Research Interests: Nuclear Structure, Exotic Modes of Excitation, Nuclear Astrophysics, Exotic Nuclei, Effective Nuclear Interactions, Weak Interaction, Neutrino-Nucleus Reactions, Nonlinear Dynamics, Mathematical Modeling, Computational Physics

# SELECTED RECENT PUBLICATIONS & ABSTRACTS:

• A. Krasznahorkay, L. Stuhl, M. Csatlós, A. Algora, J. Gulyás, J. Timár,N. Paar et al.,"Neutron-skin thickness from the study of the antianalog giant dipole resonance", submitted to Phys. Rev. Lett. (2012). nucl-th/arXiv:1205.2325

• The gamma-decay of the anti-analog of the giant dipole resonance (AGDR) has been measured to the isobaric analog state excited in the p(124Sn,n) reaction at a beam energy of 600 MeV/nucleon. The energy of the transition was also calculated with state-of-the-art self-consistent random-phase approximation (RPA) and turned out to be very sensitive to the neutron-skin thickness (\DeltaR_(pn)). By comparing the theoretical results with the measured one, the \DeltaR_(pn) value for 124Sn was deduced to be 0.18 \pm 0.02 fm, which agrees well with the previous results. The energy of the AGDR measured previously for ^(208)Pb was also used to determine the \DeltaR_(pn) for ^(208)Pb. In this way a very precise \DeltaR_(pn) = 0.18 \pm 0.02 neutron-skin thickness has been obtained for 208Pb. The present method offers new possibilities for measuring the neutron-skin thicknesses of very exotic isotopes.

• H. Djapo, N. Paar, "Neutral-current neutrino-nucleus cross sections based on relativistic nuclear energy density functional", Phys. Rev. C 86, 035804 (2012). nucl-th/arXiv:1203.5224

• Background: Inelastic neutrino-nucleus scattering through the weak neutral-current plays important role in stellar environment where transport of neutrinos determine the rate of cooling. Since there are no direct experimental data on neutral-current neutrino-nucleus cross sections available, only the modeling of these reactions provides the relevant input for supernova simulations. Purpose: To establish fully self-consistent framework for neutral-current neutrino-nucleus reactions based on relativistic nuclear energy density functional. Methods: Neutrino-nucleus cross sections are calculated using weak Hamiltonian and nuclear properties of initial and excited states are obtained with relativistic Hartree-Bogoliubov model and relativistic quasiparticle random phase approximation that is extended to include pion contributions for unnatural parity transitions. Results: Inelastic neutral-current neutrino-nucleus cross sections for 12C, 16O, 56Fe, 56Ni, and even isotopes {92-100}Mo as well as respective cross sections averaged over distribution of supernova neutrinos. Conclusions: The present study provides insight into neutrino-nucleus scattering cross sections in the neutral channel, their theoretical uncertainty in view of recently developed microscopic models, and paves the way for systematic self-consistent large-scale calculations involving open-shell target nuclei.

• T. Marketin, G. Martinez-Pinedo, N. Paar, and D. Vretenar, "Role of momentum transfer in the quenching of Gamow-Teller strength", Phys. Rev. C 85, 054313 (2012). nucl-th/arXiv:1203.3687

• The relativistic proton-neutron quasiparticle random phase approximation (pn-RQRPA) is applied in the calculation of the L=0 strength in charge-exchange reactions on $^{48}$Ca, $^{90}$Zr, $^{208}$Pb and nuclei in the Sn isotopic chain. The microscopic theoretical framework is based on the relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state. The calculation is fully self-consistent, i.e. the same interaction is used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the pn-RQRPA. The inclusion of the higher-order terms that include the effect of finite momentum transfer, primarily the isovector spin monopole (IVSM) term, in the transition operator shifts a portion of the strength to the high-energy region above the Gamow-Teller (GT) resonance. The total strength is slightly enhanced in nuclei with small neutron-to-proton ratio but remains unchanged with increasing neutron excess. Based on the strength obtained using the full L=0 transition operator in the pn-RQRPA calculation, we have estimated the impact of the IVSM on the strength measured in the charge-exchagne reactions on $^{90}$Zr and found that the data are consistent with the Ikeda sum rule.

• D. Vretenar, Y. F. Niu, N. Paar, and J. Meng, "Low-energy isovector and isoscalar dipole response in neutron-rich nuclei", Phys. Rev. C 85, 044317 (2012).arXiv:1202.5663

• The self-consistent random phase approximation (RPA), based on the framework of relativistic energy density functionals, is employed in the study of isovector and isoscalar dipole response in $^{68}$Ni, $^{132}$Sn, and $^{208}$Pb. The evolution of pygmy dipole states (PDS) in the region of low excitation energies is analyzed as a function of the density-dependence of the symmetry energy for a set of relativistic effective interactions. The occurrence of PDS is predicted in the response to both the isovector and isoscalar dipole operators, and its strength is enhanced with the increase of the symmetry energy at saturation and the slope of the symmetry energy. In both channels the PDS exhausts a relatively small fraction of the energy-weighted sum rule but a much larger percentage of the inverse energy-weighted sum rule. For the isovector dipole operator the reduced transition probability $B(E1)$ of the PDS is generally small because of pronounced cancellation of neutron and proton partial contributions. The isoscalar reduced transition amplitude is predominantly determined by neutron particle-hole configurations, most of which add coherently, and this results in a collective response of the PDS to the isoscalar dipole operator.

