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Through the S-matrix of the nuclear system, an effective nonhcrmitean hamiltonian is introduced. A matrix which measures the complexity of nuclear states from an E2 sum rule is introduced, Numerical calculations for the SU ( 3 )-U ( 5 ) transition of the interacting boson model are performed. The transition from order to chaos in nuclear spectra is discussed in terms of a participation index. A transition from order to chaos is obtained when the SU ( 3 ) symmetry is broken, in agreement with the nearest neighbour distributions, but fails to reflect the order corresponding to the U ( 5 ) symmetry. The transition from order to chaos in nuclear spectra is an intriguing question. A convenient measure of chaotic behaviour is given by the distribution of the average level distances between nearcst neighbours with the same spin and parity [ I-8 ]. Recently also a number of investigations of the behaviour of B (E2) values for regular and chaotic systems havc been made [ 9-12 ]. There have been attempts of establishing wave-function related measures of quantum chaos [13-16]. It is the purposc of this letter to introduce a quantitative measure for the degree of complexity of nuclear states and to study its behaviour for the transition from order to chaos. This measure uses the decay properties of nuclear states. It is based on the idea that a level has a complicated structure if it is connected with many other levels by strong decay width whereas it has a simple structure if it is connccted with only one or at most a few levels by strong decay widths. Due to their decay, nuclear levels are resonances rather than stationary states and are described by an effective hamiltonian which is in general nonhermitean. A convenient way to introduce an effective nonhermitean hamiltonian is through a suitable form of the S-matrix of the system. Such a form has been used by Mahaux and Weidenmiiller [ 17 ] and others [ 13,18-20 ]. The effective hamiltonian (which is obtaincd from this form of the S-matrix ) is

An average resonance capture study of Te-124 was carried out by An average resonance capture study of Te-124 was carried out by

Lifetime measurements of levels near 2 MeV in 114 Cd give quantitative evidence for collective 3-phonon vibrational states. An analysis of the level scheme reveals a remarkable ambiguity with origins in the basic properties of quantum mechanical mixing.

It is shown that isotopic sequences of 21+ level energies, for elements from Zr to the actinides, are linear against the factor P = N p N n (N p +N n ) . This linearity is interpreted in terms of a simple two-level model. The P-factor also provides a linearization scheme for intruder 0+ energies in the Pb region.

The E1 transition rates in Sm isotopes with neutron number N =86−90 are studied in the frame of the (sd) N B−1 f interacting boson model. An effective E1 operator, obtained by eliminating, by perturbation theory, the p boson from the spdf model, explains very well the E1 data in this transitional region.

The lifetimes of low-lying negative parity yrast levels have been measured in131La using the recoil distance Doppler shift method. The nuclear reaction employed was116Cd+19F at a beam energy of 80 MeV. The data were analysed using the differential decay curve method. The E2 transition strengths for negative parity yrast states and the energy spectra are well described by coupling a fermion to aγ-soft core in the frame of the interacting boson fermion approximation model.

A recently introduced way of parameterizing the energies of 3 states in many even-even nuclei, based on the microscopic structure of the low-energy octupole mode, is slightly modified so it now includes all (non-doubly magic) nuclei with A ⩾ 30.

Evidence for the first empirical example of a transitional dynamical symmetry at a critical point is discussed in the spectrum of ${}^{134}\mathrm{Ba}$. The role of such classes of symmetries in nuclear structural evolution is also discussed.

The energy of the first excited 2{sup +} state in {sup 96}Kr was measured as 241 keV. The nucleus was produced in the fission of {sup 238}U induced by a 954-MeV {sup 136}Xe beam and prompt {gamma} rays were observed using the clover array CLARA in coincidence with fission products identified with the PRISMA spectrometer. The evolution of the quadrupole collectivity in the Kr isotopes with N{>=}50 is discussed by comparison with that from the Rb to Mo isotones and with predictions of various theoretical calculations.

