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The empirical coupled-channel (ECC) model and the universal fusion function (UFF) prescription are used to analyse the data of capture cross sections for reactions ${}^{39}$K$+{}^{181}$Ta and ${}^{46}$K$+{}^{181}$Ta reported recently by A. Wakhle {\it et al.} [Phys. Rev. C 97, 021602(R) (2018)]. The results of the ECC model are in good agreement with the data of ${}^{39}$K$+{}^{181}$Ta while, for ${}^{46}$K$+{}^{181}$Ta, the predictions of the ECC model overestimate the above-barrier capture cross sections. Comparing the reduced data of these two reactions, it is found that the above-barrier cross sections of ${}^{39}$K$+{}^{181}$Ta are consistent with the UFF and are larger than those of ${}^{46}$K$+{}^{181}$Ta. This implies that the capture cross sections of ${}^{46}$K$+{}^{181}$Ta are suppressed at energies above the Coulomb barrier. Furthermore, at sub-barrier energies, the reduced calculated capture cross sections of ${}^{39}$K$+{}^{181}$Ta are a little larger than those of ${}^{46}$K$+{}^{181}$Ta, which is owing to the coupling to the positive $Q$-value two-neutron transfer channel., 6 pages, 3 figures. Accepted for publication in PRC

In the framework of the relativistic mean field theory, the isovector scalar interaction is considered by exchanging δ meson to study the influence of δ meson on the cooling properties of neutron star matter. The calculation results show that with the inclusion of δ meson, the neutrino emissivity of the direct Urca processes increases, and thus enhances the cooling of neutron star matter. When strong proton superfluidity is considered, the theoretical cooling curves agree with the observed thermal radiation for isolated neutron stars.

The nuclear and Coulomb potentials between deformed nuclei with octupole deformations and arbitrary orientations are evaluated numerically. The effects of the octupole deformation on the potential between nuclei and the potential energy surface (PES) used in the description of the production of super-heavy nuclei (SHN) by heavy-ion fusion reactions are investigated in the di-nuclear system model. It is found that the nuclear octupole deformation significantly changes the shape of the PES, which may influence the fusion probability of the SHN. Also, PESs in the tip-belly and belly-belly cases are investigated. Finally, the quasi-fission barriers in the tip-tip and belly-belly cases are evaluated. It is found that the quasi-fission barriers of the belly-belly case are generally larger than those of the tip-tip case.

In the framework of relativistic mean field theory, the condensations of K− and 0 in neutron star matter including baryon octet and Δ quartet are studied. We find that in this case K− and 0 condensations can occur at relative shallow optical potential depth of from −80 MeV to −160 MeV. Both K− and 0 condensations favor the appearances of Δ resonances. With condensations all the Δ quartet can appear well inside the maximum mass stars. The appearances of Δ resonances change the composition and distribution of particles at high densities. The populations of Δ resonances can enhance K− condensation. It is found that in the core of massive neutron stars, neutron star matter includes rich particle species, such as antikaons, baryon octet, and Δ quartet. In the presence of Δ resonances and condensation, the EOS becomes softer and results in smaller maximum mass stars. Furthermore the impact of antikaon condensations, hyperons, and Δ resonances on direct Urca process with nucleons is also discussed briefly.

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field (RAS-RMF) model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from nearly-spherical (N = 130) shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only (222,224)Rn are octupole deformed and the octupole deformations for them are small. However, more nuclei (N similar or equal to 134-148) in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant (vertical bar beta vertical bar similar to 0.1 or even larger).

alpha decay energies of 323 heavy nuclei with Z >= 82 are evaluated with a macroscopic-microscopic model. In this model, the macroscopic part is treated by the continuous medium model and the microscopic part consists of shell and pairing corrections based on the Nilsson potential. alpha decay half-lives are calculated by Viola-Seaborg formula. The results of alpha decay energies and half-lives are compared with experimental values and satisfactory agreement is found. The recoiling effect of the daughter nucleus on alpha decay half-life is also discussed.

