International Journal of Modern Physics E

Our previous experimental method and results of (EC+β⁺) decay for the medium-heavy nuclei ¹⁵³Er, ¹⁵⁷Yb, ²⁰⁹Fr, ¹²⁸Ce, ¹³⁰Ce, ¹²⁸Pr, ¹³⁰Pm and ¹⁴⁰Tb have been briefly summarized. The observed low-lying states in their daughter nuclei and a 11/2^- isomeric state in ¹³³Pr have been reviewed in a systematic way and compared with different model calculations. Finally, some questions have been put forward for further study and discussion.

This paper outlines some of the physics opportunities available with the GSI RISING active stopper and presents preliminary results from an experiment aimed at performing beta-delayed gamma-ray spectroscopic studies in heavy-neutron-rich nuclei produced following the projectile fragmentation of a 1 GeV per nucleon ²⁰⁸Pb primary beam. The energy response of the silicon active stopping detector for both heavy secondary fragments and beta-particles is demonstrated and preliminary results on the decays of neutron-rich Tantalum (Ta) to Tungsten (W) isotopes are presented as examples of the potential of this technique to allow new structural studies in hitherto experimentally unreachable heavy, neutron-rich nuclei. The resulting spectral information inferred from excited states in the tungsten daughter nuclei are compared with results from axially symmetric Hartree–Fock calculations of the nuclear shape and suggest a change in ground state structure for the N = 116 isotone ¹⁹⁰W compared to the lighter isotopes of this element.

High-spin states of ¹⁶⁰Tm are studied via in-beam gamma-ray spectroscopy. Previously known rotational bands are confirmed. These bands feed into low-lying states which are enriched in this work. A four-quasiparticle band with configuration of πg_7/2 ⊗ νh_9/2 ⊗ ν(i_13/2)² is established. Signature splitting features of πh_11/2⊗νi_13/2 and πh_11/2⊗νh_9/2 bands are presented.

We apply a simple barrier penetration approach to calculate α-decay branching ratios to members of ground-state rotational band of heavy even-even nuclei. The influence of α-decay energy, the angular momentum of α-particle, and the excitation probability of the daughter nucleus is taken into account in our calculations. The theoretical branching ratios of α-transitions are found to agree with the available experimental data well.

We review the recent progress of theoretical researches on heavy nuclei and superheavy nuclei. At first we analyze the experimental data of long lifetime heavy nuclei and discuss their stability. Then the calculated binding energies and alpha-decay energies of heavy and superheavy nuclei from different models are compared and discussed. This includes the results from the local binding energy formula of heavy nuclei with Z ≥ 90 and N ≥ 130, those from the relativistic mean-field model, and from other models. For the local binding energy formula, it can reproduce experimental binding energies of known heavy and superheavy nuclei well. The relativistic mean-field model and non-relativistic mean-field model show that there is shape coexistence in superheavy nuclei. For some superheavy nuclei, superdeformed prolate shape can be their ground states and there are isomers in lowly excited states due to shape coexistence. The properties of some unknown superheavy nuclei are predicted. Some new views on the stability and on half-lives of heavy and superheavy nuclei are presented. Possible new phenomenon in superheavy region is analyzed and discussed.

The excited states of some odd A nuclei near the stability line have been systematically investigated from light to intermediate mass with the spherical relativistic mean field (RMF) model. The ratio between the valence nucleon root-mean-square (RMS) radius and the core rms radius, the separation energy and the density distribution have been deduced as signatures for halo or skin structure. We have presented the scaling laws of the ratio of valence particle rms radii and square-potential radii versus the scaled separation energies. The probability for a valence particle being out of the binding potential has also been extracted. We proposed a relaxed necessary condition for nuclear halo occurrence.

The fusion process of ⁴⁸Ca induced reactions is studied with the two-step model. In this model, the fusion process is devided into two stages: first, the sticking stage where projectile and target come to the touching point over the Coulomb barrier from infinite distance, and second, the formation stage where the di-nucleus formed with projectile and target evolve to form the spherical compound nucleus from the touching point. By the use of the statistical evaporation model, the residue cross sections for different neutron evaporation channels are analyzed. From the results, optimum reactions are given to synthesize Z=117 element with ⁴⁸Ca induced reactions.

Based on the improved isospin dependent molecular dynamics model in which the shell correction energy of the system is calculated by using deformed two-center shell model and the surface energy of the system is improved by introducing a switch function that combines the surface energies of projectile and target with the one of the compound nucleus. The effects of the shell correction energy on synthesis of superheavy nuclei and the fusion cross sections in asymmetric and nearly symmetric reaction systems leading to the same compound nuclei ⁶²Zn, ⁷⁶Kr, and ²⁰²Pb are studied. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, Coulomb barriers and fusion cross sections. The experimental data are described quantitatively by the present model. It is found that the compound nucleus formation is favorable for the systems with larger mass asymmetry.

