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The charge exchange spin-dipole (SD) excitations of Zr are studied using the Skyrme Hartee-Fock plus proton-neutron random phase approximation with SAMi-J interactions. The experimental value of the model-independent sum rule obtained from the SD strength distributions of Zr(p, n) Nb and Zr(n, p) Y is used to deduce the neutron skin thickness. The neutron skin thickness of Zr is extracted as fm, which is similar to the results of other studies. Based on the correlation analysis of the neutron skin thickness and the nuclear symmetry energy J as well as its slope parameter L, a constraint from the extracted leads to the limitation of J to MeV and L to MeV.

Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena. In this work, the systematic evolutions of nuclear charge radii along even $Z$=84-120 isotopic chains are firstly investigated by the recently developed new ansatz under the covariant density functional. The calculated results show that the shell closure effects of nuclear charge radii are remarkably shown at the neutron numbers $N=126$ and 184. Interestingly, the arch-like shapes of charge radii between these two strong neutron closed shells are naturally observed. Across the $N=184$ shell closure, the abrupt increase in charge radii is still evidently emerged. In addition, the rapid raise of nuclear charge radii from the neutron numbers $N=138$ to $N=144$ is also disclosed clearly in superheavy regions due to the enhanced shape deformation., 23 pages, 3 figures

In a recent paper [Phys. Rev. C 101, 014305 (2020)], Dong and Shang claim that the Skyrme original tensor interaction is invalid. Their conclusion is based on the misconception that the Fourier transform of tensor interaction is difficult or even impossible, so that the Skrme-type tensor interaction was introduced in an unreasonable way. We disagree on their claim. In this note, we show that one can easily get the Skyrme force in momentum space by Fourier transformation if one starts from a general central, spin-orbit or tensor interaction with a radial dependence., 3 pages, 0 figures

Systematic trends in nuclear charge radii are of great interest due to universal shell effects and odd-even staggering (OES). The modified root mean square (rms) charge radius formula, which phenomenologically accounts for the formation of neutron-proton ($np$) correlations, is here applied for the first time to the study of odd-$Z$ copper and indium isotopes. Theoretical results obtained by the relativistic mean field (RMF) model with NL3, PK1 and NL3$^{*}$ parameter sets are compared with experimental data. Our results show that both OES and the abrupt changes across $N=50$ and $82$ shell closures are clearly reproduced in nuclear charge radii. The inverted parabolic-like behaviors of rms charge radii can also be described remarkably well between two neutron magic numbers, namely $N=28$ to $50$ for copper isotopes and $N=50$ to $82$ for indium isotopes. This implies that the $np$-correlations play an indispensable role in quantitatively determining the fine structures of nuclear charge radii along odd-$Z$ isotopic chains. Also, our conclusions have almost no dependence on the effective forces., Comment: 21 pages, 4 figures

A unified theoretical model reproducing charge radii of known atomic nuclei plays an essential role in making extrapolations for unknown nuclei. Recently developed new ansatz which phenomenologically takes into account the neutron-proton short-range correlations ($np$-SRCs) can describe the discontinuity properties and odd-even staggering (OES) effect of charge radii along isotopic chains remarkably well. In this work, we further review the modified root-mean-square (rms) charge radii formula in the framework of relativistic mean field (RMF) theory. The charge radii are calculated along various isotopic chains that include the nuclei featuring the $N=50$ and $82$ magic shells. Our results suggest that RMF with and without considering a correction term give an almost similar trend of nuclear size for some isotopic chains with open proton shell, especially the abrupt increases across the strong neutron closed shells and the OES behaviors. This reflects that the $np$-SRCs have almost no influence for some nuclei due to the strong coupling between different levels around Fermi surface. The weakening OES behavior of nuclear charge radii is observed generally at completely filled neutron shells and this may be proposed as a signature of magic indicator., Comment: 19 pages, 5 figures