• A. F. Fantina, E. Khan, G. Colo, N. Paar, and D. Vretenar, "Stellar electron-capture rates on nuclei based on microscopic Skyrme functional", Phys. Rev. C 86, 035805 (2012).

• We compute electron-capture rates for 54,56Fe and Ge isotopes using a self-consistent microscopic approach. The single-nucleon basis and the occupation factors in the target nucleus are calculated in the finite-temperature Skyrme Hartree-Fock model, and the Ji = 0±, 1±, 2± charge-exchange transitions are determined in the finite-temperature random-phase approximation (RPA). The scheme is self-consistent, i.e. both the Hartree-Fock and the RPA equations are based on the same Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on the electron-capture rates for different astrophysical conditions. Considering various models, the typical spreading of the electron-capture rates in Fe and Ge is estimated to two orders of magnitude.

• J. Piekarewicz, B. K. Agrawal, G. Colo, W. Nazarewicz, N. Paar, P.-G. Reinhard, X. Roca-Maza, and D. Vretenar, "Electric dipole polarizability and the neutron skin", Phys. Rev. C 85, 041302(R) (2012).

• The recent high-resolution measurement of the electric dipole (E1) polarizability (alphad) in 208Pb [Phys. Rev. Lett. 107, 062502 (2011)] provides a unique constraint on the neutron-skin thickness of this nucleus. The neutron-skin thickness (rskin) of 208Pb is a quantity of critical importance for our understanding of a variety of nuclear and astrophysical phenomena. To assess the model dependence of the correlation between alphad and rskin, we carry out systematic calculations for 208Pb, 132Sn, and 48Ca based on the nuclear density functional theory (DFT) using both non-relativistic and relativistic energy density functionals (EDFs). Our analysis indicates that whereas individual models exhibit a linear dependence between alphad and rskin, this correlation is not universal when one combines predictions from a host of different models. By averaging over these model predictions, we provide estimates with associated systematic errors for rskin and alphad for the nuclei under consideration. We conclude that precise measurements of rskin in both 48Ca and 208Pb---combined with the recent measurement of alphad---should significantly constrain the isovector sector of the nuclear energy density functional.

• E. Khan, N. Paar, and D. Vretenar, "Low-energy monopole strength in exotic Nickel isotopes", Phys. Rev. C 84, 051301 (2011).

• Low-energy strength is predicted in the isoscalar monopole response of neutron-rich Ni isotopes, in calculations performed using the microscopic Skyrme HF+RPA and relativistic RHB+RQRPA models. Both models, although based based on different energy density functionals, predict the occurrence of pronounced monopole states in the energy region between 10 MeV and 15 MeV, well separated from the isoscalar GMR. The analysis of transition densities and corresponding particle-hole configurations shows that these states represent almost pure neutron single hole-particle excitations. Even though their location is not modified with respect to the corresponding unperturbed states, their (Q)RPA strength is considerably enhanced by the residual interaction. The theoretical analysis predicts the gradual enhancement of low-energy monopole strength with neutron excess.

• N. Paar, T. Suzuki, M. Honma,T. Marketin, D. Vretenar, "Uncertainties in modeling low-energy neutrino induced reactions on iron group nuclei", Phys. Rev. C 84, 047305 (2011). nucl-th/arXiv:1107.4872

• Charged-current neutrino-nucleus cross sections for 54,56Fe and 58,60Ni are calculated and compared using frameworks based on relativistic and Skyrme energy density functionals, and the shell model. The current theoretical uncertainties in modeling neutrino-nucleus cross sections are assessed in relation to the predicted Gamow-Teller transition strength and available data, multipole decomposition of the cross sections, and cross sections averaged over the Michel flux and Fermi-Dirac distribution. Employing different microscopic approaches and models, the DAR neutrino-56Fe cross section and its theoretical uncertainty are estimated: sigma_th=(258+-57) 10^{-42} cm^2, in very good agreement with the experimental value: sigma_exp=(256+-108+-43) 10^{-42} cm^2.

• Y. F. Niu, N. Paar, D. Vretenar, and J. Meng, "Stellar electron-capture rates calculated with the finite-temperature relativistic random-phase approximation", Phys. Rev. C 83, 045807 (2011). nucl-th/arXiv:1104.1683

• We introduce a self-consistent microscopic theoretical framework for modeling the process of electron capture on nuclei in stellar environment, based on relativistic energy density functionals. The finite-temperature relativistic mean-field model is used to calculate the single-nucleon basis and the occupation factors in a target nucleus, and Jπ=0±, 1±, and 2± charge-exchange transitions are described by the self-consistent finite-temperature relativistic random-phase approximation. Cross sections and rates are calculated for electron capture on 54,56Fe and 76,78Ge in stellar environment, and results compared with predictions of similar and complementary model calculations.

