Investigation of the electronic structure of Be2+He and Be+He,and static dipole polarisabilities of the helium atom

The potential energy and spectroscopic constants of the ground and many excited states of the Be⁺He van der Waals system have been investigated using a one-electron pseudo-potential approach, which is used to replace the effect of the Be²⁺ core and the electron-He interactions by effective potentials. Furthermore, the core–core interactions are incorporated. This permits the reduction of the number of active electrons of the Be⁺He van der Waals system to only one electron. Therefore, the potential energy of the ground state as well as the excited states is performed at the SCF level and considering the spin–orbit interaction. The core–core interaction for Be²⁺He ground state is included using accurate CCSD (T) calculations. Then, the spectroscopic properties of the Be⁺He electronic states are extracted and compared with the previous theoretical and experimental studies. This comparison has shown a very good agreement for the ground and the first excited states. Moreover, the transition dipole moment has been determined for a large and dense grid of internuclear distances including the spin orbit effect. In addition, a vibrational spacing analysis for the Be²⁺He and Be⁺He ground states is performed to extract the He atomic polarisability.     

Structure studies of neutron-rich beryllium and carbon isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion induced transfer reactions. A strong sensitivity to the chosen core nucleus is found for the cores of ⁹Be and ¹⁰Be, respectively. With a ⁹Be core, molecular rotational bands up to high excitation energies are observed due to the pronounced 2α-cluster structure, whereas only few states at low excitation energies are populated with a ¹⁰Be core. For ¹¹Be a detailed investigation has been performed for the three states at 3.41 MeV, 3.89 MeV and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^? and 3/2^?, respectively. Furthermore we have studied particlehole states of ¹⁶C using the ¹³C(¹²C,⁹C)¹⁶C reaction and found 14 previously unknown states.     

Structure of neutron-rich Be and C isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion-induced transfer reactions. In neutron transfer reactions, the population of final states shows a strong sensitivity to the chosen core nucleus, i.e., the target nuclei ⁹Be or ¹⁰Be, respectively. Molecular rotational bands up to high excitation energies are observed with ⁹Be as the core due to its pronounced 2α-cluster structure, whereas only a few states at low excitation energies are populated with ¹⁰Be as the core. For ¹¹Be, a detailed investigation has been performed for the three states at 3.41, 3.89, and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^?, and 3/2^?, respectively. Furthermore, we have studied particle-hole states of ¹⁶C using the ¹³C(¹²C, ⁹C)¹⁶C reaction and found 14 previously unknown states. Using the ¹²C(¹²C, ⁹C)¹⁵C reaction, five new states were observed for ¹⁵C.     

Continuum shell-model calculation for 14C including core excitations

Elastic and inelastic cross sections for neutron scattering on ¹³C have been calculated up to 10 MeV including excitations of the ¹²C core. The core properties are taken from experiment while the additional neutrons are described in a shell-model basis. Antisymmetrization between the valence particles and the core is taken into account as a second-order perturbation effect. All results including those for the target and the bound states of ¹⁴C are compared to experimental data. The differences between a gaussian and a δ interaction for the valence particles is investigated. The calculation was only feasible with a modified continuum shell model, i.e. approximating the single-particle resonances by bound states. The remaining modified continuum states are damped in amplitude within the resonance region. The residual interaction between modified continuum states is neglected.     

Efimov effect in 2-neutron halo nuclei

This paper presents an overview of our theoretical investigations in search of Efimov states in light 2-neutron halo nuclei. The calculations have been carried out within a three-body formalism, assuming a compact core and two valence neutrons forming the halo. The calculations provide strong evidence for the occurrence of at least two Efimov states in ²⁰C nucleus. These excited states move into the continuum as the two-body (core-neutron) binding energy is increased and show up as asymmetric resonances in the elastic scattering cross-section of the n-¹⁹C system. The Fano mechanism is invoked to explain the asymmetry. The calculations have been extended to ³⁸Mg, ³²Ne and a hypothetical case of a very heavy core (A = 100) with two valence neutrons. In all these cases the Efimov states show up as resonances as the two-body energy is increased. However, in sharp contrast, the Efimov states, for a system of three equal masses, show up as virtual states beyond a certain value of the two-body interaction.     

Proton-neutron interactions in nuclei withA∼90

An extension of the cluster-(quadrupole-octupole) phonon model is proposed for nuclei withA～90 to describe simultaneously positive- and negative-parity states, in which quadrupole as well as octupole vibrations of the⁸⁸Sr core are allowed. The cluster states include particle and particle-hole core excitations. The residual interaction is a delta-function force with spin-spin exchange plus a quadrupole-quadrupole force. The model is applied to⁸⁷Sr,⁸⁹Sr,⁸⁸Y, and⁹⁰Y nuclei. For each case, energy levels, spectroscopic factors, and electromagnetic properties are calculated and compared with experiment.     

