Key Topics in Nuclear Structure

FOREWORD

CONTENTS

PROGRAM

Nuclear physics research is evolving into a new era. Much of our knowledge concerning nuclear matter to date has been derived from experiments involving reactions between stable projectile and target nuclei. However, new technical developments now enable intense beams of radioactive nuclei to be used as projectiles. The use of such beams enables the nuclear landscape to be investigated over a much wider range of neutron to proton ratios. Not only is this important for nuclear physics, it is also of great importance for nuclear astrophysics, use of the nucleus as a probe for fundamental symmetries, as well as using such beams to probe the atomic structure of new materials. This paper will describe progress at TRIUMF concerning the production of radioactive beams.

During the last 10 years many experiments with radioactive ion beams have been performed at the superconducting linear accelerator ATLAS at Argonne National Laboratory. The production methods employ the two-accelerator technique for long-lived isotopes or the in-flight technique for nuclei with shorter half-lives. Experiments with radioactive beams ranging in mass from ⁶He (T_1/2=0.8s) to ⁵⁶Ni (T_1/2=6.1d) have been performed so far. The experiments cover studies in nuclear structure and reactions, in nuclear astrophysics, especially in explosive nuclear synthesis, as well as in neutrino physics, which are relevant in connection with recent results from the large neutrino detectors at SNO and SUPERKAMIOKANDE.

The Radioactive beam EXperiment (REX) at ISOLDE (CERN) was conceived as a pilot experiment to demonstrate a novel technique to bunch, charge breed and accelerate radioactive ions produced by ISOL facilities. The experiment was successfully commissioned in 2002 and promoted to a CERN user facility at the end of 2003. First measurements were performed at 2.2 MeV/u in summer 2003 using the MINIBALL array, which consists of 24 individually encapsulated, 6-fold segmented high-purity Ge-detectors and allows to detect de-excitation γ-rays with high efficiency and high energy resolution. The REX-ISOLDE facility together with the MINIBALL array offers new and unique possibilities to study collective and single-particle properties of nuclei far-off stability with standard nuclear physics tools such as (safe) Coulomb excitation and single-nucleon transfer reactions in inverse kinematics, as well as with other well established experimental methods. Due to the current energy range of REX-ISOLDE (2004: 3.0MeV/u) the present experimental programme is concentrated on light to medium heavy, neutron rich nuclei. After an introduction to REX-ISOLDE and MINIBALL, the high potential and physics opportunities offered by the new facility are exemplified by first results obtained for Mg isotopes around the “island of inversion” at N = 20.

The experimental programme and associated instrumentation for the radioactive-beam facility at the future FAIR facility at GSI is briefly discussed.

The SPIRAL2 project is now close to the end of the Detailed Design Study (APD) phase. The baseline project, as well as possible extensions, was presented at various meetings and an intermediate report has been published, showing the technical solutions chosen, as well as the tentative time schedule and construction costs. The reference project, including the baseline project and the addition of a number of extensions, was discussed with the physics group and presented at the Steering Committee, held on the 5th of February 2004. A decision for the beginning of the construction in 2005 could be taken before the end of this year.

With the increasing likelihood that major next-generation radioactive beam facilities will be built in the not–too–far future, interest in exotic nuclei has become even more intense. Of course, major foci of this interest concern the frontiers, namely extremely proton rich nuclei, nuclei near the neutron drip line, and the heaviest nuclei that can exist. However, another major area of interest will be the evolution of structure between the known nuclei and those furthest from stability. Recent work has revealed several new and important facets of this structural evolution. These concern phase transitional behavior and its nature; the expected locus and the theoretical description of nuclei in phase transitional regions; new examples of evolutionary trajectories with implications for the description of nuclei in terms of regular and chaotic behavior; and new empirical signatures for such behavior. Several of these aspects of nuclei far from stability will be discussed.

The understanding of the structure of nuclei very far-from-stability constitutes the next major challenge in the description of nucleon interactions resulting in low lying excited states. New techniques of measurement of magnetic moments of short-lived nuclear states combining Coulomb excitations of beams and the transient hyperfine magnetic interaction have led to the determination of magnetic moments of low-lying, short-lived, states with a precision that can distinguish between various theoretical calculations. The technique is particularly applicable to the study of radioactive beams and was used for the first time to measure the g factor of the state of ⁷⁶Kr. The ⁷⁶Kr beam was produced and accelerated in batch mode at the Lawrence Berkeley National laboratory 88-Inch cyclotron. Peak rates of 10⁸ particles/s were obtained yielding a g factor measurement of .