• A. R. Samana, F. Krmpotic, N. Paar, and C. A. Bertulani, "Neutrino and antineutrino charge-exchange reactions on 12C", Phys. Rev. C 83, 045807 (2011). nucl-th/arXiv:1005.2134

• 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. Explicit violation of CVC hypothesis by the Coulomb field, as well as development of a sum rule approach for the inclusive cross sections have been worked out. 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 achieved in this way put in evidence the limitations of standard RPA and the QRPA models, which come from the inability of the RPA in opening the $p_{3/2}$ shell, and from the non-conservation of the number of particles in the QRPA. The inclusive neutrino/antineutrino ($\nu/\bar{\nu}$) reactions $^{12}$C($\nu,e^-)^{12}$N and $^{12}$C($\bar{\nu},e^+)^{12}$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 $\nu$ and $\bar{\nu}$, ii) they steadily increase when the size of the configuration space is augmented, and particulary for $\nu/\bar{\nu}$ energies $> 200$ MeV, and iii) converge for sufficiently large configuration space and final state spin. We study the decomposition of the inclusive cross-section based on the degree of forbiddenness of different multipoles. The $\nu/\bar{\nu}$-$^{12}$C charge-exchange reactions related with astrophysical applications are briefly discussed.

• N. Paar, "The quest for novel modes of excitation in exotic nuclei", J. Phys. G: Nucl. Part. Phys. 37, 064014 (2010). nucl-th/arXiv:1002.4776

• This paper provides an insight into several open problems in the quest for novel modes of excitation in nuclei with isospin asymmetry, deformation and finite temperature characteristics in stellar environments. 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 of supernova evolution present open problems with a 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 Vlow-k and correlated realistic nucleon- nucleon interaction VUCOM, 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.

• N. Paar, G. Colo, E. Khan, and D. Vretenar, "Calculation of stellar electron-capture cross sections on nuclei based on microscopic Skyrme functionals", Phys. Rev. C 80, 055801 (2009). nucl-th/arXiv:0909.3070

• A fully self-consistent microscopic framework for evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model, and charge-exchange transitions to excited states are computed using the finite-temperature RPA. Effective interactions are implemented self-consistently: both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is tested in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes.

• Y. F. Niu, N. Paar, D. Vretenar, and J. Meng, "Low-energy multipole response in nuclei at finite temperature", submitted to Phys. Lett. B 681, 315 (2009). nucl-th/arXiv:0906.2973

• The multipole response of nuclei at temperatures T=0-2 MeV is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=1-2 MeV additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in $^{60,62}$Ni, where no low-energy excitations occur at zero temperature. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in $^{68}$Ni and $^{132}$Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions.

• N. Paar, Y. F. Niu, D. Vretenar, and J. Meng, "On the isoscalar-isovector splitting of pygmy dipole structures", Phys. Rev. Lett. 103, 032502 (2009). nucl-th/arXiv:0905.4848

• The electric dipole response of $^{140}$Ce is investigated using the fully consistent relativistic quasiparticle random phase approximation. By analyzing the isospin structure of the E1 response, it is shown that the low-energy (pygmy) strength separates into two segments with different isospin character. The more pronounced pygmy structure at lower energy is composed of predominantly isoscalar states with surface-peaked transition densities. At somewhat higher energy the calculated E1 strength is primarily of isovector character, as expected for the low-energy tail of the giant dipole resonance. The results are in qualitative agreement with those obtained in recent $(\gamma,\gamma')$ and $(\alpha,\alpha'\gamma)$ experiments, and provide a simple explanation for the splitting of low-energy E1 strength into two groups of states with different isospin structure and radial dependence of the corresponding transition densities.

• T. Marketin, N. Paar, T. Niksic, and D. Vretenar, "Relativistic QRPA calculation of muon capture rates", Phys. Rev. C 79, 054323 (2009). nucl-th/arXiv:0812.1947

• The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of total muon capture rates on a large set of nuclei from $^{12}$C to $^{244}$Pu, for which experimental values are available. The microscopic theoretical framework is based on the Relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the PN-RQRPA. The calculation is fully consistent, i.e., the same interactions are used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the PN-RQRPA. The calculated capture rates are sensitive to the in-medium quenching of the axial-vector coupling constant. By reducing this constant from its free-nucleon value $g_A = 1.262$ by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.

• N. Paar, Comment on "Pygmy dipole response of proton-rich argon nuclei in random-phase approximation and no-core shell model", Phys. Rev. C 78, 039801 (2008). nucl-th/arXiv:0803.0274

• In recent paper by C. Barbieri, E. Caurier, K. Langanke, and G. Mart\'inez Pinedo~\cite{Bar.08}, low-energy dipole excitations have been studied in proton-rich $^{32,34}$Ar with random phase approximation (RPA) and no-core shell model (NCSM) using the correlated realistic nucleon-nucleon interactions obtained by the unitary correlation operator method (UCOM)~\cite{Fel.98}. The main objective of this comment is to argue that the paper~\cite{Bar.08} contains an inconsistency with respect to previous study of excitations in the same UCOM-RPA framework using identical correlated Argonne V18 interaction~\cite{Paa.06}, it does not provide any evidence that the low-lying state declared as pygmy dipole resonance in $^{32}$Ar indeed has the resonance-like structure, and that priror to studying exotic modes of excitation away from the valley of stability one should ensure that the model provides reliable description of available experimental data on nuclear ground state properties and excitations in nuclei.

