Abstract
The application of relativistic energy density functionals to the description of nuclei leads to the problem of solving self-consistently a coupled set of equations of motion to determine the nucleon wave functions and meson fields. In this work the Lagrange-mesh method in spherical coordinates is proposed for the numerical calculation. The essential field equations are derived from the relativistic energy density functional and the basic principles of the Lagrange-mesh method are delineated for this particular application. The numerical accuracy is studied for the case of a deformed relativistic harmonic oscillator potential with axial symmetry. Then the method is applied to determine the point matter distributions and deformation parameters of self-conjugate even-even nuclei from 4He to 40Ca.
Highlights
The theoretical description of nuclei with the help of energy density functionals (EDFs) has advanced steadily during the last decades
The motion of a fermion in a deformed harmonic oscillator potential is considered to study the numerical accuracy of solving the Dirac equation with the Lagrange-mesh method in spherical coordinates
The relativistic harmonic oscillator was often considered in the connection with pseudo-spin symmetry in different versions [44,45,46,47]
Summary
The theoretical description of nuclei with the help of energy density functionals (EDFs) has advanced steadily during the last decades. Instead of diagonalizing large matrices, imaginary time-step methods have been exploited with great success to obtain wave functions from non-relativistic EDFs; see, e.g., Davies et al [26], Reinhard and Cusson [27], and Ryssens et al [28]. Another method is based on Fourier transformation techniques [29]. The Lagrange-mesh method is applied to find solutions of the Dirac equation with non-spherical potentials that appear in the description of deformed but axially symmetric nuclei.
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