Research Interests: Nuclear Structure, Exotic Modes of Excitation, Nuclear Astrophysics, Exotic Nuclei, Effective Nuclear Interactions, Weak Interaction, NeutrinoNucleus Reactions, Nonlinear Dynamics, Computational Physics
SELECTED RECENT PUBLICATIONS & ABSTRACTS:
 D.Vale, T. Rauscher, N. Paar, "Hybrid method to resolve the neutrino mass hierarchy by supernova (anti)neutrino induced reactions", Journal of Cosmology and Astroparticle physics 02, 007 (2016).nuclth/arXiv:1509.07342
 X. RocaMaza, X. Viñas, M. Centelles, B. K. Agrawal, G. Col, N. Paar, J. Piekarewicz, D. Vretenar, Physical Review C 92, 064304 (2015).nuclth/arXiv:1510.01874
 N. Paar, Ch. C. Moustakidis, T. Marketin, D. Vretenar, G. A. Lalazissis, "Neutron star structure and collective excitations of finite nuclei", Physical Review C 90, 011304(R) (2014).nuclth/arXiv:1403.7574
 X. RocaMaza, N. Paar, G. Colo, "Covariance analysis for Energy Density Functionals and instabilities", Journal of Physics G 42, 034033 (2015).nuclth/arXiv:1212.4377
 N. Paar, H. Tutman, T. Marketin, T. Fischer, "Largescale calculations of supernova neutrinoinduced reactions in Z=882 target nuclei", Phys. Rev. C 87, 025801 (2013). nuclth/arXiv:1210.2655
 A. Krasznahorkay, N. Paar,, D. Vretenar, M.N. Harakeh, "Antianalog giant dipole resonances and the neutron skin of nuclei", Phys. Lett. B 720, 428 (2013). nuclth/arXiv:1302.6007v1
 Y.F. Niu, Z.M. Niu, N. Paar, D. Vretenar, G.H. Wang, J.S. Bai, J. Meng, "Pairing transitions in finitetemperature relativistic HartreeBogoliubov theory", Phys. Rev. C 88, 034308 (2013). nuclth/arXiv:1306.4749
 X. RocaMaza, M. Brenna, G. Colo, M. Centelles, X. Vinas, B.K. Agrawal, N. Paar, "Electric dipole polarizability in Pb208: Insights from the droplet model", D. Vretenar, J. Piekarewicz, Phys. Rev. C 88, 024316 (2013). nuclth/arXiv:1307.4806
 E. Khan, N. Paar, D. Vretenar, L.G. Cao, H. Sagawa, G. Colo, "Incompressibility of finite fermionic systems: Stable and exotic atomic nuclei", Phys. Rev. C 87, 064311 (2013). nuclth/arXiv:1304.7163
 P.G. Reinhard, J. Piekarewicz, W. Nazarewicz, B.K. Agrawal, N. Paar, X. RoccaMaza, "Information content of the weakcharge form factor", Phys. Rev. C 88, 034325 (2013). nuclth/arXiv:1308.1659
 H. Djapo, N. Paar, "Neutralcurrent neutrinonucleus cross sections based on relativistic nuclear energy density functional", Phys. Rev. C 86, 035804 (2012). nuclth/arXiv:1203.5224
 T. Marketin, G. MartinezPinedo, N. Paar, and D. Vretenar, "Role of momentum transfer in the quenching of GamowTeller strength", Phys. Rev. C 85, 054313 (2012). nuclth/arXiv:1203.3687
 D. Vretenar, Y. F. Niu, N. Paar, and J. Meng, "Lowenergy isovector and isoscalar dipole response in neutronrich nuclei", Phys. Rev. C 85, 044317 (2012).arXiv:1202.5663
 A. F. Fantina, E. Khan, G. Colo, N. Paar, and D. Vretenar, "Stellar electroncapture rates on nuclei based on microscopic Skyrme functional", Phys. Rev. C 86, 035805 (2012).
 J. Piekarewicz, B. K. Agrawal, G. Colo, W. Nazarewicz, N. Paar, P.G. Reinhard, X. RocaMaza, and D. Vretenar, "Electric dipole polarizability and the neutron skin", Phys. Rev. C 85, 041302(R) (2012).
 E. Khan, N. Paar, and D. Vretenar, "Lowenergy monopole strength in exotic Nickel isotopes", Phys. Rev. C 84, 051301 (2011).