New effective interactions, PK1, PK1r and PKDD, in the relativistic mean field (RMF) theory, are proposed with the center-of-mass correction included in a microscopic way. They are able to provide an excellent description not only for the properties of nuclear matter and neutron stars, but also for the nuclei near and far from the β-stability line, including halos and giant halos at the neutron drip line in nuclei and hypernuclei. Based on the solution of the RMF equations, a good spin symmetry is found in anti-nucleon spectra. The magic proton and neutron numbers are searched in the superheavy region by the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Spherical doubly magic superheavy nuclei are systematically investigated and their stabilities against deformation are discussed.

The non–adiabatic quasi-particle approach for proton radioactivity from deformed drip–line nuclei is discussed. All experimental data available on decay from ground and isomeric states, and fine structure of odd-even and odd–odd nuclei, are consistently interpreted without free parameters, by this theoretical approach.

An unified shell model scheme to evaluate simultaneously the contributions of bound single-particle states, Gamow resonances, antibound (virtual) states and continuum complex scattering states is presented. The formalism could be very suitable to study processes occurring in the continuum part of the nuclear spectra.

Motivated by the renormalization group (RG) and effective field theory (EFT) approach, a low-momentum NN interaction V_low–k has been derived by integrating out the high momentum components of modern NN potential models V_NN. Although the various V_NN models are significantly different, the V_low–k’s extracted from them are nearly identical to each other when a decimation momentum Λ ≈ 2fm⁻¹ or smaller is employed. Starting from the Lee-Suzuki (or folded diagram) non-Hermitian low momentum NN interactions, a family of phase-shift equivalent V_low–k’s are obtained by way of a Schmidt orthogonalization method. We have found that V_low–k can be very accurately represented by a counter term expressed as a low order momentum expansion of the form ∑C_nkⁿ.

Binding energies of ³H, ⁴He, and ¹⁶O are calculated, using low-momentum nucleon-nucleon interactions (V_low–k) for a wide range of the cutoff momentum Λ. In addition, single-particle energies in nuclei around ¹⁶O are computed. The dependence of the binding energies and the single-particle energies in these nuclei on the cutoff momentum Λ of the V_low–k is examined. Furthermore, the availability of the V_low–k in nuclear structure calculations is discussed.

We describe the development and application of the ab initio No-Core shell Model (NCSM), in which the effective Hamiltonians are derived microscopically from realistic nucleon-nucleon (NN) plus theoretical three-nucleon (NNN) potentials, as a function of the finite harmonic-oscillator (HO) basis space. For presently feasible no-core model spaces, we evaluate the effective Hamiltonians in a cluster approach, which is guaranteed to provide exact results for sufficiently large model spaces and/or sufficiently large clusters. A number of recent applications of the NCSM are given.

An elementary introduction to the monopole Hamiltonian is proposed. Emphasis is put on comparison with experimental data, especially those indicating the need of three-body interactions.

We present recent coupled-cluster studies of nuclei, with an emphasis on ground state and excited states of closed shell nuclei. Perspectives for future studies are delineated.

We present the structure of ⁶Li and ¹⁸O calculated with the use of a dynamic correlation model. In our model, the nucleon-nucleon correlations are built into a set of nonlinear equations of motion, which we solve self-consistently to obtain the eigenstates of the nucleons that are dressed by their interactions with the nuclear medium. We have found that the solution does not depend on the original choice of the two-body matrix elements. The inputs to solve the dynamical eigenvalue-equations are the n-body matrix elements. We have developed a cluster factorization method to relate the n-body matrix elements to the (n-1)-body matrix elements by recursion relations. Hence all the needed n-body matrix elements can be built up from the basic 2-body matrix elements.

Particle-number restoration before variation is implemented in the HFB method employing the Skyrme force and zero-range delta pairing. Results are compared with those obtained within the Lipkin-Nogami method, with or without the particle-number projection after variation. Shift invariance property is proven to be valid also in the case of density functional calculations which allows the well known singularity () in PNP HFB calculations to be safely avoided.

Shell-model states involving several pseudospin doublets and “intruder” levels in nuclei, are combined into larger multiplets. The corresponding single-particle spectrum exhibits a supersymmetric pattern whose origin can be traced to the relativistic pseudospin symmetry of a nuclear mean-field Dirac Hamiltonian with scalar and vector potentials.

