States In 168Er Research Articles

Collective excitations built on the 2+ γ state in 168Er

To examine the collectivity of the previously proposed K π=4+γγ-two-phonon state in 168Er at an excitation energy of 2056 keV and of the first excited K π=0+ band at 1217 keV (b-band), a Coulomb excitation experiment has been carried out at the Heidelberg-Darmstadt Crystal Ball spectrometer. The B(E2) value connecting the 4+ γγ state to the γ-band was remeasured to be B(E)2,4+ γγ→ 2+ γ)=(600± 130) e2fm4, which almost exhausts the harmonic expectation. In addition, the B(E2) values connecting the band head of the lowest lying excited 0+ b band to the 2+ g and 2+ γ states were measured to be B(E2,2+ g→ 0+ b)=(4.4±0.6) e2fm4 and B(E2, 2+ γ→ 0+ b)=(30.4±4.6) e2fm4; the latter is almost a factor of 10 smaller than the B(E2,2+ γ→ 0+ g) value, which shows that the 0+ b band head has no significant contribution of the K π= 0+γγ-two-phonon state in its wave function.

Gamma-ray transitions between excited states in 168Er

The intensities and reduced probabilities of the E1, E2, M1 and M2 transitions between excited states in 168Er are calculated within the quasiparticle-phonon nuclear model. The intensities and reduced probabilities are in reasonably good overall agreement with experimental ones. It is shown that the contribution of the two-phonon configuration to the wavefunction of excited states with energy below 2 MeV is small. The wavefunction of the first Knu pi =41+ state contains the largest double-gamma vibrational term equal to 30%. The dominance of the decay from the first excited 01+ state to the gamma vibrational state over that to the ground state band is in agreement with the experimental data. The specific features of the calculated B(E1), B(E2) and B(M1) values and the relative intensities of the gamma-ray transitions are discussed.

On the K-dependence in the gamma-decay of neutron resonances in 168Er

The intensities of the K-allowed gamma transitions from neutron resonance states to low-lying states in 168Er are analyzed. The quasiparticle selection rule is taken into account. It is shown that the K-allowed gamma transitions satisfying the quasiparticle selection rule are much faster than the K-forbidden transitions. It may indicate that the K mixing in the neutron resonance region is incomplete.

Description of low-lying vibrational and two-quasiparticle states in164Dy

The calculation with the deformed Woods-Saxon potential and residual interaction allowing for a twophonon admixture of the quadrupole, octupole and hexadecapole vibrational and two-quasiparticle states in164Dy have been made. The calculated excitation energies and B(E; λ=2, 3, 4) values are found to be in reasonable agreement with experimental data. The calculated 0+ states in168Er do not contradict experimental data. It is shown that the wave functions of states with energies below 2.3 MeV have dominating one-phonon components.

Double-γ vibrational states in 168Er and 192Os

In order to identify double-γ vibrational states in well deformed and transitional region, we have made Coulomb excitation experiments for 168Er and 192Os. The measured E2 transition probabilities support the assignment of the 2055-keV 4+ state in 168Er, the 1069-keV 4+ and 956-keV 0+ states in 192Os as the double-γ vibrational states.

Description of low-lying vibrationalK ??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.

Two-quasiproton states in 168Er studied by the [formula omitted] reaction

The 169 Tm( t , α) 168 Er reaction has been studied using 17 MeV polarized tritons from the Los Alamos National Laboratory tandem Van de Graaff accelerator. The α-spectra were analyzed with a Q3D magnetic spectrometer. The overall energy resolution was typically ~ 15 keV (FHWM) and angular distributions of cross sections and analyzing powers were obtained for levels up to ~ 2.7 MeV. The fact that spins and parities for all levels up to ⩾ 2 MeV were previously known from an extensive series of (n, γ) studies made it possible to determine specific two-quasiproton structures for many bands from the present results. The K π = 2 + γ-vibrational band was found to have a large 3 2 + [411] p + 1 2 +[411] p admixture, consistent with the predicted microscopic composition of this phonon, but no 5 2 [413] p − 1 2 + [411] p component was observed. The K π = 0 4 + band at 1833 keV has ∼ 25% of the 1 2 + [411] p − 1 2 +[411] p two-quasiproton strength. This is in excellent agreement with the Soloviev model but is inconsistent with the interacting boson model, in which the K π = 0 4 + band is composed almost completely of multiphonon configurations that should not be populated in a single-nucleon transfer reaction. The K π = 4 −, 7 2 −[523] p + 1 2 + [411] p two-quasiproton and the K π = 4 −, 7 2 +[633] n + 1 2 −[521] n two-quasineutron states are mixed strongly with each other, but the two K π = 3 − bands composed of antiparallel couplings of the same particles are not. A good qualitative explanation of this mixing pattern is provided in terms of the effective neutron-proton interaction.