The low lying states in {sup 128}Ba have been investigated for the first time with the {sup 130}Ba(p,t){sup 128}Ba reaction. The experiment was performed at the Munich Q3D magnetic spectrograph with a 25-MeV proton beam and a high-resolution, 1.5-m-long focal plane detector. As a result of this experiment 27 excited levels with energies below 3.7 MeV have been observed for the first time, significantly increasing (by {approx}50%) the number of levels observed in {sup 128}Ba. Angular distributions of tritons were measured and their comparison with the distorted wave Born approximation calculation allowed in most cases spin and parity assignments for the nuclear levels. The experimental two-neutron transition strengths with transferred angular momentum L=0 and 2 are compared with the predictions of the IBA-1 model with a new set of parameters. The results indicate for the first time from a hadronic probe perspective a transitional structure close to the O(6) symmetry for the {sup 128}Ba nucleus, confirming previous conclusions of {gamma}-ray spectroscopy studies.

It is shown that the Mallmann’s energy correlations, introduced a long time ago for the ground state bands of the even‐even nuclei are, in fact, universal. Various bands in all collective nuclei (even‐even, odd‐even, and odd‐odd) obey the same systematics. This unique, universal behaviour indicates the same spin dependence of the energy of the levels and, consequently, a common structure of all collective bands. Based on the second‐order anharmonic vibrator description, parameter‐free recurrence relations between energy ratios are deduced. These relations can be used to predict levels of higher spins in various bands.

Striking experimental differences in the signature splitting in γ-bands and negative-parity bands in the axially asymmetric A = 130 region are interpreted as manifesting the coupling of an f-boson (l = 3) to an O(6) IBM core.

Signatures of γ softness or rigid triaxiality in low energy, low spin nuclear spectra are discussed. Two classes of signatures, relating to γ-band energy staggering, are found to provide clear distinctions between these shapes. The data for even-even nuclei are compared to predictions for potentials with varying γ dependence. It is found that nuclei with large asymmetries can be characterized by potentials that are nearly γ flat, with, at most, a few percent deviation from γ independence.

The possibility of phase transitional behaviour in the Sm nuclei is discussed in relation to recent experiments on , in the context of both interacting boson model and geometric collective model calculations.

It is shown that the Mallmann's energy ratio correlations, for the first time observed for the ground state band of the even-even nuclei, are universal: various band structures in all collective nuclei obey the same systematics, and consequently the same spin dependence. Based on a second order anharmonic vibrator description, parameter-free recurrence relations between Mallmann-type energy ratios are deduced, which can be used to extrapolate bands to higher spin.

The cross sections of the $^{117}\mathrm{Sn}$($\ensuremath{\alpha},\ensuremath{\gamma}$) $^{121}\mathrm{Te}$ and $^{117}\mathrm{Sn}$($\ensuremath{\alpha},p$) $^{120}\mathrm{Sb}$ reactions have been measured in the effective center of mass energy from 11.5 to 14.6 MeV. Highly enriched self-supporting $^{117}\mathrm{Sn}$ (90%) foils were bombarded with an $\ensuremath{\alpha}$ beam delivered by the Bucharest IFIN-HH tandem accelerator. The induced activity of $^{121}\mathrm{Te}$ and $^{120}\mathrm{Sb}$ was measured with two large-volume high-purity Ge detectors in close geometry to maximize the detector efficiency. The experimental cross section and astrophysical $S$ factor are compared with statistical model predictions for different global $\ensuremath{\alpha}$-nucleus optical potentials.

We investigated the evolution of experimental two‐neutron separation energies (S2n) along the isotopic chains for the even‐even nuclei. In order to enhance the sensitivity of our search, differential variation of the S2n has been investigated. The emphasis is on finding nonmonotonic behaviors which can be correlated with phase/shape transition. Correlations of the ground state S2n values with the excited states energies R4/2 ratio are also discussed.

The effects of the neutron-proton interaction on the low-lying levels of Mo and Cd isotopes have been considered in the frame of the IBA-1 model by taking into account an effective boson number (Neff). Both an empirical procedure based on previous IBA-2 mixing calculations and the Np AT, scheme provide comparable Neff values. Level spectra and electromagnetic transitions are investigated. The results support the idea that IBA-1 calculations with a suitable Neff can largely simulate IBA-2 mixing calculations, taking advantage of simplicity and a smaller number of parameters. PACS: 21.60.Ev

