arXiv subjects

F. Krmpotić

Publications and source records attributed to F. Krmpotić.

At least 19 recordsLinked to original sources

arXiv2025

Neutrinoless $ββ$-Decay in DCEQTDA

We have recently developed a nuclear model, which is a natural extension of the $pn$-QRPA model, specially designed to describe double charge exchange (DCE) processes generated by two-body DCE transition operators. It is based on the Quasiparticle Tamm-Dancoff Approximation (QTDA) for $pn$ and $2p2n$ excitations in intermediate and final nuclei, respectively, and will be called DCEQTDA. As such, this model, having the same number of free parameters as the $pn$-QRPA, also brings into play the excitations of four quasiparticles to build up the final nuclear states, which are then used to evaluate the nuclear matrix elements (NMEs) for all $0^+$ and $2^+$ final states, including resonances, and not just for the ground state as in $pn$-QRPA. In addition, it allows us to evaluate: (a) the values of $Q_{ββ}$, (b) the excitation energies in final nuclei, and (c) the DCE sum rules, which are fulfilled in the DCEQTDA. So far, this model has been used mainly to calculate double beta decays with the emission of two neutrinos ($2νββ$-decay). Here, we extend it to the study of these processes when no neutrinos are emitted ($0νββ$-decay), evaluating them in a series of nuclei, but paying special attention to (i) $^{76}$Se, which have been measured recently in the GERDA and MAJORANA experiments, and (ii) $^{124}$Te, for which the first direct observation of the double electron capture $2ν$ has been performed with the XENON1T dark matter detector. We obtain good agreement with the data for both the ground state and the excited states. The validity of the DCEQTDA model is checked by comparing the calculation with the experimental data for the $2νββ$ NMEs, and for the $Q_{ββ}$, in a series of nuclei.

nucl-th↗

arXiv2019

A Nuclear Structure Model for Double Charge-Exchange Processes

A new model, based on the BCS approach, is specially designed to describe nuclear phenomena $(A,Z)\rightarrow (A,Z\pm 2)$ of double-charge exchange (DCE). After being proposed, and applied in the particle-hole limit, by one of the authors (F. Krmpotić [1]), so far it was never been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [2] to describe the single $β$-decays $(A,Z)\rightarrow (A,Z\pm 1)$, to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when is used in the evaluation of the double beta decay (DBD) rates. For instance, i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur, ii) it allows to study NMEs, not only for the fundamental state in daughter nuclei, as the pn-QRPA model does, but also for all final $0^+$ and $2^+$ states, accounting at the same time their excitation energies and the corresponding DBD Q-values, iii) together with the DBD-NMEs it provides also the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules, iv) the latter are relevant for both the DBD and the DCE reactions, since the involved nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the $(A,Z)\rightarrow (A,Z+ 2)$ process in $^{48}$Ca $\rightarrow ^{48}$Ti and the $(A,Z)\rightarrow (A,Z- 2)$ process in $^{96}$Ru $\rightarrow ^{96}$Mo, involving all final $0^+$ states and $2^+$ states.

nucl-th↗

arXiv2017

Nonmesonic weak decay of charmed hypernuclei

We present a study of the nonmesonic weak decay (NMWD) of charmed hypernuclei using a relativistic formalism. We work within the framework of the independent particle shell model and employ a ($π$,$K$) one-meson-exchange model for the decay dynamics. We implement a fully relativistic treatment of nuclear recoil. Numerical results are obtained for the one-neutron-induced transition NMWD rates of the $_{Λ^{+}_{c}}^{12}$N. The effect of nuclear recoil is sizable and goes in the direction to decrease the nuclear decay rate. We found that the NMWD decay rate of $_{Λ^{+}_{c}}^{12}$N is of the same order of magnitude as the partial decay rate for the corresponding mesonic decay $Λ^+_c \rightarrow Λ+ π^+$, suggesting the feasibility of experimental detection of such heavy-flavor nuclear processes.

nucl-th↗

arXiv2017

Partial restoration of spin-isospin SU(4) Symmetry and the One-QRPA method in Double Beta Decay

