenberg's. Fermi suggested that neutron and proton interaction was not based on the "migration" of neutrons and protons, but instead on the emission and absorption of two light particles. These were the neutrino and the electron. Yukawa's key idea was how the mass of the exchanged particle determines the range of the force. Basically, Yukawa's innovation was the combination of Heisenberg’s short-range interaction force concept and Fermi’s beta decay theory. With this, Yukawa also successfully predicted the meson particle, as its mass was in the middle of the proton and electron. For this, Hideki Yukawa was awarded the 1949 Nobel Prize in Physics. From that occasion, the Yukawa potential was named after Hideki Yukawa. This is also known as the screened Coulomb potential. 

The Yukawa potential system has various applications, such as complex plasma physics, colloidal suspensions, charged nanoparticles in solution, nuclear physics, and astrophysics. The renowned open-source molecular dynamics software LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) uses the Yukawa potential to simulate plasmas, colloids, and nanoparticle systems. In LAMMPS, there is a built-in pair interaction called pair_style yukawa. This style is part of the COLLOID package. This helps the investigator to study at the nano-scale in atomic style. Below, a sample Yukawa system simulation is performed in a 3D periodic box by implementing Newtonian dynamics. The script investigates how potential energy converts into kinetic energy. LJ units were used here. 

Written by:

• Mahmud Hasin Azwad

• 3rd Year 2nd Semester, Mechanical Engineering (Projjolon - 24th Batch)

• Ahsanullah University of Science and Technology (AUST)

References

• Yukawa, H. (1935). "On the interaction of elementary particles". Proc. Phys.-Math. Soc. Jpn. 17: 48. https://doi.org/10.1143/PTPS.1.1

• Miller, Arthur I. (1985). "Werner Heisenberg and the beginning of nuclear physics". Physics Today. 38 (11): 60–68. Bibcode:1985PhT....38k..60M. doi: 10.1063/1.880993

• Brown, Laurie M. (1986). "Hideki Yukawa and the meson theory". Physics Today. 39 (12): 55–62. Bibcode:1986PhT....39l..55B. doi: 10.1063/1.881048

• Müller, H.J.W.; Schilcher, K. (February 1968). "High-energy scattering for Yukawa potentials". Journal of Mathematical Physics. 9 (2): 255–259. doi: 10.1063/1.1664576.