Quantum correlations in rotating nuclei

Using the Hamiltonian that consists of the separable quadrupole + pairing forces and the cranking term, we analyze the correlations associated with shape, orientation, and particle-number fluctuations in rotating nuclei. Quantum fluctuations around mean field solutions are treated in the random phase approximation (RPA), with special emphasis on the restoration of rotational symmetry and particle number conservation. The mean field calculations have been made within the self-consistent cranking model. The effect of the RPA correlation energy for the moment of inertia is studied with the integral representation method proposed.     

Microscopic interpretation of the (<Emphasis Type="Italic">t</Emphasis>, <Superscript>3</Superscript>He) reaction at 130 MeV on <Superscript>90</Superscript>Zr and isovector monopole strength

The 130-MeV primary tritium beam of the AGOR facility with an intensity of up to 10⁸ pps and the Big Bite Spectrometer experimental setup have been used to study the (t, ³He) reaction between 0° and 5° lab angles on ¹²C and ⁹⁰Zr targets. The standard ray-tracing procedure has allowed us to obtain excitation-energy spectra up to 30 MeV in six angular bins for each residual nucleus, with an average energy resolution of 350 keV. We have used the DWBA reaction mechanism model to reproduce those spectra and their angular distributions. In this approximation, the form factor was treated as a folding of an effective projectile-nucleon interaction with a transition density. The effective projectile-nucleon interaction has been adjusted to reproduce the 0° cross section of the 1⁺ ground state of ¹²B populated in the ¹²C(t, ³He) reaction. We have employed RPA wave functions of excited states to construct the form factors. This DWBA+RPA analysis is used to compare calculated and experimental cross sections directly and to discuss the giant resonance excitations in the ⁹⁰Y nucleus. In this talk, we give some details on this analysis. We show that there are important contributions of L = 2 transitions in the observed cross sections for the 1⁺ final states that explain the previous difficulties in clearly identifying the monopole strength distributions. We then have a better indication of where the L = 0 part is located with this reaction and its microscopic analysis. The text was submitted by the author in English.     

Phase separation in La-Pr manganites and its evolution in a magnetic field

The self-consistent harmonic oscillator model including the three-dimensional cranking term is extended to describe collective excitations in the random phase approximation. It is found that quadrupole collective excitations associated with wobbling motion in rotating nuclei lead to the appearance of two-or three-dimensional rotation.     

Investigation on phase and shape transitions in the hot rotating nucleus <Superscript>154</Superscript>Dy

A statistical theory for hot rotating nuclei incorporating deformation, collective and non-collective rotational degrees of freedom, shell effects and pairing correlations is used to investigate the occurrence of phase and shape transitions in the hot rotating deformed nucleus ¹⁵⁴Dy . The interplay of various degrees of freedom and their influence on the behavior of nuclei formed as fused compounds in heavy-ion reactions are studied. A phase transition from the superfluid to normal state in the nucleus with increasing temperature and angular momentum is observed. The effect of pairing on the level density parameter and nucleon separation energy has been analyzed and is found to be substantial. The neutron and proton separation energies extracted as a function of the angular momentum and temperature is found to decrease sharply for particular angular momentum states of the nucleus due to shape transitions from prolate collective to oblate non-collective at higher temperatures.     

Structure of the isovector dipole resonance in neutron-rich <Superscript>60</Superscript><Emphasis Type="Italic">Ca</Emphasis> nuclei and direct decay from pygmy resonance

The structure of the isovector dipole resonance in neutron-rich calcium isotope, ⁶⁰Ca, has been investigated by implementing a careful treatment of the differences of neutron and proton radii in the continuum random phase approximation (RPA). The calculations have taken into account the current estimates of the neutron skin. The estimates of the escape widths for direct neutron decay from the pygmy-dipole resonance (PDR) were shown rather wide, implicating a strong coupling to the continuum. The width of the giant-dipole resonance (GDR) was evaluated, bringing on a detailed discussion about its microscopic structure.Received: 22 September 2003, Revised: 9 February 2004, Published online: 7 September 2004PACS: 21.10.Pc Single-particle levels and strength functions - 21.60.-n Nuclear structure models and methods - 24.30.Cz Giant resonances - 24.30.Gd Other resonances     

Temperature dependence of collective states in the random-phase approximation

We investigate the temperature dependence of collective states in the framework of the random-phase approximation at finite temperature. We show that sum rules can be extended to collective energies at finite temperature. Numerical methods are developed to solve the RPA equations at finite temperature. Results are presented and discussed in the case of ⁴⁰Ca for isovector dipole and isoscalar octupole vibrations, using oscillator wave functions and a zero-range force. We show that the broadening of giant dipole resonances observed experimentally, appears as a natural consequence of the structure of the RPA equations. Comparison is made with the schematic model for which the temperature dependence of collective states can be worked out analytically.     