The mean-lifetimes, \ensuremath{\tau}, of various medium-spin excited states in $^{103}\mathrm{Pd}$ and $^{106,107}\mathrm{Cd}$ have been deduced using the Recoil Distance Doppler Shift technique and the Differential Decay Curve Method. In $^{106}\mathrm{Cd}$, the mean-lifetimes of the ${I}^{\ensuremath{\pi}}={12}^{+}$ state at ${E}_{x}=5418$ keV and the ${I}^{\ensuremath{\pi}}={11}^{\ensuremath{-}}$ state at ${E}_{x}=4324$ keV have been deduced as 11.4(17)ps and 8.2(7)ps, respectively. The associated ${\ensuremath{\beta}}_{2}$ deformation within the axially-symmetric deformed rotor model for these states are 0.14(1) and 0.14(1), respectively. The ${\ensuremath{\beta}}_{2}$ deformation of 0.14(1) for the ${I}^{\ensuremath{\pi}}={12}^{+}$ state in $^{106}\mathrm{Cd}$ compares with a predicted ${\ensuremath{\beta}}_{2}$ value from total Routhian surface (TRS) calculations of 0.17. In addition, the mean-lifetimes of the yrast ${I}^{\ensuremath{\pi}}={\frac{15}{2}}^{\ensuremath{-}}$ states in $^{103}\mathrm{Pd}$ (at ${E}_{x}=1262$ keV) and $^{107}\mathrm{Cd}$ (at ${E}_{x}=1360$ keV) have been deduced to be 31.2(44)ps and 31.4(17)ps, respectively, corresponding to ${\ensuremath{\beta}}_{2}$ values of 0.16(1) and 0.12(1) assuming axial symmetry. Agreement with TRS calculations are good for $^{103}\mathrm{Pd}$ but deviate for that predicted for $^{107}\mathrm{Cd}$.

High-spin states of {sup 191,193}Au and {sup 192}Pt have been populated in the {sup 186}W({sup 11}B, xn) and {sup 186}W({sup 11}B, p4n) reactions, respectively, at a beam energy of 68 MeV and their {gamma} decay was studied using the YRAST Ball detector array at the Wright Nuclear Structure Laboratory at Yale University. The level scheme of {sup 193}Au has been extended up to I{sup {pi}}=55/2{sup +}. New transitions were observed also in {sup 191}Au and {sup 192}Pt. Particle-plus-Triaxial-Rotor (PTR) and Total Routhian Surface (TRS) calculations were performed to determine the equilibrium deformations of the Au isotopes. The predictions for oblate deformations in these nuclei are in agreement with the experimental data. Development of nonaxial shapes is discussed within the framework of the PTR model.

The experimental energy staggering in \ensuremath{\gamma} bands of rare earths and actinides exhibits three distinct patterns as a function of angular momentum that are typical of well-deformed structural benchmarks: \ensuremath{\gamma}-soft for nuclei situated between a vibrator and a deformed \ensuremath{\gamma}-soft structure, axially symmetric for those between a vibrator and a rigid rotor, and triaxial \ensuremath{\gamma}-rigid for nuclei between a vibrator and a rigid triaxial rotor. The three patterns are reproduced by appropriate special solutions of the Bohr Hamiltonian, as well as by interacting boson approximation calculations. A particular quantity called S(4), which is proportional to the displacement of the ${3}_{\ensuremath{\gamma}}^{+}$ level relative to the average of the ${2}_{\ensuremath{\gamma}}^{+}$ and ${4}_{\ensuremath{\gamma}}^{+}$ levels, can vary in magnitude and sign for different shapes and is found to give a good indication of structure and the evolution of structure. A sudden change in the \ensuremath{\gamma}-band staggering occurring between the vibrator and the axially symmetric rotor limits seems to be connected to the known presence of a first-order phase/shape transition in this region.

In this contribution, further evidence of the importance of multiphonon-octupole excitations to describe experimental data in the rare earths and actinides will be presented. First, new results of a ( p, t ) experiment at the Q3D magnetic spectrograph in Munich will be discussed, which was performed to selectively excite J π = 0 + states in 240 Pu. spdf interacting boson model (IBM) calculations suggest that the previously proposed double-octupole phonon nature of the J π = 0 + 2 state is not in conflict with its strong ( p, t ) population. Second, the framework of the IBM has been adopted for the description of experimental observables related to octupole excitations in the rare earths. Here, the IBM is able to describe the signature splitting for positiveand negative-parity states when multi-dipole and multi-octupole bosons are included. The present study might support the idea of octupole-phonon condensation at intermediate spin ( J π = 10 + ) leading to the change in yrast structure observed in 146 Nd.

