S. Leoni

Fluctuation analysis of rotational spectra

Abstract It is well established that nucleons in the atomic nucleus can organize their motion, leading to quadrupole deformed shapes of the average field and to rotations of the nucleus as a whole. At an excitation energy of few MeV above the yrast line, rotational bands become very closely spaced in energy. Any single band can be viewed as a collective sequence of related states embedded in a dense background of other (more or less complicated) states, to which it will couple by residual interactions. This coupling leads to stationary states of the system (the compound nucleus) which are complicated mixtures of unperturbed configurations. The rotational degree of freedom is “damped” in these compound states in the sense that the electric quadrupole decay of a single quantum state with angular momentum I will not go to a unique final state with spin I − 2 (as for the unperturbed bands) but will exhibit a spectrum of final states all having spin I − 2. In other words, for each compound nucleus formed in an experiment, the cascade of ∼20 γ -rays, which eventually will cool the system, will find many transitions through which to proceed in the regions where bands mix strongly (damped region) and only few in the region of discrete bands. In actual experiments, the cascade of γ-rays associated with each of the members of the ensemble of compound nuclei will use each of the “discrete” transitions many more times than the “continuum” transitions. Relatively large and small fluctuations in the recorded coincidence spectrum will ensue. respectively. The analysis of the fluctuations will be shown to be instrumental to gain insight into the phenomenon of rotational damping. For this purpose, two- and higher-fold coincidence spectra emitted from rotating nuclei are analyzed with respect to the count fluctuations. The coincidences from consecutive γ-rays emitted from discrete rotational bands generate ridges in the E γ 1 · E γ 2 spectrum, and the fluctuation analysis of the ridges is based upon the ansatz of a random selection of transition energies from band to band. This ansatz is supported by a cranked mean-field calculation for the nucleus 168 Yb, as well as by analyzing resolved bands in 168 Yb and its neighbors. Consecutive γ-rays emitted from the region of rotational damping spread out more in the E γ 1 · E γ 2 plane than those associated with transitions between members of discrete rotational bands, and are studied most clearly in the central valley ( E γ 1 = E γ 2 ). The fluctuation analysis of the valley is based upon the ansatz of fluctuations in the intensity of the transitions of Porter-Thomas type superposed on a smooth spectrum of transition energies. This ansatz is again supported by a mixed-band calculation. The mathematical treatment of count fluctuations is formulated in general terms, and the connection to earlier treatments of one-fold spectra of high level density is established. The statistical assumptions underlying the fluctuation analysis imply the existence of a principal uncertainty, which is examined in detail. In the experimental section, the fluctuation analysis is applied to two-dimensional γ-spectra, the only available data at present with sufficient intensity to warrant a meaningful analysis. Large fluctuations are observed in the ridge structures from the four cases analyzed, showing that only a rather low number (≈ 30) of discrete rotational bands exist. In contrast, only weak fluctuations are found along the central valley, revealing that the spectrum in the valley effectively contains different (of the order of 10 5 ) coincidence combinations. This number is considerably larger than what is found assuming that the rotational decay leads to a unique final state, showing that the transition strength through each decay step is spread over many states within a given energy interval, the damping width, and thus providing fairly direct evidence of the rotational damping picture.

Cd-98(48)50: The two-proton-hole spectrum in Sn-100(50)50

Excited states in {sup 98}Cd, two proton holes from {sup 100}Sn, were identified and studied for the first time, using in-beam spectroscopy with highly selective ancillary detectors. The structure of the ({pi}g{sub 9/2}){sup {minus}2} two-proton-hole spectrum below a T{sub 1/2}=0.48(16) {mu}s isomer is deduced and compared to shell-model predictions. A tentative I{sup {pi}}=(8{sup +}) assignment, as suggested by systematics, yields a strongly reduced B(E2,8{sup +}{r_arrow}6{sup +})=0.44({sup +20}{sub {minus}10}) W.u., corresponding to an effective proton charge of e{sub {pi}}=0.85({sup +20}{sub {minus}10}) e , which is at variance with existing theoretical predictions. {copyright} {ital 1997} {ital The American Physical Society}Excited states in Cd-98, two proton holes from Sn-100, were identified and studied for the first time, using in-beam spectroscopy with highly selective ancillary detectors. The structure of the (pi g(9/2))(-2) two-proton-hole spectrum below a T-1/2 = 0.48(16) mu s isomer is deduced and compared to shell-model predictions. A tentative I-pi = (8(+)) assignment, as suggested by systematics, yields a strongly reduced B(E2,8(+) --> 6(+)) = 0.44((+20)(-10)) W.u., corresponding to an effective proton charge of e(pi) = 0.85((+20)(-10))e, which is at variance with existing theoretical predictions.

THE DISTRIBUTION OF THE ROTATIONAL TRANSITION STRENGTH IN WARM NUCLEI STUDIED THROUGH GAMMA-RAY CORRELATIONS

Abstract 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.

Interactions between a multitude of rotational bands in well deformed odd nuclei: A new method for spin and parity assignment

Abstract Using the ( 18 O,5n) 163 Er reaction a multitude of rotational bands have been established with firm spin and parity assignments in 163 Er. 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.

A finite number of regular rotational bands in the superdeformed well of 143Eu

Abstract The number of excited superdeformed bands in 143 Eu is measured by use of the Fluctuation Analysis Method. Between 10 and 40 rotational bands, displaying typical rotational energy correlations over two consecutive transitions, are populated within a rather narrow range in transition energy, E γ ≈ 1300–1500 keV. These numbers are close to the values found for normally deformed nuclei and agree with microscopic cranking + band mixing calculations for the specific superdeformed nucleus, which predict the onset of rotational damping to occur at the excitation energy U 0 = 1.3–1.6 MeV above the yrast line.

Four independent decay properties in the super-deformed well of 143Eu☆

Abstract The flow of γ-transitions through the superdeformed minimum of 143Eu is investigated by studying the intensities of four different types of γ-rays of superdeformed origin, obtained with a variety of gating conditions. They can all be explained rather well by schematic simulation calculations assuming only well known statistical properties. Information on level density, competition between E1 and E2 strengths and rotational damping width in the SD well is obtained, yielding a rather complete picture of the feeding mechanism into different regions of the second minimum.

Probing the limits of complete spectroscopy in 164Yb

Abstract 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.

Multi-quasiparticle states and K-forbiddenness in 177W

Abstract 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.

In-beam study of 102Sn

Excited states in 102Sn have been identified for the first time, in an in-beam γ-ray spectroscopic experiment. Two γ-ray transitions with energies 1472 and 497 keV following the decay of the seniority 6+ isomer with t1/2 = 1.0(5) μs were unambiguously assigned to 102Sn. Due to the very low cross section of about 2 μb for producing 102Sn in the reaction 50Cr(58Ni,1α2n), a highly selective detector setup utilizing NORDBALL ancillary detectors and a recoil catcher device was used. High γ-ray detection efficiency was achieved with two EUROBALL Ge cluster detectors.

In-beam study of Sn-102

Excited states in102Sn have been identified for the first time, in an in-beamγ-ray spectroscopic experiment. Twoγ-ray transitions with energies 1472 and 497 keV following the decay of the seniority 6+ isomer with t1/2=1.0(5)μs were unambiguously assigned to102Sn. Due to the very low cross section of about 2µb for producing102Sn in the reaction50Cr(58Ni,1α2n), a highly selective detector setup utilizing NORDBALL ancillary detectors and a recoil catcher device was used. Highγ-ray detection efficiency was achieved with two EUROBALL Ge cluster detectors.