Structure of low-lying quadrupole states in nucleus <Superscript>134</Superscript>Xe

Starting from the Skyrme interaction, we study the M1 transitions between vibration quadrupole states. The finite rank separable approach for quasiparticle random phase approximation is used. As an example, we investigate the properties of the low-energy spectrum of quadrupole excitations in nucleus ¹³⁴Xe.     

Radiative strength function and the pygmy dipole resonance in <Superscript>208</Superscript>Pb and <Superscript>70</Superscript>Ni

The pygmy-resonance parameters and the E1 strength function are derived for ²⁰⁸Pb using a fully self-consistent microscopic formalism recently developed for magic nuclei, which takes into account quasiparticle phonon interactions (or coupling to phonons) in addition to the random phase approximation. For the radiative strength function of ²⁰⁸Pb at energies above 5 MeV, the experimental data of the Oslo group are adequately described by our predictions, whereby the important role of coupling to phonons is confirmed. By comparing the measurements based on the (³He, ³He′γ) and (γ, γ′) reactions, we discuss the physical properties of the radiative strength function measured for ²⁰⁸Pb. For the neutron-rich ⁷⁰Ni nucleus, predictions for the radiative strength function and the pygmy resonance are obtained using a partially self-consistent approach, which invokes the Skyrme forces in deriving the mean field, effective nucleon–nucleon interaction, and phonon characteristics.     

Effect of Sr<Superscript>2+</Superscript> ion substitution with trivalent ions (Sc<Superscript>3+</Superscript>, In<Superscript>3+</Superscript>, La<Superscript>3+</Superscript>, Bi<Superscript>3+</Superscript>) on its ferroelectric instability in SrTiO<Subscript>3</Subscript>

The vibration frequencies of unstable ferroelectric and antiferrodistortion modes and the dependences of the energy on the ion displacement amplitude have been calculated within the generalized Gordon-Kim model for distortions along eigenvectors of these modes in the mixed compounds Sr_{1 − x} A _x Ti_{1 − x} /₄□ _x/4O₃ and Sr_{1 − y} A _2y /₃□ _y/3TiO₃ (A = Sc³⁺, In³⁺, La³⁺, Bi³⁺; □ is the vacancy). To compensate an excess positive charge, vacancies are introduced into the Ti⁴⁺ or Sr²⁺ site. Calculations have been performed in the “daverage” crystal approximation for impurity concentrations of 0.25 and 0.50. To this end, a set of 40 atomic superlattices with various orderings of heterovalent ions Sr²⁺ and impurity A ³⁺ has been considered. It has been found that each impurity type, independently of charge balance, induces ferroelectric instabilities in doped compounds. In the case of doping with In³⁺ and La³⁺ for concentration x = 0.25, the possibility of rotating the polarization vector has been shown.     

Local structure of Gd<Superscript>3+</Superscript> and Eu<Superscript>2+</Superscript> impurity centers in a CdF<Subscript>2</Subscript> crystal

The local crystal structure of Gd³⁺ and Eu²⁺ cubic impurity centers in cadmium fluoride is calculated within the shell model in the pair potential approximation. The local compressibility of the cationic and anionic sublattices of the host lattice is determined in the vicinity of the Gd³⁺ (Eu²⁺) impurity ion.     

Structure of 2<Subscript>1,2</Subscript> <Superscript>+</Superscript> states in <Superscript>132,134,136</Superscript>Te

Starting fromthe Skyrme interaction f_ together with the volume pairing interaction, we study the g factors for the 2_1,2⁺ excitations of ^132,134,136Te. The coupling between one- and two-phonon terms in the wave functions of excited states is taken into account within the finite-rank separable approximation. Using the same set of parameters we describe the available experimental data and give the prediction for ¹³⁶Te, g(2₁⁺) = ?0.18 in comparison to +0.32 in the case of ¹³²Te.     