The one-QRPA method is used to describe simultaneously both double decay beta modes, giving special attention to the partial restoration of spin-isospin SU(4) symmetry. To implement this restoration and to fix the model parameters, we resort to the energetics of Gamow-Teller resonances and to the minima of the single $β^+$-decay strengths. This makes the theory predictive regarding the $ββ_{2ν}$-decay, producing the $2ν$ moments in $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{128,130}$Te, and $^{150}$Nd, that are of the same order of magnitude as the experimental ones; however, the agreement with $ββ_{2ν}$ data is only modest. To include contributions coming from induced nuclear weak currents, we extend the $ββ_{0ν}$-decay formalism employed previously in C. Barbero et. al, Nuc. Phys. A628, 170 (1998). The numerical results for the $ββ_{0ν}$ moments in the above mentioned nuclei are similar to those obtained in other theoretical studies although smaller on averag by $\sim 40\%$. We attribute this difference basically to the one-QRPA-method, employed here for the first time, instead of the currently used two-QRPA-method. The difference is partially due to the way of carrying out the restoration of the spin-isospin symmetry. It is hard to say which is the best way to make the restoration, since the $ββ_{0ν}$ moments are not experimentally measurable. The numerical uncertainties in the $ββ$ moments, related with i) their strong dependence on the residual interaction in the p-p channel when evaluated within the QRPA, and ii) lack of proper knowledge of single-particle energies, have been quantified. It is concluded that the partial restoration of the SU (4) symmetry is crucial in the description of the $ββ$-decays, regardless of the nuclear model used.

nucl-th↗

arXiv2015

Relativistic model for the nonmesonic weak decay of single-lambda hypernuclei

Having in mind its future extension for theoretical investigations related to charmed nuclei, we develop a relativistic formalism for the nonmesonic weak decay of single-$Λ$ hypernuclei in the framework of the independent-particle shell model and with the dynamics represented by the $(π,K)$ one-meson-exchange model. Numerical results for the one-nucleon-induced transition rates of ${}^{12}_Λ\textrm{C}$ are presented and compared with those obtained in the analogous nonrelativistic calculation. There is satisfactory agreement between the two approaches, and the most noteworthy difference is that the ratio $Γ_{n}/Γ_{p}$ is appreciably higher and closer to the experimental value in the relativistic calculation. Large discrepancies between ours and previous relativistic calculations are found, for which we do not encounter any fully satisfactory explanation. The most recent experimental data is well reproduced by our results. In summary, we have achieved our purpose to develop a reliable model for the relativistic calculation of the nonmesonic weak decay of $Λ$-hypernuclei, which can now be extended to evaluate similar processes in charmed nuclei.

nucl-th↗

arXiv2012

Nonmesonic Hyperon Weak Decay Spectra in $^{12}_Λ$C}

We study the nonmesonic weak decay (NMWD) $ΛN \to nN$ of the ${}^{12}_Λ C$ hypernucleus induced by the nucleon $N=n,p$ with transition rate $Γ_N$. The nuclear process is described by the interplay of two models; one describing the NMWD of hyperon $Λ$ in the nuclear environment, and the other taking into account the Final State Interaction (FSI) of the two outgoing nucleons with the residual nucleus. The first one is done in the framework of the Independent-Particle Shell-Model (IPSM), with the decay dynamics represented by the exchange of $π+ η+ K+ρ+ω+K^*$ mesons with usual parametrization. For the second one is used a time dependent multicollisional intranuclear cascade schema (implemented in the CRISP code - Collaboration Rio-São Paulo). The results obtained for inclusive and exclusive kinetic energy spectra, and the angular correlation are compared with recent data from KEK and FINUDA experiments. The calculated ratio $(Γ_n / Γ_p)^{\partial{\tiny FSI}}$, between the numbers of emitted back-to-back $nn$ and $np$ pairs, is in good agreement with the experimental data.

