Ca Ground State Research Articles

Theory ofCa10Cr7O28as a bilayer breathing-kagome magnet: Classical thermodynamics and semiclassical dynamics

Ca$_{10}$Cr$_7$O$_{28}$ is a novel spin-$1/2$ magnet exhibiting spin liquid behaviour which sets it apart from any previously studied model or material. However, understanding Ca$_{10}$Cr$_7$O$_{28}$ presents a significant challenge, because the low symmetry of the crystal structure leads to very complex interactions, with up to seven inequivalent coupling parameters in the unit cell. Here we explore the origin of the spin-liquid behaviour in Ca$_{10}$Cr$_7$O$_{28}$, starting from the simplest microscopic model consistent with experiment - a Heisenberg model on a single bilayer of the breathing-kagome (BBK) lattice. We use a combination of classical Monte Carlo (MC) simulation and (semi-)classical Molecular Dynamics (MD) simulation to explore the thermodynamic and dynamic properties of this model, and compare these with experimental results for Ca$_{10}$Cr$_7$O$_{28}$. We uncover qualitatively different behaviours on different timescales, and argue that the ground state of Ca$_{10}$Cr$_7$O$_{28}$ is born out of a slowly-fluctuating "spiral spin liquid", while faster fluctuations echo the U(1) spin liquid found in the kagome antiferromagnet. We also identify key differences between longitudinal and transverse spin excitations in applied magnetic field, and argue that these are a distinguishing feature of the spin liquid in the BBK model.

Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula * *Supported by the National Natural Science Foundation of China (U1731238, 11761161001, 11105079, 11535004, 11375086, 11975167, 12035011), the Science and Technology Development Fund (FDCT) of Macau (020/2014/A1, 008/2017/AFJ, 0042/2018/A2), the Science and Technology Foundation of Guizhou Province ((2016)4008, (2017)5726-37) and the foundation of Guizhou Provincial education Department (KY(2020)003)

A systematic analysis on experimental data of the half-lives of nuclear double- decays with two neutrinos ( ) is performed based on the analytical formula proposed by Primakoff and Rosen. We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor. This improved formula can closely describe all available experimental half-lives of decays, both for ground-state transitions and transitions from ground states of parent nuclei to the first excited states of daughter nuclei. The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an average factor of 2.3. Further predictions are provided for -decay candidates with decay energies above 0.5 MeV. We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double- transitions between the ground state of Ca, Ge, and Xe and the first excited states of their corresponding daughter nuclei, which will be very useful for understanding the underlying mechanisms of double- decays and for further studying the shell effects on nuclear transition matrix elements.

Tuning magnetic properties of CrS2 monolayer by doping transition metal and alkaline-earth atoms

In view of important role of inducing the magnetism in semiconducting transition metal dichalcogenides monolayer, the influences of a series of transition metal and alkaline-earth dopants, including Ca, Sc, Ti, V, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Cd and In, on the electronic and magnetic properties of semiconducting CrS2 monolayer are systematically investigated using first-principles calculations. The calculations show that Nb, Mo, Ru and Rh dopants cannot induce the magnetism in doped CrS2 monolayer, whereas ground states of Ca, Sc, Ti, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Pd, Ag, Cd and In-doped system are magnetic and the stability of magnetic state of V doped system is small. Furthermore the value and the distribution of the magnetic moment induced by dopant not only relate to the number of valence electrons and the occupancy of the d orbitals of dopant, but also depend on the hybridization between dopant and its neighboring S and Cr atoms. Note that it is found that the substitutional doping at the Cr site of CrS2 monolayer with numerous transition metal and alkaline-earth atoms should be possible under the Cr-poor growth conditions. Overall, the calculated results show high potential for inducing the magnetism in CrS2 monolayer by doping at the Cr site.