The evolution of nuclear structure along the Xe and Ba isotopes with N{lt}82 is studied in comparison with that in the Pt-Os isotopes and with interacting boson approximation calculations. As is well known, the Pt isotopes from {sup 188{minus}196}Pt exhibit a stable structure very close to O(6), the lighter Pt isotopes and the Os nuclei evolve towards a rotor, and the heaviest Pt nuclei, {sup 198,200}Pt, show a tendency towards vibrational character. In contrast, we show that the Ba nuclei are best described by a trajectory from U(5) towards SU(3) that passes through an intermediate structure that resembles O(6) for N{approximately}72{endash}76. The Xe appears to evolve from U(5) to O(6)-like. {copyright} {ital 1998} {ital The American Physical Society}

The parameter independent (up to overall scale factors) predictions of the X(5)-{beta}{sup 2}, X(5)-{beta}{sup 4}, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two-parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the shape/phase-transition region of the IBA for boson numbers of physical interest (close to 10). Nuclei within the rare-earth region and select Os and Pt isotopes are identified as good examples of X(3), X(5)-{beta}{sup 2}, and X(5)-{beta}{sup 4} behavior.

Recently, a set of nine nonmagic nuclei with anomalous values of the $B(E2)$ ratio ${B}_{4/2}\ensuremath{\equiv}B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})/B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{1}^{+})$ 1 were identified. Such values are outside the range allowed by current collective models. In the present work, the $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ values for two of these nuclei, $^{98}\mathrm{Ru}$ and $^{180}\mathrm{Pt}$, were re-measured to determine if the current literature values for these nuclei are correct. $^{98}\mathrm{Ru}$ was studied in a $^{27}\mathrm{Al}$($^{98}\mathrm{Ru}$,$^{98}\mathrm{Ru}$${}^{*}$) Coulomb excitation experiment in inverse kinematics, while the lifetime of the ${4}_{1}^{+}$ state in $^{180}\mathrm{Pt}$ was measured in a $^{122}\mathrm{Sn}$($^{62}\mathrm{Ni}$, $4n$)$^{180}\mathrm{Pt}$ recoil distance method (RDM) experiment. For both nuclei, the remeasured ${B}_{4/2}$ values are well above 1, removing the deviations from collective models.

Lifetime measurements of yrast levels in 162Yb and 166Hf were performed using the recoil distance Doppler-shift method in coincidence mode. Excited states in 162Yb and 166Hf were populated via the reactions 116Cd(50Ti, 4n) and 122Sn(48Ti, 4n), respectively. The resulting B(E2) values are compared with the X(5) critical point model predictions and interacting boson approximation (IBA) model calculations. The X(5) model provides a reasonable description of the yrast B(E2) values in 166Hf, whereas the IBA fails to reproduce the transition strengths from the higher spin levels. In 162Yb, some transitions agree with the X(5) predictions while others are more consistent with the predictions of the IBA or a deformed symmetric rotor.

A simple phenomenological model is discussed that simultaneously accounts for the saturation of B(E2; 0{sub 1}{sup +}{yields} 2{sub 1}{sup +}) values and the newly recognized near constancy of g(2{sub 1}{sup +}) factor values in deformed nuclei. The model invokes reduced effective contributions to these observables from the valence neutrons and protons. Empirical evidence supporting this ansatz comes from recently extracted proton-neutron interaction strengths.

Excited states in $^{209}\mathrm{Fr}$ were produced following the $^{176}\mathrm{Yb}$($^{37}\mathrm{Cl}$, $4n$) reaction. An excitation function was measured with data taken at 173, 179, and 185 MeV. Recoiling fusion-evaporation products were separated using the SASSYER gas-filled spectrometer. HPGe clover detectors of the YRAST Ball array at the target position and at the focal plane were used to detect prompt and delayed gamma ray decays, providing the first spectroscopic information about prompt and delayed transitions in $^{209}\mathrm{Fr}$. The decay from a proposed $\ensuremath{\pi}{i}_{13/2}$ configuration isomer was observed in $^{209}\mathrm{Fr}$, and its half-life was measured to be 446(14)ns. States above the isomer were also observed.