Pseudospin symmetry is a relativistic symmetry of the Dirac Hamiltonian. We show that the eigenfunctions of realistic relativistic nuclear mean fields approximately conserve pseudospin symmetry.

We have performed shell-model calculations starting from modern nucleon-nucleon potentials V_NN. We make use of a new approach to the renormalization of the short-range repulsion of V_NN in which a low-momentum potential V_low–k is derived by integrating out the high-momentum components of V_NN down to a cutoff momentum Λ. We present some results for nuclei around closed shells which have been obtained starting from the CD-Bonn potential. We have also performed calculations making use of different modern NN potentials. Comparison of the results obtained shows that they are only slightly dependent on the kind of potential used as input. The effects of changes in Λ are explored.

Recently the first excited state in ¹³⁵Sb has been observed at the excitation energy of only 282 keV and interpreted as mainly d_5/2 proton coupled to the ¹³⁴Sn core. It was suggested that its low-excitation energy is related to a relative shift of the proton d_5/2 and g_7/2 orbits induced by the neutron excess. With the aim to provide more spectroscopic information on this anomalously low-lying 5/2⁺ state, we have measured its lifetime by the Advanced Time-Delayed βγγ(t) method at the OSIRIS fission product mass separator at Studsvik. The M1 and E2 transition rates from the 282 keV state are strongly hindered, similarly to what occurs in ²¹¹Bi for the transition de-populating the first excited state at 405 keV. However, more data are needed above ¹³²Sn especially on the transition matrix elements. Thus our investigation was extended to include lifetime measurement of the 5/2⁺ 243 keV state in ¹³⁷I, which has an extra pair of protons above ¹³⁵Sb. Results of shell model calculations are presented.

In this work, μs isomers in In and Cd isotopes with A = 123 to 130 were investigated. These experiments were conducted at the ILL (Grenoble) using the LOHENGRIN mass spectrometer. The isomers were produced by thermal-neutron induced fission of Pu targets. The level schemes of the odd-mass ^123–129In and new measurements of the µs half-lives of the odd-odd ^126–130In are reported. In contrast, the expected 8⁺ isomers in the even-Cd isotopes were not observed. A shell-model study of the heaviest In and Cd nuclei was also performed using a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential. Comparison shows that the calculated levels of ¹³⁰In and ¹²⁹In are in good agreement with experimental values while some discrepancies appear for the lighter In isotopes. The collectivity of ^126,128Cd is discussed in the framework of the shell model and in comparison with ²⁰⁴Hg.

DSA lifetime measurements in the negative-parity yrast band of the odd-odd ¹⁰⁴In have given evidence for the interplay of the [] proton-neutron shears band with the remaining ν(d_5/2, g_7/2) valence neutrons. The recoupling of the ν^2,4(d_5/2,g_7/2) part of the wave functions to either seniority 2 or 4 produces a pronounced up-bend of B(M1) which is reproduced by large-scale shell model calculations with effective single-particle energies and two-body matrix elements.

The status of the experimental approach to ¹⁰⁰Sn is reviewed. In particular the nuclei in the closest vicinity of the doubly magic nucleus and with an isomeric high spin state are addressed. The nature of isomeric states is discussed, and the wave function analysed in terms of measured decay transition probabilities. The observation of the high spin isomer in ⁹⁸Cd in an experiment at EUROBALL IV yields information on single particle structure, size of the shell gap for ¹⁰⁰Sn and solves the puzzle of contradictory results of previous measurements. Experimental results are compared to the empirical and large-scale shell model calculation employing realistic interactions. The data on ⁹⁸Cd is discussed together with a survey of known and predicted isomeric states in this region.

Data from three gamma spectroscopy experiments using deep-inelastic heavy ion reactions provided new information on high-spin states in the ⁴⁸Ca core nucleus and in the N=30, ⁵⁰Ca and ⁵¹Sc isotones. Shell model calculations restricted to neutron excitations only are shown to reproduce with good accuracy some of the experimental levels. It is demonstrated that proton excitations not accounted in these calculations are abundantly present in the observed yrast structures. High energy of the 4⁺ state in ⁵⁰Ca underlines the validity of the N=32 shell closure.

