Relativistic Energy Density Research Articles

Elucidate the non-relativistic and relativistic energy density functional from momentum space to coordinate space within local density approximation

Elucidate the non-relativistic and relativistic energy density functional from momentum space to coordinate space within local density approximation

Relativistic energy density functional from momentum space to coordinate space within a coherent density fluctuation model

In this theoretical study, we have derived a simplified analytical expression for the binding energy per nucleon as a function of density and isospin asymmetry within the relativistic mean-field model. We have generated a new parameterization for the density-dependent DD-ME2 parameter set using the Relativistic-Hartree-Bogoliubov approach. Moreover, this work attempts to revisit the prior polynomial fitting in Kumar A. et al. Phys. Rev. C, 103 (2021) 024305 for the non-linear NL3 force parameter to provide a simplified set of equations for the energy density functional which is used for calculating the surface properties of finite nuclei. The current study improves the existing fitting procedure by effectively proposing a simpler model that provides comparably precise results while lowering the computational expense. To study the surface properties of finite nuclei with these parameterizations, we have adopted the coherent density fluctuation model, which effectively translates the quantities of nuclear matter from momentum space to coordinate space at local density. The isospin properties, such as symmetry energy and its surface and volume components, slope parameter, finite nuclear incompressibility, and surface incompressibility for even-even nuclei, are calculated for different mass regions. Moreover, we have studied the effect of density, weight function, and choice of relativistic force parameters on the surface properties. The significance of this work will help to determine the properties of nuclei along the nuclear landscape and can facilitate an improved understanding of the island of stability, heavy-ion collision, and nucleosynthesis, among others.

Dark radiation from the primordial thermal bath in momentum space

Motivated by the stunning projections for future CMB surveys, we evaluate the amount of dark radiation produced in the early Universe by two-body decays or binary scatterings with thermal bath particles via a rigorous analysis in momentum space. We track the evolution of the dark radiation phase space distribution, and we use the asymptotic solution to evaluate the amount of additional relativistic energy density parameterized in terms of an effective number of additional neutrino species ΔN eff. Our approach allows for studying light particles that never reach equilibrium across cosmic history, and to scrutinize the physics of the decoupling when they thermalize instead. We incorporate quantum statistical effects for all the particles involved in the production processes, and we account for the energy exchanged between the visible and invisible sectors. Non-instantaneous decoupling is responsible for spectral distortions in the final distributions, and we quantify how they translate into the corresponding value for ΔN eff. Finally, we undertake a comprehensive comparison between our exact results and approximated methods commonly employed in the existing literature. Remarkably, we find that the difference can be larger than the experimental sensitivity of future observations, justifying the need for a rigorous analysis in momentum space.

Persistence of the N=50 shell closure over the isotopic chains of Sc, Ti, V and Cr nuclei using relativistic energy density functional

The analytical expression of the density-dependent binding energy per nucleon for the relativistic mean field (RMF), the so-called relativistic energy density functional (Relativistic-EDF), is used to obtain the isospin-dependent symmetry energy and its components for the isotopic chain of Sc-, Ti-, V- and Cr-nuclei. The procedure of the coherent density fluctuation model is employed to formulate the Relativistic-EDF and Brüeckner energy density functional (Brüeckner-EDF) at local density. A few signatures of shell and/or sub-shell closure are observed in the symmetry energy and its components, i.e. surface and volume symmetry energy, far from the [Formula: see text]-stable region for odd-[Formula: see text] Sc- and V-, and even–even Ti- and Cr- nuclei with nonlinear NL3 and G3 parameter sets. A comparison is made with the results obtained from Relativistic-EDF and Brüeckner-EDF with both NL3 and G3 for the considered isotopic chains. We find Relativistic-EDF outperforms the Brüeckner-EDF in predicting the shell and/or sub-shell closure of neutron-rich isotopes at [Formula: see text] for these atomic nuclei. Moreover, a relative comparison has been made for the results obtained with the nonlinear NL3 and G3 parameter sets.