The ground state properties of Hs nuclei were studied to give an overview to the isotope chain. It is seen that more stable isotopes are located on the proton abundant side of the chain. The last stable nucleus to the proton drip line is ²⁵⁶Hs. The most stable unknown Hs nucleus may be ²⁶⁸Hs. The proton Fermi surfaces of Hs nuclei are close to zero, the conventional BCS treatment with constant pairing interaction can excite protons to the continuum, and causes the failure for pairing correction. The density dependent delta interaction results in more reasonable single-particle energy level distributions and nucleon occupation. Therefore it has improved the BCS treatment, and is available to describe the properties of nuclei in the superheavy region.

We introduce a no-core full configuration (NCFC) approach and present results for ⁴He, ¹²C, ¹⁴F and some other nuclei with the realistic NN interaction, JISP16. We obtain ground state energies and their uncertainties through exponential extrapolations that we demonstrate are reliable in ⁴He where fully converged results are obtained. We find ¹²C is overbound by 1.7 MeV and we predict the yet-to-be-measured binding energy of ¹⁴F to be 70.2±3.5 MeV. The extrapolated spectrum of ¹⁴F is in reasonable agreement with known features of the ¹⁴B spectrum. Distinctions are drawn between this approach and the no-core shell model (NCSM).

We summarize recent efforts to develop an angular-momentum-conserving variant of the Density Matrix Renormalization Group method into a practical truncation strategy for large-scale shell model calculations of atomic nuclei. Following a brief description of the key elements of the method, we report the results of test calculations for ⁴⁸Cr and ⁵⁶Ni. In both cases we consider nucleons limited to the 2p-1f shell and interacting via the KB3 interaction. Both calculations produce a high level of agreement with the exact shell-model results. Furthermore, and most importantly, the fraction of the complete space required to achieve this high level of agreement goes down rapidly as the size of the full space grows.

The symplectic no-core shell model (Sp-NCSM) is described. The theory is applied to a study of the structure of ¹²C and ¹⁶O. Results from a full 6ħΩ NCSM calculation for low-lying states in these nuclei using a realistic nucleon-nucleon interaction are found to project at approximately the 90% level onto a few of the leading 0p-0h and 2p-2h symplectic representations. The results are nearly independent of the oscillator strength parameter and whether bare or renormalized effective interactions are used in the analysis. The Sp-NCSM model space is typically only a very small fraction (under 1%) of the NCSM space, and grows slowly with increasing ħΩ. The comparisons with NCSM results suggest either the effective nucleon-nucleon interaction possesses a heretofore unappreciated symmetry, namely Sp(3,R) and the complementary (spin-isospin) supermultiplet symmetry, or the nuclear many-body system acts as a filter that allows the symplectic symmetry to propagate in a coherent way into the many-body dynamics while tending to dampen out symplectic symmetry breaking terms. Also, since the Sp-NCSM is a multi-ħΩ generalization of the Elliott SU(3) model, the results obtained to date reaffirm the relevance of SU(3) to atomic nuclei.

The spontaneously broken reflection and axial symmetries in the nuclear mean field and their necessary restorations in the laboratory frame are described in a natural way in the triaxial Reflection Asymmetric Shell Model. This recently developed theoretical model has been applied to explore the possibility that some superheavy nuclei may have an exotic shape, tetrahedral-like. The ground state band and the partner low-lying negative parity bands are calculated for the Cf isotopes and the results are in a good agreement with the available experimental data. The tetrahedral symmetry, realized at the first order with the nonaxial octupole Y₃₂ deformation, plays an important role for understanding the low-lying band structures in transfermium and superheavy nuclei, but it is significantly obscured by the competing quadrupole deformation as well as the axial octupole component. The calculated reduced E3 transition probabilities between the low lying 2^–-band states and the ground band states show a large enhancement of the nonaxial octupole collectivity.

The projected shell model (PSM) in its original version is an efficient shell model truncation scheme for well deformed nuclei. However, the model is applicable only to rotational motion, but not collective vibrations. In this paper, we discuss a scheme that extends the PSM applicability to low-lying rotational and vibrational states possibly in all kinds of heavy nuclei (from deformed via transitional to spherical), thus rendering it to be a more general multi-major-shell shell model for heavy nuclei. Three known types of vibration (β, γ, and scissors-mode) are discussed.

The K-mixing effect is investigated for triaxial deformation through the angular momentum projection technique. The mathematical nature of the norm overlap kernels is discussed in terms of the Fourier analysis. A relation between the signature symmetry and the K quantum number is discussed. A non-cranked Hartree-Fock state is shown to be a K=0 dominating state. The spread of the K distribution happens in a symmetrical manner and the K-mixing is enhanced as triaxial deformation is enlarged. On the contrary, the J=0 component is contained only slightly against a naive expectation.

