Search

The level structures of the N = 50 83As, 82Ge, and 81Ga isotones have been investigated by means of multi-nucleon transfer reactions. A first experiment was performed with the CLARA–PRISMA setup to identify these nuclei. A second experiment was carried out with the GASP array in order to deduce the γ-ray coincidence information. The results obtained on the high-spin states of such nuclei are used to test the stability of the N = 50 shell closure in the region of 78Ni ( Z = 28 ). The comparison of the experimental level schemes with the shell-model calculations yields an N = 50 energy gap value of 4.7(3) MeV at Z = 28 . This value, in a good agreement with the prediction of the finite-range liquid-drop model as well as with the recent large-scale shell model calculations, does not support a weakening of the N = 50 shell gap down to Z = 28 .

High-spin states in Lu-165 were populated in the La-139(Si-30, 4n) reaction at a beam energy of 152 MeV and gamma-ray coincidences were measured with the EUROBALL spectrometer array. Nine new rotational bands were discovered, known band structures were considerably extended and many inter-band transitions were found. Structures with normal deformation coexist with bands associated with the strongly deformed triaxial energy minima found in calculations. Three of these triaxial bands form a family of wobbling excitations with phonon quanta n(w) = 0, 1 and 2. The wobbling mode is a unique signature of nuclear triaxiality. Configuration assignments are discussed for the observed band structures. An exchange of configuration between two of the new bands due to mixing is observed, resulting in different signature partnerships at low and high spins. (Less)

Wobbling is a rotational mode unique to a triaxial body. The Lu-Hf isotopes with N similar to 94 at high spin provide a possible region of nuclei with pronounced triaxiality. We have investigated Lu-163 through the fusion-evaporation reaction La-139(Si-29,5n)Lu-163 with a beam energy of 152 MeV. Three excited bands decaying into the known, presumably triaxial, superdeformed (TSD) band built on the i(13/2) proton orbital are observed. The electromagnetic properties of the connecting transitions from the two strongest populated excited TSD bands have been investigated. New particle-rotor calculations in which one i(13/2) quasiproton is coupled to the core of triaxial shape produce a variety of bands, whose properties can clearly be interpreted either as "wobbling" or "cranking" motion of the core. Evidence for the assignment of the excited TSD bands as one, and possibly even two wobbling phonon modes built on the yrast TSD band in Lu-163 is given. These triaxial bands coexist with bands built on quasiparticle excitations in the normal deformed (ND) minimum for which new data are also presented. (Less)

165 Tm has been studied through the reactions 150 Nd( 19 F, 4n), E beam =85 MeV and 154 Sm ( 15 N, 4n), E beam =70 MeV. The level scheme has been extended to spin 71/2 − ℏ, and four new bands have been added. Two are assigned to the K =17/2, three-quasiparticle configurations, π [523]7/2 − ⊗ ν [642]5/2 + ⊗ ν [523]5/2 − and π [404]7/2 + ⊗ ν [642]5/2 + ⊗ ν [523]5/2 − , and the remaining two are assigned to γ -vibrations coupled to an h 9/2 proton. Lifetimes of high-spin states in the [541]1/2 − and [411]1/2 + bands have been measured using DSAM techniques, allowing transition quadrupole moments to be deduced. Furthermore, crossings between the [541]1/2 − and [523]7/2 − bands and between the [411]1/2 + and [404]7/2 + bands are analysed with a band-mixing calculation to obtain the quadrupole moments of the [523]7/2 − and [404]7/2 + bands. While the [523]7/2 − , [411]1/2 + and [404]7/2 + bands all have similar deformations, the [541]1/2 − band has a quadrupole moment approximately 15% larger. The relative deformations are in good agreement with diabatic potential energy surface calculations performed using the code “Ultimate Cranker”. The experimental crossing frequency, due to the alignment of i 13/2 neutrons, is found to be delayed in the [541]1/2 − band compared to the other bands. This is a universal feature in the rare-earth region, and extensive systematic Cranked Shell Model calculations have been performed to predict deformations and crossing frequencies for nuclei in the region. The model is unable to reproduce the full delay in crossing frequency, confirming that deformation alone is not responsible for the shift.

In this paper we discuss some relevant results of an experiment performed with the EUROBALL array equipped with large volume BaFz detectors in which coincidences between low-energy and high-energy y-rays from the reaction 37C1 (&,,,,=165 MeV) + ll”Pd were measured. The main goal is to search for the giant dipole resonance built on superdeformed states and to determine the role played by the y-decay of the GDR on the population of superdeformed configurations. The analysis of high-energy y-ray spectra in coincidence with low-energy transitions of normal deformed and superdeformed types indicates the presence of the giant dipole resonance built on superdeformed states. Further support for this result is given by the analysis of the intensity of the superdeformed yrast and excited bands which is found to increase by a factor of approximately two when a coincidence with a high energy y-ray is required.