In the framework of the relativistic mean field theory, we investigate K0 condensation along with K− condensation in neutron star matter including the baryon octet. The results show that both K0 and K− condensations can occur well in the core of the maximum mass stars for relatively shallow optical potentials of K in the range of −10MeV ~ −160 MeV. With the increasing optical potential of K, the critical densities of K decrease and the species of baryons appearing in neutron stars become fewer. The main role of K0 condensation is to make the abundances of particles become identical leading to isospin saturated symmetric matter including antikaons, nucleons and hyperons. K− condensation is chiefly responsible for the softening of the corresponding equation of state, which leads to a large reduction in the maximum masses of neutron stars. In the core of massive neutron stars, neutron star matter including rich particle species, such as antikaons, nucleons and hyperons, may exist.

Density-dependent parametrization models of the nucleon-meson coupling constants, including the isovector scalar delta-field, are applied to asymmetric nuclear matter. The nuclear equation of state (EOS) and the neutron star properties are studied in a relativistic Lagrangian density, using the relativistic mean field (RMF) hadron theory. It is known that the delta-fleld in the constant coupling scheme leads to a larger repulsion in dense neutron-rich matter and to a definite splitting of proton and neutron effective masses, finally influences the stability of the neutron stars. We use density-dependent models of the nucleon-meson couplings to study the properties of neutron star matter and to reexamine the delta-held effects in asymmetric nuclear matter. Our calculation shows that the stability conditions of the neutron star matter can be improved in presence of the delta-meson in the density-dependent models of the coupling constants. The EOS of nuclear matter strongly depends on the density dependence of the interactions.

We investigate the dependences of the potential energy surfaces (PES) and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy's contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding Pb-208 are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope.

The global colour model at finite temperature is further extended to study the systems at finite chemical potential. The deconfinement and chiral phase transition at finite chemical potential and at temperature T = 0 K are studied simultaneously. Meanwhile the evolution of the bag constants at finite chemical potential is calculated. The dependence of results on the model parameters are discussed in detail.

A double folding method with simplified Skyreme-type nucleon-nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this methods, the potential energy surfaces, the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.

The potential energy surface of 179Hg is traced and the multi-shape coexistence phenomenon in that nucleus is studied within the relativistic mean-field theory with quadrupole moment constraint. The calculation results of binding energies and charge radii of mercury isotopes are in good agreement with the experimental data.

In this paper a new phase structure of neutron star matter including nucleons and delta isobars is presented. Particle fractions populated and pion condensations in neutron star matter are investigated in this model, The existence of the pion condensations can postpone the appearance of delta isobars' We found that both the pion condensation and reduce of the ratio of delta isobar to nucleons couplings can soften the corresponding equation of state. The maximum masses and their corresponding radii of neutron stars are calculated, and the obtained values are in observational region.

The microscopic mechanism of the identical bands in odd–odd nucleus 194Tl and its neighbour odd-A nucleus 193Tl are investigated using the particle-number conserving method with monopole and quadrupole pairing interaction. It is found that the blocking effect plays an important role in the variation of moments of inertia (J(1) and J(2)) with rotational frequency for the superdeformed bands and identical bands. The alignment of 194Tl bands with respect to the 193Tl(1) band used as a reference is also discussed.

The survival probability of the superheavy compound nuclei with Z = 114 is studied with the statistical model. It is found that the survival probability shows drastic odd-even effects. The odd-A compound nuclei have higher survival probability by evaporating three neutrons as compared with their neigbouring even-A compound nuclei.

The global colour model in free space is extended to finite temperature to study the deconfinement and chiral phase transitions at high temperature T and zero chemical potential in the mean field approximation. Both possibilities of coincidence and non-coincidence of the two distinct phase transitions are found when the model parameters are varied in a certain range. The underlying mechanisms of the coincidence and noncoincidence are analysed and discussed. The validity of the T-dependent model propagator as the input is also discussed.

Validity of adiabatic assumption is discussed within the constrained Hartree-Fock theory for self-conjugate nucleus Kr-72. It is shown that the adiabatic assumption does not provide a correct description for the nature of nucleus when a, configuration change is involved. The excited Hartree-Fock states and the continuously-connected constrained Hartree-Fock states are given for the first time by applying the configuration dictated constrained Hartree-Fock theory with Gogny force. The importance of self-consistency between the mean-field and the single particle wave functions is emphasized even when a small number of nucleons are involved in the configuration change.