 N. Paar, T. Suzuki, M. Honma,T. Marketin, D. Vretenar, "Uncertainties in modeling lowenergy neutrino induced reactions on iron group nuclei", Phys. Rev. C 84, 047305 (2011). nuclth/arXiv:1107.4872
 Y. F. Niu, N. Paar, D. Vretenar, and J. Meng, "Stellar electroncapture rates calculated with the finitetemperature relativistic randomphase approximation", Phys. Rev. C 83, 045807 (2011). nuclth/arXiv:1104.1683
 A. R. Samana, F. Krmpotic, N. Paar, and C. A. Bertulani, "Neutrino and antineutrino chargeexchange reactions on 12C", Phys. Rev. C 83, 045807 (2011). nuclth/arXiv:1005.2134
 N. Paar, "The quest for novel modes of excitation in exotic nuclei", J. Phys. G: Nucl. Part. Phys. 37, 064014 (2010). nuclth/arXiv:1002.4776
 N. Paar, G. Colo, E. Khan, and D. Vretenar, "Calculation of stellar electroncapture cross sections on nuclei based on microscopic Skyrme functionals", Phys. Rev. C 80, 055801 (2009). nuclth/arXiv:0909.3070
 Y. F. Niu, N. Paar, D. Vretenar, and J. Meng, "Lowenergy multipole response in nuclei at finite temperature", submitted to Phys. Lett. B 681, 315 (2009). nuclth/arXiv:0906.2973
 N. Paar, Y. F. Niu, D. Vretenar, and J. Meng, "On the isoscalarisovector splitting of pygmy dipole structures", Phys. Rev. Lett. 103, 032502 (2009). nuclth/arXiv:0905.4848
 T. Marketin, N. Paar, T. Niksic, and D. Vretenar, "Relativistic QRPA calculation of muon capture rates", Phys. Rev. C 79, 054323 (2009). nuclth/arXiv:0812.1947
 N. Paar, Comment on "Pygmy dipole response of protonrich argon nuclei in randomphase approximation and nocore shell model", Phys. Rev. C 78, 039801 (2008). nuclth/arXiv:0803.0274
 N. Paar, D. Vretenar, T. Marketin, and P. Ring, "Inclusive chargedcurrent neutrinonucleus reactions calculated with the relativistic quasiparticle random phase approximation", Phys. Rev. C 77, 024608 (2008). nuclth/arXiv:0710.4881
 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). nuclth/0701081
 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). nuclth/0609039

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).nuclth/0608018
 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).nuclth/0608011
 N. Paar, D. Vretenar, T. Niksic, and P. Ring, "Relativistic quasiparticle randomphase approximation description of isoscalar compression modes in openshell nuclei in the A=60 mass region ", Phys. Rev. C 74, 037303 (2006).nuclth/0606054
 N. Paar, P. Papakonstantinou, H. Hergert, and R. Roth, "Collective multipole excitations based on correlated realistic nucleonnucleon interactions", Phys. Rev. C 74, 014318 (2006). nuclth/0601026
 N. Paar, P. Papakonstantinou, R. Roth, and H. Hergert, "Selfconsistent description of collective excitations in the unitary correlation operator model", Int. J. Mod. Phys. E 15, 346 (2006). nuclth/0511041
 R. Roth, P. Papakonstantinou, N. Paar, H. Hergert, T. Neff, and H. Feldmeier, "HartreeFock and ManyBody Perturbation Theory with Correlated Realistic NNInteractions", Phys. Rev. C 73, 044312 (2006). nuclth/0510036
 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). nuclth/0506076
 N. Paar, T. Niksic, D. Vretenar, T. Marketin, and P. Ring, "Selfconsistent relativistic QRPA studies of soft modes and spinisospin resonances in unstable nuclei", Eur. Phys. J. A 25 Suppl. 1, 531 (2005). ISSN 1434601X (Online).
 N. Paar, P. Papakonstantinou, V. Yu. Ponomarev, and J. Wambach, "Lowenergy dipole excitations towards the proton dripline: doubly magic 48Ni", Phys. Lett. B 624, 195 (2005). nuclth/0506010
 N. Paar, D. Vretenar, and P. Ring, "Proton electric pygmy dipole resonance", Phys. Rev. Lett. 94, 182501 (2005). nuclth/0504035
 T. Niksic, T. Marketin, D. Vretenar, N. Paar, and P. Ring, "Betadecay rates of rprocess nuclei in the relativistic quasiparticle random phase approximation", Phys. Rev. C 71, 014308 (2005). nuclth/0412028
 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). nuclth/0407064
 N. Paar, T. Niksic, D. Vretenar and P. Ring, "Isotopic dependence of the pygmy dipole resonance", Phys. Lett. B 606, 288 (2005). nuclth/0404055
 N. Paar, T. Niksic, D. Vretenar and P. Ring, "Quasiparticle random phase approximation based on the relativistic HartreeBogoliubov model II: Nuclear spin and isospin excitations", Phys. Rev. C 69, 054303 (2004).nuclth/0402094
 D. Vretenar, T. Niksic, P. Ring, N. Paar, G. A. Lalazissis, and P. Finelli, "Relativistic HartreeBogoliubov 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 lowlying dipole strength in neutronrich nuclei", Nucl. Phys. A 731, 281 (2004).