Gamma rays from neutron-rich Ti nuclei in the vicinity of N = 32 have been studied at Gammasphere using deep-inelastic reactions induced by a 305 MeV 48Ca beam on a thick ²⁰⁸Pb target. The yrast γ-ray cascades in ⁵³Ti were identified for the first time and the location in energy of the states with spin up to J=21/2 was determined. The yrast excitations of ⁵³Ti, together with the earlier studied yrast structure of ⁵⁴Ti, provided new tests of effective interactions for full pf-shell calculations. The data confirm the presence of a significant subshell gap at N=32. Comparisons between theory and experiment regarding the highest spin states located in ^53,54Ti suggest that energy gap at N=34 in neutron-rich nuclei is not as large as predicted by the recently proposed GXPF1 interaction.

Electromagnetic moments measurement of isomeric states produced and spin-oriented in projectile fragmentation reactions at intermediate energies have been performed using the Time Dependent Perturbed Angular Distribution (TDPAD) method. This allows the study of neutron-rich nuclei unaccessible by other kind of reaction. An important experimental achievement is presented.

A discussion is made on the status of multinucleon transfer studies performed with high resolution spectrometers and the new possible experiments to be done via γ-particle coincidences in suitable systems to elucidate the structure of interesting excited states populated via transfer reactions.

The ¹¹²Sn(p,t)¹¹⁰Sn reaction has been studied in a high resolution experiment at an incident energy of 26 MeV. Differential cross-sections for transitions to 27 levels of ¹¹⁰Sn up to an excitation energy of about 4.3 MeV have been measured. Distorted wave Born approximation analysis of experimental angular distributions, assuming a dineutron cluster pickup mechanism, has been performed, allowing confirmation of previous J^π values as well as new assignments. Moreover, a microscopic calculation of the angular distributions of ground and first excited states of ¹¹⁰Sn has been carried out. A shell-model study of ¹¹⁰Sn has been also performed using a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential.

Motivated by the problem of the relative importance of J = 1⁺ T = 0 pairing versus the better established J = 0⁺ T = 1 pairing in nuclei, we here address the problem of the number of np pairs of a given angular momentum in selected nuclei, ⁴⁴Ti, ⁴⁶Ti, and ⁴⁸Ti. The number of pairs is obviously relevant to np pickup reactions such as (p,³He). One can address also the np transfer reaction (³He,p) and indeed there is a proposal by the Berkeley group to do the reaction ⁴⁴Ti(³He,p)⁴⁶Sc. In this work we will consider the single j shell model for the Ti isotopes. In the near future more elaborate calculations are planned.

We show that a recently developed algorithm for generating a subset of eigenvalues and eigenvectors of large matrices may be used for an efficient definition of an importance sampling of the shell-model basis. The sampling so implemented allows for substantial reductions of configuration spaces, and, also, for extrapolations to exact eigenvalues and E2 strengths.

The formalism of the auxiliary-field Monte Carlo method is well suited for studying the finite-temperature properties of nuclear structure. Since this approach avoids an explicit enumeration of the many-body states, spaces larger than in the conventional methods can be reached. The nuclear implementation of the shell model Monte Carlo method is limited by the ‘sign’ problem associated with the Monte Carlo weight function when we use realistic effective two-body interactions. We consider a new approach for alleviating the ‘sign’ problem. This method is based on shifting the Monte Carlo integration to a region in the complex plane where fluctuations around the Hartree-Fock solution are minimized.

Shape phase transitions in nuclei are reviewed, with particular emphasis to the recent introduction of spectral signatures of critical behavior.

This talk focuses on three topics: the development of a program to determine SO(5) spherical harmonics and SO(5) Clebsch-Gordan coefficients; efficient ways to do collective model calculations in an SU(1,1) × SO(5) ⊃ U(1) × SO(3) basis; and quasi-dynamical symmetry in an IBM second-order phase transition.

Davidson potentials of the form , when used in the E(5) framework (i.e., in the original Bohr Hamiltonian after separating variables as in the E(5) model) bridge the U(5) and O(6) symmetries, while they bridge the U(5) and SU(3) symmetries when used in the X(5) framework (i.e., in the original Bohr Hamiltonian after separating variables as in the X(5) model). Using a variational procedure, we determine for each value of angular momentum L the value of the parameter β₀ at which the rate of change of the energy ratio R_L = E(L)/E(2) has a maximum, the collection of the values of R_L formed in this way being a candidate for describing its behavior at the relevant critical point. This procedure leads to the E(5) ground state band in the E(5) framework and to the X(5) ground state band in the X(5) framework, thus indicating that the use of an infinite well potential in β is an optimum choice in both cases.

