Influence of giant angular resonances on the electromagnetic characteristics of low-lying states

The two-rotor model0 with the Feshbach projection operator method is applied for investigating the properties of the positive parity low-lying collective states in the rare earth nuclei. The calculations of the energy spectra, E2-transition probability and magnetic properties of the states of β- and γ-bands are carried out for the isotopes ^{164, 166, 168}Er. The B(M1) values from 1⁺ states to the ground band are estimated.     

(α, 2nγ) Studies of γ-vibrational and other side-bands in 162, 164, 166Er

Levels in ^{162, 164, 166}Er have been studied using the (α, 2nγ) reaction at an energy of 24 MeV. Singles spectra, γ-γ coincidence spectra, and angular distributions were obtained using Ge(Li) detectors. Transitions from levels in the γ-vibrational bands up to the 8^+' in ^{162, 164}Er and 10^+' in ¹⁶⁶Er were observed and M1/E2 mixtures were determined for many of these transitions. There is a relative shifting upward of the even-spin levels in the γ-band of ¹⁶⁶Er while the analogous levels of ^{162, 164}Er are shifted downward with the effect being most pronounced for¹⁶²Er. The standard phenomenological band-mixing parameters z₂ and z₀₂ were obtained from γ-ray branching ratio data and the values are probably correlated with the staggering of levels in the γ-bands. The ratios of the intraband and interband E2 transition strengths which are related to the intrinsic quadrupole moments of the ground-state and γ-bands are discussed. A number of other levels are observed in ¹⁶², 164Er and some of these correspond to negative parity states reported in decay studies.     

Messung der magnetischen Momente der tiefsten 2+-Zustände für einige Dy-, Er- und Yb-Isotope

With the Mössbauer technique, the hyperfine splittings of the lowest 2⁺-states of some Dy-, Er-, and Yb-isotopes were observed at 4.2 °K in the paramagnetic compounds Dy-Al-garnet, ErCl₃·6H₂O, and YbCl₃·6H₂O. Most of the sources were produced by photonuclear reactions. Ratios ofg-factors for neighbouring isotopes could be determined with small systematic errors. The results are:g ¹⁶⁴/g ¹⁶⁶=1.103 (15),g ¹⁶⁶/g ¹⁶⁸=0.960 (13) for Er, andg ¹⁷⁰/g ¹⁷²=1.009 (15),g ¹⁷⁰/g ¹⁷⁴=0.994 (13) for Yb. Using known values for the effective magnetic fields at the nuclei, the followingg-factors were obtained:¹⁶⁴Dy 0.336 (14),¹⁶⁴Er 0.353 (10),¹⁶⁶Er 0.320 (8),¹⁶⁸Er 0.333 (8),¹⁷⁰Yb 0.335 (6),¹⁷²Yb 0.332 (8),¹⁷⁴Yb 0.337 (8).     

Interaction of slow neutrons with natural terbium,holmium and erbium and its isotopes

Coherent neutron scattering lengths and total cross sections have been measured on samples of ordinary Tb, Ho and Er and on isotopically enriched Er-compounds. From the experiment the following data were obtained:

• - the coherent scattering lengths (in fm) of the bound atoms ¹⁵⁹Tb(7.34 ± 0.02), ¹⁶⁵Ho(8.44 ± 0.03), ^ordEr(7.79 ± 0.02), ¹⁶²Er(9.01 ± 0.11), ¹⁶⁴Er(7.95 ± 0.14), ¹⁶⁶Er(10.51 ± 0.19), ¹⁶⁷Er(3.06 ± 0.05), ¹⁶⁸Er(7.43 ± 0.08), and ¹⁷⁰Er(9.61 ± 0.06)
• - the thermal absorption cross sections (in b) ¹⁴¹Pr(12.7 ± 0.6), ^ordNd(58 ± 1), ¹⁵⁹Tb(30 ± 2), ¹⁶⁵Ho (65 ± 2), ^ordEr (145 ± 2), ¹⁶⁶Er (18 ± 2), ¹⁶⁷Er(568 ± 9), ¹⁶⁸Er(2.3 ± 0.3), and ¹⁷⁰Er(15 ± 1). In combination with the resonance parameters, the measured coherent scattering lengths allowed the determination of potential scattering radii R′ which are of particular interest for the optical model theory.