 D. Vretenar, N. Paar, T. Niksic, and P. Ring, "SpinIsospin Resonances and Neutron Skin of Nuclei", Phys. Rev. Lett. 91, 262502 (2003).nuclth/0310030
 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 HartreeBogoliubov model" , Phys. Rev. C 67, 034312 (2003). nuclth/0212011
 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, 585590 (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). nuclth/0107024
 D. Vretenar, N. Paar, P. Ring and G. A. Lalazissis, "Collectivity of the lowlying dipole strength in relativistic random phase approximation", Nucl. Phys. A, 692 (34) 496517 (2001). nuclth/0101063
 D. Vretenar, N. Paar, P. Ring and G. A. Lalazissis, "Pygmy dipole resonances in relativistic random phase approximation", Phys. Rev. C 63, 047301 (2001). nuclth/0009057
 D. Vretenar, N. Paar, P. Ring, and G. A. Lalazissis, "Nonlinear dynamics of giant resonances in atomic nuclei", Phys. Rev. E 60, 308319 (1999). nuclth/9809003
 D. Vretenar, P. Ring, G. A. Lalazissis, and N. Paar, "Relativistic meanfield description of the dynamics of giant resonances", Nucl. Phys.A649, 2936 (1999). nuclth/9809036
We introduce a hybrid method to determine the neutrino mass hierarchy by simultaneous measurements of responses of at least two detectors to antineutrino and neutrino fluxes from accretion and cooling phases of corecollapse supernovae. The (anti)neutrinonucleus cross sections for 56Fe and 208Pb are calculated in the framework of the relativistic nuclear energy density functional and weak interaction Hamiltonian, while the cross sections for inelastic scattering on free protons p(ν¯e,e+)n are obtained using heavybaryon chiral perturbation theory. The modelling of (anti)neutrino fluxes emitted from a protoneutron star in a corecollapse supernova include collective and MikheyevSmirnovWolfenstein effects inside the exploding star. The particle emission rates from the elementary decay modes of the daughter nuclei are calculated for normal and inverted neutrino mass hierarchy. It is shown that simultaneous use of (anti)neutrino detectors with different target material allows to determine the neutrino mass hierarchy from the ratios of νe and ν¯einduced particle emissions. This hybrid method favors neutrinos from the supernova cooling phase and the implementation of detectors with heavier target nuclei (208Pb) for the neutrino sector, while for antineutrinos the use of free protons in mineral oil or water is the appropriate choice.
The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability αD of 68Ni, 120Sn, and 208Pb with the predictions of the Random Phase Approximation, using a representative set of nuclear energy density functionals. The calculated values of αD are used to validate different correlations involving αD, the symmetry energy at the saturation density J, the corresponding slope parameter L and the neutron skin thickness Δrnp, as suggested by the Droplet Model. A subset of models that reproduce simultaneously the measured polarizabilities in 68Ni, 120Sn, and 208Pb are employed to predict the values of the symmetry energy parameters at saturation density and Δrnp. The resulting intervals are: J=3035 MeV, L=2066 MeV; and the values for Δrnp in 68Ni, 120Sn, and 208Pb are in the ranges: 0.15\text{}0.19 fm, 0.12\text{}0.16 fm, and 0.13\text{}0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei.
A method is introduced that establishes relations between properties of collective excitations in finite nuclei and the
phase transition density $n_t$ and pressure $P_t$ at the inner edge separating the liquid core and the solid crust of a neutron star.
A theoretical framework that includes the thermodynamic method, relativistic nuclear energy density functionals and
the quasiparticle randomphase approximation
is employed in a selfconsistent calculation of $(n_t,P_t)$ and collective excitations in nuclei.
Covariance analysis shows that properties of chargeexchange dipole transitions, isovector giant dipole and quadrupole resonances, and pygmy dipole transitions
are correlated with the corecrust transition density and pressure. A set of relativistic nuclear energy density functionals, characterized by systematic variation of the density dependence of the symmetry energy of nuclear matter, is used to constrain possible values for $(n_t,P_t)$. By comparing the calculated excitation energies of giant resonances, energy weighted pygmy dipole strength, and dipole polarizability with available data, we obtain the weighted average values: $n_t = 0.0955 \pm 0.0007$ fm$^{3}$ and
$P_t = 0.59 \pm 0.05$ MeV fm$^{3}$. This approach crucially depends on experimental
results for collective excitations in nuclei and, therefore, accurate measurements
are necessary to further constrain the structure of the crust of neutron stars.
