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A microscopic calculation of half-lives for both the α and 2α decays of ^212Po and ^224Ra is performed, using a self-consistent framework based on energy density functionals. A relativistic density functional and a separable pairing interaction of finite range are used to compute axially symmetric deformation energy surfaces as functions of quadrupole, octupole, and hexadecapole collective coordinates. Dynamical least-action paths are determined, that trace the α and 2α emission from the equilibrium deformation to the point of scission. The calculated half-lives for the α decay of ^212Po and ^224Ra are in good agreement with data. A new decay mode, the symmetric 2α emission, is predicted with half-lives of the order of those observed for cluster emission.

A microscopic calculation of half-lives for the recently observed 108Xe → 104Te → 100Sn α-decay chain is performed by using a self-consistent framework based on energy density functionals. The relativistic density functional DD-PC1 and a separable pairing interaction of finite range are used to compute axially symmetric deformation-energy surfaces of 104Te and 108Xe as functions of quadrupole, octupole, and hexadecupole collective coordinates. Dynamic least-action paths are determined that trace the α-particle emission from the equilibrium deformation to the point of scission. The calculated half-lives, 197 ns for 104Te and 50 μs for 108Xe, are compared with recent experimental values of the half-lives of superallowed α decay of 104Te

Modeli koji se koriste za opis većine prirodnih pojava imaju velik broj slobodnih parametara čije vrijednosti određujemo prilagodbom teorijskih predviđanja modela empirijskim podacima. U jednostavnim modelima, promjena bilo kojeg parametra znatno utječe na kvalitetu prilagodbe predviđanja empirijskim podacima, no također postoje modeli koji sadrže i aljkavo odredive parametre. To su određeni parametri i/ili kombinacije parametara koje se mogu značajno promijeniti uz minimalnu promjenu kvalitete prilagodbe. Nedavno je razvijena aproksimacijska metoda mnogostrukosti s rubom (MBAM) kojom je moguće eliminirati što veći broj aljkavih stupnjeva slobode modela, uz minimalan gubitak na preciznosti same prilagodbe. Problem MBAM metode jest u tome što zahtijeva izračun numeričkih derivacija modela. U ovome smo diplomskom radu razvili računalnu implementaciju MBAM metode poboljšane tehnikama algoritamske diferencijacije kako bi uklonili numeričke greške nastale zbog numeričke diferencijacije. Računalnu implementaciju smo testirali na širokom rasponu modela zadanih ili kao analitički izrazi ili rješenja sustava diferencijalnih jednadžbi. U konačnici provjerili smo postoji li razlika prilikom korištenja preciznijih derivacija u MBAM redukciji na modelu atomske jezgre zasnovanom na nuklearnom energijskom funkcionalu gustoće DD-PC1. Models used in describing most physical phenomena have a large number of free parameters, usually estimated by fitting theoretical predictions to empirical data. In simple models, changes in any model parameter would produce a visible change in the quality of fit. More complex models also have degrees of freedom, called sloppy parameters, that can be significantly altered without disrupting the quality of the fit. A novel method, called the manifold boundary approximation method (MBAM), has been shown to be able to remove sloppy parameters without affecting the quality of model predictions. However, the MBAM method requires a large number of numerical derivatives, raising the question of numerical errors. In this diploma thesis, we have developed codes that improve the MBAM method using algorithmic differentiation instead of numerical approximations. We have tested this implementation on a wide variety of models, from simple analytical expressions to complex systems of differential equations. Finally, we have tested whether using algorithmic differentiation impacts results of the MBAM method applied to the model of the atomic nucleus based on the nuclear energy density functional DD-PC1.

18 pags., 7 figs., 2 tabs., The neutron skin of nuclei is an important fundamental property, but its accurate measurement faces many challenges. Inspired by charge symmetry of nuclear forces, the neutron skin of a neutron-rich nucleus is related to the difference between the charge radii of the corresponding mirror nuclei. We investigate this relation within the framework of the Hartree-Fock-Bogoliubov method with Skyrme interactions. Predictions for proton skins are also made for several mirror pairs in the middle mass range. For the first time the correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated simultaneously for nuclei and their corresponding mirror partners. As an example, the Ni isotopic chain with mass number A=48−60 is considered. These quantities are calculated within the coherent density fluctuation model using Brueckner and Skyrme energy-density functionals for isospin asymmetric nuclear matter with two Skyrme-type effective interactions, SkM* and SLy4. Results are also presented for the symmetry energy as a function of A for a family of mirror pairs from selected chains of nuclei with Z=20, N=14, and N=50. The evolution curves show a similar behavior crossing at the N=Z nucleus in each chain and a smooth growing deviation when N≠Z starts. Comparison of our results for the radii and skins with those from the calculations based on high-precision chiral forces is made., M.K.G., A.N.A., and D.N.K. are grateful for the support of the Bulgarian National Science Fund under Contract No. KP-06-N38/1. P.S. acknowledges support from Ministerio de Ciencia, Innovación y Universidades MCIU/AEI/FEDER, UE (Spain) under Contract No. PGC2018-093636-B-I00

