Li States Research Articles

Independently Optimized Orbital Sets in GRASP—The Case of Hyperfine Structure in Li I

In multiconfiguration Dirac–Hartree–Fock (MCDHF) calculations, there is a strong coupling between the localization of the orbital set and the configuration state function (CSF) expansion used to determine it. Furthermore, it is well known that an orbital set resulting from calculations, including CSFs describing core–core correlation and other effects, which aims to lower the weighted energies of a number of targeted states as much as possible, may be inadequate for building CSFs that account for correlation effects that are energetically unimportant but decisive for computed properties, e.g., hyperfine structures or transition rates. This inadequacy can be traced in irregular or oscillating convergence patterns of the computed properties as functions of the increasing orbital set. In order to alleviate the above problems, we propose a procedure in which the orbital set is obtained by merging several separately optimized, and mutually non-orthogonal, orbital sets. This computational strategy preserves the advantages of capturing electron correlation on the total energy through the variational MCDHF method and allows to target efficiently the correlation effects on the considered property. The orbital sets that are merged are successively orthogonalized against each other to retain orthonormality. The merged orbital set is used to build CSFs that efficiently lower the energy and also adequately account for the correlation effects that are important for the property. We apply the procedure to compute the hyperfine structure constants for the 1s22s2S1/2 and 1s22p2P1/2,3/2o states in 7Li and show that it leads to considerably improved convergence patterns with respect to the increasing orbital set compared to standard calculations based on a single orbital set, energy-optimized in the variational procedure. The perspectives of the new procedure are discussed in a broader context in the summary.

Fast neutron inelastic scattering from 7Li

The inelastic scattering of fast neutrons from 7Li nuclei was investigated at the nELBE neutron-time-of-flight facility. The photon production cross section of 478 keV γ-rays from the first excited state of 7Li was determined by irradiating a disc of LiF with neutrons of energies ranging from 100 keV to about 10 MeV. The target position was surounded by a setup of 7 LaBr3 scintillation detectors and 7 high-purity germanium detectors to detect the de-excitation γ-rays. A 235U fission chamber was used to determine the incoming neutron flux. The number of detected photons was corrected for the detection efficiency, multiple scattering and the time-of-flight dependent data acquisition dead time. The preliminary results show reasonable agreement with some previous measurments but are about 15 % below the recent data taken at the GELINA facility.

Study of spin-isospin responses of radioactive nuclei with the background-reduced neutron spectrometer, PANDORA

The status of a project to measure spin-isospin responses of neutron drip-line nuclei using a new low-energy neutron detector, PANDORA (Particle Analyzer Neutron Detector Of Real-time Acquisition), is reported. The performance of PANDORA was characterized by the 6He(p,n)6Li reaction in inverse kinematics at the HIMAC facility in Chiba. Observation of the strong transition to the ground state in 6Li is discussed. Preliminary results of 11Li(p,n)11Be and 14Be(p,n)14B experiments in inverse kinematics at RI Beam Factory (RIBF) of RIKEN Nishina Center are also presented including the exotic decay channel of 11Be→9Li + d. Details of the experimental setup based on PANDORA and the SAMURAI large-acceptance magnetic spectrometer, as well as the combined data-acquisition system are described. The neutron-gamma discrimination capability of PANDORA was evaluated, Figure-of-Merit (FoM) values higher than those found in the literature for similar materials were derived from experimental data.

Inelastic scattering of fast neutrons on 6Li and 7Li nuclei in three-body cluster model

The systematic approach to calculating cross section of inelastic neutron scattering on 6Li and 7Li nuclei in the range of kinetic energies En=0.1−20 MeV is presented. The reaction mechanism is described using the Faddeev equations within the problem of neutron interaction with two clusters which form the target nucleus bound state. The length anLi of elastic n−Li scattering are calculated. The coherence effect on n5Li and αd contributions to 6Li nucleus ground state is demonstrated by the example of elastic neutron scattering reaction. Total and differential cross sections of inelastic neutron scattering on 6Li and 7Li nuclei with formation of three and four particles in the final state are calculated. Three-body interaction of clusters which form the target nucleus ground state in 6Li(n,n′)dα and 7Li(n,n′α)t reactions is shown to be of great importance.