The lifetimes of excited states in ¹⁵⁴Gd were measured using the recoil distance Doppler-Shift (RDDS) method. The experiment was performed at Cologne FN Tandem accelerator where a beam of ³²S with an energy of 110 MeV was used to Coulomb excite states of ¹⁵⁴Gd. The determined transition probabilities as well as the low-spin level scheme of ¹⁵⁴Gd demonstrate a good agreement with the predictions of the critical point symmetry X(5). Comparison of specific experimental observables for the N = 90 rare earth isotones with the calculations of the X(5) model clearly show that ¹⁵⁴Gd is one of the best examples of the realization of the X(5) dynamical symmetry. In addition, the experimental data are compared to fits in the framework of the IBA and the General Collective Model (GCM).

A solution of the Bohr Hamiltonian is obtained by approximately separating variables for γ = 30°. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are found to be in good agreement with experimental data for ¹⁹⁴Pt, which is supposed to be located very close to the prolate to oblate critical point, as well as for its neighbours (¹⁹²Pt, ¹⁹⁶Pt). Hallmarks of the model are the R₄ = E(4)/E(2) ratio of 2.350, as well as the location of the γ₁- and β₁-bandheads (normalized to the 2⁺ state of the ground state band) at 1.837 and 3.913 respectively, while the selection rules for B(E2) transition rates are similar to the ones of the O(6) limit of the Interacting Boson Model.

To provide information for comparison with predictions for a dynamical supersymmetry, the odd-odd nucleus ¹⁹⁶Au was studied via transfer reactions. With a polarized deuteron beam we measured () and (), with unpolarized beams (p,d), (³He,d), and (α,d) transfer reactions. In this way we obtain for 20 out of the 26 observed states with negative parity below 500 keV safe J^π assignments. The number of states and the safe or restricted assignments are in agreement with the predictions from the dynamical supersymmetric scheme. Comparison with model predictions for spectroscopic factors will provide a further critical test to what extent this symmetry is realized in nature.

We derive a boson Hamiltonian from a Nuclear Hamiltonian whose potential is expanded in pairing multipoles and determine the fermion-boson mapping of operators. We use a new method of bosonization based on the evaluation of the partition function restricted to the bosonic composites of interest. By rewriting the partition function so obtained in functional form we get the euclidean action of the composite bosons from which we can derive the Hamiltonian. Such a procedure respects all the fermion symmetries.

The β decay from As to Ge isotopes is studied together with the energy levels and the electromagnetic properties in the interacting boson-fermion model (IBFM). The effects of the higher-order terms in the particle transfer operators that form the β-decay operators will be discussed.

In a new application of the algebraic Interacting Vector Boson Model (IVBM), we exploit the reduction of its Sp(12, R) dynamical symmetry group to , which defines basis states with fixed values of the angular momentum L. The energy distribution of collective positive parity states with L = 0, 2, 4, 6… states is studied, using the correspondence of the new reduction chain to the rotational limit of the model. Results for low-lying spectra of rare-earth nuclei show that the energies of the states with fixed L lie on second order curves with respect to the number of collective phonons n or vector bosons N = 4n from which they are built. The analysis of this behavior leads to insight regarding the common nature of collective states, tracking vibrational as well as rotational features.

Recoil-Decay-Tagging (RDT) experiments for studies of shape coexistence in neutron deficient nuclei near Z = 82 have been continued at JYFL by employing the JUROGAM gamma-ray detector array and the GREAT spectrometer at the RITU gas-filled separator. A new non-yrast band has been observed in ¹⁸⁶Pb and tentatively associated with oblate shape. New experiments for ²⁵⁴No were also carried out with the same set-up revealing feeding via highly coverted M1 transitions.

Systematic nuclear resonance fluorescence experiments (NRF) on all 7 stable even-even Xe isotopes have been performed at the bremsstrahlung facility of the 4.3 MV Stuttgart Dynamitron accelerator. For the first time thin-walled, high-pressure gas targets (about 70 bar) were used in NRF experiments. Precise excitation energies, transition strengths, spins, and decay branching ratios were obtained for numerous states, most of them unknown so far. The systematics of the observed E1 two-phonon excitations (2⁺ 3⁻) and M1 excitations to 1⁺ mixed symmetry states are discussed with respect to the new critical point symmetry E(5).

