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.     

Microscopic analysis of octupole shape transitions in neutron-rich actinides with relativistic energy density functional

Quadrupole and octupole deformation energy surfaces, low-energy excitation spectra, and electric transition rates in eight neutron-rich isotopic chains – Ra, Th, U, Pu, Cm, Cf, Fm, and No – are systematically analyzed using a quadrupole-octupole collective Hamiltonian model, with parameters determined by constrained reflectionasymmetric and axially-symmetric relativistic mean-field calculations based on the PC-PK1 energy density functional.The theoretical results of low-lying negative-parity bands, odd-even staggering, average octupole deformations β_3,and B(E3;3_1~- →0_1~+) show evidence of a shape transition from nearly spherical to stable octupole-deformed, and finally octupole-soft equilibrium shapes in the neutron-rich actinides. A microscopic mechanism for the onset of stable octupole deformation is also discussed in terms of the evolution of single-nucleon orbitals with deformation.     

The spestroscopy and structure of odd-A Fr isotopes withA=213–225

The remarkable features of the spectra of the odd-A Fr isotopes from²¹³Fr (with 126 neutrons) through²²⁵Fr (with 138 neutrons) serve as a sequence of examples for the application of a variety of nuclear models. As the shapes vary from spherical to spherical with strong octupole correlations to octupole-deformed, the corresponding symmetry breaking leads to increasingly complex spectra. Of considerable interest is the fact that the²¹⁹Fr 9/2⁻ ground state has the character of an h_9/2 shell model state while still having the rotational properties appropriate as a legitimate member of a reflection asymmetric K=1/2⁻ band. It is also possible to follow the expansion of the more degenerate shell model states into the less degenerate reflection asymmetric states. This results from dramatic decreasing in decoupling parameters with increasing mass number.     

Definition of the actinide region of static quadrupole-octupole deformation

Ground state spins of odd-A nuclei in the region just beyond ²⁰⁸Pb are compiled. They are compared with the theoretically predicted spins of an axially symmetric, reflection asymmetric nucleus with octupole deformation ϵ₃ = 0.08 to determine the region of static quadrupole-octupole deformation. Coexistence of different shapes and the corresponding spectra in the same nucleus are predicted in the transition regions.     

Systematics of low-lying octupole states in the doubly-even nuclei from Ge to Sr

Low-lying octupole states of doubly-even ^78–86Kr isotopes have been studied with inelastic scattering of 51.9 MeV protons. It is shown that in the doubly-even nuclei from Ge to Sr with N = 42–50, the lowest octupole vibrational energies of nuclei with equal neutron excess are almost the same. The transition strengths of these states increase with Z.     

Shell model and octupole states in148Gd from in-beam experiments

Through (α, 4n) and (τ, 3n) reactions the high-spin states in the two-neutron nucleus¹⁴⁸Gd were populated up toI ^π=21? at 7.2 MeV, including numerous states above the yrast line. The¹⁴⁸Gd energy spectrum is interpreted in terms of the spherical shell model. Identification of the (νf _7/2 i _{1 3/2})_10? state gives the νi _13/2 single particle energy free of octupole admixtures as 2.1(1) MeV. Eight high-spin states between 1.2 and 3.7 MeV were identified as the couplings of the two valence-particles to the¹⁴⁶Gd octupole phonon, and three above-lying levels are assigned as double-octupole excitations including a 12⁺ state which decays by anE3-E3 stretched cascade. All these octupole levels can be quantitatively predicted from the one-particle x phonon spectrum of¹⁴⁷Gd. The high-spin states above 3 MeV are four-quasiparticle excitations ofπ ⁺¹ π ^?1 ν ² andπ ² ν ² type and their energies are in good accord with shell model estimates.     