Recent improvements in the experimental determination of properties of the isovector giant quadrupole resonance (IVGQR), as demonstrated in the A=208 mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in 208Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of nonrelativistic and covariant energy density functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of state. The macroscopic approach yields an explicit dependence of the nuclear symmetry energy at some subsaturation density, for instance S(Ï=0.1 fmâ3), or the neutron skin thickness Îrnp of a heavy nucleus, on the excitation energies of isoscalar and isovector GQRs. Using available data it is found that S(Ï=0.1 fmâ3)=23.3Â±0.6 MeV. Results obtained with the microscopic framework confirm the correlation of the Îrnp to the isoscalar and isovector GQR energies, as predicted by the macroscopic model. By exploiting this correlation together with the experimental values for the isoscalar and isovector GQR energies, we estimate Îrnp=0.14Â±0.03 fm for 208Pb, and the slope parameter of the symmetry energy: L=37Â±18 MeV.
Background: In the environment of high neutrino fluxes provided in corecollapse supernovae or neutron star mergers, neutrinoinduced reactions with nuclei contribute to the nucleosynthesis processes. A number of terrestrial neutrino detectors are based on inelastic neutrinonucleus scattering and modeling of the respective cross sections allow predictions of the expected detector reaction rates.
Purpose: To provide a selfconsistent microscopic description of neutrinonucleus cross sections involving a large pool of Z=8â82 nuclei for the implementation in models of nucleosynthesis and neutrino detector simulations.
Methods: Selfconsistent theory framework based on relativistic nuclear energy density functional is employed to determine the nuclear structure of the initial state and relevant transitions to excited states induced by neutrinos. The weak neutrinonucleus interaction is employed in the currentcurrent form and a complete set of transition operators is taken into account.
Results: We perform largescale calculations of chargedcurrent neutrinonucleus cross sections, including those averaged over supernova neutrino fluxes, for the set of eveneven target nuclei from oxygen toward lead (Z=8â82), spanning N=8â182 (OPb pool). The model calculations include allowed and forbidden transitions up to J=5 multipoles.
Conclusions: The present analysis shows that the selfconsistent calculations result in considerable differences in comparison to previously reported cross sections, and for a large number of target nuclei the cross sections are enhanced. Revision in modeling rprocess nucleosynthesis based on a selfconsistent description of neutrinoinduced reactions would allow an updated insight into the origin of elements in the Universe and it would provide the estimate of uncertainties in the calculated element abundance patterns.
We examine a method to determine the neutronskin thickness of nuclei using data on the chargeexchange antianalog giant dipole resonance (AGDR). Calculations performed using the relativistic protonneutron quasiparticle randomphase approximation (pnRQRPA) reproduce the isotopic trend of the excitation energies of the AGDR, as well as that of the spinflip giant dipole resonances (IVSGDR), in comparison to available data for the eveneven isotopes Sn112124. It is shown that the excitation energies of the AGDR, obtained using a set of densitydependent effective interactions which span a range of the symmetry energy at saturation density, supplemented with the experimental values, provide a stringent constraint on value of the neutronskin thickness. For Sn124, in particular, we determine the value Delta Rpn = 0.21 +/ 0.05 fm. The result of the present study shows that a measurement of the excitation energy of the AGDR in (p, n) reactions using rareisotope beams in inverse kinematics, provides a valuable method for the determination of neutronskin thickness in exotic nuclei. (c) 2013 Elsevier B.V. All rights reserved.
We formulate the finitetemperature relativistic HartreeBogoliubov theory for spherical nuclei based on a pointcoupling functional, with the Gogny or separable pairing force. Using the functional PCPK1, the framework is applied to the study of pairing transitions in Ca, Ni, Sn, and Pb isotopic chains. The separable pairing force reproduces the gaps calculated with the Gogny force not only at zero temperature, but also at finite temperatures. By performing a systematic calculation of the eveneven Ca, Ni, Sn, and Pb isotopes, it is found that the critical temperature for a pairing transition generally follows the rule Tc=0.6În(0), where În(0) is the neutron pairing gap at zero temperature. This rule is further verified by adjusting the pairing gap at zero temperature with a strength parameter.
We study the electric dipole polarizability Î±D in 208Pb based on the predictions of a large and representative set of relativistic and nonrelativistic nuclear mean field models. We adopt the droplet model as a guide to better understand the correlations between Î±D and other isovector observables. Insights from the droplet model suggest that the product of Î±D and the nuclear symmetry energy at saturation density J is much better correlated with the neutron skin thickness Îrnp of 208Pb than the polarizability alone. Correlations of Î±DJ with Îrnp and with the symmetry energy slope parameter L suggest that Î±DJ is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of thenuclear energy density functional by comparing our theoretical predictions against measurements of both Î±D and the parityviolating asymmetry in 208Pb. We find that the recent experimental determination of Î±D in 208Pb in combination with the range for the symmetry energy at saturation density J=[31Â±(2)est.]\,MeV suggests Îrnp(208Pb)=0.165Â±(0.009)exp.Â±(0.013)theo.Â±(0.021)est.fm and L=43Â±(6)exp.Â±(8)theo.Â±(12)est. MeV.
