Isoscalar Giant Monopole Resonance in Relativistic Continuum Random Phase Approximation

The isoscalar giant monopole resonance （ISGMR） in nuclei is studied in the framework of a fully 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 technique. The negative energy states in the Dirac sea are also included in the single particle Green＇s function in the no-sea approximation. The single particle Green＇s function is calculated numerically by a proper product of the regular and irregular solutions of the Dirac equation. The strength distributions in the RCRPA calculations, the inverse energyweighted sum rule m-1 and the centroid energy of the ISGMR in ^120Sn and ^208Pb are analysed. Numerical results of the RCRPA are checked with the constrained relativistic mean field model and relativistic random phase approximation with a discretized spectrum in the continuum. Good agreement between them is achieved.     

Microscopic study of Gamow-Teller and spin-dipole states in 208Bi

Gamow-Teller (GT) and spin-dipole (SD) states in ²⁰⁸Bi are studied by using self-consistent Hartree-Fock + Tamm-Dancoff approximation taking into account the coupling to the continuum. Most of SD strength is found at the excitation energy E _x≈ 25MeV with a very broad width, which agrees with recent experimental observations. It is shown that Landau damping effect is responsible for the large width of SD peak, while the escape width is found to be at most 1MeV. We study also electric dipole (E1) transitions between GT and SD states in ²⁰⁸Bi. Main E1 transitions for 0^- and 1^- states are found near excitation energy expected from Brink's hypothesis in which SD states are considered as E1 resonances built on the GT state. Calculated E1 transition strengths between GT and SD states are compared with the analytic sum rules within one-particle one-hole (1p-1h) configuration space and within both 1p-1h and 2p-2h model space. Received: 11 April 2000 / Accepted: 30 August 2000     

Resonant and weakly-bound one-particle levels in quadrupole-deformed potentials

Both positive-energy and weakly-bound one-particle levels for neutrons in Y₂₀ deformed Woods-Saxon potentials are examined in comparison with those in spherical Woods-Saxon potentials. While s_1/2 levels play a unique role in spherical drip-line nuclei, the Ω^π = 1/2⁺ levels in Y₂₀ deformed potentials, which always contain some amount of s_1/2 component, exhibit an important role in deformed drip-line nuclei. As the potential strength becomes weaker, some weakly-bound Ω^π = 1/2⁺ levels continue to the positive-energy region as one-particle resonant levels, while others have no such continuation. Among an infinite number of one-particle levels at a given positive-energy and in a given deformed potential, only some selected levels expressed in terms of eigenphase are found to be important in the pair-correlated ground state of neutron-drip-line nuclei.     

Low-energy monopole and dipole response in nuclei at finite temperature

The multipole response of nuclei at temperatures T=0–2 MeV$T=0\text{–}2\text{MeV}$ is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=1–2 MeV$T=1\text{–}2\text{MeV}$ additional transition strength appears at low energies due to thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in ^60,62Ni. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in ⁶⁸Ni and ¹³²Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions.     

Giant resonances in exotic spherical nuclei within the RPA approach with the Gogny force

Theoretical results for giant resonances in the three doubly magic exotic nuclei ⁷⁸Ni, ¹⁰⁰Sn and ¹³²Sn are obtained from Hartree-Fock (HF) plus Random Phase Approximation (RPA) calculations using the D1S parameterization of the Gogny two-body effective interaction. Special attention is paid to full consistency between the HF field and the RPA particle-hole residual interaction. The results for the exotic nuclei, on average, appear similar to those of stable ones, especially for quadrupole and octupole states. More exotic systems have to be studied in order to confirm such a trend. The low energy of the monopole resonance in ⁷⁸Ni suggests that the compression modulus in this neutron-rich nucleus is lower than the one of stable ones.     

Magnetic dipole response in rare earth nuclei

Experimental observations in certain rare earth nuclei have established the presence of sizeable B(M1) strength of two peak structure lying in the 5–10 MeV region. The character of the states concerned, studied within a self-consistent Random Phase Approximation using Skyrme forces, are identified to be that of proton and neutron giant spin-flip resonances. Received: 14 July 1997 / Revised version: 20 October 1997     

On the difference between proton and neutron spin-orbit splittings in nuclei

The latest experimental data on nuclei at ¹³²Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly magic region and compare the case to that of ²⁰⁸Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean-field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in the framework of different theoretical approaches. Received: 13 February 2002 / Accepted: 20 February 2002     

Structure of nuclei far from the stability in relativistic approach

The recent progress of the relativistic many-body approach by the group at Peking University will be reviewed. In particular, axially deformed relativistic Hartree-Bogoliubov approach in Woods-Saxon basis aiming at halo nucleus, time-odd triaxial RMF approach, the adiabatic and configuration-fixed constrained triaxial RMF approaches, a Reflection ASymmetric RMF (RAS-RMF) approach, and a new relativistic Hartree-Fock (RHF) approach with density-dependent σ,ω,ρ and π meson-nucleon couplings for finite nuclei and nuclear matter, will be highlighted.     

Nuclear giant resonances and linear response

We search for nonlinear effects in nuclear giant resonances (GRs), in particular the isovector dipole and the isoscalar quadrupole modes. To that end, we employ a spectral analysis of time-dependent Hartree-Fock (TDHF) dynamics using Skyrme forces. Based on TDHF calculations over a wide range of excitation amplitudes, we explore the collectivity and degree of harmonic motion in these modes. Both GR modes turn out to be highly harmonic in heavy nuclei from A = 100 on. There is no trace of a transition to irregular motion and multiple resonances are predicted. Slight anharmonicities are seen for light nuclei, particularly for ¹⁶O. These are mainly caused by the spin-orbit splitting.     