Expanding the limits of nuclear stability at finite temperature

Properties of nuclei in hot stellar environments such as supernovae or neutron star mergers are largely unexplored. Since it is poorly understood how many protons and neutrons can be bound together in hot nuclei, we investigate the limits of nuclear existence (drip lines) at finite temperature. Here, we present mapping of nuclear drip lines at temperatures up to around 20 billion kelvins using the relativistic energy density functional theory (REDF), including treatment of thermal scattering of nucleons in the continuum. With extensive computational effort, the drip lines are determined using several REDFs with different underlying interactions, demonstrating considerable alterations of the neutron drip line with temperature increase, especially near the magic numbers. At temperatures T ≲ 12 billion kelvins, the interplay between the properties of nuclear effective interaction, pairing, and temperature effects determines the nuclear binding. At higher temperatures, we find a surprizing result that the total number of bound nuclei increases with temperature due to thermal shell quenching. Our findings provide insight into nuclear landscape for hot nuclei, revealing that the nuclear drip lines should be viewed as limits that change dynamically with temperature.

The optimized point-coupling interaction for the relativistic energy density functional of Hartree-Bogoliubov approach quantifying the nuclear bulk properties

We propose a newly optimized nonlinear point-coupling parameterized interaction, PC-L3R, for the relativistic Hartree-Bogoliubov framework with a further optimized separable pairing force by fitting to observables, i.e., the binding energies of 91 spherical nuclei, charge radii of 63 nuclei, and 12 sets of mean pairing gaps consisting of 54 nuclei in total. The separable pairing force strengths of proton and neutron are optimized together with the point-coupling constants, and are justified in satisfactory reproducing the empirical pairing gaps. The comparison of experimental binding energies compiled in AME2020 for 91 nuclei with the ones generated from the present and other commonly used point-coupling interactions indicates that the implementation of PC-L3R in relativistic Hartree-Bogoliubov yields the lowest root-mean-square deviation. The charge radii satisfactory agree with experiment. Meanwhile, PC-L3R is capable of estimating the saturation properties of the symmetric nuclear matter and of appropriately predicting the isospin and mass dependence of binding energy. The experimental odd-even staggering of single nucleon separation energies is well reproduced. The comparison of the estimated binding energies for 7,373 nuclei based on the PC-L3R and other point-coupling interactions is also presented.

Magnetic quadrupole transitions in the relativistic energy density functional theory

Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. Since it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited, it is interesting to study the properties of M2 transitions using the framework of relativistic nuclear energy density functional. In this work the nuclear ground state is calculated with relativistic Hartree-Bogoliubov model, while the M2 excitations are described using the relativistic quasiparticle random phase approximation with the residual interaction extended with the isovector-pseudovector term. The M2 transition strength distributions are described and analyzed for closed shell nuclei $$^{16}$$ O, $$^{48}$$ Ca, $$^{208}$$ Pb, open-shell $$^{18} \mathrm O$$ , $$^{42}$$ Ca, $$^{56}$$ Fe, and semi-magic $$^{90}$$ Zr. The evolution of M2 transition properties has been investigated within the $$^{36-64} \mathrm Ca$$ isotope chain. The main M2 transitions have rather rich underlying structure and detailed analysis shows that collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the reduction of M2 strength and shifts of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the g factors in nuclear medium.