Promising high strangeness dibaryons are studied by the extended quark delocalization and color screening model. It is shown that besides H particle and di-Omega, there might be other dibaryon candidates worth to be searched experimentally such as NOmega.

Ground-state properties of C, O, and Ne isotopes are described in the framework of Hartree–Fock–Bogoliubov theory with density-dependent finite-range Gogny interaction D1S. We include all the contributions to the Hartree–Fock and pairing field arising from Gogny and Coulomb interaction as well as the center of mass correction in the numerical calculations. These ground-state properties of C, O, and Ne isotopes are compared with available experimental results, Hartree–Fock plus BCS, shell model and relativistic Hartree–Bogoliubov calculations. The agreement between experiments and our theoretical results is pretty well. The predicted drip-line is dependent strongly on the model and effective interaction due to their sensitivity to various theoretical details. The calculations predict no evidence for halo structure predicted for C, O, and Ne isotopes in a previous RHB study.

The structure of superheavy nuclei has been studied using the macroscopic-microscopic model. The macroscopic energy was calculated with the continuous medium model in which the energy is expressed as a function of nucleon densities. The deformations and structures of superheavy nuclei were systematically investigated. Calculations reproduce well the available data of experimental α-decay energies and half-lives. The investigation of single-particle levels shows that the shell structure is deformation and isospin dependent. Potential-energy-surface calculations display that superheavy nuclei have in general harder shapes than the nuclei of other mass regions.

The survival probability of super heavy nuclei produced in cold fusion reactions is studied by using the standard Fermi gas level density formula and analyzed with fission and neutron evaporation characteristics predicted in different theoretical models. The level density formula used in this letter suppresses the ratio of neutron emission width to fission width, Gamma(n)/Gamma(f). The dependence of Gamma(n)/Gamma(f) on the saddle point level density parameter and excitation energy is also investigated.

The properties of neutron stars are studied in a relativistic mean-field model with SU(2) chiral symmetry spontaneous breaking being considered. The calculation results indicate that the effects of the chiral symmetry spontaneous breaking are not negligible.

Influence of the nuclear deformation on the potential energy surface (PES) in a di-nuclear system is studied in details. It is found that the PES shape changes greatly due to the deformation effect. The top point of the PES could be reduced significantly, which implies that the optimum excitation energy could also be reduced greatly and may enhance the formation probability of the compound nucleus. The dynamical deformation as a function of the reaction time in the reaction process is dramatic. The Z/N ratios of fragments tend to follow that of the compound nucleus during the nucleon exchange process, but to fluctuate.

A method for obtaining the small current quark mass dependence of the dressed quark propagator from an effective quark-quark interaction model is developed. Within this approach the small current quark mass effects on dressed-quark propagator have been studied. A comparison with previous results is given.

Complete fusion excitation functions of reactions involving breakup are studied by using the empirical coupled-channel (ECC) model with breakup effects considered. An exponential function with two parameters is adopted to describe the prompt-breakup probability in the ECC model. These two parameters are fixed by fitting the measured prompt-breakup probability or the complete fusion cross sections. The suppression of complete fusion at energies above the Coulomb barrier is studied by comparing the data with the predictions from the ECC model without the breakup channel considered. The results show that the suppression of complete fusion are roughly independent of the target for the reactions involving the same projectile., Comment: 9 pages, 6 figures, 3 tables

Based on QCD sum rule three-point and two-point external field formulas respectively, the vector vacuum susceptibilities are calculated at the mean-field level in the framework of the global color symmetry model. It is shown that the above two approaches of determination of the vector vacuum susceptibility may lead to different results. The reason of this contradiction is discussed.

The mixed quark-gluon condensate from the global color symmetry model is derived. It is shown that the mixed quark-gluon condensate depends explicitly on the gluon propagator. This interesting feature may be regarded as an additional constraint on the model of gluon propagator. The values of the mixed quark-gluon condensate from some ansatz for the gluon propagator are compared with those determined from QCD sum rules.