The incompressibility of finite fermionic systems is investigated using analytical approaches and microscopic models. The incompressibility of a system is directly linked to the zeropoint kinetic energy of constituent fermions, and this is a universal feature of fermionic systems. In the case of atomic nuclei, this implies a constant value of the incompressibility in mediumheavy and heavy nuclei. The evolution of nuclear incompressibility along Sn and Pb isotopic chains is analyzed using global microscopic models, based on both nonrelativistic and relativistic energy functionals. The result is an almost constant incompressibility in stable nuclei and systems not far from stability and a steep decrease in nuclei with pronounced neutron excess, caused by the emergence of a soft monopole mode in neutronrich nuclei.
Background: Parityviolating electron scattering provides a modelindependent determination of the nuclear weakcharge form factor that has widespread implications across such diverse areas as fundamental symmetries, nuclear structure, heavyion collisions, and neutronstar structure.
Purpose: We assess the impact of precise measurements of the weakcharge form factor of 48Ca and 208Pb on a variety of nuclear observables, such as the neutron skin and the electricdipole polarizability.
Methods: We use the nuclear density functional theory with several accurately calibrated nonrelativistic and relativistic energy density functionals. To assess the degree of correlation between nuclear observables and to explore systematic and statistical uncertainties on theoretical predictions, we employ the chisquare statistical covariance technique.
Results: We find a strong correlation between the weakcharge form factor and the neutron radius, that allows for an accurate determination of the neutron skin of neutronrich nuclei. We determine the optimal range of the momentum transfer q that maximizes the information content of the measured weakcharge form factor and quantify the uncertainties associated with the strange quark contribution. Moreover, we confirm the role of the electricdipole polarizability as a strong isovector indicator.
Conclusions: Accurate measurements of the weakcharge form factor of 48Ca and 208Pb will have a profound impact on many aspects of nuclear theory and hadronic measurements of neutron skins of exotic nuclei at radioactivebeam facilities.
Background: Inelastic neutrinonucleus scattering through the weak neutralcurrent plays important role in stellar environment where transport of neutrinos determine the rate of cooling. Since there are no direct experimental data on neutralcurrent neutrinonucleus cross sections available, only the modeling of these reactions provides the relevant input for supernova simulations. Purpose: To establish fully selfconsistent framework for neutralcurrent neutrinonucleus reactions based on relativistic nuclear energy density functional. Methods: Neutrinonucleus cross sections are calculated using weak Hamiltonian and nuclear properties of initial and excited states are obtained with relativistic HartreeBogoliubov model and relativistic quasiparticle random phase approximation that is extended to include pion contributions for unnatural parity transitions. Results: Inelastic neutralcurrent neutrinonucleus cross sections for 12C, 16O, 56Fe, 56Ni, and even isotopes {92100}Mo as well as respective cross sections averaged over distribution of supernova neutrinos. Conclusions: The present study provides insight into neutrinonucleus scattering cross sections in the neutral channel, their theoretical uncertainty in view of recently developed microscopic models, and paves the way for systematic selfconsistent largescale calculations involving openshell target nuclei.
The relativistic protonneutron quasiparticle random phase approximation
(pnRQRPA) is applied in the calculation of the L=0 strength in chargeexchange
reactions on $^{48}$Ca, $^{90}$Zr, $^{208}$Pb and nuclei in the Sn isotopic
chain. The microscopic theoretical framework is based on the relativistic
HartreeBogoliubov (RHB) model for the nuclear ground state. The calculation is
fully selfconsistent, i.e. the same interaction is used both in the RHB
equations that determine the quasiparticle basis, and in the matrix equations
of the pnRQRPA. The inclusion of the higherorder 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
highenergy region above the GamowTeller (GT) resonance. The total strength is
slightly enhanced in nuclei with small neutrontoproton ratio but remains
unchanged with increasing neutron excess. Based on the strength obtained using
the full L=0 transition operator in the pnRQRPA calculation, we have estimated
the impact of the IVSM on the strength measured in the chargeexchagne
reactions on $^{90}$Zr and found that the data are consistent with the Ikeda
sum rule.
The selfconsistent 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 densitydependence 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 energyweighted
sum rule but a much larger percentage of the inverse energyweighted 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 particlehole configurations, most of which
add coherently, and this results in a collective response of the PDS to the
isoscalar dipole operator.