• N. Paar, D. Vretenar, T. Marketin, and P. Ring, "Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random phase approximation", Phys. Rev. C 77, 024608 (2008). nucl-th/arXiv:0710.4881

• Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.

• N. Paar, D. Vretenar, E. Khan, and G. Colo, "Exotic modes of excitation in atomic nuclei far from stability", Rep. Prog. Phys. 70, 691 (2007). nucl-th/0701081

• We review recent studies of the evolution of collective excitations in atomic nuclei far from the valley of $\beta$-stability. Collective degrees of freedom govern essential aspects of nuclear structure, and for several decades the study of collective modes such as rotations and vibrations has played a vital role in our understanding of complex properties of nuclei. The multipole response of unstable nuclei and the possible occurrence of new exotic modes of excitation in weakly-bound nuclear systems, present a rapidly growing field of research, but only few experimental studies of these phenomena have been reported so far. Valuable data on the evolution of the low-energy dipole response in unstable neutron-rich nuclei have been gathered in recent experiments, but the available information is not sufficient to determine the nature of observed excitations. Even in stable nuclei various modes of giant collective oscillations had been predicted by theory years before they were observed, and for that reason it is very important to perform detailed theoretical studies of the evolution of collective modes of excitation in nuclei far from stability. We therefore discuss the modern theoretical tools that have been developed in recent years for the description of collective excitations in weakly-bound nuclei. The review focuses on the applications of these models to studies of the evolution of low-energy dipole modes from stable nuclei to systems near the particle emission threshold, to analyses of various isoscalar modes, those for which data are already available, as well as those that could be observed in future experiments, to a description of charge-exchange modes and their evolution in neutron-rich nuclei, and to studies of the role of exotic low-energy modes in astrophysical processes.

• P. Papakonstantinou, R. Roth, and N. Paar, "Nuclear collective excitations using correlated realistic interactions: the role of explicit RPA correlations", Phys. Rev. C 75, 014310 (2007). nucl-th/0609039

• We examine to which extent correlated realistic nucleon-nucleon interactions, derived within the Unitary Correlation Operator Method (UCOM), can describe nuclear collective motion in the framework of first-order random-phase approximation (RPA). To this end we employ the correlated Argonne V18 interaction in calculations within the so-called "Extended" RPA (ERPA) and investigate the response of closed-shell nuclei. The ERPA is a renormalized RPA version which considers explicitly the depletion of the Fermi sea due to long-range correlations and thus allows us to examine how these affect the excitation spectra. It is found that the effect on the properties of giant resonances is rather small. Compared to the standard RPA, where excitations are built on top of the uncorrelated Hartree-Fock (HF) ground state, their centroid energies decrease by up to 1 MeV, approximately, in the isovector channel. The isoscalar response is less affected in general. Thus, the disagreement between our previous UCOM-based RPA calculations and the experimental data are to be attributed to other effects, mainly to a residual three-body force and higher-order configurations. Ground-state properties obtained within the ERPA are compared with corresponding HF and perturbation-theory results and are discussed as well. The ERPA formalism is presented in detail.

• P. Ring, E. Litvinova, T. Niksic, N. Paar, D. Pena Arteaga, V. I. Tselyaev, and D. Vretenar, "Dynamics of exotic nuclear systems: covariant QRPA and extensions", Nucl. Phys. A 788, 194c (2007).

• R. Roth, H. Hergert, N. Paar, and P. Papakonstantinou, "Nuclear structure in the UCOM framework: from realistic interactions to collective excitations", Nucl. Phys. A 788, 12c (2007).nucl-th/0608018

• The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary transformation. The application of UCOM in the context of the no-core shell model provides insight into the interplay between dominant short-range and residual long-range correlations in the nuclear many-body problem. The use of the correlated interaction within Hartree-Fock, many-body perturbation theory, and Random Phase Approximation gives access to various nuclear structure observables throughout the nuclear chart.

• C. Barbieri, N. Paar, R. Roth, and P. Papakonstantinou, "Correlation energies in the random phase approximation using realistic interactions", submitted to Phys. Rev. C (2007).nucl-th/0608011

• The self-consistent random phase approximation (RPA) based on a correlated realistic nucleon-nucleon interaction is used to evaluate correlation energies in closed-shell nuclei beyond the Hartree-Fock level. The relevance of contributions associated with charge exchange excitations as well as the necessity to correct for the double counting of the second order contribution to the RPA ring summation are emphasized. Once these effects are properly accounted for, the RPA ring summation provides an efficient tool to assess the impact of long-range correlations on binding energies throughout the whole nuclear chart, which is of particular importance when starting from realistic interactions.

