The breaking of intrinsic reflection symmetry in nuclear ground states

Negative-parity excited states of doubly even nuclei have earlier been attributed to vibrational excitations. This paper shows that an interpretation starting from a reflection asymmetric intrinsic state is more appropriate for certain nuclei in the radium region. Theoretical evidence for stable octupole deformation comes from a deformed shell-model calculation in which we use a single-particle potential with a realistic radial shape and a finite-range interaction for the surface energy. The octupole effect systematically improves the agreement between theoretical and experimental masses. The low-lying O⁺ excitations observed in experiment are compatible with the calculated collective octupole potentials. The possibility of obtaining further evidence from the spectroscopy of odd-mass nuclei is considered in an exactly solvable model, which shows that the smaller energy splitting observed in odd-A parity doublets mainly reflects single-particle fragmentation of the collective mode. The systematics of theoretical shell structure and experimental spectroscopy suggests the presence of other regions of octupole collectivity near the limits of stability.     

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.     

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.     

Collective states of odd nuclei in a model with quadrupole-octupole degrees of freedom

We apply the collective axial quadrupole—octupole Hamiltonian to describe the rotation—vibration motion of odd nuclei with Coriolis coupling between the even-even core and the unpaired nucleon.We consider that the core oscillates coherently with respect to the quadrupole and octupole axialdeformation variables. The coupling between the core and the unpaired nucleon provides a split paritydoublet structure of the spectrum. The formalism successfully reproduces the parity-doublet splitting in a wide range of odd-A nuclei. It provides model estimations for the third angular-momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure. The text was submitted by the authors in English.     

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.     

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.     

Rotational motion of triaxial shape in unfavoured-signature states of odd-A nuclei

In the region of the angular momentum where the intrinsic energy (namely, the odd-quasiparticle energy) plays a more important role than the collective rotational energy, we point out that the way of rotation in unfavoured-signature states of odd-A nuclei, which is clearly different from that in the usual cranking approximation, can be realized for triaxial intrinsic shape and leads to a peculiar signature dependence of B(E2;I→I - 1) values.     

Excitation of 3−1, 5−1 and 7−1 states in Te isotopes A = 120, 122; 124, 126, 128 WITH (p,t) reactions

The reactions ^ATe(p, t)^A?2Te have been studied with even-A targets using 51.9 MeV protons. Three or more strongly excited triton peaks were observed in the spectra of the ^A-2Te nuclei at energies of ≈ 2–3 MeV excitation. Angular distributions are analyzed using DWBA theory. The lowest octupole (3^?₁) states of five Te isotopes are strongly excited. The lowest 3^? state in ¹²⁰Te is established at 2.09 ±0.02 MeV. The systematics of excitation energies and cross sections for the lowest 5^? and 7^? states are interpreted by a quasiparticle model.     

Mean square charge radii of radium isotopes and octupole deformation in the 220–228Ra region

The first investigation of isotope shifts in both the atomic and ionic resonance lines of radium has been carried out using the technique of on-line collinear fast-beam laser spectroscopy at the ISOLDE facility at CERN. The measurements cover 19 isotopes in the mass range 208⩽A⩽232 with half-lives between 23 ms and 1600 y. The differences in the nuclear mean square charge radii δ〈r²〉 have been evaluated and - together with earlier published spins and moments from the hyperfine structure - related to nuclear deformation. In particular the inversion of the odd-even staggering effect for the isotopes ²²¹Ra, ²²³Ra and ²²⁵Ra can be interpreted by the presence of octupole instability and adds weight to the concept of near-stable octupole deformation in the odd-A isotopes which already explained their spins and magnetic moments.     

On octupole alignment in actinides

The alignment of the octupole angular momentum in the rotational states of the K^π = 0⁻ band is analysed in the microscopic model. The model describes qualitatively the branching ratio for the E1-transitions from these states to the ground band states.     