The effective isospin-density-dependent pairing interaction (P1) [S. S. Zhang, U. Lombardo, and E. G. Zhao, Sci. Chin. Phys. Mech. Astron. 54, 236 (2011)] extracted from neutron pairing gaps for $^{1}S_{0}$ in asymmetric nuclear matter calculations [S. S. Zhang, L. G. Cao, U. Lombardo, E. G. Zhao, and S. G. Zhou, Phys. Rev. C 81, 044313 (2010)] is employed to study the bulk properties of Ca, Ni, Zr, and Sn isotopes. The odd-even mass (OEM) staggering is calculated by the Skyrme Hartree-Fock plus BCS method ($\text{SHF}+\text{BCS}$) with the SkP force. For comparison, we study two other types of isovector effective pairing interactions. One is also extracted from pairing gaps of infinite nuclear matter by the Brueckner-Hartree-Fock (BHF) method but for free spectrum (P2). The other is obtained by fitting the empirical OEM (P3). An isoscalar effective pairing interaction (P4) is also adopted, which is determined by fitting the empirical OEM. We find that interaction P1 can better describe the OEM staggering of Ni, Zr, and Sn isotopes by $14.3%, 41%$, and $30.4%$ compared with interaction P2, in terms of root-mean-square deviations to the empirical OEM, respectively. On the other hand, the performance of P1 and P2 is comparable for Ca isotopes. For Ca and Ni isotopes, P1 behaves similarly to P3, but for Zr isotopes P1 is better than P3 by $\ensuremath{\approx}34%$. One may conclude that the isovector pairings are preferred over the isoscalar one for neutron pairings in finite nuclei with the SkP force. It is quite interesting to note that the pairing interaction P1 extracted from nuclear matter calculations can describe pairing gaps of finite nuclei as well as or even better than the interaction P3 directly fitted to finite nuclei. To study the influence from the mean fields on the OEM, we perform the same analysis using the SLy4 and SkI4 forces as well. It turns out that pairing gaps described by these two forces with four pairing interactions are underestimated, so that P2 seems to be better than P1 and is comparable with P3.

We examined the low-lying quadrupole states in Sn isotopes in the framework of fully self-consistent Hartree-Fock+BCS plus QRPA. We focus on the effect of the density-dependence of pairing interaction on the properties of the low-lying quadrupole state. The SLy5 Skyrme interaction with surface, mixed, and volume pairings is employed in the calculations, respectively. We find that the excitation energies and the corresponding reduced electric transition probabilities of the first 2+ state are different, given by the three pairing interactions. The properties of the quasiparticle state, two-quasiparticle excitation energy, reduced transition amplitude, and transition densities in 112Sn are analyzed in detail. Two different mechanisms, the static and dynamical effects, of the pairing correlation are also discussed. The results show that the surface, mixed, and volume pairings indeed affect the properties of the first 2+ state in the Sn isotopes.

We critically examine nuclear matter and neutron matter equation of state (EoS) parameters by using best available terrestrial experimental results. The nuclear incompression modulus $K_{\infty}$ is re-examined in comparisons with RPA results of modern relativistic and non-relativistic EDF and up-to-date experimental data of isoscalar giant monopole resonance energy of $^{208}$Pb. The symmetry energy expansion coefficients $J$, $L$ and $K_{sym}$ are examined by recent FRDM mass model and the neutron skin of $^{48}$Ca extracted from $(p,p')$ experiments., 13 pages, 6figures, To appear in the AIP Conference Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy (January 3 - 7, 2019, Xiamen, China

The isovector giant dipole resonances (IVGDR) in proton-rich Ar and Ca isotopes have been systematically investigated using the resonant continuum Hartree-Fock+BCS (HF+BCS) and quasiparticle random phase approximation (QRPA) methods. The Skyrme SLy5 and density-dependent contact pairing interactions are employed in the calculations. In addition to the giant dipole resonances at energy around 18 MeV, pygmy dipole resonances (PDR) are found to be located in the energy region below 12 MeV. The calculated energy-weighted moments of PDR in nuclei close to the proton drip-line exhaust about 4% of the TRK sum rule. The strengths decrease with increasing mass number in each isotopic chain. The transition densities of the PDR states show that motions of protons and neutrons are in phase in the interiors of nuclei, while the protons give the main contribution at the surface. By analyzing the QRPA amplitudes of proton and neutron 2-quasiparticle configurations for a given low-lying state, we find that only a few proton configurations give significant contributions. They contribute about 95% to the total QRPA amplitudes, which indicates that the collectivity of PDR states is not strong in proton-rich nuclei in the present study.

