cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.1012103.v1
title: Energy levels (in Ry) of the target states of Ne<sup>3 +</sup> and comparison with available NIST data [37]

description: <b>Table 1.</b> Energy levels (in Ry) of the target states of Ne<sup>3 +</sup> and comparison with available NIST data [37]. The values with superscript '*' are deduced from the experimental results of the x-ray emission spectrum [38]. <strong>Abstract</strong> A close-coupling calculation is performed for the photoionization cross section of the high-lying core-excited state 1s2s<sup>2</sup>2p<sup>5</sup> <sup>1</sup>P<sup>o</sup> of Ne<sup>2 +</sup> in the energy region of the double <em>K</em>-vacancy resonance 1s<sup>0</sup>2s<sup>2</sup>2p<sup>6</sup> <sup>1</sup>S. The calculation is carried out by using the <em>R</em>-matrix method in the <em>LS</em>-coupling scheme, which includes 27 target states and extensive configuration interaction. The <em>KK</em>-<em>KL</em> x-ray energy, rate and autoionization width of the double <em>K</em>-vacancy state, together with <em>KK</em>-<em>KLL</em> Auger energies and branching ratios of the main channels, are obtained from the cross sections and the contributions of these channels. The calculated resonance energy and x-ray rate are in good agreement with the existing experimental and theoretical results. For the Auger width, our result agrees well with the available experimental result and it is very close to the average of other theoretical data, which shows considerable differences with each other. The Auger energy of the predominate channel <em>KK</em>-<em>KL</em><sub>23</sub><em>L</em><sub>23</sub> <sup>2</sup>D is in rather good agreement with recent experiments on the Auger spectra. Our branching ratios for the channels <em>KK</em>-<em>KL</em><sub>23</sub><em>L</em><sub>23</sub> <sup>2</sup>D and <em>KK</em>-<em>KL</em><sub>23</sub><em>L</em><sub>23</sub> <sup>2</sup>S are larger than the results obtained by the multi-configuration Dirac–Fock method by ~20% on average, which may be due to the coupling of the continuum channels.
DOI: 10.6084/m9.figshare.1012105.v1
title: Auger energies <em>E<sub>a</sub></em> (in Ry) and branching ratios (BR in %) of the channels shown in figure 4

description: <b>Table 3.</b> Auger energies <em>E<sub>a</sub></em> (in Ry) and branching ratios (BR in %) of the channels shown in figure 4. Available experimental and theoretical data are given for comparison. <strong>Abstract</strong> A close-coupling calculation is performed for the photoionization cross section of the high-lying core-excited state 1s2s<sup>2</sup>2p<sup>5</sup> <sup>1</sup>P<sup>o</sup> of Ne<sup>2 +</sup> in the energy region of the double <em>K</em>-vacancy resonance 1s<sup>0</sup>2s<sup>2</sup>2p<sup>6</sup> <sup>1</sup>S. The calculation is carried out by using the <em>R</em>-matrix method in the <em>LS</em>-coupling scheme, which includes 27 target states and extensive configuration interaction. The <em>KK</em>-<em>KL</em> x-ray energy, rate and autoionization width of the double <em>K</em>-vacancy state, together with <em>KK</em>-<em>KLL</em> Auger energies and branching ratios of the main channels, are obtained from the cross sections and the contributions of these channels. The calculated resonance energy and x-ray rate are in good agreement with the existing experimental and theoretical results. For the Auger width, our result agrees well with the available experimental result and it is very close to the average of other theoretical data, which shows considerable differences with each other. The Auger energy of the predominate channel <em>KK</em>-<em>KL</em><sub>23</sub><em>L</em><sub>23</sub> <sup>2</sup>D is in rather good agreement with recent experiments on the Auger spectra. Our branching ratios for the channels <em>KK</em>-<em>KL</em><sub>23</sub><em>L</em><sub>23</sub> <sup>2</sup>D and <em>KK</em>-<em>KL</em><sub>23</sub><em>L</em><sub>23</sub> <sup>2</sup>S are larger than the results obtained by the multi-configuration Dirac–Fock method by ~20% on average, which may be due to the coupling of the continuum channels.
DOI: 10.6084/m9.figshare.1012098
title: Lifetime (in ms) and transition rate (in s<sup>−1</sup>) of the hyperfine level of 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> either with or without nuclear quadrupole HFI