Energy level statistics of a system consisting of six particles interacting by delta force in a two-j model coupled with a deformed core is studied in particle-rotor model. For single-j shell (i(13/2)) and two-j shell (g(7/2) + d(5/2)) the exact energies for our statistical analysis are obtained from a full diagonalization of the Hamiltonian, while in two-j case (i(13/2) + g(9/2)) the configuration truncation is used. The nearest-neighbor distribution of energy levels and spectral rigidity are studied as the function of spin. The results of single-j shell are compared with those in two-j case. It is showed that the system becomes more regular when single-j space (i(13/2)) is replaced by two-j shell (g(7/2) + d(5/2)) although the basis size of the configuration space is unchanged. The degree of chaoticity of the system, however, changes slightly when configuration space is enlarged by extending single-j shell (i(13/2)) to two-j shell (i(13/2) + g(9/2)).

It is shown how the axial vector current of current quarks is related to that of constituent quarks within the framework of the global color symmetry model. Gluon dressing of the axial vector vertex and the quark self-energy functions are described by the inhomogeneous Bethe-Salpeter equation in the ladder approximation and the Schwinger-Dyson equation in the rainbow approximation, respectively.

The chaotic properties for six particles interacting by a monopole pairing force in a two-j shell model coupled with a deformed core are studied in the frame of particle-rotor model. The nearest-neighbor distribution of energy levels and spectral rigidity in the two-j shell are compared with those in the single-j case. The results show that the system is more regular in the two-j model than that in the single-j case.

In the framework of the extended relativistic mean-field theory with hyperons, the properties of neutron star matter have been investigated. It is, found that at a density of four to five times that of nuclear matter saturation density po, a neutron star will become a hyperon star. This transition is strongly influenced by the coupling constants of hyperons to mesons and a different parameter set. For a given parameter set, a minimum transition baryon density exists when the hyperon coupling ratios satisfy x(H sigma) = x(H omega) = x(H rho) = 0.65 or x(H sigma) = x(H omega) = 0.62,x(H rho) = 0.7.

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the quark condensate ((q) over bar q), the mixed quark gluon condensate g(s)((q) over bar G(mu nu)sigma(mu nu)q) and the four-quark condensate ((q) over bar Gamma q (q) over bar Gamma q) at the mean-field level in the framework of global color symmetry model. The numerical calculation shows that our result is compatible with the range obtained within other nonperturbative approaches. In particular, we have found that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.

Based on the quark propagator in the instanton dilute liquid approximation, we have determined the nonlocal four-quark condensate at the mean-field level in the framework of global color symmetry model. By making use of this formula, the vacuum susceptibility (pion susceptibility) was calculated in this paper. The theoretical analysis and numerical calculation show that even at the mean-field level the naive vacuum saturation approximation is not a good approximation when we consider nonlocal four-quark condensate.

A nonlinear chiral quark model with topological ghost terms is proposed. The couplings among the light-flavor quarks, the Goldstone boson nonet and the topological ghost field are consistently incorporated in the model. The inclusion of the ghost field coupling is demanded by describing correctly the effect of the axial anomaly Some features of the model are discussed.

The properties of thermal protoneutron star matter including hyperons are investigated in the framework of the relativistic mean field theory (RMFT). In protoneuron star matter, with the increase of the temperature, the critical densities of hyperons decrease, the sequence for appearances of hyperons change, the abundances of hyperons as well as neutrinos increase, and the strong interactions between baryons get weaker. Meanwhile, the abundances of isospin multiple states for nucleons, Σ, and Ξ become identical, leading to isospin saturated symmetric matter, respectively. Moreover, if a protoneutron star is born with higher temperature, it is less likely to convert to a black hole.

Based on random matrix theory and reduced BS equation, it is found that the regular motion of system can be expected at a small value of color screening mass but the chaotic motion at a large one. It is shown that the level mixing due to color screening serves as a new mechanism resulting in J/ψ suppression. Moreover, this kind of suppression can occur before the color screening mass reaches its critical value for J/ψ dissociation. In addition, it is implied that a strong J/ψ suppression is possible in the absence of dissociation of J/ψ.