Relativistic Quasiparticle Random Phase Approximation with a Separable Pairing Force

In our previous work [Phys. Lett. （to be published）, Chin. Phys. Lett. 23 （2006） 3226], we introduced a separable pairing force for relativistic Hartree-Bogoliubov calculations. This force was adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. By using the well known techniques of Talmi and Moshinsky it can be expanded in a series of separable terms and converges quickly after a few terms. It was found that the pairing properties can be depicted on almost the same footing as the original pairing interaction, not only in nuclear matter, but also in finite nuclei. In this study, we construct a relativistic quasiparticle random phase approximation （RQRPA） with this separable pairing interaction and calculate the excitation energies of the first excited 2^＋ states and reduced B（E2; 0^＋ → 2^＋） transition rates for a chain of Sn isotopes in RQRPA. Compared with the results of the full Gogny force, we find that this simple separable pairing interaction can describe the pairing properties of the excited vibrational states as well as the original pairing interaction.     

The “island of inversion" from a nuclear moments perspective and the g factor of 35Si

This paper reviews recent results from electromagnetic moment measurements on isotopes in the island of inversion around N=20. The obtained moments on neutron rich Na, Mg, Al and Si isotopes allow to draw conclusions on the amount of intruder components in their ground state wave function, demonstrating a gradual transition from the normal sd-shell region into the island of inversion, starting at N=18 for Na, N=19 for Mg and N=20 for Al isotopes. A measurement of the ground state g factor of ³⁵Si (N=21), using a polarized fragment beam at GANIL, is discussed in more detail. The magnetic moment μ(³⁵Si, I^π= 7/2^-) = (-)1.638(4) μ_N is consistent with a normal ground state structure, dominated by a νf_7/2 neutron.     

High-spin nuclear states and persistent currents in mesoscopic rings

An analogy is presented between periodic persistent currents in mesoscopic rings and staggerings of gamma energy transitions from some nuclear high-spin states. Various sources of damping of the expected periodic structures in both physical systems are compared. This discussion provides, in the nuclear case, a tentative explanation of the scarcity of such staggerings, their appearance near ¹⁵⁰Gd and the existence of a spin-window for their observation. Received: 21 July 1997 / Revised version: 13 October 1997     

High-spin isomers in Rn in the region of triple neutron core-excitations

The level scheme of ²¹²Rn has been extended to spins of ∼38?$\sim 38?$ and excitation energies of about 13 MeV using the ²⁰⁴Hg(¹³C, 5n)²¹²Rn reaction and γ-ray spectroscopy. Time correlated techniques have been used to obtain sensitivity to weak transitions and channel selectivity. The excitation energy of the 22⁺ core-excited isomer has been established at 6174 keV. Two isomers with τ=25(2) ns$\tau =25(2)\text{ns}$ and τ=12(2) ns$\tau =12(2)\text{ns}$ are identified at 12211 and 12548 keV, respectively. These are the highest-spin nuclear isomers now known, and are attributed to configurations involving triple neutron core-excitations coupled to the aligned valence protons. Semi-empirical shell-model calculations can account for most states observed, but with significant energy discrepancies for some configurations.     

Decoupling and coherence in E1 and E2 moments in drip line nuclei

I discuss first the effect of decoupling of extended wave functions and the coherence in the low-energy E1 strength in drip line nuclei ¹²Be and ¹³O, which are studied by large-scale shell model calculations including 3 ?ω configuration space. The calculated results are compared to recent experimental data of Coulomb excitations. The quenching of the core polarization charges in drip line nuclei is also discussed in relation to recent observations of quadrupole moments in B-isotopes. Received: 1 May 2001 / Accepted: 4 December 2001     

Stability of Strutinsky Shell Correction Energy in Relativistic Mean Field Theory

The single-particle spectrum obtained from the relativistic mean field （RMF） theory is used to extract the shell correction energy with the Strutinsky method. Considering the delicate balance between the plateau condition in the Strutinsky smoothing procedure and the convergence for the total binding energy, the proper space sizes used in solving the RMF equations are investigated in detail by taking ^208 Pb as an example. With the proper space sizes, almost the same shell correction energies are obtained by solving the RMF equations either on basis space or in coordinate space.     

A Hartree-Fock nuclear mass formula

We recall the main features of the recently published mass formula, HFBCS-1, based on the Hartree-Fock-BCS method, and compare its extrapolations out to the neutron drip line with those given by the fine-range droplet model. A new Hartree-Fock-Bogolyubov mass formula, HFB-1, is described: the rms error of the fit to 1888 masses is 0.766 MeV, compared with 0 .738 MeV for HFBCS-1, but there are no substantial changes in the predictions relevant to the r-process. After a critical examination of various questions relating to the effective nucleon mass and to the requirements of the relativistic mean-field theory, we conclude that the greatest remaining ambiguity concerns the nature of the pairing force. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: pearson@lps.umontreal.ca     

Effect of tensor correlations on Gamow–Teller states in Zr and Pb

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree–Fock plus Random Phase Approximation (HF + RPA) model. The Gamow–Teller (GT) strength function of ⁹⁰Zr and ²⁰⁸Pb are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA.     

Study of N = 16 for Ne isotopes

²⁷Ne has been investigated through the one neutron transfer reaction ²⁶Ne(d,p)²⁷Ne in inverse kinematics at 9.7 MeV/nucleon. The results support the existence of a low lying negative parity state in ²⁷Ne which is a signature of a reduced sd-fp shell gap in the N = 16 neutron rich region, at variance with stable nuclei.