Phase shift analysis of the <Superscript>6</Superscript>He+<Superscript>208</Superscript>Pb and the <Superscript>6</Superscript>He+<Superscript>197</Superscript>Au systems

We present the elastic scattering of the ⁶He+²⁰⁸Pb and the ⁶He+¹⁹⁷Au systems at the laboratory energy of E _lab=27 MeV within the framework of the McIntyre parametrization, and systematically investigate χ ²/N analysis of both systems to obtain an excellent agreement between the theoretical results and the experimental data. We find large diffusivity parameters indicating long range absorption mechanisms. We also show that both systems lack both the nuclear and the Coulomb rainbow scattering for obtained S-matrix parameters.     

Microscopic description of collective states near the yrast line of nuclei with stable octupole deformation

Collective states near the yrast line in nuclei with stable octupole deformation are discussed in the framework of the random phase approximation (RPA) based on the cranking model. These vibrational states are characterized by the quantum number of generalized signature (eigenvalue of the operator S_x = PR_x^?1(π)). In the zero-octupole deformation limit the RPA equations of motion are reduced to the well-known ones characterized by both values of parity and signature, respectively. The connection of the translational and rotational symmetry of the model hamiltonian with the spurious solutions of the RPA equation of motion is discussed. Expressions for the reduced probabilities B(E1), B(E2) and B(E3) are obtained. These expressions confirm the conclusions of phenomenological models for the strong E1 and E3 intraband transitions in nuclei with stable octupole deformation.     

Comparison of halo of <Superscript>11</Superscript>Be, <Superscript>15</Superscript>C,and <Superscript>19</Superscript>C

We have compared the halo of ¹¹Be, ¹⁵C, and ¹⁹C nuclei by analyzing the one-neutron stripping reaction data on the Be target at 60-, 54-, and 57-MeV/A beam energies, respectively, within the framework of the eikonal approximation approach. The determination of effective range through the comparison of the total cross section data and prediction has revealed that the halo of ¹⁹C is the well developed, while that of ¹⁵C is the least and that of ¹¹Be lies in between these two. The longitudinal momentum distribution data also strengthen these observations. The text was submitted by the authors in English.     

QRPA coordinate space calculations of 2<Superscript>+</Superscript> states in <Emphasis Type="Italic">N</Emphasis>=20 isotones

The first 2⁺ states in N=20 isotones are studied within the self-consistent quasiparticle random phase approximation based on the Green’s function method. The residual interaction between quasiparticles with full velocity dependence is consistently derived from the Skyrme interaction plus pairing interaction energy density functional. The B(E2, 0 ₁ ⁺ → 2 ₁ ⁺ ) transition probabilities and the excitation energies of the first 2⁺ states are well described within a single framework. We discuss mainly the microscopic origin of the anomalously large B(E2) value and the very low excitation energy in ³²Mg.     

Mass distribution studies in the <Superscript>19</Superscript>F + <Superscript>197</Superscript>Au reaction

Mass distribution and evaporation residue measurements have been carried out in the reaction ¹⁹F + ¹⁹⁷Au using the recoil catcher technique followed by off-line γ-ray spectrometry. The random neck rupture model (RNRM) has been used to compute the variance of the mass distribution ( σ²_A) and the average kinetic energy ( ˉ) of the fission fragments for the present system. The results of model calculations have been found to be in good agreement with the experimental observations. Measured evaporation residue cross-sections have been compared with the statistical model calculations.     

Blocking of coupling to the 0<Subscript>2</Subscript><Superscript>+</Superscript> excitation in <Superscript>154</Superscript>Gd by the [505]11/2<Superscript>-</Superscript> neutron in <Superscript>155</Superscript>Gd

The concept that the first excited 0⁺ states in N = 90 nuclei are not a b \beta -vibration but a second vacuum formed by the combination of the quadrupole pairing force and the low density of oblate orbitals near the Fermi surface is supported by the blocking of this collective mode in ¹⁵⁴Gd from coupling to the [505]11/2^- single-particle quasi-neutron orbital in ¹⁵⁵Gd . The coupling of this orbital to the 2⁺ g \gamma -vibration in ¹⁵⁴Gd is observed since this coupling is not Pauli-blocked.