We compute electroncapture rates for 54,56Fe and Ge isotopes using a selfconsistent microscopic
approach. The singlenucleon basis and the occupation factors in the target nucleus are calculated
in the finitetemperature Skyrme HartreeFock model, and the Ji = 0±, 1±, 2± chargeexchange
transitions are determined in the finitetemperature randomphase approximation (RPA). The
scheme is selfconsistent, i.e. both the HartreeFock and the RPA equations are based on the same
Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on
the electroncapture rates for different astrophysical conditions. Considering various models, the
typical spreading of the electroncapture rates in Fe and Ge is estimated to two orders of magnitude.
The recent highresolution measurement of the electric dipole (E1)
polarizability (alphad) in 208Pb [Phys. Rev. Lett. 107, 062502 (2011)] provides
a unique constraint on the neutronskin thickness of this nucleus. The
neutronskin 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 nonrelativistic 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 208Pbcombined with the recent measurement of alphadshould
significantly constrain the isovector sector of the nuclear energy density
functional.
Lowenergy strength is predicted in the isoscalar monopole response of
neutronrich 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
particlehole configurations shows that these states represent almost
pure neutron single holeparticle 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 lowenergy monopole strength with neutron excess.
Chargedcurrent neutrinonucleus 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 neutrinonucleus cross sections are assessed in relation to the predicted GamowTeller transition strength and available data, multipole decomposition of the cross sections, and cross sections averaged over the Michel flux and FermiDirac distribution. Employing different microscopic approaches and models, the DAR neutrino56Fe 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.
We introduce a selfconsistent microscopic theoretical framework for modeling the process of electron capture on nuclei in stellar environment, based on relativistic energy density functionals. The finitetemperature relativistic meanfield model is used to calculate the singlenucleon basis and the occupation factors in a target nucleus, and Jπ=0±, 1±, and 2± chargeexchange transitions are described by the selfconsistent finitetemperature relativistic randomphase 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.
We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrinonucleus 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 nonconservation 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 crosssections: i) are close to the sumrule 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 crosssection based on the degree of forbiddenness of different multipoles. The $\nu/\bar{\nu}$$^{12}$C chargeexchange reactions related with astrophysical applications are briefly discussed.
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 spinisospin excitations both in neutronrich and proton dripline 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
selfconsistent manybody theory frameworks at the frontiers of ongoing
research, including nuclear energy density functionals, both phenomenological
and constrained by the strong interaction physics of QCD, models based on low momentum
twonucleon interaction Vlowk and correlated realistic nucleon
nucleon interaction VUCOM, supplemented by threebody force, as well as
twonucleon and threenucleon 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.
A fully selfconsistent microscopic framework for evaluation of nuclear
weakinteraction rates at finite temperature is introduced, based on Skyrme functionals.
The singlenucleon basis and the corresponding thermal occupation factors of the initial nuclear
state are determined in the finitetemperature Skyrme HartreeFock model, and
chargeexchange transitions to excited states are computed using the
finitetemperature RPA. Effective interactions are implemented selfconsistently:
both the finitetemperature singlenucleon HartreeFock 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 electroncapture cross sections for selected nuclei in the iron mass group
and for neutronrich Ge isotopes.
The multipole response of nuclei at temperatures T=02 MeV is studied using a selfconsistent finitetemperature 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 lowenergy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=12 MeV additional transition strength appears at low energies because of thermal unblocking of singleparticle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in $^{60,62}$Ni, where no lowenergy excitations occur at zero temperature. The principal effect of finite temperature on lowenergy 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.
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 lowenergy
(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 surfacepeaked transition densities. At
somewhat higher energy the calculated E1 strength is primarily of isovector
character, as expected for the lowenergy 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 lowenergy E1 strength into two groups
of states with different isospin structure and radial dependence of the
corresponding transition densities.
The relativistic protonneutron quasiparticle random phase approximation (PNRQRPA) 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 HartreeBogoliubov (RHB) model for the nuclear ground state, and transitions to excited states are calculated using the PNRQRPA. 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 PNRQRPA. The calculated capture rates are sensitive to the inmedium quenching of the axialvector coupling constant. By reducing this constant from its freenucleon value $g_A = 1.262$ by 10% for all multipole transitions, the calculation reproduces the experimental muon capture rates to better than 10% accuracy.
In recent paper by C. Barbieri, E. Caurier, K. Langanke, and
G. Mart\'inez Pinedo~\cite{Bar.08}, lowenergy
dipole excitations have been studied in protonrich $^{32,34}$Ar
with random phase approximation (RPA)
and nocore shell model (NCSM) using the correlated
realistic nucleonnucleon 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 UCOMRPA framework using
identical correlated Argonne V18 interaction~\cite{Paa.06},
it does not provide any evidence that the lowlying state declared as
pygmy dipole resonance in $^{32}$Ar indeed has the resonancelike
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.