     

High-spin structure of neutron-rich Dy isotopes

In view of recent experimental progress on production and spectroscopy of neutron-rich isotopes of Dy with mass number A =166 and 168, we have made theoretical investigations on the structure of high spin states of^164-170Dy isotopes in the cranked Hartree-Fock-Bogoliubov (CHFB) theory employing a pairingquadrupolehexadecapole model interaction. With the increase of neutron number the rotation alignment of the proton orbitals dominates the structure at high spins, which is clearly reflected in the spin dependence of the rotational g-factors. A particularly striking feature is the difference in the spin-dependent properties of¹⁶⁶Dy as compared to that of¹⁶⁴Dy     

Towards a shell model description of the low-energy structure of deformed nuclei I. Even-even systems

A microscopic shell model theory for the low-lying collective states of heavy deformed nuclei is described. Basis selection is guided by the Bohr-Mottelson-Nilsson picture of collective motion in nuclei. The necessary further truncation is achieved by exploiting an SU(3) symmetry inherent to the structure of the normal parity states and by restricting abnormal parity configurations to states with low seniority. An effective interaction comprised of operators which form an integrity basis for the SU(3) → R(3) algebra is shown to be sufficient to reproduce almost exactly, within a single leading irreducible representation of SU(3), the ground and gamma band rotational structure of eight rare earth (¹⁶⁰Dy, ¹⁶²Dy, ¹⁶⁴Dy, ¹⁶⁴Er, ¹⁶⁶Er, ¹⁶⁸Er, ¹⁶⁶Yb, ¹⁶⁸Yb) and four actinide (²³²Th, ²³⁴U, ²³⁶U, ²³⁸U) nuclei. The concomitant interband and intraband E2 strengths are also shown to be accurately reproduced. Extensions of the theory and necessary further theoretical investigations are reviewed.     

The phenomenon of nucleon emission at high angular momentum states of fused compound systems

Nucleon emission from high spin fused compound systems is analyzed in the framework of the statistical theory of hot rotating (STHR) nuclei. This is an elaborate version of our earlier work and we present our results for¹⁵⁶Er,¹⁶⁶Er,¹⁶⁸ Yb and¹⁸⁸Hg. We predict an increase in neutron emission for¹⁶⁶Er due to the abrupt decrease in neutron separation energy aroundI ≈55ℏ. Since the drop in the separation energy is closely associated with the structural changes in the rotating nuclei, relative increase in neutron emission probability around certain values of angular momentum may be construed as evidence for the shape transition. A similar effect is predicted for¹⁶⁸Yb aroundI ≈55ℏ. We also extend the microscopic cranked Nilsson method (CNM) to hot nuclear systems and compare the results with that of the STHR method. The two methods yield different results for triaxially deformed nuclei although for biaxial deformations the results are identical. This is illustrated for¹⁸⁶Hg.     

Anharmonicities of γ-vibrations in deformed nuclei

The anharmonicities of γ-vibrations are studied within the multiphonon method in different even-even deformed nuclei where the first K^π = 2⁺ vibrational state appears well below the energy gap: ¹³⁰Ce, ^162–164Dy, ^164–168Er, ¹⁸⁶Os. The anharmonicities previously obtained in ¹⁶⁸Er appear to be a general property of these nuclei.     

Symmetry-conserving Hartree-Fock-Bogoliubov theory: (II). Number-projected cranked Hartree-Fock-Bogoliubov calculations in the rare earth region

The yrast line of the nuclei ¹⁶⁴Er and ¹⁶⁸Er is investigated within the cranking approximation by a full variation after exact number projection. The results are compared with those of the cranked shell model and of a self-consistent solution without number projection. In particular we discuss the behavior of pairing correlations in the region of very high spins, where a phase transition is expected.     