The neutron thermal pairing gap determined from the modified BCS theory is included in the calculation of the width of the giant dipole resonance (GDR) at finite temperature T in ¹²⁰Sn within the Phonon Damping Model. The results obtained show that thermal pairing causes a smaller GDR width at T ≤ 2 MeV as compared to the one obtained neglecting pairing. This effect improves significantly the agreement between theory and experiment including the most recent data point at T = 1 MeV.

The results are presented from the experiments using the EUROBALL and RFD/HECTOR arrays, concerning various aspects of collectivity in light nuclei. A superdeformed band in ⁴²Ca was found. A comparison of the GDR line shape data with the predictions of the thermal shape fluctuation model, based on the most recent rotating liquid drop LSD calculations, shows evidence for a Jacobi shape transition in hot, rapidly rotating ⁴⁶Ti and strong Coriolis effects in the GDR strength function. The preferential feeding of the SD band in ⁴²Ca by the GDR low energy component was observed

A dipole degree of freedom, a most natural concept in molecular physics, is also essential for describing certain states near threshold in light and heavy nuclei. Much like for the Ar-benzene molecule, it is shown that molecular configurations are important near threshold as exhibited by states with a large halo and strong electric dipole transitions. After its first observation in ¹⁸O it was also shown to be relevant for the structure of heavy nuclei (e.g. ²¹⁸Ra). The Molecular Sum Rule derived by Alhassid, Gai and Bertsch (AGB) is shown to be a very useful model independent tool for examining such dipole molecular structure near threshold. Accordingly, the dipole strength observed in the halo nuclei such as ⁶He, ¹¹Li, ¹¹Be, ¹⁷O, as well as the N=82 isotones is concentrated around threshold and it exhausts a large fraction (close to 100%) of the AGB sum rule, but a small fraction (a few percent) of the TRK sum rule. This is suggested as an evidence for a new soft dipole Vibron like oscillations in nuclei.

A semiclassical model based on the solution of the Vlasov equation for finite systems with a sharp moving surface has been used to study the isoscalar quadrupole and octupole collective modes in heavy spherical nuclei. Within this model, a unified description of both low-energy surface modes and higher-energy giant resonances has been achieved by introducing a coupling between surface vibrations and the motion of single nucleons. Analytical expressions for the collective response functions of different multipolarity can be derived by using a separable approximation for the residual interaction between nucleons. The response functions obtained in this way give a good qualitative description of the quadrupole and octupole response in heavy nuclei. Although shell effects are not explicitly included in the theory, our semiclassical response functions are very similar to the quantum ones. This happens because of the well known close relation between classical trajectories and shell structure. The role played by particular nucleon trajectories and their connection with various features of the nuclear response is displayed most clearly in the present approach, we discuss in some detail the damping of low-energy octupole vibrations and give an explicit expression showing that only nucleons moving on triangular orbits can contribute to this damping.

The excitation of a multiple giant resonance is studied within the framework of a semiclassical model. We make use of an extended RPA to treat anharmonicities and non liner terms in the external field. Successful applications to double giant resonances to both relativistic and lower incident energies are reviewed. We have extended this method to the calculation of the triple giant resonance. We show that large amplitude motion induce a strong coupling to giant monopole and quadrupole vibrations.

New level schemes to high spin are extracted for ^99,101Y, ^101,105Nb, ^105,107,109Tc, ^111,113Rh and ^115,117Ag from prompt γ–γ–γ coincidences studies of ²⁵²Cf with Gammasphere. The π5/2⁺[422] bands in ^99,101Y and ^101,105Nb and 7/2⁺[413] bands in ^105,107,109Tc, ^111,113Rh and ^115,117Ag exhibit a smooth evolution from strong prolate deformation with very little signature splittings in ^99,101Y to triaxial deformation with large and near maximum splitting in the Tc, Rb and Ag nuclei. These splitting data along with the presence of an excited 11/2⁺ bands with almost no decay to the 7/2⁺ levels in the Tc and Rh nuclei indicate the increasing importance of rigid triaxial shapes in these nuclei. The Nb isotopes having intermediate splitting between Y and Tc, Rh isotopes may suggest that they are transitional nuclei with regard to triaxial deformation. Triaxial-rotor-plus-particle model calculations yielded best fits to the energies, signature splitting and transition probabilities for ∈(≈ β₂)≈0.32 and γ = −22.5° for ¹⁰⁷Tc and β₂ = 0.28 and near maximum triaxiality, γ = −28°, for ^111,113Rh. A K=1/2 band based on the 1/2⁺[431] intruder orbital with large deformation is seen in ^105,107Tc and ^111,113Rh with anomalous spaces where the 1/2, 5/2, … are above the 3/2, 7/2, … levels. Band crossings are seen in ^105,107,109Tc and ^111,113Rh with spin alignments that indicate the alignment of a h_11/2 neutron pair.