• N. Paar, D. Vretenar, T. Niksic, and P. Ring, "Relativistic quasiparticle random-phase approximation description of isoscalar compression modes in open-shell nuclei in the A=60 mass region ", Phys. Rev. C 74, 037303 (2006).nucl-th/0606054

• Very recent inelastic $\alpha$-scattering data on the isoscalar monopole and dipole strength distributions in $^{56}$Fe, $^{58}$Ni, and $^{60}$Ni are analyzed in the relativistic quasiparticle random-phase approximation (RQRPA) with the DD-ME2 effective nuclear interaction (nuclear matter compression modulus K$_{nm}= 251$ MeV). In all three nuclei the calculation nicely reproduces the observed asymmetric shapes of the monopole strength, and the bimodal structure of the dipole strength distributions. The calculated centroid and mean energies are in very good qualitative agreement with the experimental values both for the monopole, and for the low- and high-energy components of the dipole transition strengths. It is noted, however, that while DD-ME2 reproduces in detail the excitation energies of the giant monopole resonances (GMR) in nuclei with $A \ge 90$, the theoretical centroids are systematically above the experimental values in lighter nuclei with $A \leq 60$. The latter can be reproduced with an effective interaction with a lower value of K$_{nm} \approx$ 230 MeV but, because of the asymmetric shapes and pronounced fragmentation of the monopole strength distributions, isoscalar GMR data in light nuclei cannot provide accurate estimates of the nuclear matter compression modulus.

• N. Paar, P. Papakonstantinou, H. Hergert, and R. Roth, "Collective multipole excitations based on correlated realistic nucleon-nucleon interactions", Phys. Rev. C 74, 014318 (2006). nucl-th/0601026

• We investigate collective multipole excitations for closed shell nuclei from 16O to 208Pb using correlated realistic nucleon -nucleon interactions in the framework of the random phase approximation (RPA). The dominant short-range central and tensor correlations a re treated explicitly within the Unitary Correlation Operator Method (UCOM), which provides a phase-shift equivalent correlated interaction V_UCOM adapted to simple uncorrelated Hilbert spaces. The same unitary transformation that defines the correlated interaction is used to derive correlated transition operators. Using V_UCOM we solve the Hartree-Fock problem and employ the single-particle state s as starting point for the RPA. By construction, the UCOM-RPA is fully self-consistent, i.e. the same correlated nucleon-nucleon interact ion is used in calculations of the HF ground state and in the residual RPA interaction. Consequently, the spurious state associated with t he center-of-mass motion is properly removed and the sum-rules are exhausted within +-3%. The UCOM-RPA scheme results in a collective character of giant monopole, dipole, and quadrupole resonances in closed-shell nuclei across the nuclear chart. For the isoscalar giant monopole resonance, the resonance energies are in agreement with experiment hinting at a reasonable compressibility. However, in the 1- and 2+ channels the resonance energies are overestimated due to missing long-range correlations and three-body contributions.

• N. Paar, P. Papakonstantinou, R. Roth, and H. Hergert, "Self-consistent description of collective excitations in the unitary correlation operator model", Int. J. Mod. Phys. E 15, 346 (2006). nucl-th/0511041

• The fully self-consistent Random Phase Approximation (RPA) is constructed within the Unitary Correlation Operator Method (UCOM), which describes the dominant interaction-induced short-range central and tensor correlations by a unitary transformation. Based on the correlated Argonne V18 interaction, the RPA is employed in studies of multipole response in closed-shell nuclei across the nuclide chart. The UCOM-RPA results in a collective character of giant resonances, and it describes rather well the properties of isoscalar giant monopole resonances. However, the excitation energies of isovector giant dipole resonances and isoscalar giant quadrupole resonances are overestimated due to the missing long-range correlations and three-body contributions.

• R. Roth, P. Papakonstantinou, N. Paar, H. Hergert, T. Neff, and H. Feldmeier, "Hartree-Fock and Many-Body Perturbation Theory with Correlated Realistic NN-Interactions", Phys. Rev. C 73, 044312 (2006). nucl-th/0510036

• We employ correlated realistic nucleon-nucleon interactions for the description of nuclear ground states throughout the nuclear chart within the Hartree-Fock approximation. The crucial short-range central and tensor correlations, which are induced by the realistic interaction and cannot be described by the Hartree-Fock many-body state itself, are included explicitly by a state-independent unitary transformation in the framework of the unitary correlation operator method (UCOM). Using the correlated realistic interaction V_UCOM resulting from the Argonne V18 potential, bound nuclei are obtained already on the Hartree-Fock level. However, the binding energies are smaller than the experimental values because long-range correlations have not been accounted for. Their inclusion by means of many-body perturbation theory leads to a remarkable agreement with experimental binding energies over the whole mass range from He-4 to Pb-208, even far off the valley of stability. The observed perturbative character of the residual long-range correlations and the apparently small net effect of three-body forces provides promising perspectives for a unified nuclear structure description.