To improve measurement accuracy of safety belt pin, the size-sorting system which mainly includes a machine vision subsystem and a driving subsystem, is researched. The machine vision subsystem includes a industry camera, a double telecentric lens and a backlight. Image process steps that have sub-pixel accuracy are presented. The driving subsystem is designed with Atmega128L MCU. The state machine is designed for safety pin control logic. The two sub systems communicate with RS232 serial port. The test shows that the system has a maximum accuracy error of 0.05mm, repeatability error of 0.013mm.

Glazing is a key procedure in ceramic product surface decorating processing. Recently, robots are gradually utilized to fulfill the glazing work instead of manual work. However, the researches on freeform surface glazing technology lag behind the research on robotics technology, thus limits the application of glazing robot in ceramic industry. In order to improve the quality and efficiency of robot glazing, this paper presents a new method which is base on STL model to generate trajectory for glazing spray gun. The whole procedures of this method have been discussed explicitly.

To acquire torque performance in seat belt conveniently and precisely, the measurement scheme based on stepper motor was established. The hardware was developed with high-speed data acquisition unit based on PCI protocol. The software which includes user interface and data acquisition control module etc was developed with multithread technique and document-view architecture. The experiments with seat belt spring show that the max torque error of the system is 0.08N.cm. The system has merits of high precision, easy operation and can provide reliable data for spring torque performance in seat belt.

Random Phase Approximation (RPA) calculations are nowadays an indispensable tool in nuclear physics studies. We present here a complete version implemented with Skyrme-type interactions, with the spherical symmetry assumption, that can be used in cases where the effects of pairing correlations and of deformation can be ignored. The full self-consistency between the Hartree–Fock mean field and the RPA excitations is enforced, and it is numerically controlled by comparison with energy-weighted sum rules. The main limitations are that charge-exchange excitations and transitions involving spin operators are not included in this version.

To improve the efficiency and accuracy of porcelain appearance evaluation, a kind of automatic evaluation system was presented, which composed with industrial cameras, USB(Universal Serial Bus) data acquisition card and step motor etc. The software was mainly developed with C# language. Modules such as image pre-processing and evaluation algorism etc, were developed with matlab program language. Communication between C# program and matlab program was implemented with component technology. Experiments with bowls show that the system can conveniently evaluate the porcelain by its appearance and the result is accurate.

The effect of the tensor force on the properties of finite nuclei is discussed by analyzing the multipole giant resonances in 208 Pb. It is found that the tensor force has a larger effect on the spin-flip magnetic dipole and Gamow-Teller resonances than on the natural parity low-lying isoscalar quadrupole (2 + ) and octupole (3 � ) states. By analyzing the modifications to the Hartree-Fock mean field induced by the tensor terms, and the specific features of the residual particle-hole tensor interaction, we find that the tensor force gives an attractive contribution to the particle-hole matrix elements.

The isoscalar giant monopole resonance (ISGMR) in Cd, Sn and Pb isotopes has been studied within the self-consistent Skyrme Hartree-Fock+BCS and quasi-particle random phase approximation (QRPA). Three Skyrme parameter sets are used in the calculations, i.e., SLy5, SkM* and SkP, since they are characterized by different values of the compression modulus in symmetric nuclear matter, namely K=230, 217, and 202 MeV, respectively. We also investigate the effect of different types of pairing forces on the ISGMR in Cd, Sn and Pb isotopes. The calculated peak energies and the strength distributions of ISGMR are compared with available experimental data. We find that SkP fails completely to describe the ISGMR strength distribution for all isotopes due to its low value of the nuclear matter incompressibility, namely K=202 MeV. On the other hand, the SLy5 parameter set, supplemented by an appropriate pairing interaction, gives a reasonable description of the ISGMR in Cd and Pb isotopes. A better description of ISGMR in Sn isotopes is achieved by the SkM* interaction, that has a somewhat softer value of the nuclear incompressibility., Submitted to Phys. Rev. C

A microscopic analysis of the asymmetry energy is performed through the investigation of nuclear giant resonances in the relativistic approach. Nuclear ground state properties are calculated in an extended relativistic mean-field theory plus BCS method, where the contribution of the resonant continuum to pairing correlations is properly treated. The nuclear giant resonances are investigated in the relativistic random phase approximation (RRPA) or quasi-particle RRPA. Special emphases are paid to the correlation between the giant dipole resonance or pygmy resonance and the density dependence of the asymmetry energy.