Ab initio study of spectroscopic properties of the calcium hydride molecular ion

In the present work, all adiabatic potential energy curves, spectroscopic constants and dipole moments of CaH⁺ molecular ion dissociating below the ionic limit Ca²⁺H⁻ are presented. These curves are determined by an ab initio approach involving a non-empirical pseudo-potential for the Ca core, core-valence correlation accounted in operator form with two types of core polarization potentials (CPP) and full valence Configuration Interaction. The molecule is thus treated as a two-electron system. The potential energy curves and the spectroscopic constants are presented. In addition, the permanent and transition dipole moments are calculated for most of the states and reveal the underlying ionic states. A rather good agreement with the available theoretical works in the literature is obtained for the spectroscopic constants of the lowest states of the CaH⁺ molecule.     

Origin of three-body resonances

We expose the relation between the properties of the three-body continuum states and their two-body subsystems. These properties refer to their bound and virtual states and resonances, all defined as poles of the S-matrix. For one infinitely heavy core and two non-interacting light particles, the complex energies of the three-body poles are the sum of the two two-body complex pole-energies. These generic relations are modified by center-of-mass effects which alone can produce a Borromean system. We show how the three-body states evolve in ⁶He, ⁶Li, and ⁶Be when the nucleon-nucleon interaction is continuously switched on. The schematic model is able to reproduce the main properties in their spectra. Realistic calculations for these nuclei are shown in detail for comparison. The implications of a core with non-zero spin are investigated and illustrated for ¹⁷Ne ( ¹⁵O + p + p). Dimensionless units allow predictions for systems of different scales.     

Low-energy spectrum of one-neutron halo nucleus 11Be

We investigate the low-energy spectrum of the one-neutron halo nucleus ¹¹Be using the complex scaled coupled channel method for a ¹⁰Be + n model, paying attention to the effects of the deformation of the ¹⁰Be-core and the Pauli principle between the core and a valence neutron. For positive parity states of ¹¹Be, our calculation well reproduces the experimental results, but for negative parity states, not so well. With reducing the coupling between the core deformation and a valence neutron, the negative parity levels of the ¹¹Be nucleus are much improved.     

β delayed emission of a proton by a one-neutron halo nucleus

Some one-neutron halo nuclei can emit a proton in a β decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core + neutron bound state and final core + proton scattering states. The decay probability per second is evaluated for the ¹¹Be, ¹⁹C and ³¹Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.     

Neutron-proton transfer reactions leading toT=1 particle-hole states of56Co

Zero range DWBA analysis for two-particle (neutron and proton) transfer reactions is carried out, using simple shell model structure wave functions for⁵⁴Fe,⁵⁶Co and⁵⁸Ni, with⁵⁶Ni inert core. In this structure calculation, a microscopic set of two-body interaction matrix elements derived from the non-local separable potential of Tabakin are employed. These matrix elements include in the perturbation theory two corrections (i) the second-order Börn term and (ii) the appropriate core excitations. Unlike the situation in many two-particle transfer reactions, the fragmentation of the reaction strengths to the excited states with respect to the lowest states of same spin and parity in the above transfer processes is satisfactorily borne out from this analysis.     

Calculation of Be in an α-α-Λ Three-Body Model Using the Faddeev Equations

 The hypernucleus Be is investigated in an α-α-Λ three-body model using the Faddeev formalism. We use an α-α interaction in which the Pauli-forbidden states are correctly taken into account and we employ some phenomenological potentials between the α and Λ particles. We obtained two bound states for and , and three resonance states of . We studied the properties of these states by calculating the components and the expectation values of the potential for each partial wave. It is found that a few channels dominate in the α (α, Λ) and states, so that the alpha-clusters or the ⁸Be core are still alive in the nucleus. In a case where the two alpha particles are fixed on an axis the contour plots of the distribution of the Λ particle are shown. With the assistance of these plots one can visually understand that some of them are shell-model-like states while others are well developed cluster-model-like states. For the structure of Be, it is concluded that the Λ particle is loosely coupled in S- and P-wave orbits about the ⁸Be(0⁺) and ⁸Be(2⁺) core states. Finally, we discuss a redundant state in the Faddeev amplitude which could arise from the treatment of symmetrization. Received June 25, 1998; revised April 13, 1999; accepted for publication December 29, 1999     

Quasi-relativistic treatment of the low-lying KCs states

The potential energy curves, permanent and transition dipole moments as well as spin-orbit and angular coupling matrix elements between the KCs electronic states converging to the lowest three dissociation limits were evaluated in the basis of the spin-averaged wavefunctions corresponding to pure Hund’s coupling case (a). The quasi-relativistic matrix elements have been obtained for a wide range of internuclear distance by using of small (9-electrons) effective core pseudopotentials of both atoms. The core-valence correlation has been accounted for a large scale multi-reference configuration interaction method combined with semi-empirical core polarization potentials. The static dipole polarizabilities of the ground X¹Σ⁺ and a³Σ⁺ states were extracted from the closed-shell coupled-cluster energies by the finite-field method. Among the singlet and triplet Σ⁺ states manifold the pronounced avoided crossing effect between repulsive walls of the (2,3)³Σ⁺ states has been discovered and analyzed by finite-difference calculation of radial coupling matrix elements. The resulting transition dipole moments and potentials were used to predict radiative lifetimes and emission branching ratios of excited vibronic states while the calculated angular coupling matrix elements were transformed to Λ-doubling constants of the (1,2)¹Π states and magnetic g-factor of the ground state. The accuracies of the present results are discussed by comparing with experimental data and preceding calculations.     