• N. Paar, P. Papakonstantinou, H. Hergert, and R. Roth, "Collective excitations in the Unitary Correlation Operator Method and relativistic QRPA studies of exotic nuclei", Physics of Atomic Nuclei 69, 1345 (2006). nucl-th/0506076

• The collective excitation phenomena in atomic nuclei are studied in two different formulations of the Random Phase Approximation (RPA): (i) RPA based on correlated realistic nucleon-nucleon interactions constructed within the Unitary Correlation Operator Method (UCOM), and (ii) relativistic RPA (RRPA) derived from effective Lagrangians with density-dependent meson-exchange interactions. The former includes the dominant interaction-induced short-range central and tensor correlations by means of an unitary transformation. It is shown that UCOM-RPA correlations induced by collective nuclear vibrations recover a part of the residual long-range correlations that are not explicitly included in the UCOM Hartree-Fock ground state. Both RPA models are employed in studies of the isoscalar monopole resonance (ISGMR) in closed-shell nuclei across the nuclide chart, with an emphasis on the sensitivity of its properties on the constraints for the range of the UCOM correlation functions. Within the Relativistic Quasiparticle RPA (RQRPA) based on Relativistic Hartree-Bogoliubov model, the occurrence of pronounced low-lying dipole excitations is predicted in nuclei towards the proton drip-line. From the analysis of the transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.

• N. Paar, T. Niksic, D. Vretenar, T. Marketin, and P. Ring, "Self-consistent relativistic QRPA studies of soft modes and spin-isospin resonances in unstable nuclei", Eur. Phys. J. A 25 Suppl. 1, 531 (2005). ISSN 1434-601X (Online).

• N. Paar, P. Papakonstantinou, V. Yu. Ponomarev, and J. Wambach, "Low-energy dipole excitations towards the proton drip-line: doubly magic 48Ni", Phys. Lett. B 624, 195 (2005). nucl-th/0506010

• The properties of the low-energy dipole response are investigated for the proton-rich doubly magic nucleus $^{48}$Ni, in a comparative study of two microscopic models: fully self-consistent Relativistic Random-Phase Approximation(RRPA) based on the novel density-dependent meson-exchange interactions, and Continuum Random-Phase Approximation(CRPA) using Skyrme-type interactions with the continuum properly included. Both models predict the existence of the low-energy soft mode, i.e. the proton pygmy dipole resonance (PDR), for which the transition densities and RPA amplitudes indicate the dynamics of loosely bound protons vibrating against the rest of the nucleons. The CRPA analysis indicates that the escape width for the proton PDR is rather large, as a result of the coupling to the continuum.

• N. Paar, D. Vretenar, and P. Ring, "Proton electric pygmy dipole resonance", Phys. Rev. Lett. 94, 182501 (2005). nucl-th/0504035

• The evolution of the low-lying E1 strength in proton-rich nuclei is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov (RHB) model and the relativistic quasiparticle random-phase approximation (RQRPA). Model calculations are performed for a series of N=20 isotones and Z=18 isotopes. For nuclei close to the proton drip-line, the occurrence of pronounced dipole peaks is predicted in the low-energy region below 10 MeV excitation energy. From the analysis of the proton and neutron transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance

• T. Niksic, T. Marketin, D. Vretenar, N. Paar, and P. Ring, "Beta-decay rates of r-process nuclei in the relativistic quasiparticle random phase approximation", Phys. Rev. C 71, 014308 (2005). nucl-th/0412028

• The fully consistent relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is employed in the calculation of beta-decay half-lives of neutron-rich nuclei in the N$\approx$50 and N$\approx$82 regions. A new density-dependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic Hartree-Bogoliubov calculation of nuclear ground states and in the particle-hole channel of the PN-RQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a proton-neutron particle-particle interaction. The theoretical half-lives reproduce the experimental data for the Fe, Zn, Cd, and Te isotopic chains, but overestimate the lifetimes of Ni isotopes and predict a stable 132Sn.

• N. Paar, T. Niksic, D. Vretenar and P. Ring, "Relativistic description of exotic collective excitation phenomena in atomic nuclei", Int. J. Mod. Phys. E 14, 1 (2005). nucl-th/0407064

• The low-lying dipole and quadrupole states in neutron rich nuclei, are studied within the fully self-consistent relativistic quasiparticle random-phase approximation (RQRPA), formulated in the canonical basis of the Relativistic Hartree-Bogoliubov model (RHB), which is extended to include the density dependent interactions. In heavier nuclei, the low-lying E1 excited state is identified as a pygmy dipole resonance (PDR), i.e. as a collective mode of excess neutrons oscillating against a proton-neutron core. Isotopic dependence of the PDR is characterized by a crossing between the PDR and one-neutron separation energies. Already at moderate proton-neutron asymmetry the PDR peak is calculated above the neutron emission threshold, indicating important implications for the observation of the PDR in (gamma,gamma') scattering, and on the theoretical predictions of the radiative neutron capture rates in neutron-rich nuclei. In addition, a novel method is suggested for determining the neutron skin of nuclei, based on measurement of excitation energies of the Gamow-Teller resonance relative to the isobaric analog state.