nucl-th↗

arXiv2012

Neutrino and antineutrino cross sections in $^{12}$C

We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrino-nucleus reactions and muon capture. We have done a thorough study of exclusive (ground state) properties of $^{12}$B and $^{12}$N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data is achieved in this way. The inclusive neutrino/antineutrino ($ν/\tildeν$) reactions $^{12}$C($ν,e^-)^{12}$N and $^{12}$C($\tildeν,e^+)^{12}$B are calculated within both the PQRPA, and the relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for $ν$ and $\tildeν$, ii) they steadily increase when the size of the configuration space is augmented, and particulary for $ν/\tildeν$ energies $> 200$ MeV, and iii) converge for sufficiently large configuration space and final state spin.

nucl-th↗

arXiv2008

Gross Theory Model for Neutrino-Nucleus Cross Section

The nuclear gross theory, originally formulated by Takahashi and Yamada for the $β$-decays, is applied for the electronic-neutrino nucleus reactions, employing a more realistic description to the energetics of the Gamow-Teller resonances. The model parameters are gauged from the most recent experimental data, both for $β^-$ decay and electron-capture, separately for even-even, even-odd, odd-odd, odd-even nuclei. The numerical estimates for neutrino-nucleus cross sections agree fairly well with previous evaluations done within the framework of microscopic models. The formalism presented here can be extended to the heavy nuclei mass region, where weak processes are quite relevant, which is of astrophysical interest because of its applications in supernova explosive nucleosynthesis.

nucl-th↗

arXiv2007

Pairing Correlations in Odd-Mass Carbon Isotopes and Effect of Pauli Principle in Particle-Core Coupling in 13C and 11Be

We present an exploratory study of structure of 13C, 15C, 17C and 19C, showing that the simple one-quasiparticle projected BCS (PBCS) model is capable to account for several important properties of these nuclei. Next we discuss the importance of the Pauli Principle in the particle-core models of normal-parity states in 13C and 11Be. This is done by considering the pairing interaction between nucleons moving in an over-all deformed potential. To assess the importance of pairing correlations in these light nuclei we use both the simple BCS and the PBCS approximations. We show that the Pauli Principle plays a crucial role in the parity inversion in 11Be. It is also found that the effect of the particle number conservation in relatively light and/or exotic nuclei is quite significant. Comparison of our results with several recent papers on the same subject, as well as with some experimental data, is presented.

nucl-th↗

arXiv2006

A Reanalysis of the LSND Neutrino Oscillation Experiment

We reanalyse the LSND neutrino oscillation results in the framework of the Projected Quasiparticle Random Phase Approximation (PQRPA), which is the only RPA model that treats the Pauli Principle correctly, and accounts satisfactorily for great majority of the weak decay observables around 12C. We have found that the employment of the PQRPA inclusive DIF 12C(nu_e,e-)12N cross-section, instead of the CRPA used by the LSND collaboration in the (nu_mu ->nu_e) oscillations study of the 1993-1995 data sample, leads to the following: 1) the oscillation probability is increased from (0.26 +/- 0.10 +/- 0.05) percents to (0.33 +/- 0.10 +/- 0.13) percents, and 2) the previously found consistence between the (sin^2 2theta, Delta m^2) confidence level regions for the (nu_mu -> nu_e) and the (bar{nu}_mu -> bar{nu}_e) oscillations is significantly diminished. These effects are not due to the difference in the uncertainty ranges for the neutrino-nucleus cross-section, but to the difference in the cross-sections themselves.

nucl-th↗

arXiv1999

Nuclear moments for the neutrinoless double beta decay II

The recently developed formalism for the evaluation of nuclear form factors in neutrinoless double beta decay is applied to $^{48}Ca$, $^{76}Ge$, $^{82}Se$, $^{100}Mo$, $^{128}Te$ and $^{130}Te$ nuclei. Explicit analytical expressions that follows from this theoretical development, in the single mode model for the decay of $^{48}Ca$, have been worked out. They are useful both for testing the full numerical calculations, and for analytically checking the consistency with other formalisms. Large configuration space calculations are compared with previous studies, where alternative formulations were used. Yet, besides using the G-matrix as residual interaction, we here use a simple $δ$-force. Attention is paid to the connected effects of the short range nuclear correlations and the finite nucleon size. Constraints on lepton number violating terms in the weak Hamiltonian (effective neutrino Majorana mass and effective right-handed current coupling strengths) are deduced.