Many neutron hole and particle states were identified in ^93,95Sr by using the spontaneous fission of ²⁵²Cf and Gammasphere array. 21 and 20 new gamma transitions were observed in ⁹³Sr and ⁹⁵Sr, respectively. The level schemes of ⁹³Sr and ⁹⁵Sr are interpreted in part as the weak coupling of the 2d_5/2 neutron hole and 1g_7/2 neutron particle, respectively, to the excited configurations of ⁹⁴Sr core. Also, the shell model calculations have been done for comparison with the levels of ⁹³Sr. Half-lives (T_1/2) of several states which decay by delayed γ transitions were determined from time-gated triple γ coincidence method. We determined, for the first time, the half-life of 330.6+x state in ¹⁰⁸Tc and the half-life of 19/2⁻ state in ¹³³Te based on the new level schemes. Five half-lives of ^95,97Sr, ⁹⁹Zr, ¹³⁴Te and ¹³⁷Xe are consistent with the previously reported ones. These results indicate that this new method is useful for measuring the half-lives.

From the Brookhaven and Lawrence Berkeley National Laboratory Data Retrieval websites, we present new insights into shape coexistence in the Pt to Pb region. The phenomenon of shifted identical bands is now found in proton-rich nuclei in the Pt to Pb region. Shifted identical bands are bands of two neighboring nuclei differing by 2n, 2p, α, n, p, and other combinations, where the transition energies in the bands differ by the same constant fraction over a range of spins. Identical bands and SIBs are found above spins of 6⁺ in even-even nuclei or equivalent in odd-A nuclei, where the well-deformed structures become yrast with little mixing between the shape-coexisting structures. As an example, E_γ(¹⁸⁰Hg) = 1-0.022(⁺³₋₁)E_γ(¹⁸²Hg) from 6⁺ to 16⁺.

From prompt γ – γ – γ coincidence studies with a ²⁵²Cf source, the yrast levels were identified from 2⁺ to 16⁺ and 14⁺ in neutron-rich ^162,164Gd, respectively. Transition energies between the same spin states are higher and moments of inertia lower at every level in N = 100 ¹⁶⁴Gd than in N = 98 ¹⁶²Gd. The same trend is seen in ^164,166Dy. These observations are in contrast to the continuous decrease in the 2+ energy to a minimum at neutron midshell (N = 104) in Er, Yb, and Hf nuclei. The lowest known 2⁺ energy in this region now occurs for N = 96 ¹⁵⁶Nd and next for N = 98 ¹⁶⁰Sm, which are well removed from midshell for both protons and neutrons.

Some results for two distinct but complementary exactly solvable algebraic models for pairing in atomic nuclei are presented: 1) binding energy predictions for isotopic chains of nuclei based on an extended pairing model that includes multi-pair excitations; and 2) fine structure effects among excited 0⁺ states in N ≈ Z nuclei that track with the proton-neutron (pn) and like-particle isovector pairing interactions as realized within an algebraic sp(4) shell model. The results show that these models can be used to reproduce significant ranges of known experimental data, and in so doing, confirm their power to predict pairing-dominated phenomena in domains where data is unavailable.

Many-body effects associated with the coupling of particles and vibrations contribute in an important way to pairing correlations in finite nuclei.

The microscopic structure of the 14 low-lying excited 0⁺ states, observed recently in ¹⁵⁸Gd, is investigated within the quasiparticle-phonon model. The results are compared with the predictions by other approaches for a complete characterization of these states.

We studied in a microscopic multiphonon approach the proton-neutron symmetry and phonon structure of some low-lying states recently discovered in ⁹²Zr. We confirm the breaking of F-spin symmetry, but argue that the breaking mechanism is more complex than the one suggested in the original shell model analysis of the data. We found other new intriguing features of the spectrum, like a pronounced multiphonon fragmentation of the states and a tentative evidence of a three-phonon mixed symmetry state.