Exciton and phonon spectra of acoustooptic Tl3AsS3 crystals

The λ-modulated exciton reflection spectra of Tl₃AsS₃ crystals are investigated at 8 and 77 K, in which the ground (n=1) and excited (n=2, 3) exciton states are revealed. Taking into account the spatial dispersion, the shapes of λ-modulated reflection spectra of the n=1 line are calculated and the basic parameters of excitons and bands are determined (the translational and reduced masses of excitons and the effective masses of electrons and light and heavy holes). The one-phonon reflection spectra are studied in the region from 50 to 500 cm^?1 in polarizations E ∥ c and E ⊥ c. The shapes of one-phonon reflection spectra are calculated and the parameters of vibrational modes E and A ₂ are determined.     

Boson description of nuclear collective motion

Nuclear system interacting via quadrupole and octupole particle-hole forces is studied by the boson expansion technique. Energy spectra of the negative parity yrast band and the ground state band are calculated and compared with experiment for¹⁰⁰Ru,¹¹²Cd,¹⁵⁰Sm and¹⁵⁰Gd. ExperimentalB(E1)/B(E2) ratios show strong hindrance for E1 transitions, and are used to deduce the static polarizability of E1 transitions.     

Incipient octupole and 26-pole deformation in the mass region 220 < A < 230

The increase in calculated binding energies of nuclides in the mass region 220<A<230 due to varying the 2⁶-pole deformation parameter is found to be ∽1.0 MeV. The implications of this finding for octupole deformation are discussed.     

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.     

Reflection K-matrices for 19-vertex models

We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or A₁⁽¹⁾ model, Izergin-Korepin or A₂⁽²⁾ model, sl(2|1) model and the osp(2|1) model. We find that there is a general solution for A₁⁽¹⁰⁾ and sl(2|1) models. In both models it is a complete K-matrix with three free parameters. For the A₂⁽²⁾ and os(2|1) models we find three general solutions, being two complete reflection K-matrices solutions and one incomplete reflection K-matrix solution with some null entries. In both models these solutions have two free parameters. Integrable spin-1 Hamiltonians with general boundary interactions are also presented. Several reduced solutions from these general solutions are presented in the appendices.     

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.     

Microscopic structures of parity doublets in the151Pm,153Eu and155Eu nuclei

Microscopic structures of the proposed parity doublet bands in the odd-proton Z=61¹⁵¹Pm and Z=63^{153, 155}Eu nuclei are examined using the quasiparticle phonon nuclear model Hamiltonian including the residual pairing and multipole-multipole interactions. Octupole correlations between intrinsic nonrotational states are studied to check the suggested assignments of parity doublet partners in these nuclei. We conclude significant octupole correlations between a pair ofK ^π = 1/2^± doublets in each of these nuclei, with somewhat weaker correlations betweenK ^π = 3/2^± bands in both the Eu isotopes. No octupole connection between the lowestK ^π = 5/2^± bands is found; however, significant octupole collectivity, built on the low-lying 5/2^? bands, is predicted in the higher-lying 5/2⁺ bands which contain the 5/2⁺ [402] fragmented strength.     

High-K isomers as probes of octupole collectivity in heavy nuclei

The influence of the octupole deformation on the structure of high-K isomeric states in the region of heavy even–even actinide nuclei is studied through a reflection asymmetric deformed shell model (DSM). Two-quasiparticle states with high-K values are constructed by taking into account the pairing effect through a DSM + BCS procedure with constant pairing interaction. The behaviour of two-quasiparticle energies and magnetic dipole moments of Kπ=⁶⁺$K^{\pi }=6^{+}$, ⁶⁻$6^{-}$ and ⁸⁻$8^{-}$ configurations, applicable to mass numbers in the range A=234–252$A=234\text{–}252$, was examined over a wide range of quadrupole and octupole deformations. A pronounced sensitivity of the magnetic moments to the octupole deformation is found. The result suggests a possibly important role for high-K isomers in determining the degree of octupole deformation in heavy actinide nuclei.     

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.