The nuclear structure of 168Er studied with the 170Er(p,t)168Er and 166Er(t,p)168Er reactions

The 170Er(p,t)168Er and 166Er(t,p)168Er reactions have been studied using 18-MeV protons and 17-MeV tritons, respectively. The reaction products were analyzed with magnetic spectrographs providing overall resolutions ranging from 10 to 15 keV full width at half maximum. The chief aim of these studies was to search for previously unknown 0+ states in 168Er, and one new 0+ level, at 1833.5 keV, has been identified. All the known excited 0+ states were populated much more strongly in the (t,p) reaction than in the (p,t) reaction. Numerous natural parity states in known bands were also observed in both reactions. The significance of these results for some recently proposed interpretations of 168Er is discussed. The states with I,Kπ = 0,0+ at 1422 keV and 2,2+ at 1848 keV are both populated much more strongly in the (t,p) reaction than the single-phonon γ vibration. Thus the interpretation given these levels in the interacting boson description, as predominantly multiple-phonon excitations involving at least one γ phonon, does not satisfactorily describe these data. The quasiparticle-phonon model of Soloviev and co-workers is the only model that does not conflict in some way with the presently available experimental data.

Two-quasineutron states in 168Er populated by the 167Er(d, p) and 167Er(t, d) reactions

The nuclear structure of 168Er has been studied with the 167Er(d, p) 168Er and 167Er(t, d) 168Er reactions, using 12 MeV deuterons and 15 MeV tritons from the McMaster tandem Van de Graaff accelerator. The reaction products were analyzed with an Enge split-pole magnetic spectrograph and detected with photographic emulsions. Angular distributions were obtained for levels up to ∼2.5 MeV excitation, with typical resolutions of ∼9 keV and ∼11 keV (FHWM) for the (d, p) and (t, d) reactions, respectively. Since the I, K π values for all levels up to ∼2 MeV were known from previous ( n, γ) studies, the main contribution of this study was to determine the admixtures of specific two-quasineutron configurations to the various bands. Earlier {7/2 +[633]±1/2 −[521]} assignments for the 1094.0, K π = 4 − and 1541.5 keV, K π = 3 − bands have been confirmed, although the full {7/2 +[633]+1/2 −[521]} strength is not observed in the 1094.0 keV band. The K π = 1 − octupole band at 1358.8 keV has a dominant {7/2 +[633] − 5/2 −[512]} component, as predicted by the Soloviev model. The K π = 6 −, {7/2 +[633] + 5/2 −[512]} configuration has been assigned in this work to the 1773.2 keV level. The K π = 4 − band at 2059.9 keV is found to contain ∼35% of the {7/2 +[633] + 1/2 −[510]} strength, and a ∼25% admixture of the {7/2 +[633] − 1/2 −[510]} configuration is tentatively assigned in the K π = 3 − band at 1828.0 keV. Relative cross sections for members of the 168Er ground state band suggest the presence of a mixed wave function for the 167Er target ground state. The K π = 0 +, 1217.1 keV band exhausts the {7/2 +[633] − 7/2 +[633]} strength which does not go to the ground band, while the K π = 0 +, 1422.0 keV band was not observed. The Soloviev model is the only one which has made quantitative predictions that can be compared with the present results. In general, it is quite successful in explaining the experimental data.

Anharmonicities of the Double Gamma-Vibrational States in 168Er

Anharmonicities of the Double Gamma-Vibrational States in 168Er

Anharmonicities of the Double Gamma-Vibrational States in 168Er

Anharmonicities of the Double Gamma-Vibrational States in 168Er

Two-quasiparticle states in 168Er

Abstract The level structure of 168Er and the de-excitation mechanism in this nucleus have been studied by radiative capture of thermal neutrons in samples of natural erbium which give a cross-section contribution of 89.8±2.3 % for 167Er. Interference from the 9.1±2.1 % capture contribution of 166Er was well known from a separate study with enriched 166Er samples. Highresolution measurements of the γ-ray spectrum have been performed using the Karlsruhe Ge(Li) anti-Compton spectrometer below 2 MeV and a Ge(Li) double-escape spectrometer above 5.16 MeV. The high accuracy of the data allows the construction of a considerably extended transition diagram up to 2 MeV excitation energy. A large number of new levels has been assigned to specific configurations and their superimposed rotational bands. Conclusive evidence is given that the previously known states at 1094 keV and 1542 keV are the two-quasiparticle neutron levels [633 ↑ + 524 ↓]nn and [633↑−521↓]nn, respectively. Some aspects of the corresponding log ft values are discussed in detail. Rotational bands at 1354 keV, 1569 keV and 1542 keV have to be identified with the Kπ = 1−,2− and 3− octupole vibrational bands. The properties of the Kπ = 1− state are presumably close to those of the neutron level [512 ↑–633↓]nn. The 3− rotational member of the Kπ = 0− octupole band probably occurs at 1914 keV. The simple model of pairing plus state-independent octupole force provides a surprisingly good microscopic description of the octupole excitation energies. The first Kπ = 0+ band has been well established to occur at 1217 keV. Within the model of pairing plus quadrupole and spin-quadrupole force one obtains the interaction constants kq = 5.3 and kt = 8.8 (in units of A − 1 3 h ω 0 ). The neutron level [521↓ + 642 ↑]nn has been tentatively assigned to a rotational band at 1893 keV. The properties of some other more or less collective states are discussed. No positive evidence has been found for the occurrence of two-quasiparticle proton levels below 1820 keV excitation energy. The neutron separation energy was determined to be 7771.24 ±0.48 keV.