Starting from an effective Skyrme interaction we present a method to take into account the coupling between one- and two-phonon terms in the wave functions of excited states. The approach is a development of a finite rank separable approximation for the quasiparticle RPA calculations proposed in our previous work. The influence of the phonon-phonon coupling on energies and transition probabilities for the low-lying quadrupole in the neutron-rich Sn isotopes is studied.

A matrix element of the γ transition operator between the states of “quasiparticle ⊗ phonon” type is evaluated and analyzed. A contribution of transitions of this type to the total M2 and E3 transition probabilities between states of different structure in several odd-mass spherical nuclei is computed. A role of these transitions appears to be somewhat stronger for magnetic transitions than for electric ones. Their effect is much more pronounced if states with dominating components of “quasiparticle ⊗ phonon” type are involved in the γ transition.

We report on a microscopic study of the electromagnetic response in fast rotating nuclei undergoing backbending with special attention at the orbital M1 excitations known as scissors mode. We find that the overall strength of the orbital M1 transitions evolves with the rotational frequency in parallel with the nuclear moment of inertia and, eventually, gets enhanced by more than a factor four above the critical backbending region. The physical implications of this result are discussed.

The rare ternary fission (TF) process has been studied in a number of correlation experiments that have included registration of neutrons and γ-rays along with the light charged particles (LCPs) or coincident emission of two LCPs. Highly efficient detector setups have permitted, for the fission reactions ²⁵²Cf(sf) and ^233,235U(n_th,f), to identify the population of excited states in LCPs, the formation of neutron-unstable nuclei as short-lived intermediated LCPs, as well as the sequential decay of particle-unstable LCP species into charged particle pairs. Quaternary fission with an apparently independent emission of two charged particles has also been observed. The applied technologies are briefly summarized, and particular results are presented and discussed.

The deformation energy of actinides in the fusionlike deformation path has been determined from a generalized liquid drop model taking into account both the proximity energy, the asymmetry and an accurate nuclear radius and from the shell and pairing energies. Double and triple-humped potential barriers appear. The second maximum corresponds to the transition from compact and creviced one-body shapes to two touching ellipsoids. Third minimum and peak appear in certain asymmetric exit channels where one fragment is almost a double magic nucleus with a quasi-spherical shape while the other one evolves from oblate to prolate shapes. The heights of the double and triple-humped fission barriers agree with the experimental results. The predicted half-lives follow the experimental data trend.

As is well know, also if the exact energy spectrum of the triaxial rigid rotator cannot be analytically determined, the classical Hamiltonian of the triaxial top is integrable and depends only on two action variables. We use the classical integrability of the triaxial top to analytically calculate the semiclassical energy spectrum via torus quantization. We analyze the global (number of states and density of states) and the local (single energy levels and their fluctuations) properties by using both the semiclassical approximation and the exact diagonalization. The agreement betweeen exact and semiclassical global properties is excellent, while for single energy levels the agreement is not so good. Note that among the spectral fluctuations we have also investigated a new statistic recently proposed in Phys. Rev. Lett. 89, 244102 (2002).

Many complex systems in nature and in human society exhibit time fluctuations characterized by a power spectrum which is a power function of the frequency f. We show that the energy spectrum fluctuations of quantum systems can be formally considered as a discrete time series. The power spectrum behavior of such a signal for paradigmatic quantum systems suggests the following conjecture: The energy spectra of chaotic quantum systems are characterized by 1/f noise.

The phenomenon of super-radiance in quantum optics predicted by Dicke 50 years ago and observed experimentally has its counterparts in many-body systems on the borderline between discrete spectrum and continuum. The interaction of overlapping resonances through the continuum leads to the redistribution of widths and creation of broad super-radiant states and long-lived compound states. We explain the physics of super-radiance and discuss applications to weakly bound nuclei, giant resonances and widths of exotic baryons.

The problem of protein folding consists in understanding how the aminoacid sequence of a protein (primary structure) determines its unique, biological active equilibrium conformation (tertiary structure). By mean of simplified models, we explore the dynamical processes which are at the basis of the folding of model proteins and find a simple hierarchical mechanism which governs the folding phenomenon. Exploiting this result, it is possible not only to develop an algorithm to determine the equilibrium conformation of a protein from its sequence, that is to solve the protein folding problem provided one knows the interaction among the amino acids, but also to design a novel class of drugs which interfere with the folding mechanism and whose inhibitor effect cannot be neutralized through mutations, as it is the case with standard drugs acting, as a rule, on the active site of enzymes.

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