Microscopic aspects of identical bands in 78Sr and 78Rb

Recent investigations of the shape transition and shape coexistence phenomena dominating the structure of the even-even N ? Z nuclei in the A ? 80 mass region are extended to the odd-odd nucleus ⁷⁸Rb. Special attention is paid to the structure of some “identical” bands which have been recently identified in ⁷⁸ Sr and ⁷⁸Rb. The ground band of⁷⁸ Sr and the yrast as well as excited negative parity bands in ⁷⁸Rb are studied within the EXCITED VAMPIR approximation using complex Hartree-Fock-Bogoliubov transformations in a relatively large model space. The results are compared with the available experimental data. The emerging picture reveals the role played by the strong quadrupole deformation on the appearance of identical bands as well as the influence of the shape coexistence on their evolution. Predictions for the electromagnetic and alignment properties of the bands are presented.     

Calculation of charge and transition charge densities in some even mass Ge isotopes from microscopic nuclear structure wave functions

Microscopic nuclear structure wave functions obtained within the EXCITED FED VAMPIR approach are used to calculate the charge densities for the ground states as well as the transition charge densities for the transitions from the ground to the first and second 2⁺ states in some doubly even Ge isotopes. The results are compared with the data extracted from elastic and inelastic electron scattering experiments. Except for the heavier isotopes, where the calculations fail to yield enough collectivity, rather nice agreement is obtained. This result strongly supports the theoretically predicted shape coexisting structures in the low spin states of the nuclei in this mass region.     

Complex mean fields and unnatural parity pairing in the Hartree-Fock-Bogoliubov problem with symmetry-projection before the variation

The Hartree-Fock-Bogoliuboy problem with restoration of the broken symmetries before the variation as it has been formulated recently within the VAMPIR and EXCITED VAMPIR approaches is studied in more detail. Special emphasis is put on the implications of various symmetry restrictions imposed on the quasiparticle transformations. It is shown that the use of essentially complex transformations provides a possibility to account for time-odd unnatural parity pairing correlations in the wavefunctions without being forced to give up axial and time-reversal symmetry. It is illustrated that together with parity and neutron-proton mixing the use of such complex mean fields extends the applicability of the VAMPIR and EXCITED VAMPIR approaches to states with arbitrary spin and parity in both doubly even and doubly odd nuclear systems. The corresponding variational equations are explicitly evaluated and the numerical feasibility of their solution is investigated.     

VAMPIR calculations for 128Ba and 130Ce: Two mechanisms of backbending

Hartree-Fock-Bogoliubov calculations with spin and number projection before the variation (VAMPIR) are performed for the nuclei ¹²⁸Ba and ¹³⁰Ce using a slightly renormalized Brueckner G-matrix as effective interaction in a rather large single-particle basis. The results are compared to those of Hartree-Fock-Bogoliubov calculations with projection after the variation, those of multiconfiguration calculations (MONSTER) and to experiment. In both nuclei the VAMPIR and the MONSTER approaches turn out to be of about the same quality and agree rather well with the experimental data. Analysis of the VAMPIR mean fields reveals that two somewhat different mechanisms are responsible for the backbending observed in the yrast bands of the two nuclei. While in ¹³⁰Ce the well-known alignment of two high-j quasiparticles (proton $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$) is found, in ¹²⁸Ba first a neutron pair is scattered from the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ to the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ orbit, and then the larger alignment energy of the less occupied neutron $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ states produces the backbend. This latter effect is in agreement with the predictions of a simple model presented by us some years ago.     

Research on High Spin States in 68Ge,65Ga and 67Ga

The high spin states in ⁶⁸Ge,⁶⁵Ga and ⁶⁷Ga were studied through in-beam gamma-ray spectroscopy experiment.The reaction ⁴⁶Ti(²⁵Mg,xpxn) was used with beam energy 68MeV.In ⁶⁸Ge the new multiplicity of band structures,the crossing transitions among the bands and a new band with possible big diformation were observed.The experiment results agree with a new microscopic model calculation (EXCITED FED VAMPIR).In ⁶⁵Ga and ⁶⁷Ga a few band structures with strong collectivity were observed and the new level schemes were given.     