Number-conserving treatment of the BCS-Tamm-Dancoff approximation for deformed rare-earth nuclei

The formulation for the exact number-conserving treatment of the BCS-Tamm-Dancoff approximation (NTDA) in deformed even nuclei is given. It is applied to theK ^π=0^? octupole vibrations of rare-earth nuclei and is also compared with the ordinary TDA or RPA method based on the Bogoliubov transformation which has the defect of mixing of the particle number in the wave functions. The excitation energies andB(E3) calculated by NTDA method show rather stronger dependence on the Nilsson orbits than those calculated by the usual TDA or RPA methods, especially atN=94 nuclei.     

Semimicroscopic description of giant octupole resonances in deformed nuclei

The strength functions b(E3, ω) are calculated, and the positions and widths of giant octupole resonances in deformed nuclei are found. It is shown that the giant octupole isoscalar resonances have energies (19–20) MeV for the rare-earth nuclei and (17–18) MeV for the actinides and the widths (5–7) MeV. The energies of the giant octupole isovector resonances are defined by the value of the isovector constant κ⁽³⁾₁.     

Octupole vibrations of deformed nuclei

The octupole vibrations of deformed nuclei are studied. A strong coupling between the harmonic octupole vibrations and the quadrupole ellipsoid is assumed. This interaction gives rise to a splitting of octupole bands with different projection quantum numberK. TheE1-transitions of the octupole states are explained within the frame of the Dynamic Collective Theory ofDanos andGreiner by calculating the Coulomb interaction between octupole vibrations and giant resonances. Furthermore, theE2- andE3-transitions of the octupole states are studied. The spectrum of W¹⁸² is investigated in detail. A fair agreement between theory and experiment is obtained. Predictions for the octupole spectra of Sm¹⁵² and Gd¹⁵⁶ are given.     

Effect of N-substitution in multinuclear complexes allows interplay between magnetic states and multistability investigated by Mössbauer spectroscopy

A series of pentadentate ligands N–X–⁵LH₂ (X?=?H, Methyl, Benzyl)?=?N–X–saldptn (4-X-N,N′-bis(1-hydroxy-2-benzylidene)-1,7-diamino-4-azaheptane) has been prepared by a Schiff base condensation between 1,7-diamino-4-X-azaheptane and salicylaldehyde. Complexation with Fe(III) yields a series of high-spin (S?=?5/2) complexes of [Fe^III(N–X–⁵L)Cl]. Such precursors were combined with [Mo(CN)₈]^4? and a series of blue nonanuclear cluster compounds [Mo^IV{(CN)Fe^III(N–X–⁵L)}₈]Cl₄ resulted. Such star-shaped nonanuclear compounds are high-spin systems at room temperature. On cooling to 10 K some of the iron(III) centers switched to the low-spin state as proven by Mössbauer spectra, i.e. multiple electronic transitions. Parts of the compounds perform a high-spin to high-spin transition. Under light irradiation the populations are altered slightly.     

Crossing of negative parity bands in even-even nuclei around A≈150

Level energies of negative parity yrast bands (NPB) have been studied with a recently proposed, sensitive method. The irregular behaviour of the NPB's in theN=88 nuclei around spin 9–11 and the smooth behaviour in¹⁵⁶Dy (up toI=13) and in²³⁸U (up to I=19) support calculations by Vogel, where NPB's are described as aligned octupole bands up to a critical spin where intersection with two-quasiparticle bands takes place. Considering the NPB levels (I≦13) in¹⁵⁶Dy as members of an aligned octupole band, we obtain a remarkably good reproduction of their decay properties and energies using the VMI model.     

The subshell closure at N = 56 and the deformation of neutron-rich isotopes from Ge to Zr

The microscopic energy density method is applied to the study of nuclei with N ? 50 and Z = 32?40. The experimental Subshell effect at N = 56, which is not found in many previous works about this region, is well reproduced by the present self-consistent calculation. The existence of strongly deformed prolate isotopes of Zr and Sr for N ? 60 is also explained. A wide region of oblate shapes is predicted for N ? 60 and Z ? 36. The results also support the interpretation of low-energy isomers in the shape transition region as shape isomers.     

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.     