nucl-th↗

arXiv1998

Weak Magnetism in Two Neutrino Double Beta Decay

We have extended the formalism for the two-neutrino double beta decay by including the weak-magnetism term, as well as other second-forbidden corrections. The weak magnetism diminishes the calculated half-lives in $\sim 10%$, independently of the nuclear structure. Numerical computations were performed within the pn-QRPA, for $^{76}Ge$, $^{82}Se$, $^{100} Mo$, $^{128}Te$ and $^{130}Te$ nuclei. No one of the second-forbidden corrections modifies significantly the spectrum shapes. The total reduction in the calculated half lives varies from 6% up to 32%, and strongly depend on the nuclear interaction in the particle-particle $S=1,T=0$ channel. We conclude that the higher order effects in the weak Hamiltonian would hardly be observed in the two-neutrino double beta experiments.

nucl-th↗

arXiv1998

Competition between standard and exotic double beta decays

We discuss the contributions of higher order terms in weak Hamiltonian to the standard two-neutrino double beta decay. The formalism for the unique first forbidden transitions has been developed, and it is shown that they can alter the two-electron energy spectrum. Yet, their effect is too small to screen the detection of exotic neutrinoless double beta decays, which are candidates for testing the physics beyond the standard model.

nucl-th↗

arXiv1998

Self Consistent and Renormalized particle-particle RPA in a Schematic Model

The dynamical effects of ground state correlations for excitation energies and transition strengths near the superfluid phase transition are studied in the soluble two level pairing model, in the context of the particle-particle self consistent Random Phase Approximation (SCRPA). Exact results are well reproduced across the transition region, beyond the collapse of the standard particle-particle Random Phase Approximation. The effects of two-body correlation in the SCRPA are displayed explicitly.

nucl-th↗

arXiv1994

Two neutrino double beta decay within the $ξ$-approximation

We examine the contributions of odd-parity nuclear operators to the two-neutrino double beta decay $0^+\rightarrow 0^+$ amplitude, which come from the $P$-wave Coulomb corrections to the electron wave functions and the recoil corrections to the nuclear currents. Although they are formally of higher order in $αZ/2$ or $v/c$ of the nucleon than the usual Fermi and Gamow-Teller matrix elements, explicit calculations performed within the QRPA show that they are significant when confronted with the experimental data.

nucl-th↗

arXiv1994

Double beta decay transition mechanism

After briefly reviewing $ββ$ decay as a test of the neutrino mass, I examine the nuclear structure involved in this process. Simple formulas (à la Padé) are designed for the transition amplitudes and the general behavior of $ββ$ decay amplitudes in the quasiparticle random phase approximation are discussed. Results of a calculation for $^{48}Ca$, $^{76}Ge $, $^{82}Se$, $^{100}Mo$, $^{128}Te$ and $^{130}Te$ nuclei are presented, in which the particle-particle interaction strengths have been fixed by invoking the partial restoration of the isospin and Wigner SU(4) symmetries. An upper limit of $ \approx 1$ eV is obtained for the effective neutrino mass.

nucl-th↗

arXiv1994

Ground-state Correlation Effects in Extended RPA Calculations

We study normalization problems associated with use of perturbatively correlated ground-states in extended RPA schemes in the context of a specific but typical example. The sensitivity of the results to the amount of $2p2h$ admixtures to the correlated ground state is also investigated in terms of a modification of the standard perturbative approach.

nucl-th↗

arXiv1994

On the energy-shell contributions of the three-particle~-~ three-hole excitations

The response functions for the extended second and third random phase approximation are compared. A second order perturbation calculation shows that the first-order amplitude for the direct $3p3h$ excitation from the ground state cancels with those that are engendered by the $1p1h$-$3p3h$ coupling. As a consequence nonvanishing $3p3h$ effects to the $1p1h$ response involve off energy shell renormalization only. On shell $3p3h$ processes are absent.

nucl-th↗