Electric monopole transitions from low energy excitations in nuclei

Electric monopole (E0) properties are studied across the entire nuclear mass surface. Besides an introductory discussion of various model results (shell model, geometric vibrational and rotational models, algebraic models), we point out that many of the largest E0 transition strengths, ϱ²(E0), are associated with shape mixing. We discuss in detail the manifestation of E0 transitions and present extensive data for single-closed shell nuclei, vibrational nuclei, well-deformed nuclei, nuclei that exhibit sudden ground-state changes, and nuclei that exhibit shape coexistence and intruder states. We also pay attention to light nuclei, odd-A nuclei, and illustrate a suggested relation between ϱ²(E0) and isotopic shifts.     

Description of low-lying vibrationalK π≠0+ states of deformed nuclei in the quasiparticle-phonon nuclear model

The QPNM equations are derived taking account of p-h and p-p interactions. The calculated quadrupole, octupole and hexadecapole vibrational states in¹⁶⁸Er,¹⁷²Yb and¹⁷⁸Hf are found to be in reasonable agreement with experimental data. It is shown that distribution of theEλ strength in some deformed nuclei differs from the standard one. There are cases when for a givenK ^π theEλ strength is concentrated not on the first but on higher-lying states. The assertion made earlier about the absence of collective two-phonon states in deformed nuclei is confirmed.     

Nuclear pears: Recent developments and future prospects

We report studies of examples of reflection-asymmetric nuclei which are difficult to access using compound nucleus reactions. The octupole radium isotopes withN>132 and radon isotopes are not accessible by reactions employing stable targets and beams; we have shown that multinucleon transfer reactions can populate these nuclei with sufficient yield for their structure to be determined. We report high-spin studies in^{218, 220, 222}Rn and^{222, 224, 226, 228, 230}Ra: these show that the Ra isotopes withA<228 have the characteristics of octupole deformed nuclei whereas the Rn isotopes behave like octupole vibrators. Measurements of theB(E1)/B(E2) ratios indicate that the electric dipole moment in these nuclei is constant with spin. The most octupole deformed nuclei are predicted to be uranium isotopes withN≈132; measurements of the very fissile nucleus²²⁶U suggest that it is octupole deformed and has a large intrinsic electric dipole moment. Finally, we speculate that the best examples of pear shapes are the hyperdeformed minima predicted to lie low in uranium isotopes withN≈140; their signature of high-multiplicity low-energyE1 photon cascades should be detectable using present-day high-efficiency germanium arrays.     

Semi microscopic description of84Kr

The experimental information on the⁸⁴Kr nuclei is compared with the model calculation in which two neutron holes are coupled to the vibrational field. Based on the lower-order terms of a perturbative expansion of theE2 andM1 transition matrix elements, a simple rule is obtained for the sign and the magnitude of theδ (E2/M1) ratios for the transitions between the second and first 2⁺ states in some vibrational nuclei. [Nuclear structure⁸⁴Kr, calculated levelsJ, π and δ(E2/M1), Cluster-phonon model. Pairing interaction].     

The supersymmetry scheme and E2 transition rates in the Pt region

Elastic and inelastic proton scattering from ¹⁹¹Ir, ¹⁹³Ir and ¹⁹⁴Pt have been studied at E_p = 50 MeV. The E2 reduced transition rates obtained for the low-lying states in these nuclei agree qualitatively with the predictions of the supersymmetry scheme recently proposed for these nuclei.     