Precise measurement of hyperfine structure in the 3S1/2 state of 7Li

We report a precise measurement of hyperfine structure in the 3S1/2 state of the odd isotope of Li, namely 7Li. The state is excited from the ground 2S1/2 state (which has the same parity) using two single-photon transitions via the intermediate 2P3/2 state. The value of the hyperfine constant we measure is A = 93.095(52) MHz, which resolves two discrepant values reported in the literature measured using other techniques. Our value is also consistent with theoretical calculations.

Effect of breakup and resonance states of6Li on fusion

CDCC calculations of total fusion cross sections are presented for reactions of the weakly bound6Li with targets144Sm and154Sm at energies around the Coulomb barrier. Couplings to the low-lying excited states 2+, 3− of144Sm and 2+, 4+ of154Sm are included in the calculations. In the cluster structure frame of6Li → α + d, short range absorption potentials are considered for the interactions between α- and d- with the target to account for fusion. The effect of the excited states of the target on total fusion is investigated, as well as, that from couplings of resonance states of6Li, namely, l = 2, Jπ = 3+, 2+, 1+. The latter effect is calculated by two different approaches, (a) by considering only resonance states couplings and (b) by omitting these states from the full discretized energy space. Among other things, it is found that resonance and non-resonance continuum couplings give rise to small and similar fusion suppression at the higher energies.

Emergence of Simple Patterns in Complex Atomic Nuclei from First Principles

We study the structure of low-lying states in 6Li, 6He, 8Be, 8B, 12C, and 16O, using ab initio symmetry-adapted no-core shell model. The results of our study demonstrate that collective modes in light nuclei emerge from first principles. We investigate the impact of the symmetry-adapted model space on spectroscopic properties and, in the case of the ground state of 6Li, on elastic electron scattering charge form factor. The results confirm that only a small symmetry-adapted subspace of the complete model space is needed to accurately reproduce complete-space observables and the form factor momentum dependence.

Elastic and inelastic scattering of 14N ions by 7Li at 80 MeV (c.m. 26.7 MeV)

New angular distribution data for 7Li + 14N elastic and inelastic scattering at the energy $ E_{lab}$ $({}^{14}N) = 80$ MeV (c.m. 26.7MeV) are presented. The data were analyzed within the optical model and the coupled-reaction-channels method using a channels-coupling scheme that included the 7Li and 14N inelastic scattering channels, spin reorientations of 7Li and 14N as well as most important transfer reactions. The low-energy excited states of 7Li and 14N were assumed to be collective in nature. The 7Li + 14N potential parameters as well as deformation parameters of 7Li and 14N were deduced. The 7Li + 14N potential and the data were compared with those of 6Li + 14N to observe isotopic differences. The enhanced large-angle elastic and inelastic scattering data are shown to have a large contribution from the ground-state reorientation of 7Li.

Spatial periphery of lithium and beryllium isotopes

The spatial structure of the periphery of lithium and beryllium isotopes is studied by means of charge-exchange reactions and the (t, p) and (d, p) reactions on their nuclei. It is shown that the 0+ isobaric-analog state of 6Li at 3.56 MeV has a halo structure formed by a proton and a neutron, that there is virtually no manifestation of a neutron halo in the ground state of the 9Li nucleus, and that the 11Li nucleus has a Borromean halo structure that two neutrons form with respect to the 9Li core and which manifests itself in cigar and dineutron configurations. The 10Be nucleus has a substantial two-neutron periphery in either configuration both in the ground and in the 2+ excited state at 3.37MeV.

Characteristics of d + α Bound and Resonant States from Analytic Continuation of the Effective-Range Expansion

In the present work one- and two-channel approaches using the expansion of the effective-range function K(E) in powers of energy E are applied to obtain the asymptotic normalization coefficients (ANCs) and vertex constants (VCs) for the d + α system. The coefficients of the K(E) expansion are found by fitting the dα phase shifts. By analytic continuation of K(E) thus obtained to the corresponding poles the ANCs and VCs for D wave dα resonances with Jπ = 1+, 2+, 3+ are calculated for the first time. The 1+-resonance and the bound state of 6Li (Jπ = 1+) are considered jointly in the two-channel (S + D) effective-range approach and the ANCs and VCs for the ground 6Li state are found.