Rotational bands based on the deformation driving 7rTi1312 intruder configuration have been observed in several even-N Lu isotopes [l-3] and in odd-odd 164Lu where the i13/2 proton is coupled to different neutron orbitals [4]. The quadrupole moment is only measured in 163Lu (Qt = lib) [l], however, the dynamical moments of inertia are very similar in all these bands, and larger than those of the bands built on the normal deformed (ND) structures. For nuclei with N-94 and Z-71-72, calculations predict stable triaxial shapes with large quadrupole deformation (E:, N 0.38 and y N f20”) for all symmetry groups of parity and signature [2,5]. In Fig. 1 the potential energy surface of 163Lu shows a rather deep

Two aspects of rotational motion of thermally excited nuclei are discussed. First, the schematic cases of ordered or chaotic motion of intrinsic and rotational motion are presented: discrete rotational bands, ergodic bands, damping of the rotational motion. Secondly, the strength functions of mixing of basis bands and of EP-transitions over one or two decay steps are discussed. The two-step E2-strength displays both a narrow and wide component, yielding different types of information about the basis bands and their interaction. Indications of the presence of a narrow component is found in energy correlations of consecutive transitions on displaced rotational bands of a three dimensional spectrum for the nucleus “‘Yb.

Unresolved γ transitions of 114 Te and of 112 Sn sorted into one-dimensional and two-dimensional spectra have been studied. The reaction 64 Ni + 54 Cr at bombarding energies 230, 240, 250, 260, 270 MeV was used and the γ -rays were detected with the EUROBALL array. In the case of the nucleus 114 Te the values of the multiplicity as a function of bombarding energy and of the moment of inertia were obtained. The effective moment of inertia was found to be almost constant in the interval I=20 – 40 ℏ , in contrast to the decreasing behaviour of the dynamic moment of inertia for the terminating yrast band. The ridge valley structures in E γ 1 ×E γ 2 spectra of 114 Te and of 112 Sn were analysed with the fluctuation analysis technique. The analysis of the two nuclei are compared to simulations based on microscopic cranking calculations with residual interactions included. A rather good agreement is found between data and predictions.

The γ-cascades feeding specific intrinsic configurations of 164Yb are studied making use of a statistical analysis of counts fluctuations in γ–γ coincident spectra. In particular, variance and covariance spectra are obtained starting from the measured (0,+), (0,−) and (1,−) gate-selected matrices. The analysis of the first ridge of the spectra yields about 25 excited bands carrying rotational energy correlations for the total spectrum, and about 10 in coincidence with each of the (α,π) configurations. The covariance of count fluctuations between the different (α,π) gates is expressed by an experimental correlation coefficient, r, which measures the degree of sharing of decay paths through the excited bands, and thereby the extent to which selection rules are obeyed by the decay. The correlation coefficient is around r≈0.3 for the ridge, and also in general rather small for valley fluctuations. Only at the highest valley energies, a tendency to larger correlation coefficients is seen, indicating some weakening of the selection rules over longer decay cascades. The results of the experimental analysis are compared to rotational damping model predictions based on cranked shell model plus residual interactions, and rather good agreement is found.

The lifetime of the unresolved transitions forming the rotational quasi-continuum spectra has been measured in 164 Yb using the Doppler shift attenuation method. The valley structure in E γ 1 × E γ 2 spectra was analysed using a new technique, based on fluctuation patterns, which provided for the first time experimental lifetimes for rotational damped transitions. The present results show, as predicted by the rotational damping model, that the collectivity persists for highly excited bands. In particular, agreement is found between the experimental results, for discrete and damped transitions, and the predictions corresponding to Q t = 5.5 eb, for the entire interval of γ-ray energies studied.

The γ-decay of excited rotating nuclei in the high level density region a few MeV above the yrast line has been studied through a statistical analysis of the fluctuation of counts in γ-γ coincident spectra. In particular, making use of the covariance technique between spectra gated by different intrinsic configurations, one can measure how the cascades feeding into different selected bands are similar. The aim is to learn about the transition between order to chaos in the nuclear many-body system, in terms of the validity of selection rules associated with the quantum numbers of the intrinsic structure. Experimental results on the nucleus 164Yb are presented and compared to model predictions based on cranked shell model calculations including a two-body residual interaction.