Fragmentation of giant multipole resonances in deformed nuclei

The fragmentation of the giant monopole resonance in deformed nuclei is first studied by coupling the monopole oscillation with the quadrupole oscillation by means of the variational procedure for resonance frequencies. It is shown that, for non-axial symmetry, the monopole oscillation couples with both m = 0 and 2 modes of the quadrupole oscillation and the giant monopole resonance is split into three components, whereas for axial symmetry, the fragmentation is given by E₀(1 + 0.86δ² ± 1.25δ³) and E₀(0.74 ± 0.22δ ? 0.21δ² ± 0.57δ³), where E₀ is the g monopole resonance energy for spherical nuclei, δ is the deformation parameter, and the upper and lower signs stand for prolate and oblate deformations, respectively. The initial fragmentation of the giant quadrupole resonance is seen to be little modified by the coupling, except for the m = 0 mode which is split into two components. The variational method is extended to general multipoles for an ellipsoid and the fragmentation of giant multipole resonances in deformed nuclei is investigated for both axial and non-axial symmetries. A brief discussion is also made about the meaning of the energy eigenvalue involved in the model wave equation in terms of multipole sum rules. The giant dipole resonance for the static octupole deformation is shortly considered. The giant E0 and E3 resonances for largely deformed nuclei are finally examined by solving the spheroidal eigenvalue equation and they are compared with the results of the giant dipole and quadrupole resonances.     

Structure of even-even actinides in the interacting boson model and the N = 152 subshell closure

We show that a wide range of deformed actinides can be described in terms of an interacting boson model hamiltonian with three parameters, two of them [including the coefficient of the only SU(3) symmetry breaking term] remaining almost constant over the whole region. In addition to ground γ₁ and β₁ spectra, B(E2:0_g⁺ → 2_g⁺) values are well reproduced with no extra adjustable parameters for nuclei with 136⩽N⩽146, while for nuclei beyond N = 146 an effective boson number has to be considered in order to fit the observed in the B(E2:0⁺_g → 2⁺_g) values, which is due to the presensce of a subshell closure at N = 152. The sensitive dependence of the B(E2:0_g⁺→2_g⁺) values on the effective boson numbers is emphasized. β₁ → ground and β₁ → ground transitions are fitted by breaking the SU(3) symmetry of the E2 transition operator.     

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.     

Quadrupole excitations in the two-center shell model (II)

The distribution of the isoscalar, T = 0, and isovector T = 1, strength of quadrupole modes in the deformed nucleus ²⁴Mg is investigated. A finite-range residual interaction is used in the particle-hole basis of a rotating two-center shell-model potential of two ¹²C nuclei. The model calculation describes semi-quantitatively the main features of the available experimental data for the T = 0, E2 excitations and predicts the location and structure of the isovector, T = 1, E2 strength for which no data has been published to date.     

The E2 transition probability and effective charge for the neutron i132 subshell in lead isotopes

In (heavy ion, xn) reactions, X-rays and low energy γ-rays emitted by the compound nuclei are investigated using a catcher system for recoiling nuclei within the 10–100 keV energy range. The nucleide ¹⁹⁸Pb is studied by means of this technique. A 90 keV E2 (or E2 + M1) transition is identified together with information related to the 12⁺ → 10⁺E2 transition energy. The B(E2; 12⁺ → 10⁺) value is deduced. The effective charge extracted from the analysis of the reduced transition probability between two members of the ($\text{vi}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?2}}$ multiplet is compared to the corresponding values for other lead isotopes.     

Signature-dependent ml and e2 transition probabilities in 155ho and 157ho

¹⁵⁵Ho and ¹⁵⁷Ho have been populated in the reactions ¹⁴¹Pr(¹⁸O,4n) and ¹⁴⁶Nd(¹⁵N, 4n) at 85 and 74 MeV, respectively. In both nuclei bands built on the $\text{7}\text{2}$?[523] configuration were established to spin values considerably above the first backbend. A signature dependence in the excitation energies as well as in the ratio of M1 to E2 transition rates is observed below, but not above, the backbend in both nuclei. In ¹⁵⁷Ho lifetimes were measured with the recoil-distance method. The ΔI = 2; E2 transition probabilities obtained show very little variation with either signature or spin and no irregularity at the backbend. The signature dependence and strong rise in the ratio B(M1)/B(E2) observed at the backbend in ¹⁵⁷Ho therefore must be caused by the B(M1) values. A signature dependence in the B(E2, I → I ?1)/B(E2, I → I ?2) ratios also found in ¹⁵⁷Ho below the backbend is mainly the result of signature dependence in the ΔI = 1 ; E2 transition rates. Qualitatively, most of the features observed can be explained by nonaxial deformations, which change from large negative to slightly positive values of γ at the backbend.