A correct determination of the isospin and spin-isospin properties of the nuclear effective interaction should lead to an accurate description of the Gamow-Teller resonance (GT), the Spin Dipole Resonance (SDR), the Giant Dipole Resonance (GDR) or the Antianalog Giant Dipole Resonance (AGDR), among others. A new Skyrme energy density functional named SAMi is introduced with the aim of going a step forward in setting the bases for a more precise description of spin-isospin resonances [1, 2]. In addition, we will discuss some new features of our analysis on the AGDR in 208Pb [3] as compared with available experimental data on this resonance [4, 5, 6], and on the GDR [7]. Such study, guided by a simple yet physical pocket formula, has been developed by employing the so called SAMi-J family of systematically varied interactions. This set of interactions is compatible with experimental data for values of the symmetry energy at saturation J and slope parameter L falling in the ranges 31−33 MeV and 75−95 MeV, re...

We investigate the impact of the neutron-skin thickness Delta(R) on the energy difference between the anti-analog giant dipole resonance (AGDR), E(AGDR), and the isobaric analog state (IAS), E(IAS), in a heavy nucleus such as 208Pb. For guidance, we first develop a simple and analytic, yet physical, approach based on the Droplet Model that linearly connects the energy difference E(AGDR)-E(IAS) with Delta(R). To test this correlation on more fundamental grounds, we employ a family of systematically varied Skyrme energy density functionals where variations on the value of the symmetry energy at saturation density J are explored. The calculations have been performed within the fully self consistent Hartree-Fock (HF) plus charge-exchange random phase approximation (RPA) framework. We confirm the linear correlation within our microscopic apporach and, by comparing our results with available experimental data in 208Pb, we find that our analysis is consistent with Delta(R) = 0.204 \pm 0.009 fm, J = 31.4 \pm 0.5 MeV and a slope parameter of the symmetry energy at saturation of L = 76.4 \pm 5.4 MeV - the attached errors correspond to a lower-limit estimate of the systematic plus experimental uncertainties. These results are in agreement with those extracted from different experimental data albeit, L and Delta(R) are somewhat large when compared to previous estimations based on giant resonance studies., Comment: Submitted to Phys. Rev. C

Energies, widths and wave functions of the single-particle resonant continuum are determined by solving scattering status of the Dirac equation with proper asymptotic conditions for the continuous spectrum in the relativistic mean-field theory. The relativistic regular and irregular Coulomb wave functions are calculated numerically. The resonance states in the continuum for some closed- or sub-closed-shell nucleus in Sn-isotopes, such as Sn-114, Sn-116, Sn-118, and Sn-120 arc calculated. Results show that the S-matrix method is a reliable and straightforward way in determining energies and widths of resonant status.

The pygmy and giant dipole resonances in proton-rich nuclei 17,18Ne are investigated with a fully self-consistent approach. The properties of ground states are calculated in the Skyrme Hartree–Fock with the Bardeen–Cooper–Schrieffer approximation to take into account the pairing correlation. The quasiparticle random phase approximation (QRPA) method is used to explore the properties of excited dipole states. In the calculations the SLy5 Skyrme interaction is employed. In addition to the giant dipole resonances, pygmy dipole resonances (PDR) are found to be located in the energy region below 10 MeV in both 17,18 Ne. The strength and transition density show that the low-lying states are typical PDR states. However, analyzing the QRPA amplitudes of proton and neutron 2 quasiparticle (2qp) configurations for a given low-lying state in 17,18 Ne, we find that the PDR state is less collective, more like a single 2qp excitation.

