ON INVARIANT RANDOM APPROXIMATIONS

A result regarding invariant random approximation is proved.

Extended Quark Potential Model From Random Phase Approximation

The quark potential model is extended to include the sea quark excitation using the random phase approximation. The effective quark interaction preserves the important QCD properties — chiral symmetry and confinement simultaneously. A primary qualitative analysis shows that the π meson as a well-known typical Goldstone boson and the other mesons made up of valence quark pair such as the ρ meson can also be described in this extended quark potential model.

Thied—Order Approximation of 0^＋＋ Glueball Mass and Wavefunction of （2＋1）—Dimensional SU（3） Lattice Gauge Theory

The random phase approximation is applied to the coupled-cluster expansions of lattice gauge theory (LGT). Using this method, wavefunctions are approximated by linear combination of graphs consisting of only one connected Wilson loop. We study the excited state energy and wavefunction in (2+1)-D SU(3) LGT up to the third order. The glueball mass shows a good scaling behavior.

Velocity Form Calculations of Generalized Oscillator Strengths for 3s→ (3p, 4p, 5p, 6p) Dipole Transitions of Atomic Sodium in Debye Plasma

In this paper, the generalized oscillator strengths (GOSs) of excitations of atomic sodium from ground state to 2p63s0 (3p, 4p, 5p, 6p) states, immersed in Debye plasma, were calculated by using wavefunctions which were obtained numerically from the restricted Hartree-Fock (RHF) equation. This RHF equation employs the local density approach for exchange interactions including plasma Debye screening. Theoretical RHF and random phase approximation with exchange (RPAE) velocity calculations have shown that the GOSs for excitations to 3 s0(3 p,4 p,5 p,6 p)depend on the plasma Debye screening effects, as shown by the reduction in the GOS amplitude with decreasing Debye length λD. The agreement between the present RPAE V results for the transitions 3 s→3 s0(3 p,4 p,5 p)and the length calculations of Martínez-Flores was satisfactory. Correlation effects were found quite to be significant in the vicinity of the maxima of the GOS of the 3 s→3 s0(4 p,5 p,6 p)excitations by using the RPAE V approach. We note the poor influence of many electron correlations on the GOS of (3 s→3 p)transition with the same principal quantum number. Finally, we comment that the RPAE V calculations are useful in investigating electron correlation effects on the transition GOS of atomic sodium planted in Debye plasma. The present velocity results also reveal that the 3 s→3 s0(5p, 6p)transition GOSs tend to be delocalized due to more significant screening effects at Debye lengths λD=20and 30 a.u. for excited subshells 5p and 6p, respectively. We report here novel results of GOS for 3 s→3 s06ptransition obtained from different Debye lengths.

Rigorous spectral representation of relativistic random phase approximation for finite nuclei

By using the rigorous spectral representation of relativistic random phase approximation, the low-lying excitation of finite nuclei and its longitudinal response function for quasielastic electron scattering are calculated in the σ-ω model of quantum hadrodynamics. It is shown that the reproduction of the correct order of the 1- and 3- excitation states of 16O is due to the contribution of the exchange vertex. There is no significant influence of the retardation effect on the low-lying excitation states. In contrast, the retardation effect plays an important role in the electron scattering process of nuclei. The theoretical longitudinal responses of 12C and 40Ca, including the contributions of the exchange vertex and the retardation effect, are suppressed and reproduce the experimental data better than the results excluding them.

Ferromagnetism in one-dimensional Hubbard model induced by the next-nearest-neighbor hopping at electron density 3/2

Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest- neighbor hopping amplitude tl tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the tl-U plane.

Soft Giant Dipole Modes in Ca Isotopes in the Relativistic RPA

The isovector giant dipole resonance in Ca isotopes is investigated in the framework of the fully consistent relativistic random phase approximation. The calculations are performed in an effective Lagrangian with a parameter set , which was proposed for satisfactorily describing nuclear ground state properties. It is found that a soft isovector dipole mode for Ca isotopes near drip lines exists at energy around . The soft dipole states are mainly due to the excitation of the weakly bound and pure neutron (proton) states near Fermi surface as well as the correlation of isoscalar and isovector operators. For nuclei with the extreme value of , the contributions of isoscalar mesons in the isovector mode play a non-negligible role.