The γ-decay of the GDR in hot Hg and Eu isotopes has been measured in coincidence with selected low-energy γ-transitions of the evaporation residues. In the Hg case, the GDR width at finite temperature and at different spins was studied by analyzing simultaneously with the statistical model the high-energy γ-ray spectra associated with different residual nuclei and the fractions of residue cross-sections. The measured GDR width was found in good agreement with the predictions of the thermal fluctuations model. In the case of Eu, we have measured the high-energy γ-rays in coincidence with low-energy γ-transitions from different nuclear configurations of 143 Eu in order to search for the GDR decay built on a superdeformed state. The analysis of the data shows a possible evidence of this state. The measured intensity indicates that the superdeformation survives only few MeV above the yrast line.

The nucleus 162Tm has been populated by the 130Te(37Cl,5n) reaction, and the γ-cascades detected with the NORDBALL array. Eight coupled rotational bands involving the proton orbitals, g 7 2 [404] 7 2 + , d 3 2 [411] 1 2 + , d 5 2 [402] 5 2 + , h 11 2 [523] 7 2 − and h 9 2 [541] 1 2 − and neutron orbitals i 13 2 [642] 5 2 + , h 9 2 [523] 5 2 − and f 7 2 [521] 3 2 − have been established in 162Tm, to spins varying from 18 to 47ℏ. Various phenomena which can be related to residual neutron-proton interactions are discussed. In particular, signature inversion in the π [541]1 2 − ⊗ ν [642]5 2 + bands based on the h 9 2 quasiproton and i 13 2 quasineutron, rewpectively, may be explained by a fairly large p-n interaction. In addition, interactions at the crossings of bands with constituent quasiparticles differing both in parity and signature have been extracted with strength of the order of a few (4–12) keV. Such interactions also require terms beyond the standard mean field description.

High-spin states in 177 W have been populated using the 164 Dy( 18 O,5n) reaction at a beam energy of 83 MeV. Six new high- K bands based on 3-, 5- and 7-quasiparticle excitations have been observed. Nilsson configurations for these bands are discussed, and experimental and calculated g -factors are compared. Decays of the K π = 29 2 + 5-quasiparticle state to the members of the K π = 7 2 + band have been observed. The decay rates are compared with predictions calculated within a tunneling model where the nuclear shapes are considered to change along the γ direction in the ( ϵ 2 , γ) deformation plane.

Using the (18O,5n) 163Er reaction a multitude of rotational bands have been established with firm spin and parity assignments in 163Er. In 17 out of 24 band crossings E2 cross-band transitions have been observed. The interaction strength varies between ∼ 1 and ∼ 50 keV with many of the values in the range 10–15 keV. These interactions sample a variety of the lowest (multi) -quasiparticle configurations. For some bands, in particular those with high K-values, the configurations can be established rather well. Quite complicated changes in the wavefunctions must occur at these crossings, and to explain the observed interaction strengths coupling to various vibrational degrees of freedom, in addition to possible residual neutron-proton interactions, may be needed.

An experimental investigation of the nucleus 165Lu, using the reactions 138Ba(31P,4n) 165Lu and 150Sm(19F,4n) 165Lu at beam energies of E = 155 and 95 MeV, respectively, has been performed. Among other additions to the existing level scheme, a new band, with transition energies almost identical to a strongly deformed (β2 0.42) πi13/2[660 1/2+] band recently discovered in 163Lu has been established. A theoretical analysis of the structure of the two Lu isotopes, 165Lu and 163Lu is carried out by detailed calculations of total potential energy surfaces for specific configurations. By a diabatic treatment of crossings specific proton configurations as πi13/2[660 1/2+] are identified throughout the deformation space and as a function of spin. It is found as a general feature that well deformed local minima of considerable nonaxial symmetry coexist with a normal deformed global minimum. The depth of these local minima depend on configuration. The structure of the different global and local minima found in these surfaces are analysed and discussed in terms of occupation of available basis configurations and their orientation relative to the rotation axis. The strongly deformed minima are found to belong to a group of superdeformed triaxial structures, expected to appear at low energies for certain favourable combinations of proton and neutron numbers.

The level scheme of 177Re has been extended extensively, with fragments of more than thirty bands, characterised by a given signature, observed. Alignments at low frequency in one-quasiparticle bands are interpreted as deformation effects and compared with the predictions of cranking calculations. The previously assigned one-quasiparticle π i 13 2 band is shown to be a mixture of three-quasiparticle and vibrational character. The non-observation of the one-quasiparticle π i 13 2 band is explained as being due to crossings of its s-band by competing bands. A number of high-K bands are also reported, including five- and seven-quasiparticle bands. Configuration assignments for these bands are aided by comparing experimental gκ values with “effective” gκ values, calculated with a semi-classical expression taking Coriolis mixing into account. The population of the yrast band was observed to oscillate with every four units of spin.