Change of nuclear radii due to rotation: Calculation of Mössbauer and muonic isomer shifts

Mössbauer and muonic isomer shifts of 2⁺ rotational states are calculated for rare-earth nuclei in good agreement with experiment using Migdal's effective p-h and p-p interactions. The second-order cranking equations are developed in the framework of the theory of finite Fermi systems. In contrast to the pairing-plus-quadrupole model, the results of this work show a small stretching contribution for most nuclei, but a dominating role for the Coriolis antipairing effect. Shrinking charge radii are found for Dy and Os isotopes and some other nuclei as a consequence of the CAP mechanism. Detailed information is given about the redistribution of protons and neutrons due to rotation. It is seen that only a few levels within the range of the diffuse Fermi edge take part in the redistribution and determine the isomer shifts. Shrinking m.s. proton radii and, at the same time, increasing m.s. neutron radii are obtained for the “back-bending” nuclei ^{158, 160, 162}Dy ^{160, 162}Er and ^{164, 166}Yb.     

Near-Yrast spectroscopy of 164Yb and neighbouring nuclei: Systematics of octupole bands and bandcrossings

High-spin states in ¹⁶⁴Yb have been populated in the ¹⁵²Sm(¹⁶O, 4n) and ¹⁵⁰Sm(¹⁸O, 4n) reactions. From studies of γγ coincidences, γ-ray angular distributions and conversion electron measurements the level scheme has been constructed. The g-band and the S-band have been established to spin and parity 22⁺ and 26^+', respectively, and the rotational sequences (π, α) = (−, 1)₁, (−, 0)₁ and (−, 0)₂ to 23⁻, 24⁻ and 18⁻, respectively. Constructed two-quasineutron configurations and cranked shell model calculations are compared with the experimental results. Residual interactions between quasiparticles are extracted from data. The side-bands in ^{162, 164}Er and ^{164, 166}Yb are discussed, putting a special emphasis on the octupole bands and their interaction with the two-quasiparticle bands. Crossing frequencies and the gain in alignment are summarized for the Yb isotopes and the main features are discussed.     

The change of sign of E2 and M1 matrix elements,and of δ-values of166Er at high spins

Calculations of the Dynamic Deformation Model for the E2/M1 mixing ratios for ψ-band to ground-band transitions in¹⁶⁶Er have been extended to higher spins (up to I=20). Previous comparisons with the experimental values and with the IBA-1 predictions, available at present up to spins 8 only, are also included for the sake of completeness. Additional comparison with the Frankfurt Model is also given. While all three models give reasonable magnitudes of the mixing ratios, only the DDM gives the sign changes at the correct spin values. Predictions are presented for additional sign changes of the mixing ratios, as well as those of the E2 and the M1 transition moments.     

IBA-2 model calculation on even mass tellurium isotopes compared with results of recent nuclear orientation experiments

Calculations using the IBA-2 model code are presented for even-even tellurium isotopes¹¹⁸Te to¹²⁴Te. Three parameter sets are used, two from previous work and a third chosen to give optimum fit to experimental positive parity energy levels and B(E2) ratios. With only two additional parameters, each with simple physical interpretation, the three parameter sets are shown to give excellent fits to the known collective negative parity states in these isotopes. Failure to fit the O ₂ ⁺ ,O ₃ ⁺ and 2 ₃ ⁺ levels suggests these may be 4p-2h intruder states, although their Behaviour with varying neutron number is not as clearly characteristic of such configurations as is found for the 2p-4h states in Cd isotopes.     

Study of complete and incomplete fusion for loosely bound projectiles 6He and 6Li on 165Ho and 166Er targets

Complete fusion (CF) and incomplete fusion (ICF) reactions were studied for the cases of the loosely bound ⁶He and ⁶Li projectiles bombarding ¹⁶⁶Er and ¹⁶⁵Ho targets at energy of about 10 MeV/nucleon. Experiments were carried out to test an approach exploiting the measured intensities of ?? rays emitted at the transitions between the yrast-band levels of reaction products formed after the termination of neutron evaporation. Partial waves feeding the CF reactions ¹⁶⁵Ho (⁶Li, ⁵ n) ¹⁶⁶Yb and ¹⁶⁶Er(⁶He, ⁶ n) ¹⁶⁶Yb as well as ICF ¹⁶⁵Ho (⁶Li, ??3n) ¹⁶⁴Er and ¹⁶⁶Er(⁶He, ??4n) ¹⁶⁴Er reaction channels were revealed from the obtained ??-ray data. The method of exit channel identification via the triple coincidence (??1-??2-light charged particle) was employed for these reactions study.     