Quasielastic electron scattering in a derivative coupling model with relativistic random phase approximation

We apply the derivative coupling model with ZM and ZM3 parameters to investigate the longitudinal response function in quasielastic electron scattering in the relativistic random phase approximation. The non-spectral method is chosen to describe the nucleon Green＇s function in a finite nucleus. Some remarks have been made in conclusion.

Neutron star core-crust transition and the crustal moment of inertia in the nonlinear relativistic Hartree approximation

We investigate the effects of theσmeson mass(m_(σ)),symmetry energy,and slope of the symmetry energy on the neutron star core-crust transition density and the crustal moment of inertia(ΔI/I)in the nonlinear relativistic Hartree approach(RHA),which includes vacuum polarization.Although the core-crust transition density(ρ_(t)),pressure(P_(t)),and neutron star radius(R),which are all dependent on the symmetry energy,contribute to determiningΔI/I,we find that changing only the slope of symmetry energy within a reasonable range is not sufficient to reachΔI/I≥7%to achieve the large glitches of the Vela pulsar.However,since all three factors(ρ_(t),P_(t),and R)increase with the increase in mσthrough scalar vacuum polarization,adjusting mσcan easily achieveΔI/I≥7%.

Superallowed Fermi transitions in RPA with a relativistic point-coupling energy functional

The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic pointcoupling energy functional is applied to evaluate the isospin symmetry-breaking corrections δ c for the 0+ → 0+ superallowed Fermi transitions.With these δ c values,together with the available experimental f t values and the improved radiative corrections,the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined.Even with the consideration of uncertainty,the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% for all the employed relativistic energy functionals.

Neutron skin thickness of ^(90)Zr and symmetry energy constrained by charge exchange spin-dipole excitations

The charge exchange spin-dipole(SD) excitations of ^(90)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 ^(90)Zr(p,n) ^(90)Nb and ^(90)Zr(n,p) ^(90)Y is used to deduce the neutron skin thickness.The neutron skin thickness Δr_(np) of ^(90)Zr is extracted as 0.083±0.032 fm,which is similar to the results of other studies.Based on the correlation analysis of the neutron skin thickness Δr_(np) and the nuclear symmetry energy J as well as its slope parameter L,a constraint from the extracted Δr_(np) leads to the limitation of J to 29.2±2.6 MeV and L to 53.3±28.2 MeV.

p+ip-wave pairing symmetry at type-II van Hove singularities

Based on the random phase approximation calculation in two-orbital honeycomb lattice model,we investigate the pairing symmetry of Ni-based transition-metal trichalcogenides by electron doping access to type-II van Hove singularities(vHs).We find that chiral even-parity d+id-wave(Eg)state is suppressed by odd-parity p+ip-wave(Eu)state when electron doping approaches the type-II vHs.The type-II vHs peak in density of states(DOS)enables to strengthen the ferromagnetic fluctuation,which is responsible for triplet pairing.The competition between antiferromagnetic and ferromagnetic fluctuation results in pairing phase transition from singlet to triplet pairing.The Ni-based transition-metal trichalcogenides provide a promising platform to unconventional superconductor emerging from electronic DOS.

2νββ-decay to first 2^+states with partial isospin symmetry restoration from spherical QRPA calculations

Using partially restored isospin symmetry,we calculate the nuclear matrix elements for a special decay mode of a two-neutrino double beta decay–the decay to the first 2+excited states.Employing the realistic CD–Bonn nuclear force,we analyze the dependence of the nuclear matrix elements on the isovector and isoscalar parts of proton–neutron particle–particle interactions.The dependence on the different nuclear matrix elements is observed,and the results are explained.We also provide the phase space factors using numerical electron wavefunctions and properly chosen excitation energies.Finally,we present our results for the half-lives of this decay mode for different nuclei.

Stagnancy of the pygmy dipole resonance

The pygmy dipole resonance（PDR） of nickel isotopes is studied using the deformed random phase approximation method. The isoscalar character of the pygmy resonance is confirmed, and the correlation between the pygmy resonance and neutron skin thickness is discussed. Our investigation shows a linear correlation between PDR integral cross section and neutron skin thickness when the excess neutrons lie in pf orbits, with a correlation rate of about 0.27 fm^（-1）. However, in more neutron-rich nickel isotopes, the growth of the pygmy dipole resonance is stagnant. Although the neutron skin thickness increases, the whole skin is not active. There is an inertial part in the nuclei^（70-78）Ni which does not participate in the pygmy resonance actively and as a result, contributes little to the photo-absorption cross section.