High spin states of 164Yb have been populated using the 152Sm(16O,4n) reaction. Analysis has been made using γγ coincidences and, for the first time in a large detector array, angular correlations. The experimental level scheme has been extended to include a total of 15 decay cascades, for some of which the spins have been measured. Extensive cranked shell model calculations have been performed to map the quasiparticle rotational bands in a window, reaching up to 1 MeV above the yrast line, in the spin-energy plane. The experimental data are compared with the calculated bands, and most of the experimental bands are interpreted in terms of quasiparticle excitations. It is also found that the number of experimentally detected bands is in good agreement with the calculated number of bands in the observed spin-energy region.

The study of damping of rotational motion applying te rotational plane mapping (RPM) method is presented and discussed. The aim of this technique is to extract the distribution of the rotational transition strength from an analysis of the shape of the “central valley” of two- and three-dimensional γ-ray spectra. The method is applied to a triple γ-coincidence data set of 162,163Tm nuclei formed in 37Cl+130Te reactions. The rotational transition strength is obtained as a function of rotational frequency for selected regions of entry states, and the width is found to be rather constant and approximately equal to 80 keV. This value is significantly smaller than the value predicted theoretically for the rotational damping width Γrot. Also the ratio between the observed depth and width of both the 2D and 3D valleys does not agree with the simple model adopted in the RPM method. These discrepancies point to the presence of both a wide and a narrow component in the distribution of rotational strength as extracted by the RPM method. The analysis of simulated spectra obtained on the basis of realistic band-mixing calculations, including residual interactions, confirms this behaviour.

High-spin states in 167Yb and 168Yb have been investigated using the 124 Sn( 48 Ca, x n ) reaction at a bombarding energy of 210 MeV. The level sequences of the two nuclei were established from a large set of high-fold γ-ray coincidence data detected in the EUROGAM spectrometer. The experimentally observed upbends at high rotational frequency are discussed in terms of the cranked shell model for protons both with and without pairing. An unpaired crossing involving interchange of proton orbitals is tentatively identified. No evidence was found for hyperdeformation.

The experimental data emerging from the fluctuation analysis of the rotational γ-decay are used to provide evidence for three regimes in the rotational spectrum. Namely discrete bands, fragmented transitions and rotational damping. The mechanisms which are expected to be at work in the damping of rotational motion are briefly reviewed and a parallel is made with the relaxation of giant resonances, focusing on the interplay of mean field (average) effects and of chaotic (fluctuation) behaviour. A simple, yet accurate model of rotational damping where chaotic behaviour emerges from effective, though realistic, two-body interactions acting among unperturbed rotational bands indicates the possibility of obtaining novel insight on the nuclear structure, through the study of rotational motion. In particular, the onset of chaos can be related to the high-multipole components of the nuclear force which are not able to generate mean field effects.

Several new methods for the study of nuclear structure at low temperature are reviewed. The methods analyze the fluctuations of the intensity of E γ 1 · E γ 2 spectra, and the shape and width Γ rot of the correlated patterns with different characteristics of the rotational motion in cold and warm nuclei. New results are given for the rotational damping width, and the number of 2-step-paths below and above U 0 ≈ 800 keV, considered to be the energy of the borderline between undamped and damped rotational motion. The rotational damping width Γ rot is studied as function of rotational frequency for selected regions of entry states in 163 Tm , and found to be rather constant ≈ 80 keV, significantly smaller than current theoretical predictions. The fluctuation analysis supports the damping picture in general, and confirms that a strong branching of the transition strength for each step in the E2 cascades exists at high spin. This can be taken as evidence for damping of the rotational motion in warm nuclei.

The structure of excited rotational bands in well deformed nuclei is discussed. It is shown how fluctuations of 2-dimensional energy-energy γ-ray spectra can give quite detailed information about both the region of discrete bands and the region of rotational damping.

The mixing of rotational bands in warm nuclei was first considered by Georg Leander [1]. He pointed very early to the posibility that "the in-band decay of any given state may be spread over a broad spectrum". The B(E2) matrix elements governing the rotational decay out of a mixed band state may be distributed over all final states of the given parity within a certain energy interval. The width of this interval is defined as the rotational damping width Frot [2]. Close to the yrast line, on the other hand, the bands are believed to retain their structure, allowing essentially only one final state for each decay step. Figure 1 illustrates the rotational decay within the two regions of rotational motion, the unmixed region at low excitation energy, below U0 ~ 1 MeV , and the region of rotational damping at higher excitation energy above U0 (also shown schematically in the insert). The intensity distributions of the flow of E2 transitions along the Yrast line are also indicated on this figure with the dark area representing the expected decreasing intensity in the discrete region, for increasing spin.