Mean field with tensor force and shell structure of exotic nuclei

Effects of the Tensor Force on the Ground Properties of Zr Isotopes

The effects of the tensor force on the ground properties of Zr isotopes are studied in the framework of the Skyrme–Hartree–Fock approach. It is found that the tensor force strongly affects the ground state energies and the geometric symmetry properties, in particular for those isotopes near N=60 region. The effects are attributed to the fact that the tensor force enlarges the spin and pseudospin symmetry breaking and therefore results in a ∼2 MeV sub-shell gap between d3/2 and s1/2 single-particle levels.

Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of ^{110}Zr

The first measurement of the low-lying states of the neutron-rich ^{110}Zr and ^{112}Mo was performed via in-beam γ-ray spectroscopy after one proton removal on hydrogen at ∼200  MeV/nucleon. The 2_{1}^{+} excitation energies were found at 185(11) keV in ^{110}Zr, and 235(7) keV in ^{112}Mo, while the R_{42}=E(4_{1}^{+})/E(2_{1}^{+}) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of ^{110}Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z=40 and N=70. The present data also invalidate predictions for a tetrahedral ground state symmetry in ^{110}Zr.

Microscopic theory of nuclear fission: a review

This article reviews how nuclear fission is described within nuclear density functional theory. A distinction should be made between spontaneous fission, where half-lives are the main observables and quantum tunnelling the essential concept, and induced fission, where the focus is on fragment properties and explicitly time-dependent approaches are often invoked. Overall, the cornerstone of the density functional theory approach to fission is the energy density functional formalism. The basic tenets of this method, including some well-known tools such as the Hartree-Fock-Bogoliubov (HFB) theory, effective two-body nuclear potentials such as the Skyrme and Gogny force, finite-temperature extensions and beyond mean-field corrections, are presented succinctly. The energy density functional approach is often combined with the hypothesis that the time-scale of the large amplitude collective motion driving the system to fission is slow compared to typical time-scales of nucleons inside the nucleus. In practice, this hypothesis of adiabaticity is implemented by introducing (a few) collective variables and mapping out the many-body Schrödinger equation into a collective Schrödinger-like equation for the nuclear wave-packet. The region of the collective space where the system transitions from one nucleus to two (or more) fragments defines what are called the scission configurations. The inertia tensor that enters the kinetic energy term of the collective Schrödinger-like equation is one of the most essential ingredients of the theory, since it includes the response of the system to small changes in the collective variables. For this reason, the two main approximations used to compute this inertia tensor, the adiabatic time-dependent HFB and the generator coordinate method, are presented in detail, both in their general formulation and in their most common approximations. The collective inertia tensor enters also the Wentzel-Kramers-Brillouin (WKB) formula used to extract spontaneous fission half-lives from multi-dimensional quantum tunnelling probabilities (For the sake of completeness, other approaches to tunnelling based on functional integrals are also briefly discussed, although there are very few applications.) It is also an important component of some of the time-dependent methods that have been used in fission studies. Concerning the latter, both the semi-classical approaches to time-dependent nuclear dynamics and more microscopic theories involving explicit quantum-many-body methods are presented. One of the hallmarks of the microscopic theory of fission is the tremendous amount of computing needed for practical applications. In particular, the successful implementation of the theories presented in this article requires a very precise numerical resolution of the HFB equations for large values of the collective variables. This aspect is often overlooked, and several sections are devoted to discussing the resolution of the HFB equations, especially in the context of very deformed nuclear shapes. In particular, the numerical precision and iterative methods employed to obtain the HFB solution are documented in detail. Finally, a selection of the most recent and representative results obtained for both spontaneous and induced fission is presented, with the goal of emphasizing the coherence of the microscopic approaches employed. Although impressive progress has been achieved over the last two decades to understand fission microscopically, much work remains to be done. Several possible lines of research are outlined in the conclusion.

Spins and magnetic moments of 49K and 51K: establishing the 1/2+ and 3/2+ level ordering beyond N = 28

The ground-state spins and magnetic moments of (49,51)K have been measured using bunched-beam high-resolution collinear laser spectroscopy at ISOLDE CERN. For 49K a ground-state spin I = 1/2 was firmly established. The observed hyperfine structure of 51K requires a spin I > 1/2 and strongly suggests I = 3/2. From its magnetic moment μ(51K) = +0.5129(22)μ(N) a spin-parity I(π) = 3/2+ with a dominant π1d(3/2)(-1) hole configuration was deduced. This establishes for the first time the reinversion of the single-particle levels and illustrates the prominent role of the residual monopole interaction for single-particle levels and shell evolution.

Impact of tensor force on β decay of magic and semimagic nuclei

The effect of the tensor force on β decay is studied in the framework of the proton-neutron random phase approximation with the Skyrme force. The investigation is performed for even-even semimagic and magic nuclei, (34)Si, (68,78)Ni, and (132)Sn. The tensor correlation induces strong impact on the low-lying Gamow-Teller state. In particular, it improves the β-decay half-lives. Q and ft values are also investigated and compared with experimental data.

Exploring the low-Z shore of the island of inversion at n=19

The technique of invariant mass spectroscopy has been used to measure, for the first time, the ground state energy of neutron-unbound (28)F, determined to be a resonance in the (27)F+n continuum at 220(50) keV. States in (28)F were populated by the reactions of a 62 MeV/u (29)Ne beam impinging on a 288 mg/cm(2) beryllium target. The measured (28)F ground state energy is in good agreement with USDA/USDB shell model predictions, indicating that pf shell intruder configurations play only a small role in the ground state structure of (28)F and establishing a low-Z boundary of the island of inversion for N=19 isotones.