The isotope dependence of the deformation in carbon and neon isotopes is studied in deformed Skyrme Hartree–Fock model. We find that the deformations of C and Ne isotopes have a strong isotope dependence as a manisfestation of spontaneous breaking effect in nuclear physics. By extending the deformed Skyrme Hartree–Fock model, we studied the properties of Λ hypernuclei in a broad mass region. The results suggest that the core nuclei and the corresponding hypernuclei have similar deformations with the same sign. Some light single-Λ hypernuclei are substantially deformed and the Λ binding energy is modified by the deformation.

The ground state bands observed in even-even transfermium nuclei ²⁵⁰Fm and ^252,254No are investigated by the cranked shell model with the particle-number conserving treatment for the monopole and quadrupole pairing correlations. The experimental variations of the kinematic moment of inertia with rotational frequency are reproduced very well in our calculation. Our results show bankbendings of at ħω ≈ 0.275 and 0.300 MeV in ²⁵²No and ²⁵⁴No, respectively. The detailed information about the contribution to alignment from each cranked single particle level exhibits that the backbending is mainly due to the rapidly aligned angular momentum of proton 1j_15/2 [770]1/2 pairs and neutron 2h_11/2 [761]3/2, 1j_15/2 [734]9/2 pairs the band crossing.

We focus on exotic structure and dynamics of N ≃ Z nuclei in the A ~ 80 mass region described within the complex Excited Vampir variational approach. We report on the effect of isospin-symmetry breaking on the superallowed Fermi β decay of the ground state of ⁸²Nb to ⁸²Zr. Results on the analog as well as non-analog β decay branches are self-consistently obtained. The ⁸²Nb→⁸²Zr β decay to the first two excited 0⁺ states with significant strength is predicted to coexist with the superallowed decay. The structure and electromagnetic properties of the low- and high-spin isobaric analog states in ⁸²Nb and ⁸²Zr are presented and compared with the available experimental data. The influence of shape coexistence and mixing on the Gamow–Teller strength distributions for the β⁺ decay of the ground state as well as the lowest-excited states in ⁷²Kr to the 1⁺ states in the beta window in ⁷²Br are self-consistently described using a rather large model space and realistic effective interactions. Predictions concerning the β decay half-life of the first excited 0⁺ state of ⁷²Kr relevant for the rp-process are presented.

We present a brief introduction of the nucleon pair approximation (NPA) of the shell model in this paper. We review our recent calculated results which include level spectra and electromagnetic properties of low-lying states, by applying the NPA to even-even nuclei and to odd-A nuclei. We also apply this method to a few schematic systems such as single-j shell, to investigate the validity of SD-pair truncation of the shell model.

A nucleon-pair shell model was proposed in 1993 by J. Q. Chen. Due to the success of the interacting boson model, the full shell model space in the nucleon-pair shell model was truncated to SD-pair subspace, called SD-pair shell model. Within this model, the experimental spectra in medium-weight and heavy nuclei, limiting cases in the interacting boson model, phase transitions, etc. can be reproduced approximately.

We report our research work on the equation of state (EOS) and single-particle (s.p.) properties of neutron-rich nuclear matter within the framework of the Brueckner–Bethe–Goldstone approach extended to include a microscopic three-body force (TBF). We show that inclusion of the TBF provide a largely improvement of the predicted nuclear matter saturation properties and leads to a strongly stiffening of the density dependence of symmetry energy at high densities. The neutron effective mass turns out to be greater than the proton one in neutron-rich nuclear matter in both cases of including and not including the TBF. The TBF induces a strongly repulsive rearrangement contribution to nucleon s.p. potential at high densities and large momenta. The TBF rearrangement contribution reduces considerably the attraction of the neutron and proton s.p. potentials and enhances strongly their momentum-dependence at high densities and high momenta. The TBF effect on nucleon superfluidity in neutron star matter has also been discussed.

Low-frequency modes of excitation in deformed neutron-rich nuclei are studied by the use of the deformed quasiparticle-random-phase approximation (QRPA) based on the coordinate-space Hartree–Fock–Bogoliubov formalism. We investigate the microscopic structure of the low-lying K^π = 0⁺ modes in neutron-rich Mg, Cr and Fe isotopes. It is found that the spatially extended structure of neutron quasiparticle wave functions around the Fermi level brings about a striking enhancement of the transition strengths. It is also found that the fluctuation of the pairing field plays an important role in generating coherence among two-quasiparticle excitations of neutron. Recent progress towards the self-consistent deformed QRPA calculation using the Skyrme density functional is also presented.