Ground-state electromagnetic moments of calcium isotopes

High-resolution bunched-beam collinear laser spectroscopy was used to measure the optical hyperfine spectra of the $^{43-51}$Ca isotopes. The ground state magnetic moments of $^{49,51}$Ca and quadrupole moments of $^{47,49,51}$Ca were measured for the first time, and the $^{51}$Ca ground state spin $I=3/2$ was determined in a model-independent way. Our results provide a critical test of modern nuclear theories based on shell-model calculations using phenomenological as well as microscopic interactions. The results for the neutron-rich isotopes are in excellent agreement with predictions using interactions derived from chiral effective field theory including three-nucleon forces, while lighter isotopes illustrate the presence of particle-hole excitations of the $^{40}$Ca core in their ground state.

Three-photon resonances due to autoionizing states incalcium

In the present study we have investigated three-photon ionization inCa in which autoionizing states are engaged. The two-photon resonantprocess (from the Ca ground state 4s2 1S0) occurredthrough or at least in the vicinity of one of the following states:4s4d 1D2, 4p2 3P2, 4s6s 1S0, 4p2 1D2 and 4p2 1S0, with the third photon either reachingthe continuum directly or one of the autoionizing states. The three-photonresonant transitions to 3dmp, mf: 1P1, 3P1 and 3D1 autoionizing states for m up to 21 have beenobserved. Some of the autoionizing resonances which we have found hadnot been observed before in a high-resolution one-photon absorptionexperiment (for J = 1) and in multiphoton experiments (for J = 3). We have compared the ionization signal as a function of thelaser detuning and the laser intensity with theoretical curvesobtained within a simple model (three-level atom + one-mode laserfield). This gives information about the order of magnitude of thethree-photon ionization probability through autoionizing states.

Level Energies and Oscillator Strengths for Fine-Structure Transitions from the 3s23p5 2P Ground State of Ca IV

Configuration interaction wavefunctions have been calculated and used to evaluate oscillator strengths from the ground state levels to those of the 3s3p6, 3s23p43d and 3s23p44s of Ca IV, in both LS and LSJ coupling schemes. The calculated excited energies are in close agreement with measurement. Small adjustment to the diagonal elements of the Hamiltonian matrices are made to further bring calculated energy separations between the levels as close as possible to the measured values. The present results are compared with other available calculations and experiments.

Theoretical investigation of the Ca +–N 2 and Ca 2+–N 2 complexes

The structures, harmonic frequencies and binding energies for the ground states of Ca +–N 2 and Ca 2+–N 2 are computed at several theoretical levels, including Møller–Plesset second-order perturbation with full electron correlation and density functional theory. The charge–quadrupole interaction yields linear geometries as minima for both complexes, while the C 2v geometries are transition states. At the MP2 level, Ca +–N 2 has a dissociation energy ( D e) of 5.3 kcal/mol and a Ca +–N bond distance of 2.78 Å. Ca 2+–N 2 has a dissociation energy ( D e) of 23.8 kcal/mol and a shorter metal–ligand bond of 2.48 Å.

Isospin mixing in37K and spin decomposition of Gamow-Teller strength in37Ca decay

We measured ${}^{36}$Ar$(p\ensuremath{\rightarrow}{,p}_{0})$ cross sections and analyzing powers for ${E}_{p}$ between 3.22 and 5.98 MeV, and used these data to deduce spin, parity, and widths of 17 levels in ${}^{37}$K. Our results, combined with existing information on ${}^{37}$Ca ${\ensuremath{\beta}}^{+}$ decay, yield information on the distribution of Fermi and Gamow-Teller strength in this decay. A $T=1/2$ level lying 31 keV below the ${J}^{\ensuremath{\pi}}{=3/2}^{+}$, $T=3/2$ analog of the ${}^{37}$Ca ground state was found to have ${J}^{\ensuremath{\pi}}{=3/2}^{+}$. The relative proton widths of the two levels imply an isospin-mixing matrix-element of $4.84\ifmmode\pm\else\textpm\fi{}0.43$ keV. This agrees with the value ${5.93}_{\ensuremath{-}0.65}^{+0.23}$ keV extracted from the ${\ensuremath{\beta}}^{+}$-decay intensities to the two levels, plus the Gamow-Teller to Fermi strength ratio for the 5018 keV level. We decompose the Gamow-Teller strength in ${}^{37}$Ca decay into components feeding daughter levels with ${J}^{\ensuremath{\pi}}{=1/2}^{+}$, ${3/2}^{+}$, or ${5/2}^{+}$, and compare the results to theory. None of the available shell-model calculations gives a satisfactory account of the data.

