Deuteron structure and form factors: Using an inverse potential approach
Anil Khachi, Lalit Kumar, M. R. Ganesh Kumar, O. S. K. S. Sastri
Abstract
Background: The ground-state wave function of deuteron is required to obtain its structure and form factors. Currently, an accurate analytical expression for the wave function is not available.Purpose: In this paper, we determine the deuteron's static properties, low-energy scattering parameters, and form factors using an analytical ground-state wave function.Methods: An inverse $S$-wave potential is constructed using the Morse function as the zeroth reference potential. The scattering phase shifts (SPSs) at different laboratory energies are determined using phase function method. The model parameters are optimized using least-squares minimization by both global optimization and combinatorial data analysis techniques.Results: The mean absolute error between experimental and obtained SPSs for the state $^{3}S_{1}$, using global optimization, is found to be 0.35. The low-energy scattering parameters match well with the expected values. The analytical ground-state deuteron wave function (DWF) is obtained by utilizing the experimental value for the quadrupole moment. Other static properties and form factors determined from the obtained DWF are found to be in close agreement with experimental ones.Conclusions: Modeling $np$ interaction using the Morse potential has been reasonably successful in explaining all static and low-energy parameters as well as SPSs for laboratory energies up to 350 MeV. The obtained electromagnetic form factors using an analytical deuteron ground-state wave function are found to closely match with experimental data.