Microscopic description of α, 2α , and cluster decays of Rn216−220 and Ra220−224

$\ensuremath{\alpha}$ and cluster decays are analyzed for heavy nuclei located above $^{208}\mathrm{Pb}$ on the chart of nuclides: $^{216--220}\mathrm{Rn}$ and $^{220--224}\mathrm{Ra}$, which are also candidates for observing the $2\ensuremath{\alpha}$ decay mode. A microscopic theoretical approach based on relativistic energy density functionals (EDF), is used to compute axially symmetric deformation-energy surfaces as functions of quadrupole, octupole, and hexadecupole collective coordinates. Dynamical least-action paths for specific decay modes are calculated on the corresponding potential-energy surfaces. The effective collective inertia is determined using the perturbative cranking approximation, and zero-point and rotational energy corrections are included in the model. The predicted half-lives for $\ensuremath{\alpha}$ decay are within one order of magnitude of the experimental values. In the case of single-$\ensuremath{\alpha}$ emission, the nuclei considered in the present study exhibit least-action paths that differ significantly up to the scission point. The differences in $\ensuremath{\alpha}$-decay lifetimes are not only driven by $Q$ values, but also by variances of the least-action paths prior to scission. In contrast, the $2\ensuremath{\alpha}$ decay mode presents very similar paths from equilibrium to scission, and the differences in lifetimes are mainly driven by the corresponding $Q$ values. The predicted $^{14}\mathrm{C}$ cluster decay half-lives are within three orders of magnitudes of the empirical values, and point to a much more complex pattern compared with the $\ensuremath{\alpha}$-decay mode.

Stability of the manifold boundary approximation method for reductions of nuclear structure models

The framework of nuclear energy density functionals has been employed to describe nuclear structure phenomena for a wide range of nuclei. Recently, statistical properties of a given nuclear model, such as parameter confidence intervals and correlations, have received much attention, particularly when one tries to fit complex models. We apply information-theoretic methods to investigate stability of model reductions by the manifold boundary approximation method (MBAM). In an illustrative example of the density-dependent point-coupling model of the relativistic energy density functional, utilizing Monte Carlo simulations, it is found that main conclusions obtained from the MBAM procedure are stable under variation of the model parameters. Furthermore, we find that the end of the geodesic occurs when the determinant of the Fisher information metric vanishes, thus effectively separating the parameter space into two disconnected regions.

Optimization of the generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double- β decay: Ridge regression for nuclei with axial deformation

Background: The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. Recently, it has attracted increasing interest as it can be exploited to extend ab initio methods to the collective excitations of medium-mass and heavy deformed nuclei, as well as the nuclear matrix elements (NME) of candidates for neutrinoless double-beta ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) decay.Purpose: The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. We aim to exploit statistical machine-learning (ML) algorithms to speed up GCM calculations and ultimately provide a more efficient description of nuclear energy spectra and other observables such as the NME of $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay without loss of accuracy.Method: In this work, we propose a subspace-reduction algorithm that employs optimal statistical ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay based on the orthogonality condition (OC) and the energy-transition-orthogonality procedure (ENTROP), respectively. Nuclear energy spectra are determined by the GCM through the configuration mixing within this subspace. For simplicity, the polynomial ridge regression (RR) algorithm is used to learn the norm and Hamiltonian kernels of axially deformed configurations. The efficiency and accuracy of this algorithm are illustrated for $^{76}\mathrm{Ge}$ and $^{76}\mathrm{Se}$ by comparing results obtained using the optimal RR models to direct GCM calculations. The nonrelativistic Gogny force D1S and relativistic energy density functional PC-PK1, a valence-space shell-model Hamiltonian, and a modern nuclear interaction derived from chiral effective field theory are employed.Results: The low-lying energy spectra of $^{76}\mathrm{Ge}$ and $^{76}\mathrm{Se}$, as well as the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay NME between their ground states, are computed. The results show that the performance of the $\mathrm{GCM}+\text{OC/ENTROP}+\mathrm{RR}$ is more robust than that of the $\mathrm{GCM}+\mathrm{RR}$ alone, and the former can reproduce the results of the original GCM calculation accurately with a significantly reduced computational cost.Conclusions: Statistical ML algorithms, when implemented properly, can accelerate GCM calculations without loss of accuracy. In applications with axially deformed states, the computation time can be reduced by a factor of three to nine for energy spectra and NMEs, respectively. This factor is expected to increase significantly with the number of employed generator coordinates.