The strength of octupole correlations in neutron-rich Xe isotopes

Excited levels in ¹⁴⁰Xe and ¹⁴²Xe nuclei, populated in the spontaneous fission of ²⁴⁸Cm, were studied by means of prompt γ-ray spectroscopy, using EUROGAM2 array. We report the first observation of an octupole band in ¹⁴²Xe and extend the octupole band in ¹⁴⁰Xe. Level schemes of ¹⁴⁰Xe and ¹⁴²Xe obtained in this work show patterns characteristic of ocupole-vibrational bands. Properties of octupole bands in Xe isotopes indicate that octupole correlations in these nuclei are lower than in the corresponding Ba nuclei. The electric dipole moment of ¹⁴²Xe was found to be larger than in other Xe isotopes, contrary to theoretical predictions. This may be due to the special role of the N = 88 neutron number. Received: 18 November 2002 / Accepted: 15 December 2002 / Published online: 25 February 2003 RID="a" ID="a"e-mail: urban@fuw.edu.pl Communicated by D. Schwalm     

Magnetic moments of K isomers as indicators of octupole collectivity

The relation between the quadrupole-octupole deformation and the structure of high-K isomers in heavy even-even nuclei is studied through a reflection asymmetric deformed shell model including a BCS procedure with constant pairing interaction. Two-quasiparticle states with K ^?? = 4^?, 5^?, 6^?, 6⁺ and 7^? are considered in the region of actinide nuclei (U, Pu and Cm) and rare-earth nuclei (Nd, Sm and Gd). The behaviour of two-quasiparticle energies and magnetic dipole moments of these configurations is examined over a wide range in the plane of quadrupole and octupole deformations (?? ₂ and ?? ₃. In all considered actinide nuclei, the calculations show that there is pronounced sensitivity of the magnetic moments to the octupole deformation. In the rare-earth nuclei, the calculations for ^{154, 156}Gd show stronger sensitivity of the magnetic moment to the octupole deformation than in the other considered cases.     

Chemical tuning of high-spin complexes based on 3- and 4-hydroxy-pentadentate-Fe (III) complex-units investigated by Mössbauer spectroscopy

The pentadentate ligands 3-OH-⁵L?=?[N,N′-Bis(1,3-dihydroxy-2-benzylidene)-1,7-diamino-4-azaheptane] and 4-OH-⁵L?=?[N,N′-Bis(1,4-dihydroxy-2-benzylidene)-1,7-diamino-4-azaheptane] has been prepared by a Schiff base condensation between 1,7-diamino-4-azaheptane and the dihydroxybenzaldehyde. Complexation with Fe(III) yields high-spin (S?=?5/2) complexes of [Fe^III(3-OH-⁵L)Cl] and [Fe^III(4-OH-⁵L)Cl]. These precursors were combined with [M(CN) _x ] ^y? (M?=?W(IV), Mo(IV), Ru(II), Co(III)) and heptanuclear and nonanuclear clusters of [M{(CN-Fe^III(3-OH-⁵L)} _x ]Cl _y and [M{(CN-Fe^III(4-OH-⁵L)} _x ]Cl _y resulted. Such starshaped hepta- and nonanuclear compounds are high-spin systems at room temperature. On cooling to 10 K some of the iron(III) centers switch to a second high-spin state as proven by Mössbauer spectra, i.e. multiple electronic transitions. Parts of the compounds perform a high-spin to high-spin transition.     

