Relativistic mean field and some recent applications
- PDF / 632,979 Bytes
- 46 Pages / 612 x 792 pts (letter) Page_size
- 96 Downloads / 219 Views
elativistic Mean Field and Some Recent Applications¶ Y. K. Gambhir and A. Bhagwat Department of Physics, I.I.T. Powai, Bombay 400076, India; e-mail: [email protected] Abstract—The essentials of the Relativistic Mean Field (RMF) theory and some of its recent applications are presented. The explicit calculations are carried out for a few selected isotopic, isotonic and isobaric chains of nuclei covering the entire periodic table. The calculated ground state properties are found to be in good agreement with the corresponding experiment: the binding energies are reproduced within 0.25%, on average, and the charge radii differ only in the second decimal place of fermi. The relativistic origin of the pseudo-spin symmetry is briefly discussed. The density distributions obtained, are found to be in good agreement with the experiment (where available). The peripheral factor, the ratio of neutron and proton densities on the nuclear periphery, extracted in the anti-proton annihilation experiments are well reproduced. The RMF densities are used to calculate the reaction (σR) and charge changing (σcc) cross sections in the Glauber model, as well as the α (cluster)-daughter interaction energy. The latter is then employed to estimate the decay half lives of Super-Heavy (trans-actinide) nuclei in the WKB approximation. The calculations are found to agree well with the experiment. This success of the RMF in accurately describing the nuclear properties with only a few fixed parameters is indeed remarkable. PACS numbers: 24.10.Jv; 21.60.Cs DOI: 10.1134/S106377960602002X
1. INTRODUCTION The formulation and application of the Relativistic Mean Field (RMF) theory has had the most striking development in the field of nuclear structure. The RMF [1–8] has been established to be one of the most successful and adequate theories for the description of nuclear structure properties. The RMF still works at the level of nucleons and mesons. It starts with Lagrangian density, describing the Dirac spinor nucleons interacting via the meson and photon fields. The classic Euler– Lagrange variation principle yields the equations of motion. At this stage, the mean field approximation is introduced, i.e., the fields are not quantized, but rather their expectation values or c-numbers are replaced. This then leads to the Dirac equation, with potential terms describing nucleon dynamics and the Klein–Gordon type equations, involving nucleonic currents and densities as source terms for mesons and the photon. This set of coupled, nonlinear differential equations, known as the Relativistic Mean Field (RMF) equations, is required to be solved self-consistently. The vacuum polarization effects are not included (no sea approximation) and the Fock exchange terms are ignored. The parameters of the effective Lagrangian of this relativistic Hartree RMF theory are fitted and are expected to
¶ The
text was submitted by the authors in English.
include vacuum polarization phenomenologically and the exchange contributions. The pairing correlations are important for the
Data Loading...