Inclusive neutrinonucleus cross sections are calculated using a consistent relativistic meanfield theoretical framework. The weak leptonhadron interaction is expressed in the standard currentcurrent form, the nuclear ground state is described with the relativistic HartreeBogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for chargedcurrent 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 neutrinonucleus 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.
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 weaklybound 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 lowenergy dipole response in unstable neutronrich 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 weaklybound nuclei. The review focuses on the applications of these models to studies of the evolution of lowenergy 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 chargeexchange modes and their evolution in neutronrich nuclei, and to studies of the role of exotic lowenergy modes in astrophysical processes.
We examine to which extent correlated realistic nucleonnucleon interactions, derived within the Unitary Correlation Operator Method (UCOM), can describe nuclear collective motion in the framework of firstorder randomphase approximation (RPA). To this end we employ the correlated Argonne V18 interaction in calculations within the socalled "Extended" RPA (ERPA) and investigate the response of closedshell nuclei. The ERPA is a renormalized RPA version which considers explicitly the depletion of the Fermi sea due to longrange 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 HartreeFock (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 UCOMbased RPA calculations and the experimental data are to be attributed to other effects, mainly to a residual threebody force and higherorder configurations. Groundstate properties obtained within the ERPA are compared with corresponding HF and perturbationtheory results and are discussed as well. The ERPA formalism is presented in detail.
The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant shortrange central and tensor correlations are described explicitly by a unitary transformation. The application of UCOM in the context of the nocore shell model provides insight into the interplay between dominant shortrange and residual longrange correlations in the nuclear manybody problem. The use of the correlated interaction within HartreeFock, manybody perturbation theory, and Random Phase Approximation gives access to various nuclear structure observables throughout the nuclear chart.
The selfconsistent random phase approximation (RPA) based on a correlated realistic nucleonnucleon interaction is used to evaluate correlation energies in closedshell nuclei beyond the HartreeFock 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 longrange correlations on binding energies throughout the whole nuclear chart, which is of particular importance when starting from realistic interactions.
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 randomphase approximation (RQRPA) with the DDME2 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 highenergy components of the dipole transition strengths. It is noted, however, that while DDME2 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.
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 shortrange central and tensor correlations a re treated explicitly within the Unitary Correlation Operator Method (UCOM), which provides a phaseshift 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 HartreeFock problem and employ the singleparticle state s as starting point for the RPA. By construction, the UCOMRPA is fully selfconsistent, i.e. the same correlated nucleonnucleon 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 centerofmass motion is properly removed and the sumrules are exhausted within +3%. The UCOMRPA scheme results in a collective character of giant monopole, dipole, and quadrupole resonances in closedshell 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 longrange correlations and threebody contributions.
The fully selfconsistent Random Phase Approximation (RPA) is constructed within the Unitary Correlation Operator Method (UCOM), which describes the dominant interactioninduced shortrange 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 closedshell nuclei across the nuclide chart. The UCOMRPA 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 longrange correlations and threebody contributions.
We employ correlated realistic nucleonnucleon interactions for the description of nuclear ground states throughout the nuclear chart within the HartreeFock approximation. The crucial shortrange central and tensor correlations, which are induced by the realistic interaction and cannot be described by the HartreeFock manybody state itself, are included explicitly by a stateindependent 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 HartreeFock level. However, the binding energies are smaller than the experimental values because longrange correlations have not been accounted for. Their inclusion by means of manybody perturbation theory leads to a remarkable agreement with experimental binding energies over the whole mass range from He4 to Pb208, even far off the valley of stability. The observed perturbative character of the residual longrange correlations and the apparently small net effect of threebody forces provides promising perspectives for a unified nuclear structure description.
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 nucleonnucleon interactions constructed within the Unitary Correlation Operator Method (UCOM), and (ii) relativistic RPA (RRPA) derived from effective Lagrangians with densitydependent mesonexchange interactions. The former includes the dominant interactioninduced shortrange central and tensor correlations by means of an unitary transformation. It is shown that UCOMRPA correlations induced by collective nuclear vibrations recover a part of the residual longrange correlations that are not explicitly included in the UCOM HartreeFock ground state. Both RPA models are employed in studies of the isoscalar monopole resonance (ISGMR) in closedshell 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 HartreeBogoliubov model, the occurrence of pronounced lowlying dipole excitations is predicted in nuclei towards the proton dripline. 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.
