The deuteron: numerical bound-state solution
A program describing the deuteron as a proton–neutron bound state with both s-wave and d-wave components, computing its properties from the wave function.
2nd place, Open Science conference 2024
- Where
- Open Science internship, Institute of Physics of the Czech Academy of Sciences
- Supervisor
- Ing. Martin Schäfer, Ph.D.
- When
- 01/2024 – 11/2024
The deuteron is the simplest nucleus. The tensor part of the nuclear force mixes the s-wave (l = 0) and the d-wave (l = 2), so the radial Schrödinger equation becomes two coupled equations.
I implemented a matrix Numerov method for coupled channels with a realistic potential (central, tensor and spin–orbit parts). The binding energy is found by matching the outward and inward solutions; the normalized wave function then gives further properties of the deuteron.
During the internship I also applied the methods to nucleon–nucleon scattering phase shifts and to quarkonium (exotic meson) spectra.
EB = −2.23 MeV (experiment −2.2246 MeV) PD ≈ 6.5 % rrms ≈ 1.92 fm Q ≈ 0.274 fm²
Key results
- Binding energy −2.23 MeV (experiment −2.2246 MeV)
- Wave function with s- and d-wave components
- D-state probability P_D ≈ 6.5 %
- RMS radius ≈ 1.92 fm (experiment 1.97 fm), quadrupole moment Q ≈ 0.274 fm² (experiment 0.286 fm²)