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The processes mediated by the weak interaction have significant implications in nuclear physics, astrophysics, and particle physics. In particular, the electron capture (EC) plays a prominent role in driving the dynamics of core-collapse supernovae, while the β-decay determines the time scale of the nuclear r-process. Both processes are influenced by the underlying nuclear structure through the spin-isospin excitations and the associated resonances. The main aim of this work is to establish a theoretical framework for obtaining the spin-isospin transition strength at finite temperature and its extension to the description of stellar electron capture and β-decay. The nuclear ground state at finite temperature is determined by solving either the relativistic Hartree-Bogoliubov (FT-RHB) or Hartree Baarden-Cooper-Schrieffer (FT-HBCS) equations, while the relativistic quasiparticle random-phase approximation (FT-pnRQRPA) in the charge-exchange channel is developed to determine the excited states. The new theoretical approach combines the effects of nuclear pairing, finite temperature, and deformation. The limits of nuclear stability (drip lines) for hot nuclei are studied within the FT-RHB supplemented with the subtraction of continuum. Investigated spin-isospin excitations include the Fermi and Gamow-Teller (GT) transitions. While the Fermi transitions display one resonance peak independent of temperature and deformation, the GT transition strength has a much richer structure, more sensitive to the temperature and deformation effects. When considering the spherically symmetric nuclei, the GT strength separates into a low-lying, and a resonance region, as exemplified for even-even tin isotopes. However, the deformation effects lead to a substantial fragmentation of the GT transition strength, as demonstrated for selected pf-shell nuclei, exhibiting a crucial role of the nuclear shape. Results are presented for the EC rates of nuclei near the N = 50 shell closure, with subsequent implications for the supernovae simulations. The large-scale β-decay rate calculations are shown for even-even nuclei in the range 8 ≤ Z ≤ 82, displaying how the β-decay half-lives change with temperature and stellar density. Our study highlights the complex interplay between temperature, nuclear pairing, and deformation effects with subsequent implications for weak-interaction rates and their implementation in astrophysical models. Rad ne sadrži sažetak na drugom jeziku.

We have analyzed milimeter-wave spectra of the hot cores G327.3-0.6 and NGC 6334 I, which were taken by the SHeFI instrument at the APEX telescope in Chile. Rotational and population diagrams were used to derive the gas kinetic temperatures and column densities of the detected molecules in the sources. We have identified the following molecular species in the observed hot cores: acetone, carbonyl sulfide, dimethyl ether, ethanol, ethyl cyanide, formic acid, ketene, methanol, methyl acetylene, methylamine, methyl cyanide, methyl formate, sulfur dioxide, and vinyl cyanide along with some of their isotopologues. Analizirali smo spektre vrućih jezgri G327.3-0.6 i NGC 6334 I u milimetarskom području koje su bile opažane pomoću SHeFI instrumenta na APEX teleskopu u Čileu. Rotacijski i populacijski dijagrami su korišteni pri odredivanju kinetičkih temperatura plina i stupčanih gustoća detektiranih molekula u izvorima. Identificirali smo sljedeće molekularne vrste u promatranim vrućim jezgrama: aceton, karbonil sulfid, dimetil eter, etanol, etil cijanid, mravlju kiselinu, keten, metanol, metil acetilen, metilamin, metil cijanid, metil format, sumporov dioskid, vinil cijanid kao i neke od njihovih izotopologa.