The mass spectrum and binding radii of heavy-quark bound states are analyzed in terms of the reduced Bethe-Salpeter equation. The critical values of screening masses for and bound states at finite temperature are obtained and compared with the previous results given by nonrelativistic models.

Based on the determined bilocal field in the global color symmetry model, the effective quark-quark interaction is deduced explicitly in this letter. The result shows that, except for the normal one-pi and one-sigma exchange terms, the confinement terms with screening factors can automatically be obtained.

In the framework of two-center shell model the nearest neighboring level spacing distribution and spectral rigidity of the nucleon in heavy nuclei are calculated when the shape parameters are changed systematically Two regions of shape parameter in which the chaotic motion of the nucleon occurs are found. It is shown that the chaotic motion appears not only in the heavy nuclei with oblate shapes but also in prolate ones with a considerable neck, which is quite different from the conclusions of Ref. [2]. Bohigas Giannoni Schmit conjecture is corroborated once again by the good quantum-classical correspondence of nucleonic regular (chaotic) motion. In addition, the present work suggests that nuclear dissipation is shape-dependent, strong dissipation is expected for medium or larger separations, and provides nuclear dissipation with a dynamical understanding.

The π+-13C elastic scattering at 162 MeV and 13C(π+,π0)13N at 165 MeV are analyzed in a model in which the nuclear state is assumed to consist of a valence nucleon and a 12C core described by a three α-cluster wavefunction and the cross section is calculated in the Glauber theory. A good agreement between theory and experiment is obtained and the results also indicate the important influence of the core on the processes.

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin $ST$ channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force (TBF). It is shown that the potential energy per nucleon in the isospin-singlet T=0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities, the TBF effect on the isospin-triplet T=1 channel contribution turns out to be much larger than that on the T=0 channel contribution. At low densities around and below the normal nuclear matter density, the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T=1 component is almost independent of isospin-asymmetry. As the density increases, the T=1 channel contribution becomes sensitive to the isospin-asymmetry and at high enough densities its isospin-dependence may even become more pronounced than that of the T=0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories., 5 pages, 3 figures

The non-axial reflection-asymmetric $\beta_{32}$ shape in some transfermium nuclei with N=150, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No are investigated with multidimensional constrained covariant density functional theories. By using the density-dependent point coupling covariant density functional theory with the parameter set DD-PC1 in the particle-hole channel, it is found that, for the ground states of $^{248}$Cf and $^{250}$Fm, the non-axial octupole deformation parameter $\beta_{32} > 0.03$ and the energy gain due to the $\beta_{32}$ distortion is larger than 300 keV. In $^{246}$Cm and $^{252}$No, shallow $\beta_{32}$ minima are found. The occurrence of the non-axial octupole $\beta_{32}$ correlations is mainly from a pair of neutron orbitals $[734]9/2$ ($\nu j_{15/2}$) and $[622]5/2$ ($\nu g_{9/2}$) which are close to the neutron Fermi surface and a pair of proton orbitals $[521]3/2$ ($\pi f_{7/2}$) and $[633]7/2$ ($\pi i_{13/2}$) which are close to the proton Fermi surface. The dependence of the non-axial octupole effects on the form of energy density functional and on the parameter set is also studied., Comment: 5 pages, 2 figures

By using a newly developed di-nuclear system model with a dynamical potential energy surface---the DNS-DyPES model, hot fusion reactions for synthesizing superheavy nuclei (SHN) with the charge number Z = 112-120 are studied. The calculated evaporation residue cross sections are in good agreement with available data. In the reaction 50Ti+249Bk -> (299-x)119 + xn, the maximal evaporation residue (ER) cross section is found to be about 0.11 pb for the 4n-emission channel. For projectile-target combinations producing SHN with Z=120, the ER cross section increases with the mass asymmetry in the incident channel increasing. The maximal ER cross sections for 58Fe+244Pu and 54Cr + 248Cm are relatively small (less than 0.01 pb) and those for 50Ti+249Cf and 50Ti+251Cf are about 0.05 and 0.25 pb, respectively., 6 pages, 5 figures; Phys. Rev. C, in press