• N. Paar, T. Niksic, D. Vretenar and P. Ring, "Isotopic dependence of the pygmy dipole resonance", Phys. Lett. B 606, 288 (2005). nucl-th/0404055

• The isotopic dependence of the excitation energies of the pygmy dipole resonance (PDR) is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov (RHB) model and the relativistic quasiparticle random-phase approximation (RQRPA). The DD-ME1 density-dependent meson-exchange interaction is used in the effective mean-field Lagrangian, and pairing correlations are described by the pairing part of the finite-range Gogny interaction D1S. Model calculations reproduce available experimental data on charge radii, the neutron skin, neutron separation energies, and excitation energies of isovector giant dipole resonances in Ni, Sn and Pb nuclei. In all three isotopic chains the one-neutron separation energies decrease with mass number much faster than the excitation energies of the PDR. As a result, already at moderate proton-neutron asymmetry the PDR peak energy is calculated above the neutron emission threshold. This result has important implications for the observation of the PDR in (gamma,gamma') experiments.

• N. Paar, T. Niksic, D. Vretenar and P. Ring, "Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model II: Nuclear spin and isospin excitations", Phys. Rev. C 69, 054303 (2004).nucl-th/0402094

• The proton-neutron relativistic quasiparticle random phase approximation (PN-RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov (RHB) model, for an effective Lagrangian characterized by density-dependent meson-nucleon couplings. The model includes both the T=1 and T=0 pairing channels. Pair configurations formed from the fully or partially occupied states of positive energy in the Fermi sea, and the empty negative-energy states from the Dirac sea, are included in PN-RQRPA configuration space. The model is applied to the analysis of charge-exchange modes: isobaric analog resonances and Gamow-Teller resonances.

• D. Vretenar, T. Niksic, P. Ring, N. Paar, G. A. Lalazissis, and P. Finelli, "Relativistic Hartree-Bogoliubov and QRPA description of exotic nuclear structure", Eur. Phys. J. A 20, 75 (2004).

• D. Vretenar, T. Niksic, N. Paar, and P. Ring, "Relativistic QRPA description of low-lying dipole strength in neutron-rich nuclei", Nucl. Phys. A 731, 281 (2004).

• D. Vretenar, N. Paar, T. Niksic, and P. Ring, "Spin-Isospin Resonances and Neutron Skin of Nuclei", Phys. Rev. Lett. 91, 262502 (2003).nucl-th/0310030

• The Gamow-Teller resonances (GTR) and isobaric analog states (IAS) of a sequence of even-even Sn target nuclei are calculated by using the framework of the relativistic Hartree-Bogoliubov model plus proton-neutron quasiparticle random-phase approximation. The calculation reproduces the experimental data on ground-state properties, as well as the excitation energies of the isovector excitations. It is shown that the isotopic dependence of the energy spacings between the GTR and IAS provides direct information on the evolution of neutron skin-thickness along the Sn isotopic chain. A new method is suggested for determining the difference between the radii of the neutron and proton density distributions along an isotopic chain, based on measurement of the excitation energies of the GTR relative to the IAS.

• P. Ring, N. Paar, T. Niksic and D. Vretenar "Collective excitations far from the valley of stability" , Nucl. Phys. A 722, 372c (2003).

• N. Paar, T. Niksic, D. Vretenar and P. Ring "Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model" , Phys. Rev. C 67, 034312 (2003). nucl-th/0212011

• The relativistic quasiparticle random phase approximation (RQRPA) is formulated in the canonical single-nucleon basis of the relativistic Hartree-Bogoliubov (RHB) model. For the interaction in the particle-hole channel effective Lagrangians with nonlinear meson self-interactions are used, and pairing correlations are described by the pairing part of the finite range Gogny interaction. The RQRPA configuration space includes the Dirac sea of negative energy states. Both in the particle-hole and particle-particle channels, the same interactions are used in the RHB calculation of the ground state and in the matrix equations of the RQRPA. The RHB+RQRPA approach is tested in the example of multipole excitations of neutron rich oxygen isotopes. The RQRPA is applied in the analysis of the evolution of the low-lying isovector dipole strength in Sn isotopes and N=82 isotones.

• G. A. Lalazissis, D. Vretenar, N. Paar, and P. Ring "Relativistic description of regular and chaotic dynamics in the giant monopole resonances ", Chaos, Solitons & Fractals. 17, 585-590 (2003).

• D. Vretenar, N. Paar, P. Ring, and T. Niksic "Toroidal dipole resonances in the relativistic random phase approximation ", Phys. Rev. C 65, 021301(R), (2002). nucl-th/0107024

• The isoscalar toroidal dipole strength distributions in spherical nuclei are calculated in the framework of a fully consistent relativistic random phase approximation. It is suggested that the recently observed "low-lying component of the isoscalar dipole mode" might in fact correspond to the toroidal giant dipole resonance. Although predicted by several theoretical models, the existence of toroidal resonances has not yet been confirmed in experiment. The strong mixing between the toroidal resonance and the dipole compression mode might help to explain the large discrepancy between theory and experiment on the position of isoscalar giant dipole resonances.