Spatial periphery of lithium isotopes

The spatial structure of lithium isotopes is studied with the aid of the charge-exchange and (t, p) reactions on lithium nuclei. It is shown that an excited isobaric-analog state of 6Li (0+, 3.56MeV) has a halo structure formed by a proton and a neutron, that, in the 9Li nucleus, there is virtually no neutron halo, and that 11Li is a Borromean nucleus formed by a 9Li core and a two-neutron halo manifesting itself in cigar-like and dineutron configurations.

Study of the Isospin Mixing in 6Li with α + p + n Three-Body Model

We calculate the isospin mixing probabilities for both T = 0 and T = 1 states of 6Li systematically, and compare them to clarify the relation between the structure of 6Li and the isospin mixing probabilities. As a result, the effect of halo structure on the isospin mixing cannot be seen clearly. The effect of the coupling to the continuum states such as of 5He + p and 5Li + n is suggested.

Frequency stabilization of multiple lasers and Rydberg atom spectroscopy

In this paper we report details of the apparatus and experimental techniques used to excite Rydberg states of 7Li using multiple diode lasers. Special attention is paid to frequency stabilization of the lasers and we show how three lasers can be stabilized using the fluorescence from a single atomic state. Laser spectroscopy of the 8p,9p, and 11p–15p states is then performed to determine the quantum defects of these states. Our measurement precision exceeds that of previous measurements of these defects by as much as a factor of 25. This work substantially extends our previous measurement of the 10p quantum defect, and we compare our measured defects with recent theoretical calculations for the np states across the range 8≤n≤15. The agreement with theory is excellent.

Neutron Spectroscopic Factors of 7Li and Astrophysical 6Li(n,γ)7Li Reaction Rates

Angular distributions of the 7Li(6Li, 6Li)7Li elastic scattering and the 7Li(6Li, 7Lig.s.)6Li, 7Li(6Li, 7Li0.48)6Li transfer reactions at Ec.m. = 23.7 MeV are measured with the Q3D magnetic spectrograph. The optical potential of 6Li + 7Li is obtained by fitting the elastic scattering differential cross sections. Based on the distorted wave Born approximation (DWBA) analysis, spectroscopic factors of 7Li = 6Li ⊗ n are determined to be 0.73 ± 0.05 and 0.90 ± 0.09 for the ground and first exited states in 7Li, respectively. Using the spectroscopic factors, the cross sections of the 6Li(n, γ0, 1)7Li direct neutron capture reactions and the astrophysical 6Li(n, γ)7Li reaction rates are derived.

Double-Differential Neutron Emission Cross-Section Measurements of 6Li and 7Li at Incident Neutron Energies of 8.17 and 10.27 MeV

Energy angular neutron emission double-differential cross sections (DDXs) of 6Li and 7Li were measured at incident neutron energies of 8.17 and 10.27 MeV, respectively, using normal and normal + abnormal fast neutron time-of-flight (TOF) spectrometers. The effects of breakup neutrons from a D(d,n) source and the influence of an aluminum container of Li samples, as well as 7Li in the 6Li sample and 6Li in the 7Li sample, on the secondary neutron spectra were eliminated. The data were derived by comparing the net TOF spectra with the calculated spectra using a realistic Monte Carlo simulation. The differential cross sections were determined by comparing the measured and simulated TOF spectra with respect to specific scattering fractions, i.e., with respect to the elastic lines and the resolved inelastic lines related to single levels or level groups, and normalized to n-p scattering. The angular distributions for the 6Li and 7Li elastic and inelastic neutron scattering were obtained also. The angle-integrated cross sections were derived for elastic scattering from 6Li and for the sum of elastic and 0.478-MeV state inelastic scattering from 7Li. Inelastic scattering cross sections were obtained for the 2.186-MeV state in 6Li and the 4.652-MeV state in 7Li. Meanwhile, based on the unified Hauser-Feshbach and exciton model, the calculated results of the DDXs for n + 6,7Li were compared with measurements.