Large-scale collisional energy transfer in laser-pumped metastable Ca atoms: Excitation of resonance states of Ca II

We report the first experimental observation of the excitation of the 4p2P3/2, 1/2 resonance states of Ca II (located at 74 720.4 and 74 497.5 cm−1 above the ground state of Ca I) following pulsed-laser pumping of the 4s21SO−4s4p3P1 intercombination transition of Ca I (Eex = 15 210 cm−1). Large scale collisional transfer of energy between the laser-excited atoms is believed to be responsible for this. This is possibly because sufficient time is available (τrad of the 4s4p3P1 state is approximately 350 µs) for collisions to build such a high level of excitation. Some interesting additional features of the fluorescence spectra of the laser-pumped Ca vapor, such as temperature dependence of the fluorescence intensities and evolution in time of some selected states, are also presented.

Role of some selected intermediate states of Ca I in the collisional excitation of 4p 2P states of Ca II in a laser-pumped Ca vapour

The role of some intermediate states, e.g. 4s5p 3P, 3d4p(1D,3F) of Ca I in the collisional excitation of the 4p 2P3/2,1/2 states of Ca II (located at 74720.35 and 74497.46 cm-1 above the ground state of Ca I) following pulsed-laser pumping of the 4s4p 3P1 state of Ca I (Eex=15210.063 cm-1), is investigated. A 'pump' and 'probe' technique is employed together with the study of fluorescent emission. The 'probe' laser selectively prepares a substantially higher population of a specific intermediate state in Ca I and the increase in the fluorescent intensity of the 4p 2P3/2 - 4s 2S1/2 transition of Ca II is read as the relative strength of the particular collision channel utilizing that intermediate state. It is found that the 3d4p 1D2 state has the strongest influence.

Experimental and MCHF isotope shifts of strongly perturbed levels in Ca I and Sr I

Theoretical and experimental isotope shifts for Ca I and Sr I levels are presented. The isotope shifts of the levels 4s6s 1S0, 4p2 1S0 and 4p2 1D2 of calcium have been measured between the isotopes 40, 42, 43, 44 and 48 in two-photon transitions from the Ca ground state using two lasers with different wavelengths. Results of ab initio mass and field shift calculations are presented for these levels as well as for a number of other strongly perturbed low-lying levels in calcium and strontium using the multiconfiguration Hartree-Fock method. The 'gradient' and the alternative 'Slater' forms of the specific mass shift operator have been tested; the latter is found to be unreliable with the MCHF expansions which are limited to valence correlation effects.

Photoionization of the ground state of singly ionized calcium

Calculations of the absolute photoionization cross section of the ground state of Ca+ (3p64s2Se) have been performed over the energy range above the first ionization threshold up to a photon energy of 3.2 Ryd, using the R-matrix method. The core excited states in the form 3p5nl (nl=4s, 4p, 3d and 4d, where 4d is a pseudo-orbital) have been included in the R-matrix expansion. The corresponding Rydberg series of resonances have been analysed and compared with experimental data. The LS coupling scheme has been used throughout and relativistic effects have been neglected.

Evidence for proton ground state correlations in48Ca

In a high resolution48Ca(d,3He) experiment at 80 MeV evidence has been found for a 7/2− state at 1.97 MeV in47K with a spectroscopic factor of C2S=0.08 corresponding to a ~4% admixture of πf2(s,d)−2 configurations in the ground state of Ca.

Ground state and excited state sputtering Doppler-shift laser-fluorescence studies of Cr and Ca targets