Collective-model description of shape coexistence and intruder states in cadmium isotopes based on a relativistic energy density functional

Low-energy structure of even-even $^{108-116}$Cd isotopes is analyzed using a collective model that is based on the nuclear density functional theory. Spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with parameters determined by the constrained self-consistent mean-field calculations within the relativistic Hartree-Bogoliubov method employing a universal energy density functional and a pairing force. The collective Hamiltonian reproduces the observed quadrupole phonon states of vibrational character, which are based on the moderately deformed equilibrium minimum in the mean-field potential energy surface. In addition, the calculation yields a low-lying excited $0^+$ band and a $\gamma$-vibrational band that are associated with a deformed local minimum close in energy to the ground state, consistently with the empirical interpretation of these bands as intruder bands. Observed energy spectra, $B(E2)$, and $\rho^2(E0)$ values are, in general, reproduced reasonably well.

Isotopic Shift in Hg-Isotopes within Brückner versus Relativistic Energy Density Functional

The present study is focused on revealing a characteristic kink of the neutron shell closure N = 126 across the Hg-isotopic chain within the relativistic mean-field (RMF) approach with the IOPB-I, DD-ME2, DD-PC1 and NL3 parameter sets. The RMF densities are converted to their spherical equivalence via the Wood–Saxon approximation and used as input within the parametrization procedure of the coherent density fluctuation model (CDFM). The nuclear matter symmetry energy is calculated using the Brückner energy density functional, and its surface, as well as volume components, are evaluated within Danielwicz’s liquid drop prescription. In addition, a comparison between Brückner and relativistic energy density functionals using the NL3 parameter set is shown as a representative case. The binding energy, charge distribution radius and symmetry energy are used as indicators of the isotopic shift in both ground and isomeric states. We have found the presence of a kink at the shell/sub-shell closure at N = 126 for neutron-rich 206Hg. The formation of the kink is traceable to the early filling of the 1i11/2 orbitals rather than 2g9/2, due to the large spin-orbit splitting. As such, the link between the occupational probability and the magicity of nuclei over the Hg-isotopic chain is established.

Probing physics beyond the standard model: limits from BBN and the CMB independently and combined

We present new Big Bang Nucleosynthesis (BBN) limits on the cosmic expansion rate or relativistic energy density, quantified via the number Nν of equivalent neutrino species. We use the latest light element observations, neutron mean lifetime, and update our evaluation for the nuclear rates d + d ⟶ 3He + n and d + d ⟶ 3H+ p. Combining this result with the independent constraints from the cosmic microwave background (CMB) yields tight limits on new physics that perturbs Nν and η prior to cosmic nucleosynthesis: a joint BBN+CMB analysis gives Nν = 2.898 ± 0.141, resulting in Nν < 3.180 at 2σ. We apply these limits to a wide variety of new physics scenarios including right-handed neutrinos, dark radiation, and a stochastic gravitational wave background. The strength of the independent BBN and CMB constraints now opens a new window: we can search for limits on potential changes in Nν and/or the baryon-to-photon ratio η between the two epochs. The present data place strong constraints on the allowed changes in Nν between BBN and CMB decoupling; for example, we find -0.708 < Nν CMB - Nν BBN < 0.328 in the case where η and the primordial helium mass fraction Yp are unchanged between the two epochs; we also give limits on the allowed variations in η or in (η, Nν ) jointly. We discuss scenarios in which such changes could occur, and show that BBN+CMB results combine to place important constraints on some early dark energy models to explain the H0 tension. Looking to the future, we forecast the tightened precision for Nν arising from both CMB Stage 4 measurements as well as improvements in astronomical 4He measurements. We find that CMB-S4 combined with present BBN and light element observation precision can give σ(Nν ) ≃ 0.03. Such future precision would reveal the expected effect of neutrino heating (Neff -3 = 0.044) of the CMB during BBN, and would be near the level to reveal any particle species ever in thermal equilibrium with the standard model. Improved Yp measurements can push this precision even further.

Two-neutrino double- β decay matrix elements based on a relativistic nuclear energy density functional

Nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy density functional (REDF). The properties of nuclei involved in the decay are obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation based on relativistic energy density functional (REDF-QRPA). Three effective interactions have been employed, including density-dependent meson-exchange (DD-ME2) and point coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are described consistently both in $T=1$ and $T=0$ channels using a separable pairing interaction. The optimal values of $T=0$ pairing strength parameter $V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives. The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe, $^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained using optimal values of $V_{0pp}$ are discussed in comparison to previous studies. The results of the present work represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay.