Study of Pt isotopes in the core excited interacting boson model 1

The core exited IBM model was applied to the Pt isotopes. It was found that the energy spectra of the high-spin states as well as those of the low-spin states can be reproduced quite well. Also, it was found that there is a structure transition between ¹⁸⁶Pt and ¹⁸⁸Pt. The B(E2) values of ¹⁸⁴Pt were calculated and compared with recent experimental data. It was found that the general features of the B(E2) values can be reproduced qualitatively. The need of more boson core excitations is also discussed.     

Photoionization cross sections of Fe XXI

Total and partial photoionization cross sections for (Fe XXI+hν→Fe XXII+e) are presented for the ground and excited bound states with n?10 and l?9. Fe XXI is prevalent in high-temperature astrophysical plasmas as well as in photoionized plasmas excited by hard X-rays. Results are reported for the first time for the high-energy photoionization with core excitations to n=2,3 states. Details of photoionization, especially the high-energy features that often dominate considerably over the low energy ones, are illustrated. These prominent features will affect the photoionization and the recombination rates in high-temperature plasmas. Calculations are carried out in the close coupling (CC) approximation using the R-matrix method. A large CC wavefunction expansion for Fe XXII which includes the ground and 28 excited core states from n=2 and 3 complexes and spans over a wide energy range is used. A total of 835 discrete bound states of Fe XXI in the singlet, triplet, and quintet symmetries are obtained. Total photoionization cross sections, σ_PI(nLS), for ionization into all 29 states are presented for all 835 final bound states and partial photoionization cross sections, σ_PI(g,nLS), for ionization into the ground ²P⁰ state of the core are presented for 685 states. While the n=2 core excitations are at relatively lower energy range (within 15 Ry from the ionization threshold), the n=3 excitations lie at considerably higher energy, 73 Ry and above, yet introduce resonant features and enhancements more prominent than those of n=2 states. Larger numbers of resonances are formed due to Rydberg series of autoionizing states converging on to the 29 core states. However, most noticeable structures are formed in the excited state cross sections by the photoexcitation-of-core (PEC) resonances in the photon energy range of 73-82 Ry. All these high-energy features are absent in the currently available results. The present results should enable more accurate modeling of the emission spectrum of highly excited plasma from the optical to far-ultraviolet region.     

Radii of the bound states in 16N from the asymptotic normalization coefficients

The asymptotic normalization coefficients (ANCs) of the virtual decay ¹⁶N→¹⁵N+n are extracted from the ¹⁵N(⁷Li, ⁶Li)¹⁶N reaction populating the ground and first three excited states in ¹⁶N. The root-mean-square (rms) radii of the valence neutron in these four low-lying ¹⁶N states are then derived by using the ANCs. The probabilities of the valence neutron staying out of the core potentials are found to be 31%±8%, 58%±12%, 32%±8%, and 60%±12%. The present results support the conclusion that a one-neutron halo may be formed in the ¹⁶N first and third excited states, while the ground and second excited states do not have a one-neutron halo structure. However, the core excitation effect has a strong influence on the one-neutron halo structure of the ground and first excited states in ¹⁶N.     

A microscopic calculation for n-3H scattering

Starting from a nucleon-nucleon soft core potential, the³H-n scattering states were calculated in the refined cluster model framework. Phase shifts and angular distributions resulting from these calculations are compared with experiments and agree well. In all states except theJ ^π=1^? state the coupling of channels is extremely small, but in this state considerable spin-mixing is found.     

Evidence for localized excitations in MgO from electron energy-loss spectroscopy

The excited electronic states in the ionic crystal MgO have been studied by electron energy-loss spectroscopy. Structure observed above the thresholds for excitation from the Mg 2p, 2s and 1s core levels shows the final states to be predominantly excitonic levels of the Mg²⁺ ion. Comparison with the known states of the Mg²⁺ free ion indicates that solid-state shifts and splittings are small.     

Intermediate coupling model description of55Fe and57Fe

The properties of the negative parity states of⁵⁵Fe and⁵⁷Fe are investigated in the framework of the intermediate coupling model. In the model, a neutron or a quasineutron is coupled to anharmonic vibrations of the core. Anharmonicities of the vibrations are estimated through the observed properties of the core. Energy levels, spectroscopic factors and electromagnetic properties have been calculated. The results of the present calculations are also compared with available experimental results and other theoretical results. The model reasonably accounts for many of the properties of the low-lying states.