The magnetic dipole (M1) and the Gamow-Teller (GT) excitations of finite nuclei have been studied in a fully self-consistent Hartree-Fock (HF) plus random phase approximation (RPA) approach by using a Skyrme energy density functional with spin and spin-isospin densities. To this end, we adopt the extended SLy5st interaction which includes spin-density dependent terms and stabilize nuclear matter with respect to spin instabilities. The effect of the spin-density dependent terms is examined in both the mean field and the spin-flip excited state calculations. The numerical results show that those terms give appreciable repulsive contributions to the M1 and GT response functions of finite nuclei., 6 pages, 2 figures

The properties of single-particle states in the magic nuclei $^{40}$Ca and $^{208}$Pb, in particular the energies, spectroscopic factors and the effective mass, have been studied in a fully self-consistent particle-vibration coupling (PVC) approach within the framework of Skyrme energy density functional theory. All selected phonons are obtained by the Random Phase Approximation and the same Skyrme interaction is also used in the PVC vertex. We focus on the effect of the non-central two-body spin-orbit and tensor interactions on the single-particle properties. It has been found that the contributions of those terms are important to improve the results of $^{208}$Pb. The calculated single-particle energies and spectroscopic factors are compared to available experimental data. The single-particle level density around the Fermi surface is significantly increased due to the effect of PVC., Comment: 9 pages, 2 figures

Journal of Combinatorial Theory, Series B, 98(1):173-225, 2008n exotic nuclei are studied in the framework of a fully self-consistent relativistic continuum random phase approximation (RCRPA). In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function. Different from the cases in stable nuclei, there are strong low-energy excitations in neutron-rich nuclei and proton-rich nuclei. The neutron or proton excess pushes the centroid of the strength function to lower energies and increases the fragmentation of the strength distribution. The effect of treating the contribution of continuum exactly are also discussed., 8pages, 4 figures

Experimental and theoretical efforts are being devoted to the study of observables that can shed light on the properties of the nuclear symmetry energy. We present our new results on the excitation energy [X. Roca-Maza et al., Phys. Rev. C 87, 034301 (2013)] and polarizability of the Isovector Giant Quadrupole Resonance (IVGQR), which has been the object of new experimental investigation [S. S. Henshaw et al., Phys. Rev. Lett. 107, 222501 (2011)]. We also present our theoretical analysis on the parity violating asymmetry at the kinematics of the Lead Radius Experiment [S. Abrahamyan et al. (PREx Collaboration), Phys. Rev. Lett. 108, 112502 (2012)] and highlight its relation with the density dependence of the symmetry energy [X. Roca-Maza et al., Phys. Rev. Lett. 106, 252501 (2011)]., Proceedings - International Nuclear Physics Conference (INPC), Firenze 2 - 7 June 2013

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 non-relativistic 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(\rho=0.1 fm^{-3}), or the neutron skin thickness \Delta r_{np} of a heavy nucleus, on the excitation energies of isoscalar and isovector GQRs. Using available data it is found that S(\rho=0.1 fm{}^{-3})=23.3 +/- 0.6 MeV. Results obtained with the microscopic framework confirm the correlation of the \Delta r_{np} 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 \Delta r_{np} = 0.14 +/- 0.03 fm for 208Pb, and the slope parameter of the symmetry energy: L = 37 +/- 18 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 zero-point 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 medium-heavy and heavy nuclei. The evolution of nuclear incompressibility along Sn and Pb isotopic chains is analyzed using global microscopic models, based on both non-relativistic 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 neutron-rich nuclei., Comment: 7 pages, 5 figures

A fully consistent relativistic random phase approximation is applied to study the systematic behavior of the isovector giant dipole resonance of nuclei along the $\beta$-stability line in order to test the effective Lagrangians recently developed. The centroid energies of response functions of the isovector giant dipole resonance for stable nuclei are compared with the corresponding experimental data and the good agreement is obtained. It is found that the effective Lagrangian with an appropriate nuclear symmetry energy, which can well describe the ground state properties of nuclei, could also reproduce the isovector giant dipole resonance of nuclei along the $\beta$-stability line., Comment: 4 pages, 1 Postscript figure, to be submitted to Chin.Phys.Lett

Effects of Skyrme tensor interactions on the spin-orbit splittings are studied by using Hartree-Fock-Bogoliubov model. The charge-exchange spin-dipole (SD) excitations of 208 Pb are also studied by using a fully self-consistent Skyrme Hartree-Fock plus Random Phase Approximation (HF+RPA) formalism including the tensor interaction. It is found that the tensor correlations have a unique, multipole-dependent effect on the SD excitations, that is, they produce softening of 1− states, but hardening of 0− and 2− states. This paves the way to a clear assessment of the strength of the tensor terms.