Complexes based on ethylene- and propylene-bridged-pentadentate-Fe(III)-units allow interplay between magnetic centers and multistability investigated by Mössbauer spectroscopy

The propylene-based ⁵3,3-L?=?[N,N′-Bis(1-hydroxy-2-benzylidene)-1,7-diamino-4-azaheptane] and ethylene-based pentadentate ligand ⁵2,2-L?=?[N,N′-Bis(1-hydroxy-2-benzylidene)-1,5-diamino-3-azapentane] has been prepared. Complexation with Fe(III) yields high-spin (S?=?5/2) complexes of [Fe^III(⁵2,2-L)Cl] and [Fe^III(⁵3,3-L)Cl]. Such precursors were combined with [M(CN) _x ] ^y? (M?=?W(IV), Mo(IV), Ru(II), Co(III)) and heptanuclear and nonanuclear clusters of [M{(CN-Fe^III(⁵2,2-L)} _x ]Cl _y and [M{(CN-Fe^III(⁵3,3-L)} _x ]Cl _y resulted. Such starshaped hepta- and nonanuclear compounds are high-spin systems at room temperature. On cooling to 20 K in all presented ethylene compounds the iron(III) centers switch to a second high-spin state as proven by Mössbauer spectra with a yield of about 30%, i.e., multiple electronic transitions. The propylene compounds, however, perform a high-spin to low-spin transition. Mössbauer spectra taken during green light irradiation indicate changes in the population of the different electronic states, i.e. concerted inorganic reaction.     

The (p,t) reactions on nuclei in the rare earth region

The (p, t) reactions on isotopic targets of ^{178, 180}Hf and all the stable isotopes of Yb and on natural targets of Gd, Dy, Er, Hf, Ta, W, Os and Au were studied at a beam energy of 19 MeV with an average resolution of 12 keV. A split-pole magnetic spectrometer was used to measure (p, t) Q-values and absolute differential cross sections. On the basis of angular distribution shapes definite 0⁺ and tentative 2⁺ assignments were made. Rotational bands were identified assuming an I(I+1) spacing. The (p, t) reaction populates excited 0⁺ states strongly in ¹⁷⁴Yb, ¹⁷⁶Hf, ¹⁶⁶Yb and several Gd, Dy and Er isotopes. The ¹⁷⁴Yb and ¹⁷⁶Hf 0⁺ states are discussed in terms of the pairing phase transition and in terms of Nilsson orbitals with unequal (p, t) reaction amplitudes. Members of gamma and octupole vibrational bands were observed in the even-N nuclei. The lowest L = 0 transfers to states in ^{169, 171}Yb were found to have less than 55% of the strength to ground states in adjacent even-N nuclei. A strong L = 0 transfer to a state at 1513 keV in ¹⁷¹Yb indicates the presence of a possible K = 0 core vibration coupled to the unpaired $\text{5}\text{2}$[512] neutron. The natural targets have furnished information on trends in cross sections for members of ground bands, gamma bandheads, 3^? octupole states, and strongly excited 0⁺ states.     

Nuclear structure effects in the feeding of yrast states of Gd,Dy and Er nuclei

The population of the yrast and near-yrast levels in Gd, Dy and Er nuclei has been investigated experimentally in (heavy ion, xn) reactions through high-resolution γ-ray intensity measurements. A clear difference between non-rotor (N ? 86) and rotor nuclei (N > 86) is evident from the data. For the non-rotor nuclei we define the spin value I_sat below which the yrast population saturates. One finds that I_sat is independent of the bombarding energy when the latter becomes sufficiently high. We discuss the feeding pattern in relation to the single-particle structure of the yrast and near-yrast levels and in relation to the effect of shape changes, including the possibility of superdeformed shapes at high spin.     

Evolution of proton shells in 20 ⩽ Z ⩽ 28 and 20 ⩽ N ⩽ 50 nuclei and dispersive optical model

Experimental single-particle proton energies in spherical and nearly spherical 20 ? Z ? 28 medium-mass nuclei and their counterparts evaluated with the aid of data formirror nuclei were analyzed on the basis of the dispersive optical model. The parameters of the dispersive optical potential were extrapolated to the region of unstable nuclei, and the values obtained in this way were then used to predict the single-particle proton energies in the 20 ? N ? 50 nuclei under study. The evolution of the particle-hole energy gap was traced, and features peculiar to single-particle spectra of magic and nonmagic nuclei were revealed by comparing single-particle energies with proton-separation energies.