The recently much debated problem of excited state sputtering has been investigated for Cr and Ca targets using Doppler-shift laser-fluorescence spectroscopy (DSLFS). Using this sensitive and level selective method, sputtered densities for Ca and Cr atoms in the electronic ground and excited metastable states have been investigated as a function of oxygen background pressure. Furthermore, their velocity distributions have been measured for increasing oxygen coverage. In general the population of the ground state during sputtering of Cr and Ca decreases drastically by a factor greater than 50 for Cr or 20 for Ca, respectively, when the clean target is exposed to an oxygen partial pressure between 5×10−8 and 1×10−6 Torr. At the same time the maximum of the velocity distribution shifts from about 2 km/s to values between 3 and 5 km/s for Cr as well as for Ca. Thus, the velocity distribution of the Ca ground state becomes similar to the one obtained for metastable states of Ca. In addition, the light of short-lived excited states produced during the sputtering process has been monitored for different transition lines of Ca and Cr for different oxygen pressures. A quartz microbalance was used to monitor relative sputtering yields as a function of the oxygen partial pressure. For high oxygen coverage the total sputtering yield for Ca and Cr decreases by a factor of about 3. The contribution of charged particles remains below 20%. The majority of sputtered products are molecules or clusters.

RECENT PROGRESS IN THE STUDIES OF ATOMIC IONIZATION PROCESSES INVOLVING SYNCHROTRON AND LASER RADIATIONS

This paper reviews recent results obtained in photoelectron spectrometry studies carried out on atoms with the synchrotron radiation emitted by the ACO storage ring in Orsay, combined, in some cases, with the use of a cw tunable dye laser. Photoionization from the ground state of Ca and He and from laser excited sodium atoms serves to illustrate the present status of the experimental studies in atomic photoionization.

A theoretical investigation of the origins of the green and red spectra of Ca 2

The potential energy curves and transition moments of the ground state of Ca 2 and 1Σ + u states correlating with the 1S + 1P and 1S + 1D calcium atoms have been calculated. The calculations support the assignment of the observed emission spectra of Ca 2 in the red and in the green to transitions between the ground state and the 1,2 1Σ + u states. Predissociation of the 1 1Σ + u state is also shown to be possible from an interaction with the 1 3Π u state.

Hyperfine structure of the X 2Σ+ ground state of Ca 35Cl and Ca 37Cl by molecular-beam, laser-rf double resonance

The hyperfine structure of the X 2Σ+ state of Ca 35Cl and Ca 37Cl, unresolved in previous studies, has been investigated in detail by the molecular-beam, laser-rf, double-resonance technique. Results for the spin-rotation interaction and the dipole and quadrupole hfs constants are given in the form of Dunham coefficients so that the N\ and v\ dependence of each constant can be explicitly exhibited. The results, after dividing out the purely nuclear effects, fall between the corresponding values for CaF and CaBr, as expected.

Reactions of metastable calcium 3P: quenching by Ca( 1S), Mg 1S) and inert gases

Rate constants have been measured (by laser induced fluorescence) for the quenching of metastable Ca( 3P) by the ground states of Ca and Mg and by the inert gases. Rate constants for the metals were considerably larger than for the inert gases. The cross sections for the inert gases are well correlated by an orbiting model.

Correlation in thens2S1ground states of Ca, Sr, Ba, Zn, Cd, and Hg as determined by multiconfiguration Hartree-Fock calculations and photoelectron spectroscopy

On the basis of improved multiconfiguration Hartree-Fock calculations for the ground states of Ca, Sr, Ba, Zn, Cd, and Hg it is confirmed that recent photoelectron satellite spectra obtained by S\"uzer, Lee, and Shirley do require for the interpretation of the observed satellite intensities knowledge of more than just the ground-state composition. The relevant dipole matrix elements between initial and final states are also needed. It is noticed that photoelectron spectroscopy allows the observation of the relaxation of atomic orbitals on a time scale determined by the kinetic energy of the photoelectron.

Spin-Parity Assignments of the 49Sc Levels from the Gamma-Decay of the 3/2- Isobaric Analogue State In 49Sc

Gamma ray spectra and the angular distributions for the 1975 keV resonance, which is the strongest of the seven resonances associated with the 49 Ca ground state analogue in the 48 Ca( p , γ) reaction, have been measured with Ge(Li) detector. Gamma-gamma coincidence spectra have also been measured to confirm the decay scheme. To identify the transitions between the low-lying states, gamma rays from the 48 Ca( d , n γ) 49 Sc reaction have been measured at E d =3.0 MeV. Spins and parities of some of the levels in 49 Sc as well as the tentative gamma decay scheme have been determined from these data with the aids of previous reaction data.