In the framework of a Skyrme-Hartree-Fock approach combined with BCS method, the role of the tensor force on the pseudospin energy splitting for tin isotope chain is investigated. The tensor force turns out to obviously affect the pseudospin energy splitting of the spin-unsaturated nuclei. Since the tensor force shifts the single-particle levels, it modifies the single-particle level density and the shell correction energy thereof. The influence of the tensor interaction on shell correction energy is considerable according to our analysis taking a magic nucleus $^{132}$Sn as well as a superheavy nucleus $^{298}114$ as examples. This modification of the shell correction energy due to the tensor component affects the stability of the superheavy nuclei., 7 figures

We present a systematic analysis of the effects induced by tensor correlations on low-lying collective states of magic nuclei, by using the fully self-consistent random phase approximation (RPA) model with Skyrme interactions. The role of the tensor correlations is analyzed in detail in the case of quadrupole (2${}^{+}$) and octupole (3${}^{\ensuremath{-}}$) low-lying collective states in $^{208}\mathrm{Pb}$. The example of $^{40}\mathrm{Ca}$ is also discussed, as well as the case of magnetic dipole states (1${}^{+}$).

Using computer information technology and data mining technology can automatic identification of underground abnormal body. Comparing the Correlation algorithm of advantages and disadvantages, take a small area of archaeological sites in the magnetic data as the sample data, the training model using fuzzy clustering algorithm, and then modified with the actual situation. A large area of the site use K nearest neighbor algorithm. The method of classification results according with the experts explain and match the actual excavation. The efficiency of the identification and work has been improved significantly. Data mining techniques applied to archaeological exploration geophysical data processing is the future of intelligent data-processing development trend.

Since ancient ritual is usually near the water, so, there are large quantities of precious cultural relic buried ancient river. Search for ancient river has a great significance in the archaeological exploration. Traditional methods of the search ancient river entirely by manual interpretation. Interpretation by using a lot of consecutive geological cross-section diagram. The interpretation work need a professional knowledge and rich experience. Using of data mining and database technology can quickly identify the direction of ancient river. The paper based on the physical differences between the ancient river geological characteristics, propose using K-means algorithm to quickly identify the direction of ancient river. The clustering results according with the experts explain and match the actual excavation. The efficiency of the identification has been improved significantly. Data mining techniques applied to archaeological exploration geophysical data processing is the future of intelligent data-processing development trend.

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

The isospin dependence of the effective pairing interaction is discussed on the basis of the Bardeen, Cooper, and Schrieffer theory of superfluid asymmetric nuclear matter. It is shown that the energy gap, calculated within the mean field approximation in the range from symmetric nuclear matter to pure neutron matter, is not linearly dependent on the symmetry parameter owing to the nonlinear structure of the gap equation. Moreover, the construction of a zero-range effective pairing interaction compatible with the neutron and proton gaps in homogeneous matter is investigated, along with some recent proposals of isospin dependence tested on the nuclear data table.

The Landau parameters of Skyrme interactions in the spin and spin-isospin channels are studied using various Skyrme effective interactions with and without tensor correlations. We focus on the role of the tensor terms on the spin and spin-isospin instabilities that can occur in nuclear matter above saturation density. We point out that these instabilities are realized in nuclear matter at the critical density of about two times the saturation density for all the adopted parameter sets. The critical density is shown to be very much dependent not only on the choice of the Skyrme parameter set, but also on the inclusion of the tensor terms.

Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the pygmy dipole resonance (PDR) in $^{68}\mathrm{Ni}$ and $^{132}\mathrm{Sn}$ are investigated by using different random phase approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.

We present a thorough analysis of the effects of the tensor interaction on the multipole response of magic nuclei, using the fully self-consistent Random Phase Approximation (RPA) model with Skyrme interactions. We disentangle the modifications to the static mean field induced by the tensor terms, and the specific features of the residual particle-hole (p-h) tensor interaction, for quadrupole (2+), octupole (3-), and also magnetic dipole (1+) responses. It is pointed out that the tensor force has a larger effect on the magnetic dipole states than on the natural parity states 2+ and 3-, especially at the mean field level. Perspectives for a better assessment of the tensor force parameters are eventually discussed.