The ground state band was recently observed in the superheavy nucleus 256Rf. We study the rotational properties of 256Rf and its neighboring even-even nuclei by using a cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The kinematic and dynamic moments of inertia of the ground state bands in these nuclei are well reproduced by the theory. The spin of the lowest observed state in 256Rf is determined by comparing the experimental kinematic moments of inertia with the PNC-CSM calculations and agrees with previous spin assignment. The effects of the high order deformation varepsilon6 on the angular momentum alignments and dynamic moments of inertia in these nuclei are discussed., Comment: 7 pages, 6 figures; References and discussion about the cranking Nilsson model added, Fig. 3 modified and Figs. 5 and 6 added; Phys. Rev. C, in press

Multi-quasiparticle high-K states in Hf-174 are studied in the framework of the projected shell model. The calculation reproduces well the observed ground-state band as well as most of the two- and four-quasiparticle rotational bands. Some as yet unobserved high-K isomeric states in Hf-174 are predicted. Possible reasons for the existing discrepancies between calculation and experiment are discussed. It is suggested that the projected Shell model may be a useful method for studying multi-quasiparticle high-K isomers and the K-mixing phenomenon in heavy deformed nuclei.

The difference of spectral statistics properties between single-j and two-j shell models has been studied in the frame of the cranking model. The results show that the system becomes more regular when single-j space (i13/2) is replaced by a two-j shell (g7/2 + d5/2), although the basis size of the configuration space is unchanged. However, the degree of chaos of the system changes slightly when configuration space is enlarged by extending the single-j shell (i13/2) to two-j (i13/2 + g9/2) shell.

The shapes of light normal nuclei and $\Lambda$ hypernuclei are investigated in the $(\beta, \gamma)$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $\gamma$ direction, differ a lot for several nuclei. For $\Lambda$ hypernuclei, in most cases, the addition of a $\Lambda$ hyperon alters slightly the location of the ground state minimum towards the direction of smaller $\beta$ and softer $\gamma$ in the potential energy surface $E \sim (\beta, \gamma)$. There are three exceptions, namely, $^{13}_\Lambda$C, $^{23}_\Lambda$C, and $^{31}_\Lambda$Si in which the polarization effect of the additional $\Lambda$ is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei., Comment: 11 pages, 3 figures; added references and arguments in Sections III and IV; to be published in Phys. Rev. C

The recently observed high-spin rotational bands in odd-$A$ nuclei $^{247, 249}$Cm and $^{249}$Cf [Tandel \textit{et al.}, Phys. Rev. C 82 (2010) 041301R] are investigated by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method in which the blocking effects are taken into account exactly. The experimental moments of inertia and alignments and their variations with the rotational frequency $\omega$ are reproduced very well by the PNC-CSM calculations. By examining the $\omega$-dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals to the angular momentum alignment in each major shell, the level crossing and upbending mechanism in each nucleus is understood clearly., Comment: 6 pages, 5 figures, to be published in Phys. Rev. C

The shapes of light normal nuclei and $��$ hypernuclei are investigated in the $(��, ��)$ deformation plane by using a newly developed constrained relativistic mean field (RMF) model. As examples, the results of some C, Mg, and Si nuclei are presented and discussed in details. We found that for normal nuclei the present RMF calculations and previous Skyrme-Hartree-Fock models predict similar trends of the shape evolution with the neutron number increasing. But some quantitative aspects from these two approaches, such as the depth of the minimum and the softness in the $��$ direction, differ a lot for several nuclei. For $��$ hypernuclei, in most cases, the addition of a $��$ hyperon alters slightly the location of the ground state minimum towards the direction of smaller $��$ and softer $��$ in the potential energy surface $E \sim (��, ��)$. There are three exceptions, namely, $^{13}_��$C, $^{23}_��$C, and $^{31}_��$Si in which the polarization effect of the additional $��$ is so strong that the shapes of these three hypernuclei are drastically different from their corresponding core nuclei., 11 pages, 3 figures; added references and arguments in Sections III and IV; to be published in Phys. Rev. C