Signatures of shape phase transitions in krypton isotopes based on relativistic energy density functionals

Spectroscopic properties that characterize the shape phase transitions in krypton isotopes with the mass $A\approx80$ region are investigated within the framework of the nuclear density functional theory. Triaxial quadrupole constrained self-consistent mean-field calculations that employ relativistic energy density functionals and a pairing interaction are carried out for the even-even nuclei $^{76-86}$Kr. The spectroscopic properties are computed by solving the triaxial quadrupole collective Hamiltonian, with the ingredients, i.e., the deformation-dependent moments of inertia and mass parameters, and the collective potential, determined by using the SCMF solutions as microscopic inputs. Systematic behaviors of the SCMF potential energy surfaces, the corresponding low-energy spectra, electric quadrupole and monopole transition probabilities, and the fluctuations in the triaxial quadrupole deformations indicate evolution of the underlying nuclear structure as functions of the neutron number, that is characterized by a considerable degree of shape mixing. A special attention is paid to the transitional nucleus $^{82}$Kr, which has been recently identified experimentally as an empirical realization of the E(5) critical-point symmetry.

Dynamical Synthesis of ^{4}He in the Scission Phase of Nuclear Fission.

In the exothermic process of fission decay, an atomic nucleus splits into two or more independent fragments. Several aspects of nuclear fission are not properly understood, in particular the formation of the neck between the nascent fragments, and the subsequent mechanism of scission into two or more independent fragments. Using an implementation of time-dependent density functional theory, based on a relativistic energy density functional and including pairing correlations, we analyze the final phase of the process of induced fission of ^{240}Pu, and show that the timescale of neck formation coincides with the assembly of two α-like clusters. Because of its much larger binding energy, the dynamical synthesis of ^{4}He in the neck predominates over other light clusters, e.g., ^{3}H and ^{6}He. At the instant of scission the neck ruptures exactly between the two α-like clusters, which separate because of the Coulomb repulsion and are eventually absorbed by the two emerging fragments. The mechanism of light charged clusters formation at scission could also be linked to ternary fission.

What can CMB observations tell us about the neutrino distribution function?

Cosmic Microwave Background (CMB) observations have been used extensively to constrain key properties of neutrinos, such as their mass. However, these inferences are typically dependent on assumptions about the cosmological model, and in particular upon the distribution function of neutrinos in the early Universe. In this paper, we aim to assess the full extent to which CMB experiments are sensitive to the shape of the neutrino distribution. We demonstrate that Planck and CMB-S4-like experiments have no prospects for detecting particular features in the distribution function. Consequently, we take a general approach and marginalise completely over the form of the neutrino distribution to derive constraints on the relativistic and non-relativistic neutrino energy densities, characterised by N eff = 3.0 ± 0.4 and ρν,0 NR < 14 eV cm-3 at 95% CL, respectively. The fact that these are the only neutrino properties that CMB data can constrain has important implications for neutrino mass limits from cosmology. Specifically, in contrast to the ΛCDM case where CMB and BAO data tightly constrain the sum of neutrinos masses to be ∑m ν < 0.12 eV, we explicitly show that neutrino masses as large as ∑ m ν∼ 3 eV are perfectly consistent with this data. Importantly, for this to be the case, the neutrino number density should be suitably small such that the bound on ρν,0 NR = ∑ m ν n ν,0 is still satisfied. We conclude by giving an outlook on the opportunities that may arise from other complementary experimental probes, such as galaxy surveys, neutrino mass experiments and facilities designed to directly detect the cosmic neutrino background. GitHub: Parameter files for MCMC analysis and code to reproduce all plots can be found here.