The properties of the lowenergy dipole response are investigated for the protonrich doubly magic nucleus $^{48}$Ni, in a comparative study of two microscopic models: fully selfconsistent Relativistic RandomPhase Approximation(RRPA) based on the novel densitydependent mesonexchange interactions, and Continuum RandomPhase Approximation(CRPA) using Skyrmetype interactions with the continuum properly included. Both models predict the existence of the lowenergy 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.
The evolution of the lowlying E1 strength in protonrich nuclei is analyzed in the framework of the selfconsistent relativistic HartreeBogoliubov (RHB) model and the relativistic quasiparticle randomphase approximation (RQRPA). Model calculations are performed for a series of N=20 isotones and Z=18 isotopes. For nuclei close to the proton dripline, the occurrence of pronounced dipole peaks is predicted in the lowenergy 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
The fully consistent relativistic protonneutron quasiparticle random phase approximation (PNRQRPA) is employed in the calculation of betadecay halflives of neutronrich nuclei in the N$\approx$50 and N$\approx$82 regions. A new densitydependent effective interaction, with an enhanced value of the nucleon effective mass, is used in relativistic HartreeBogoliubov calculation of nuclear ground states and in the particlehole channel of the PNRQRPA. The finite range Gogny D1S interaction is employed in the T=1 pairing channel, and the model also includes a protonneutron particleparticle interaction. The theoretical halflives 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.
The lowlying dipole and quadrupole states in neutron rich nuclei, are studied within the fully selfconsistent relativistic quasiparticle randomphase approximation (RQRPA), formulated in the canonical basis of the Relativistic HartreeBogoliubov model (RHB), which is extended to include the density dependent interactions. In heavier nuclei, the lowlying E1 excited state is identified as a pygmy dipole resonance (PDR), i.e. as a collective mode of excess neutrons oscillating against a protonneutron core. Isotopic dependence of the PDR is characterized by a crossing between the PDR and oneneutron separation energies. Already at moderate protonneutron 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 neutronrich nuclei. In addition, a novel method is suggested for determining the neutron skin of nuclei, based on measurement of excitation energies of the GamowTeller resonance relative to the isobaric analog state.
The isotopic dependence of the excitation energies of the pygmy dipole resonance (PDR) is analyzed in the framework of the selfconsistent relativistic HartreeBogoliubov (RHB) model and the relativistic quasiparticle randomphase approximation (RQRPA). The DDME1 densitydependent mesonexchange interaction is used in the effective meanfield Lagrangian, and pairing correlations are described by the pairing part of the finiterange 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 oneneutron separation energies decrease with mass number much faster than the excitation energies of the PDR. As a result, already at moderate protonneutron 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.
The protonneutron relativistic quasiparticle random phase approximation (PNRQRPA) is formulated in the canonical singlenucleon basis of the relativistic HartreeBogoliubov (RHB) model, for an effective Lagrangian characterized by densitydependent mesonnucleon 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 negativeenergy states from the Dirac sea, are included in PNRQRPA configuration space. The model is applied to the analysis of chargeexchange modes: isobaric analog resonances and GamowTeller resonances.
The GamowTeller resonances (GTR) and isobaric analog states (IAS) of a sequence of eveneven Sn target nuclei are calculated by using the framework of the relativistic HartreeBogoliubov model plus protonneutron quasiparticle randomphase approximation. The calculation reproduces the experimental data on groundstate 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 skinthickness 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.
The relativistic quasiparticle random phase approximation (RQRPA) is formulated in the canonical singlenucleon basis of the relativistic HartreeBogoliubov (RHB) model. For the interaction in the particlehole channel effective Lagrangians with nonlinear meson selfinteractions 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 particlehole and particleparticle 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 lowlying isovector dipole strength in Sn isotopes and N=82 isotones.
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 "lowlying 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.
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 selfconsistent framework of relativistic meanfield theory, which has been very successfully applied in the description of groundstate properties of nuclei far from the valley of $\beta$stability, is extended to study the possible onset of lowenergy collective isovector dipole modes in nuclei with extreme isospin values.
The isovector dipole response in $^{208}$Pb is described in the framework of a fully selfconsistent relativistic random phase approximation. The NL3 parameter set for the effective meanfield Lagrangian with nonlinear meson selfinteraction 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 lowlying 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.
The dynamics of monopole giant resonances in nuclei is analyzed in the timedependent relativistic meanfield model. The phase spaces of isoscalar and isovector collective oscillations are reconstructed from the timeseries 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. Informationtheoretic functionals identify and quantify the nonlinear dynamics of giant resonances in quantum systems that have spatial as well as temporal structure.
The relativistic meanfield theory provides a framework in which the nuclear manybody problem is described as a selfconsistent system of nucleons and mesons. In the meanfield approximation, the selfconsistent 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.