• D. Vretenar, N. Paar, P. Ring and G. A. Lalazissis, "Collectivity of the low-lying dipole strength in relativistic random phase approximation", Nucl. Phys. A, 692 (3-4) 496-517 (2001). nucl-th/0101063

• The relativistic random phase approximation is applied in the analysis of the evolution of the isovector dipole response in nuclei with a large neutron excess. The self-consistent framework of relativistic mean-field theory, which has been very successfully applied in the description of ground-state properties of nuclei far from the valley of $\beta$-stability, is extended to study the possible onset of low-energy collective isovector dipole modes in nuclei with extreme isospin values.

• D. Vretenar, N. Paar, P. Ring and G. A. Lalazissis, "Pygmy dipole resonances in relativistic random phase approximation", Phys. Rev. C 63, 047301 (2001). nucl-th/0009057

• The isovector dipole response in $^{208}$Pb is described in the framework of a fully self-consistent relativistic random phase approximation. The NL3 parameter set for the effective mean-field Lagrangian with nonlinear meson self-interaction terms, used in the present calculations, reproduces ground state properties as well as the excitation energies of giant resonances in nuclei. In addition to the isovector dipole resonance in $^{208}$Pb, the present analysis predicts the occurrence of low-lying E1 peaks in the energy region between 7 and 11 MeV. In particular, a collective state has been identified whose dynamics correspond to that of a dipole pygmy resonance: the vibration of the excess neutrons against the inert core composed of equal number of protons and neutrons.

• D. Vretenar, N. Paar, P. Ring, and G. A. Lalazissis, "Nonlinear dynamics of giant resonances in atomic nuclei", Phys. Rev. E 60, 308-319 (1999). nucl-th/9809003

• The dynamics of monopole giant resonances in nuclei is analyzed in the time-dependent relativistic mean-field model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the time-series of dynamical variables that characterize the proton and neutron density distributions. The analysis of the resulting recurrence plots and correlation dimensions indicate regular motion for the isoscalar mode, and chaotic dynamics for the isovector oscillations. Information-theoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.

• D. Vretenar, P. Ring, G. A. Lalazissis, and N. Paar, "Relativistic mean-field description of the dynamics of giant resonances", Nucl. Phys.A649, 29-36 (1999). nucl-th/9809036

• The relativistic mean-field theory provides a framework in which the nuclear many-body problem is described as a self-consistent system of nucleons and mesons. In the mean-field approximation, the self-consistent time evolution of the nuclear system describes the dynamics of collective motion: nuclear compressibility from monopole resonances, regular and chaotic dynamics of isoscalar and isovector collective vibrations.

# List of Contents:

SUPPORTED BY:

"On the isoscalar-isovector splitting of pygmy dipole structures", by N. Paar, Y. F. Niu, D. Vretenar, and J. Meng, Phys. Rev. Lett. 103, 032502 (2009).
nucl-th/arXiv:0905.4848

"Neutrino and antineutrino charge-exchange reactions on 12C", by A. R. Samana, F. Krmpotic, N. Paar, and C. A. Bertulani, submitted to Phys. Rev. C (2010).
nucl-th/arXiv:1005.2134

"The quest for novel modes of excitation in exotic nuclei", by N. Paar, J. Phys. G: Nucl. Part. Phys. 37, 064014 (2010).
nucl-th/arXiv:1002.4776

REVIEW: Exotic modes of excitation in atomic nuclei far from stability by N. Paar, D. Vretenar,
E. Khan, and G. Colo,
Rep. Prog. Phys. 70, 691 (2007).                                                                      Review is focused towards modern theoretical models for studies of multipole response in unstable nuclei and possible occurrence of new exotic modes of excitation in weakly-bound nuclear systems. Of particular interest are low-energy dipole modes from stable nuclei to systems near the particle emission threshold, various isoscalar modes, charge exchange excitations and their evolution in neutron-rich nuclei, the role of exotic low-energy modes in astrophysical processes, etc.

# University of Zagreb

The University of Zagreb is one of the oldest universities in Europe, it was officially founded on 23 September 1669 by Emperor and King Leopold I Habsburg who issued a decree granting the status and privileges of a university to the Jesuit Academy of the Royal Free City of Zagreb. In naturalist field the teaching started in 1896, with first lectures in mineralogy and geology, and then in botanic, physics, mathematics, chemistry, zoology and geography. Today, the University of Zagreb is the largest university in Croatia with more than 50000 full-time students.

# Physics Department

The Physics department at the Faculty of Science has a long tradition in teaching and in scientific research. Since 1991, after moving to the new building on Horvatovac, the Department had its renaissance. The new equipment considerably improved the practical side of the education process and experimental research. Studies of the Departments theoretical physicists have led to new discoveries in the process of neleptonic decay, research of cosmology of neutrino, nuclear structures, theory of classic and quantum chaos, low dimensional systems, and electron dynamics on the surfaces of conductor and isolators. Since 2005, the Physics department consolidated its transition towards Bologna system of study programmes. Within the academic year around 700 students are pursuing one of the various theoretical, experimental, computational and educational physics programmes.