Towards a solution to the H0 tension

The tension between current expansion rate H$_0$ using Planck data and direct model-independent measurements in the local universe has reached a tension above 5$\sigma$ in the context of the $\Lambda$CDM model. The growing tension among early time and local measurements of H$_0$ has not ameliorated and remains a crucial and open question in cosmology. Solutions to understand this tension are possible hidden sources of systematic error in the observable measurements or modifications to the concordance $\Lambda$CDM model. In this work, we investigate a solution to the H$_0$ tension by modifying $\Lambda$CDM and we add at early times extra relativistic energy density $\rho_{ex}$. In some context this $\rho_{ex}$ corresponds to EDE or Bound Dark Energy. We implement our model in CAMB and perform a full COSMO-MC (MCMC) allowing to simultaneously fit the latest data from CMB anisotropies and the value of H$_0 = 74.03\pm 1.42,\mathrm{km\, s^{-1}Mpc^{-1}}$ from A. Riess [R-19] \ci{Riess:2019cxk}. The inclusion of $\rho_{ex}$ ameliorates the tension between early and late time measurements only slightly and we obtain a value H$_0 = (68.70\pm 0.45$\ksm) still in conflict with local measurements [R-19]. We follow up our analysis by proposing two forecasting standard deviation $\sigma_H=1$ and $\sigma_H=0.5$ (in units of \ksm) for local distance measurements H$_0 = (74.03\pm \sigma_H)$ \ksm. From MCMC we obtain a value of H$_0 =(72.83\pm 0.47)$ \ksm\, at 68\% confidence level for $\sigma_H =0.5$, fully consistent with [R-19], while the price to pay is a percentage increase of $0.12\%$ in CMB $\chi_{cmb}^2$. Finally, the extra energy density $\rho_{ex}$ leaves distinctive imprints in the matter power spectrum at scales $k \sim k_c$ with $k_c=a_cH(a_c)$ and in the CMB power spectrum, allowing for independent verification of our analysis.

Appearance of a peak in the symmetry energy at N=126 for the Pb isotopic chain within the relativistic energy density functional approach

The newly derived relativistic energy density functional [\textcolor{blue}{ Phys. Rev. C \textbf{103}, 024305 (2021)}], which stems from the effective field theory motivated relativistic mean-field (E-RMF) is employed to establish the appearance of peak/kink in the symmetry energy over the isotopic chain of Pb-nuclei. The coherent density fluctuation model parametrization procedure for finite nuclei is adopted here to obtain the relativistic energy density functional at local density. The relativistic energy density functional from E-RMFT takes precedence over the Br\"uckner energy density functional as it accurately predicts the empirical saturation density and binding energy per nucleon $E/A$, so-called 'Coester Band Problem'. Interestingly, using the relativistic energy density functional, it is possible to predict the peak at $N=126$ for recently developed G3 and widely used NL3 parameter sets, which is not observed for Br\"uckener's functional in-spite of using the E-RMF density. From the present analysis, the newly fitted energy density functional is found to be minutely sensitive to the choice of the parameter sets employed.

Description of weak-interaction rates within the relativistic energy density functional theory

A new theoretical framework has been established and applied in the calculation of electron capture (EC) and β-decay rates in stellar environment, characterized by high density and temperature. For the description of the nuclear properties, the finite-temperature Hartree Bardeen-Cooper-Schrie_er (FTHBCS) theory based on the relativistic derivative-coupling D3C* interaction is employed. In order to describe the charge-exchange transitions, the finitetemperature proton-neutron quasi-particle random-phase approximation is developed (FT-PNRQRPA) which includes both temperature and pairing correlations. In the FT-HBCS calculations, only the isovector pairing is included, while in the residual interaction of the FT-PNRQRPA both the isovector and isoscalar pairing contribute. In this work, results for EC and β-decay rates are presented in the temperature interval T = 0–1.5 MeV and stellar density ρYe = 107 and 109 g/cm3. Both allowed 0+, 1+ and first-forbidden transitions 0−, 1− and 2− are included in the calculations. It is shown that interplay between pairing correlations and finite-temperature effects can lead to significant changes in rates. It is also important to include de-excitations, i.e. transitions with negative Q-value, that become increasingly significant at higher temperatures especially for p f -shell nuclei.