The isovector giant and pygmy dipole resonances in even-even Ni isotopes are studied within the framework of a fully consistent relativistic random-phase approximation built on the relativistic mean field ground state. An additional isoscalar-isovector nonlinear coupling term is adopted in the standard effective mean field Lagrangian, which could modify the density dependence of the symmetry energy and soften the symmetry energy at the saturation density without changing the agreement with experimentally existing data of ground state properties. We found that the centroid energy of the isovector giant dipole resonance is tightly correlated to the neutron skin thickness. In contrast, the centroid energy of the isovector pygmy resonance is insensitive to the density dependence of the symmetry energy by tuning the isoscalar-isovector nonlinear coupling.

Soft dipole modes in neutron rich nuclei are investigated in the quasi‐particle relativistic random phase approximation. Nuclear ground state properties are calculated in an extended relativistic mean‐field theory plus BCS method where the contribution of the resonant continuum to pairing correlations is properly treated. Specially emphases are paid on the correlation between the dipole modes and the density dependence of the symmetry energy.

The low-lying isovector dipole strengths in the neutron-rich nuclei Ne-26 and Ne-28 are investigated in the quasiparticle relativistic random phase approximation. Nuclear ground-state properties are calculated in an extended relativistic mean field theory plus Bardeen-Cooper-Schrieffer (BCS) method where the contribution of the resonant continuum to pairing correlations is properly treated. Numerical calculations are tested in the case of isovector dipole and isoscalar quadrupole modes in the neutron-rich nucleus O-22. It is found that in the present calculation, low-lying isovector dipole strengths at E-x < 10 MeV in nuclei Ne-26 and Ne-28 exhaust about 4.9% and 5.8% of the Thomas-Reiche-Kuhn dipole sum rule, respectively. The centroid energy of the low-lying dipole excitation is located at 8.3 MeV in Ne-26 and 7.9 MeV in Ne-28.

The soft dipole modes in neutron rich even-even Ni-isotopes are investigated in the quasiparticle relativistic random phase approximation. We study the evolution of strengths distribution, centroid energies of dipole excitation in low-lying and normal GDR regions with the increase of the neutron excess. It is found in the present study that the centroid energies of the soft dipole strengths strongly depend on the thickness of neutron skin along with the neutron rich even-even Ni-isotopes., 14 pages, 7 figures

A proper treatment of the resonant continuum is to take account of not only the energy of the resonant state, but also its width. The effect of the resonant states on pairing correlations is presented based on the relativistic mean field theory plus Bardeen-Cooper-Schrieffer(BCS) approximation with a constant pairing strength. The study is performed in an effective Lagrangian with the parameter set NL3 for neutron rich even-even Ni isotopes. The results show that the contribution of the proper treatment of the resonant continuum to pairing correlations for those nuclei close to neutron drip line is important. The pairing gaps, Fermi energies, pairing correlation energies, and binding energies are considerably affected with a proper consideration of the width of resonant states. The problem of an unphysical particle gas, which may appear in the calculation of the traditional mean field plus BCS method for nuclei in the vicinity of drip line could be well overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum., Comment: 19 pages, 8 Postscript figure

A fully consistent relativistic random phase approximation (RRPA) built on the relativistic mean field (RMF) ground state is applied to study the giant multipole resonances of stable nuclei. The fully consistent RRPA requires that the nuclear RMF wave function and the RRPA renormalization are calculated in a same effective Lagrangian. A theoretically complete treatment of the RRPA at the mean-field level must include not only the usual particle-hole states, but also the pairs formed from the occupied Fermi states and Dirac states. Effects of inclusion of Dirac sea states in various multipole excitations are investigated. Applications to exotic nuclei, such as Ca-isotopes are presented.

Single-particle resonant-states in the continuum are determined by solving scattering states of the Dirac equation with proper asymptotic conditions in the relativistic mean field theory (RMF). The regular and irregular solutions of the Dirac equation at a large radius where the nuclear potentials vanish are relativistic Coulomb wave functions, which are calculated numerically. Energies, widths and wave functions of single-particle resonance states in the continuum for ^{120}Sn are studied in the RMF with the parameter set of NL3. The isoscalar giant octupole resonance of ^{120}Sn is investigated in a fully consistent relativistic random phase approximation. Comparing the results with including full continuum states and only those single-particle resonances we find that the contributions from those resonant-states dominate in the nuclear giant resonant processes., 16 pages, 2 figures