Preliminary lifetime values have been measured for a number of near-yrast states in the odd-A transitional nuclei 107Cd and 103Pd. The reaction used to populate the nuclei of interest was 98Mo( 12C,3nxα)107Cd, 103Pd, with the beam delivered by the tandem accelerator of the Wright Nuclear Structure Laboratory at an incident beam energy of 60 MeV. Our experiment was aimed at the investigation of collective excitations built on the unnatural parity, ν h11/2 orbital, specifically by measuring the B(E2) values of decays from the excited levels built on this intrinsic structure, using the Doppler Recoil Distance Method. We report lifetimes and associated transition probabilities for decays from the 15/2- and the 19/2- states in 107Cd and the first measurement of the 15/2- state in 103Pd. These results suggest that neither a simple rotational or vibrational interpretation is sufficient to explain the observed structures. © 2006 American Institute of Physics.

Lifetimes of excited states in 128 Ce were measured using the recoil distance Doppler-shift (RDDS) and the Doppler-shift attenuation (DSAM) methods. The experiments were performed at the Wright Nuclear Structure Laboratory of Yale University. Excited states of 128 Ce were populated in the 100 Mo (32 Si ,4 n ) reaction at 120 MeV and the nuclear γ decay was measured with an array of eight Clover detectors positioned at forward and backward angles. The deduced yrast transition strengths together with the energies of the levels within the ground-state (gs) band of 128 Ce are in agreement with the predicted values for the X (5) critical point symmetry. Thus, we suggest 128 Ce as a benchmark X (5) nucleus in the mass A ≈ 130 region.

Microscopic models suggest the occurrence of strong octupole correlations in nuclei with $N\ensuremath{\approx}88$. To examine the signatures of octupole correlations in this region, the spdf interacting boson approximation model is applied to Sm isotopes with $N=86\text{\ensuremath{-}}92$. The effects of including multiple negative-parity bosons in this basis are compared with more standard one negative-parity boson calculations and are analyzed in terms of signatures for strong octupole correlations. It is found that multiple negative-parity bosons are needed to describe properties at medium spin. Bands with strong octupole correlations (multiple negative-parity bosons) become yrast at medium spin in $^{148,150}\mathrm{Sm}$. This region shares some similarities with the light actinides, where strong octupole correlations were also found at medium spin.

The g factor of the 2{sub 1}{sup +} state of {sup 160}Er was measured by perturbed {gamma}-{gamma} angular correlation in a static external magnetic field of 5.82 T. The result, g(2{sub 1}{sup +})=0.33(6), is discussed within the systematics of g factors of even-even isotopes for the Ba-Pt region.

The most commonly accepted interpretation of the light Pt isotopes invokes the coexistence and mixing with proton intruder states from above the Z = 82 shell gap. Using an alternative description, interacting boson model (IBA) calculations are performed for the Pt isotopes with a simple, single configuration, two-parameter Hamiltonian. Excellent agreement is obtained for energies and electromagnetic transition strengths over the entire isotopic chain, spanning a wide variety of structures, and suggesting that these nuclei can be described more simply without the introduction of an intruder configuration. The Pt nuclei close to midshell are found to lie close to a region of phase/shape coexistence.

A simple, two-parameter IBA-1 Hamiltonian is applied to light W, Os, and Pt nuclei with N {

Following Coulomb excitation of the radioactive ion beam (RIB) $^{132}\mathrm{Te}$ at HRIBF we report the first use of the recoil-in-vacuum (RIV) method to determine the $g$ factor of the ${2}_{1}^{+}$ state: $g(973.9\text{ }\text{ }\mathrm{keV}\text{ }{2}^{+}\text{ }^{132}\mathrm{Te})=(+)0.35(5)$. The advantages offered by the RIV method in the context of RIBs and modern detector arrays are discussed.

