Relativistic Hartree-Fock Calculations of Deformed Nuclei in the S-D Shell
A systematic structure study of deformed nuclei in the s-d shell is performed in the relativistic quantum field framework; the model Lagrangian couples the nucleon to four mesons (sigma,omega,rho and pi) and the photon. The coupling constants of these mesons are known, except for the sigma and omega which are determined by applying the same model to the empirical nuclear matter saturation data; in this sense there is no free parameter in the calculation. The calculations are carried out in the intrinsic frame and the deformation is solely determined by the self-consistency of the solutions. The states in the deformed nuclei are expanded in a spherical basis, which is the set of Hartree solutions of the same nuclei constrained to be spherical; both the positive and negative energy wavefunction are included in the expansion. The final results are confirmed by a convergence test. By performing the variational procedure, the relativistic Hartree-Fock equation is obtained and solved; both the even-even and odd-A deformed nuclei are tackled. By using a non-spectral approach, the non-local problem of the exchange terms was avoided; this was also an advantage for deformed nuclei calculation, since otherwise one had to solve coupled differential equations. Our calculations show that for even-even deformed nuclei, going from Hartree to Hartree-Fock the total bindings are improved about 10%, however no appreciable deformation improvement is observed for Hartree-Fock calculation; also we find the deformation pattern in the s-d shell cannot be reproduced in a non -linear model (without self-couplings for sigma field). For odd-A nuclei we find magnetic moment values are worsened when the exchange terms are included. Extensions of the work to take into account the tensor coupling of the rho meson and the meson exchange current contribution in the current operator, are discussed and suggested for further investigations.
- Pub Date:
- HARTREE FOCK;
- Physics: Nuclear