We investigate analytically and numerically a random-matrix model for m fermions occupying ℓ₁ single-particle states with positive parity and ℓ₂ single-particle states with negative parity and interacting through random two-body forces that conserve parity. The single-particle states are completely degenerate and carry no further quantum numbers. We compare spectra of many-body states with positive and with negative parity. We show that in the dilute limit defined by 1 « m « ℓ₁, ℓ₂, ground states with positive and with negative parity occur with equal probability. Differences in the ground-state probabilities are, thus, a finite-size effect and are mainly due to different dimensions of the Hilbert spaces of either parity.

Originally, random matrix theory (RMT) was designed by Wigner to deal with the statistics of eigenvalues and eigenfunctions of complex many-body quantum systems in 1950s. During the last two decades, the RMT underwent an unexpected and rapid development: The RMT has been successfully applied to an ever increasing variety of physical problems, and it has become an important tool to attack many-body problems. In this contribution I briefly outline the development of the RMT and introduce its basics. Its application to the decay out of a Superdeformed band and a comparison of the approach used in Ref. 34 with that proposed by Vigezzi et al are presented. Current theoretical activities on the decay out problem are reviewed, and the influence of the degree of chaoticity of the normally deformed states on the decay out intensity is examined systematically.

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

Spectral distribution theory, based on average-fluctuation separation and trace propagation, is applied in the analysis of some properties of a system of m (identical) nucleons in shell model j-orbits with random interactions preserving angular momentum J-symmetry. Employing the bivariate Gaussian form with Edgeworth corrections for fixed E (energy) and M (J_z eigenvalue) density of states ρ(E,M), analytical results, in the form of expansions to order [J(J+1)]², are derived for energy centroids E_c(m,J) and spectral variances σ²(m,J). They are used to study distribution of spectral widths, J=0 preponderance in energy centroids, lower order cross correlations in states with different J's and so on. Also, an expansion is obtained for occupation probabilities over spaces with fixed M. All the results obtained with spectral distribution theory compare well with those obtained recently using quite different methods. In addition, using trace propagation methods, a regular feature, that they are nearly constant, of spectral variances generated by random interactions is demonstrated using several examples. These open a new window to study regular structures generated by random interactions.

Functional dependences of eigenvalues as functions of sorted diagonal elements are given for realistic nuclear shell model (NSM) hamiltonian, the uniform distribution hamiltonian and the GOE hamiltonian. In the NSM case, the dependence is found to be linear. We discuss extrapolation methods for more accurate predictions for low-lying states.

In this paper we study robustness of strong correlation between eigenvalues and diagonal matrix elements sorted from the smallest to the largest, in the presence of large single-particle splittings for both realistic and schematic systems. We also study the nearest level spacing distribution obtained by the linear correlation.

We have reviewed the study on the signatures of shape phase transition in even-even nuclei and investigated the statistical properties of the E(5) and X(5) symmetries and their location in the Casten's triangle and the effect of some modes of nucleon-nucleon interaction on the nuclear shape phases and their transitions. We show that the ratios of the E2 transition rates and the ratio of the energies of state and the state can serve as the effective order parameters not only identifying the nucleon number driven phase transition but also distinguishing the first order one form the second order one. Our calculations show that the states in E(5) and X(5) symmetries are almost regular ones and the X(5) symmetry may actually locate at the middle of the "AW arc" inside the Casten's triangle and the E(5) symmetry at the U(5)-O(6) chain. Our study also indicates that strong or weak monopole-pair interaction leads to a vibration or an axially oblate deformation. While quadrupole-pair and QQ interactions induce deformations. Then a complete shape phase structure of nucleus is given in a study at nucleon level.

The exchange interactions proper to the proton-neutron version of the interacting boson-fermion-fermion model are derived from the proton-neutron quadrupole-quadrupole interaction. The influence of the exchange interactions on the F-spin content of wave functions is analysed for a typical odd-odd nucleus.

Exact solutions of Nilsson mean-field plus various type of pairing interactions are briefly reviewed. Some even-odd mass differences and moment of inertia of low-lying states for rare earth and actinide nuclei calculated in nearest-orbit pairing and extended pairing models and comparison with the corresponding experimental data are shown. An exact boson mapping of the reduced BCS pairing Hamiltonian is reported. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping.

A review of recent advances in the theoretical analysis of nuclear mass models and their predictive power is presented. After introducing two tests which probe the ability of nuclear mass models to extrapolate, three models are analyzed in detail: the liquid drop model (LDM), the liquid drop model plus empirical shell corrections (LDMM) and the Duflo–Zuker mass formula (DZ). The DZ model is exhibited as the most predictive model. The Garvey–Kelson mass relations are also discussed. It is shown that their fulfillment probes the consistency of the most commonly used mass formulae, and that they can be used in an iterative process to predict nuclear masses in the neighborhood of nuclei with measured masses, offering a simple and reproducible procedure for short range mass predictions.