{gamma}-ray spectroscopy of {sup 132}Te, obtained from {beta}{sup -} decay of a {sup 132}Sb radioactive beam at the Holifield Radioactive Ion Beam Facility, was performed using the Clarion array. A significantly revised {gamma}-decay scheme for {sup 132}Te was obtained including a number of new, likely 2{sup +}, states below 2.5 MeV and the removal of a 3{sup -} state at 2280 keV. A simple shell-model interpretation is discussed for the low-lying levels.

Phase transitional behavior in the evolution of nuclear structure from spherical to deformed shapes is often investigated in two seemingly different contexts: within the framework of the interacting boson approximation (IBA) model, or using a geometric approach such as the X(5) or E(5) solutions. To study the connection between these two different models, two-parameter IBA-1 calculations were performed and compared to the parameter-free predictions of the X(5) model. The results show that the X(5) solution cannot be exactly reproduced by any point in the two-parameter space and that the best agreement is close to, but does not coincide with, the phase transitional region for a finite number of particles. Comparison of these two approaches with experimental data on X(5)-type nuclei shows that while X(5) and the two-parameter IBA can reproduce characteristic energy ratios in these nuclei, the IBA calculations give better agreement with the experimental electromagnetic transition strengths.

Excited states in {sup 166}Hf were populated in the {beta}{sup +}/{epsilon} decay of {sup 166}Ta and studied through off-beam {gamma}-ray spectroscopy at the Yale moving tape collector. New coincidence data found no support for two previously reported excited 0{sup +} states and led to a substantially revised level scheme. Similarities between the revised level scheme of {sup 166}Hf and the X(5) critical point symmetry are discussed, and the extent of X(5) behavior in this mass region is explored through the W and Os isotopes. Among X(5) candidates with N>90, good agreement is observed for most energies and interband B(E2) strengths, while all exhibit similar disagreements with other key observables, in particular, yrast B(E2) values and spacing in the excited K = 0{sup +} sequence.

A study of the energies of the first excited 0{sup +} states in all even-even Z{>=}8 nuclei reveals an anomalous behavior in some nuclei with N=Z,Z{+-} 2. We analyze these irregularities in the framework of the shell model. It is shown that proton-neutron correlations play an important role in this phenomenon.

Low-energy excited states of {sup 208}Ra were investigated using the {sup 182}W({sup 30}Si, 4n) reaction at the Wright Nuclear Structure Laboratory of Yale University. Fusion evaporation recoils were selected using the gas-filled spectrometer SASSYER. Delayed {gamma} rays, following isomeric decays, were detected at the focal plane of SASSYER with a small array of three clover Ge detectors. Transitions following a proposed J{sup {pi}}=8{sup +} isomer were observed, and the half-life was measured.

The results from two surrogate reaction experiments using the STARS (Silicon Telescope Array for Reaction Studies) spectrometer are presented. The surrogate method involves measuring the particle and/or γ‐ray decay probabilities of excited nuclei populated via a direct reaction. These probabilities can then be used to deduce neutron‐induced reaction cross sections that lead to the same compound nuclei. In the first experiment STARS coupled to the GAMMASPHERE γ‐ray spectrometer successfully reproduce surrogate (n,γ), (n,n′γ) and (n,2nγ) cross sections on 155,156Gd using 3He‐induced reactions. In the second series of experiments an energetic deuteron beam from the ESTU tandem at the Wright Nuclear Structure Lab at Yale University was used to obtain the ratio of fission probabilities for 238U/236U and 237U/239U populated using the 236,238U(d,d′f) and 236,238U(d,pf) reactions. Results from these experiments are presented and the implications for the surrogate reaction technique are discussed.

Following Coulomb excitation of the radioactive ion beam (RIB) Te-132 at HRIBF, we report the first use of the recoil-in-vacuum (RIV) method to determine the g-factor of the 2(1)(+) state to be (+)0.35(5). The advantages offered by the RIV method in the context of RIBs and modern detector arrays are discussed.

Following Coulomb excitation of the radioactive ion beam (RIB) 132Te at HRIBF we report the first use of the recoil-in-vacuum (RIV) method to determine the g factor of the 2(+)(1) state: g(973.9 keV 2(+) 132Te) = (+)0.35(5). The advantages offered by the RIV method in the context of RIBs and modern detector arrays are discussed.