Improved molecular constants for low vibrational levels of the [formula omitted] state of 7Li 2

We report new high resolution spectroscopic data for the lowest vibrational levels v = 0–3 for the F ( 4 ) 1 Σ g + state of 7Li 2. A new ab initio potential energy curve, that covers a wide range of internuclear distance, is also reported.

Application of direct potential fitting to line position data for the [formula omitted] and [formula omitted] states of Li 2

A collection of 15 222 spectroscopic Li 2 line positions, all with measurement precision in the range 0.005–0.02 cm −1, and which sample 99.97 and 99.98% of the A and X state well depths, respectively, have been employed in a direct least squares fit of the effective potential energy and Born–Oppenheimer breakdown functions for the two states. The fully analytical potential function for the A state of 6Li 2 is determined out to R ≈ 55 Å, well into the long-range region. For the three isotopologues, 6Li 2, 6Li 7Li, and 7Li 2, most of the data are comprised of rotationally resolved transitions in the A– X system recorded by Fourier transform spectroscopies. For 6Li 2 and 7Li 2, complementary fluorescence data are also included for high vibrational levels of both the A and X states. The reduced standard deviation of the fit was close to unity, indicating that the quantum mechanical eigenvalues calculated from the analytical functions of the Hamiltonians of the two states, which are described by a total of only 45 fitted parameters, represent the line positions, on average, to within the estimated uncertainties. The dissociation energies for 6Li 2 are estimated precisely as D e( X) = 8516.74(1) cm −1 and D e( A) = 9351.96(1) cm −1.

Isobaric analog states of neutron-rich nuclei. Doppler shift as a measurement tool for resonance excitation functions

We present a new approach for the measurement of resonance excitation functions of neutron-rich nuclei using Doppler shift information. Preliminary data from the first application of the method is presented in the spectroscopy studies of 7He isobaric analog states in 7Li.

Sequential decay reactions induced by a 18 MeV 6He beam on 6Li and 7Li

The 6He + 6Li and 6He + 7Li reactions have been studied using a 18 MeV 6He radioactive beam and a highly efficient and segmented detector set-up. Triple coincidence events corresponding to the 6He + 6Li → 6He + α + d , 6He + 6Li → 2 α + t + n and 6He + 7Li → 6He + α + t reactions have been clearly observed. The dominant mechanism of these reactions has been found to be a sequential decay through the known cluster states in 6Li, 7Li, 8Be, 9Be and 10Be. In particular, the sequential α-decay of the 10Be state at E x = 7.54 MeV has been observed although its decay energy is much smaller (130 keV) than the decay energy for neutron emission (730 keV). Furthermore, the 10Be state at E x ≈ 10.2 MeV has been found to be strongly populated in the reactions with both used targets. Angular correlations analysis of the events corresponding to the 10.2 MeV state α-decay suggests the 4 + assignment. Both of these observations indicate a special, well-developed 6He+ α cluster structure of the 10Be states involved. The structure of several low-lying 9Be states is also discussed.

Spectroscopy of 6Li using the ³He(7Li, alpha)6Li reaction

The spectroscopic study of unbound states in the 6Li nucleus was performed by measuring the energy spectrum of the alpha-particles emitted from the transfer reaction ³He(7Li, alpha)6Li. The 7Li beam at E Lab = 31.2MeV was produced at the São Paulo Pelletron accelerator. A ³He gas cell was used as target. alpha-Particle spectra were measured from thetaLab = 8º up to thetaLab = 20º with steps of 1º. Due to its positive Q = +13.3MeV, the ³He(7Li, alpha)6Li reaction favours the population of states in 6Li at high excitations energies up to about 20MeV. We observed resonances at 17.29MeV, 15.31MeV, and a new state at 12.45MeV, in addition to all previously known states of 6Li. An <FONT FACE=Symbol>Â</FONT>-Matrix analysis was performed and the positions and widths of these states were extracted.