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Register a new userProton radioactivity described by covariant density functional theory with Similarity Renormalization Group method
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Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confirms the validity of the CDF theory in describing the proton-rich nuclei, but also indicates the prediction power of present approach to calculate the half-lives and in turn to extract the structural information of proton emitters.
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The neutron and proton drip lines represent the limits of the nuclear landscape. While the proton drip line is measured experimentally up to rather high $Z$-values, the location of the neutron drip line for absolute majority of elements is based on theoretical predictions which involve extreme extrapolations. The first ever systematic investigation of the location of the proton and neutron drip lines in the covariant density functional theory has been performed by employing a set of the state-of-the-art parametrizations. Calculated theoretical uncertainties in the position of two-neutron drip line are compared with those obtained in non-relativistic DFT calculations. Shell effects drastically affect the shape of two-neutron drip line. In particular, model uncertainties in the definition of two-neutron drip line at $Zsim 54, N=126$ and $Zsim 82, N=184$ are very small due to the impact of spherical shell closures at N=126 and 184.
Modern applications of Covariant Density Functional Theory (CDFT) are discussed. First we show a systematic investigation of fission barriers in actinide nuclei within constraint relativistic mean field theory allowing for triaxial deformations. In the second part we discuss a microscopic theory of quantum phase transitions (QPT) based on the relativistic generator coordinate method.
We investigate the role of the pion in Covariant Density Functional Theory. Starting from conventional Relativistic Mean Field (RMF) theory with a non-linear coupling of the $sigma$-meson and without exchange terms we add pions with a pseudo-vector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the non-central contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.
In contrast to the non-relativistic approaches, three-dimensional (3D) mesh calculations for the {it relativistic} density functional theory have not been realized because of the challenges of variational collapse and fermion doubling. We overcome these difficulties by developing a novel method based on the ideas of Wilson fermion as well as the variational principle for the inverse Hamiltonian. We demonstrate the applicability of this method by applying it to $^{16}$O, $^{24}$Mg, and $^{28}$Si nuclei, providing detailed explanation on the formalism and verification of numerical implementation.
The similarity renormalization group is used to transform a general Dirac Hamiltonian into diagonal form. The diagonal Dirac operator consists of the nonrelativistic term, the spin-orbit term, the dynamical term, and the relativistic modification of kinetic energy, which are very useful to explore the symmetries hidden in the Dirac Hamiltonian for any deformed system. As an example, the relativistic symmetries in an axially deformed nucleus are investigated by comparing the contributions of every term to the single particle energies and their correlations with the deformation. The result shows that the deformation considerably influences the spin-orbit interaction and dynamical effect, which play a critical role in the relativistic symmetries and its breaking.
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