We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials., Comment: 24 LaTeX pages, 9 figures, 4 tables, and supplemental material, version accepted for publication in Journal of Physics G

We have performed calculations based on the Skyrme energy density functional (EDF) that includes arbitrary mixing between protons and neutrons. In this framework, single-particle states are generalized as mixtures of proton and neutron components. The model assumes that the Skyrme EDF is invariant under the rotation in isospin space and the Coulomb force is the only source of the isospin symmetry breaking. To control the isospin of the system, we employ the isocranking method, which is analogous to the standard cranking approach used for describing high-spin states. Here, we present results of the isocranking calculations performed for the isobaric analog states in A = 40 and A = 54 nuclei.

We have performed calculations based on the Skyrme energy density functional (EDF) that includes arbitrary mixing between protons and neutrons. In this framework, single-particle states are generalized as mixtures of proton and neutron components. The model assumes that the Skyrme EDF is invariant under the rotation in isospin space and the Coulomb force is the only source of the isospin symmetry breaking. To control the isospin of the system, we employ the isocranking method, which is analogous to the standard cranking approach used for describing high-spin states. Here, we present results of the isocranking calculations performed for the isobaric analog states in $A = 40$ and $A = 54$ nuclei., Comment: 6 pages, 7 figures, talk given at the 2nd Conference on "Advances in Radioactive Isotope Science 2014" (ARIS 2014), Tokyo, Japan, Jun. 1-6, 2014

In Landau theory of Fermi liquids, the particle-hole interaction near the Fermi energy in different spin-isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to constrain properties of nuclear energy density functionals in symmetric nuclear matter and finite nuclei. In this study, we present general expressions for Landau parameters corresponding to a two-body central local regularized pseudopotential. We also show results obtained for two recently adjusted NLO and N$^2$LO parametrizations. Such pseudopotentials will be used to determine mean-field and beyond-mean-field properties of paired nuclei across the entire nuclear chart., Comment: 12 pages, 4 figures, 1 table

We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one more, or one less neutron or proton. Theoretically, bare SPEs, before being confronted with experiment, must be corrected for the effects of the particle-vibration-coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this way, the agreement with experiment, on average, improves; nevertheless, large discrepancies still remain. We conclude that the main source of disagreement is still in the underlying mean fields, and not in including or neglecting the PVC corrections., 5 pages, 5 figures, extended supplemental material

A microscopic theoretical framework based on relativistic energy density functionals (REDFs) is applied to studies of shape evolution, excitation spectra, and decay properties of transactinide nuclei. Axially symmetric and triaxial relativistic Hartree-Bogoliubov (RHB) calculations, based on the functional DD-PC1 and with a separable pairing interaction, are performed for the even-even isotopic chains between Fm and Fl. The occurrence of a deformed shell gap at neutron number $N=162$ and its role on the stability of nuclei in the region around $Z=108$ is investigated. A quadrupole collective Hamiltonian, with parameters determined by self-consistent constrained triaxial RHB calculations, is used to examine low-energy spectra of No, Rf, Sg, Hs, and Ds with neutron number in the interval $158\ensuremath{\le}N\ensuremath{\le}170$. In particular, we analyze the isotopic dependence of several observables that characterize the transitions between axially symmetric rotors, $\ensuremath{\gamma}$-soft rotors, and spherical vibrators. An interesting example of a possible occurrence of shape-phase transitions and critical-point phenomena in this mass region is explored.

The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of -stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.

This article provides an insight into several open problems in the quest for novel modes of excitation in nuclei with isospin asymmetry, deformation and finite temperature characteristic in stellar environment. Major unsolved problems include the nature of pygmy dipole resonances, the quest for various multipole and spin-isospin excitations both in neutron-rich and proton drip-line nuclei mainly driven by loosely bound nucleons, excitations in unstable deformed nuclei and evolution of their properties with the shape phase transition. Exotic modes of excitation in nuclei at finite temperatures characteristic for supernova evolution present open problems with possible impact in modeling astrophysically relevant weak interaction rates. All these issues challenge self-consistent many body theory frameworks at the frontiers of on-going research, including nuclear energy density functionals, both phenomenological and constrained by the strong interaction physics of QCD, models based on low-momentum two-nucleon interaction V_{low-k} and correlated realistic nucleon-nucleon interaction V_{UCOM}, supplemented by three-body force, as well as two-nucleon and three-nucleon interactions derived from the chiral effective field theory. Joined theoretical and experimental efforts, including research with radioactive isotope beams, are needed to provide insight into dynamical properties of nuclei away from the valley of stability, involving the interplay of isospin asymmetry, deformation and finite temperature., 14 pages, submitted to the Journal of Physics G special issue on Open Problems in Nuclear Structure (OPeNST)

The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of -stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino- nucleus cross sections.