Effect of the tensor force on the charge exchange spin-dipole excitations of 208Pb

The charge exchange spin-dipole (SD) excitations of 208Pb are studied by using a fully self-consistent Skyrme Hartree-Fock plus random phase approximation formalism which includes the tensor interaction. It is found, for the first time, that the tensor correlations have a unique, multipole-dependent effect on the SD excitations; that is, they produce a softening of 1{-} states, but a hardening of 0{-} and 2{-} states. This paves the way to a clear assessment of the strength of the tensor terms. We compare our results with a recent measurement, showing that our choice of tensor terms improves the agreement with experiment. The robustness of our results is supported by the analytic form of the tensor matrix elements.

Evidence for a change in the nuclear mass surface with the discovery of the most neutron-rich nuclei with 17<or=Z<or=25

The results of measurements of the production of neutron-rich nuclei by the fragmentation of a 76Ge beam are presented. The cross sections were measured for a large range of nuclei including 15 new isotopes that are the most neutron-rich nuclides of the elements chlorine to manganese (50Cl, 53Ar, ;{55,56}K, ;{57,58}Ca, ;{59,60,61}Sc, ;{62,63}Ti, ;{65,66}V, 68Cr, 70Mn). The enhanced cross sections of several new nuclei relative to a simple thermal evaporation framework, previously shown to describe similar production cross sections, indicates that nuclei in the region around 62Ti might be more stable than predicted by current mass models and could be an indication of a new island of inversion similar to that centered on 31Na.

Development of large deformation in 62Cr

The structure of neutron-rich isotopes 60Cr and 62Cr was studied via proton inelastic scattering in inverse kinematics. The deformation lengths (delta) for 60Cr and 62Cr were extracted as 1.12(16) and 1.36(14) fm, respectively, providing evidence for enhanced collectivity in these nuclei. An excited state at 1180(10) keV in 62Cr was identified for the first time. We adopted 4;{+} as its spin and parity, leading to the rapid increase of the Ex(4;{+})/E_{x}(2;{+}) ratio, which indicates the development of large deformation in 62Cr near N=40. Importance of the admixture of the gd-shell component above N=40 is also discussed by comparing with a modern shell model calculation.

Evolution of the N=50 shell gap energy towards 78Ni

Atomic masses of the neutron-rich isotopes (76-80)Zn, (78-83)Ga, (80-85)Ge, (81-87)As, and (84-89)Se have been measured with high precision using the Penning trap mass spectrometer JYFLTRAP at the IGISOL facility. The masses of (82,83)Ga, (83-85)Ge, (84-87)As, and 89Se were measured for the first time. These new data represent a major improvement in the knowledge of the masses in this neutron-rich region. Two-neutron separation energies provide evidence for the reduction of the N=50 shell gap energy towards germanium (Z=32) and a subsequent increase at gallium (Z=31). The data are compared with a number of theoretical models. An indication of the persistent rigidity of the shell gap towards nickel (Z=28) is obtained.

First measurement of the giant monopole and quadrupole resonances in a short-lived nucleus: 56Ni

The isoscalar giant monopole resonance (GMR) and giant quadrupole resonance (GQR) have been measured in the 56Ni unstable nucleus by inducing the 56Ni(d,d') reaction at 50A MeV in the Maya active target at the GANIL facility. The GMR and GQR centroids are measured at 19.3+/-0.5 MeV and 16.2+/-0.5 MeV, respectively. The corresponding angular distributions are extracted from 3 degrees to 7 degrees . A multipole decomposition analysis using distorted wave Born approximation with random phase approximation transition densities shows that both the GMR and the GQR exhaust a large fraction of the energy-weighted sum rule. The demonstration of this new method opens a broad range of giant resonance studies at intermediate-energy radioactive beam facilities.

Coulomb excitation of neutron-rich Zn isotopes: first observation of the 2(1)+ state in 80Zn

Neutron-rich, radioactive Zn isotopes were investigated at the Radioactive Ion Beam facility REX-ISOLDE (CERN) using low-energy Coulomb excitation. The energy of the 2(1)+ state in 78Zn could be firmly established and for the first time the 2+ --> 0(1)+ transition in 80Zn was observed at 1492(1) keV. B(E2,2(1)+ --> 0(1)+) values were extracted for (74,76,78,80)Zn and compared to large scale shell model calculations. With only two protons outside the Z=28 proton core, 80Zn is the lightest N=50 isotone for which spectroscopic information has been obtained to date. Two sets of advanced shell model calculations reproduce the observed B(E2) systematics. The results for N=50 isotones indicate a good N=50 shell closure and a strong Z=28 proton core polarization. The new results serve as benchmarks to establish theoretical models, predicting the nuclear properties of the doubly magic nucleus 78Ni.

Selective population and neutron decay of an excited state of 23O

We have observed a resonance in neutron-fragment coincidence measurements that is presumably the first excited state of 23O at 2.8(1) MeV excitation energy which decays into the ground state of 22O. This interpretation is consistent with theory. The reaction mechanism supports the assignment of the observed state as the 5/2+ hole state. This assignment and the recently observed 3/2+ particle state advance the understanding of 23O.

Single-neutron states in (101)Sn

The first data on the relative single-particle energies outside the doubly magic (100)Sn nucleus were obtained. A prompt 171.7(6) keV gamma-ray transition was correlated with protons emitted following the beta decay of (101)Sn and is interpreted as the transition between the single-neutron g(7/2) and d(5/2) orbitals in (101)Sn. This observation provides a stringent test of current nuclear structure models. The measured nug(7/2)-nud(5/2) energy splitting is compared with values calculated using mean-field nuclear potentials and is used to calculate low-energy excited states in light Sn isotopes in the framework of the shell model. The correlation technique used in this work offers possibilities for future, more extensive spectroscopy near (100)Sn.