Feeding and lifetimes of yrast levels in Hf nuclei

Feeding intensities and times, as well as lifetimes of yrast levels in doubly even ^{166, 168, 170}Hf nuclei have been measured. The reactions ^{122, 124}Sn(^{48, 50}Ti, 4n)^166–170₇₂Hf have been investigated using the recoil-distance Doppler-shift method. The lifetimes, and hence the B(E2) values measured, show the same trends of rather small deviations from the rigid rotor as in the known ₆₈Er and ₇₀Yb cases. In addition to the fast feeding component, showing behaviour rather similar to that of the Yb nuclei, another type of slow feeding, related to the low spin yrast levels, is observed.     

Decay properties of neutron-deficient nuclei in the region Z = 86–92

Neutron deficient isotopes of elements Z = 86-92 have been produced by heavy-ion fusion reactions ¹²C + ²⁰⁸Pb, ²⁰⁹Bi, ²²Ne + ²⁰⁸Pb, ⁵¹V + ¹⁷⁰Er, and ⁵⁰Ti + ¹⁷⁰Er. The evaporation residues were investigated by means of α- and α-γ-spectroscopy after in-flight separation from the projectile beam by the velocity filter SHIP and implantation into a 16-strip position-sensitive Si-detector. New or improved decay data for ^{225, 226}U, ^{216, 217m, 218}Pa, ^{215, 216, 217}Th, ^{214, 215, 216, 216m}Ac, ²¹⁴Ra and ²¹³Rn have been obtained. Received: 5 April 2000 / Accepted: 28 July 2000     

High spin rotational states in 154Dy, 164Er And 162Yb

High spin rotational states in ¹⁵⁴Dy, ¹⁶⁴Er and ¹⁶²Yb have been investigated with (α, 4nγ) and (α, 6nγ) reactions. The ground state rotational bands have been identified up to spin 14 for ¹⁵⁴Dy and ¹⁶²Yb and spin 16 for ¹⁶⁴Er. Anomalous behaviour of the moment of inertia has been observed in ¹⁶⁴Er.     

Observation of a long relaxation time of the hyperfine field of Dy and Er after recoil implantation in iron and derivation of g-factors of rotational states in 164Er and 164Dy

After heavy ion multiple Coulomb excitation of ^162,164Dy and ^164,166Er and recoil implantation in iron the integral rotations of \gamma--\gamma directional correlations in the static hyperfine field were measured for the 4₁ ⁺, 6₁ ⁺ and 8₁ ⁺ states. The targets were cooled by liquid nitrogen and magnetized in beam direction by an external magnetic field of ± 4.5 T. With the known g-factors of ¹⁶⁶Er (A. Alzner et al., Z. Phys. A 322 (1985) 467) and ¹⁶²Dy (I. Alfter et al., Z. Phys. A 357 (1997) 13) effective average hyperfine fields were derived. They are smaller than the equilibrium values known from Mössbauer experiments (H.P. Wit et al., Hyp. Interact. 5 (1978) 233; L. Niesen et al., Hyp. Interact. 3 (1977) 109) and increase with the mean lives of the states. A possible explanation of the observed slow relaxation may be the hindrance of exchange within the spin system by the antiferromagnetic coupling between impurity atom and host. The data obtained for ¹⁶⁴Er and ¹⁶⁴Dy were used to derive the g-factors: g(4₁ ⁺,¹⁶⁴Er) = +0.365(38), g(4₁ ⁺,¹⁶⁴Dy) = +0.251(31), and g(6₁ ⁺, ¹⁶⁴Dy) = +0.272(50).