description: <b>Table 4.</b> Lifetime (in ms) and transition rate (in s<sup>−1</sup>) of the hyperfine level of 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> either with or without nuclear quadrupole HFI. Notation <em>f</em> denotes the natural abundance of a different isotope with nuclear spin <em>I</em> and µ denotes the magnetic dipole moment in nuclear magnetons. Notation <em>Q</em> denotes the nuclear electric quadrupole moment in barns. Values of <em>I</em>, µ and <em>Q</em> are referred from [27], where the uncertainties of µ and <em>Q</em> values are quoted in parentheses. The values of <em>f</em> are referred from [28]. All lifetimes are given in ms (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>). <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012097
title: Calculated transition rates (in s<sup>−1</sup>) of the M3 transition and two E2 transitions in ions along the Ni-like isoelectronic sequence

description: <b>Table 3.</b> Calculated transition rates (in s<sup>−1</sup>) of the M3 transition and two E2 transitions in ions along the Ni-like isoelectronic sequence. Each E2 transition rate is given in both Babushkin and Coulomb gauges (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>). <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012098.v1
title: Lifetime (in ms) and transition rate (in s<sup>−1</sup>) of the hyperfine level of 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> either with or without nuclear quadrupole HFI

description: <b>Table 4.</b> Lifetime (in ms) and transition rate (in s<sup>−1</sup>) of the hyperfine level of 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> either with or without nuclear quadrupole HFI. Notation <em>f</em> denotes the natural abundance of a different isotope with nuclear spin <em>I</em> and µ denotes the magnetic dipole moment in nuclear magnetons. Notation <em>Q</em> denotes the nuclear electric quadrupole moment in barns. Values of <em>I</em>, µ and <em>Q</em> are referred from [27], where the uncertainties of µ and <em>Q</em> values are quoted in parentheses. The values of <em>f</em> are referred from [28]. All lifetimes are given in ms (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>). <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012095
title: Excitation energies of levels in the 3d<sup>9</sup>4s configuration for W<sup>46+</sup> from different theoretical approaches compared to experiment and other calculations

description: <b>Table 1.</b> Excitation energies of levels in the 3d<sup>9</sup>4s configuration for W<sup>46+</sup> from different theoretical approaches compared to experiment and other calculations. <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012096
title: Convergence of the calculated transition rates for two E2 transitions and one M3 transition in W<sup>46+</sup>

description: <b>Table 2.</b> Convergence of the calculated transition rates for two E2 transitions and one M3 transition in W<sup>46+</sup>. All transition rates are given in s<sup>−1</sup>. Each E2 transition rate is given in both Babushkin and Coulomb gauges (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>). <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012097.v1
title: Calculated transition rates (in s<sup>−1</sup>) of the M3 transition and two E2 transitions in ions along the Ni-like isoelectronic sequence

description: <b>Table 3.</b> Calculated transition rates (in s<sup>−1</sup>) of the M3 transition and two E2 transitions in ions along the Ni-like isoelectronic sequence. Each E2 transition rate is given in both Babushkin and Coulomb gauges (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>). <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012096.v1
title: Convergence of the calculated transition rates for two E2 transitions and one M3 transition in W<sup>46+</sup>

description: <b>Table 2.</b> Convergence of the calculated transition rates for two E2 transitions and one M3 transition in W<sup>46+</sup>. All transition rates are given in s<sup>−1</sup>. Each E2 transition rate is given in both Babushkin and Coulomb gauges (<em>a</em>[<em>b</em>] = <em>a</em> <b>×</b> 10<sup><em>b</em></sup>). <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012095.v1
title: Excitation energies of levels in the 3d<sup>9</sup>4s configuration for W<sup>46+</sup> from different theoretical approaches compared to experiment and other calculations

description: <b>Table 1.</b> Excitation energies of levels in the 3d<sup>9</sup>4s configuration for W<sup>46+</sup> from different theoretical approaches compared to experiment and other calculations. <strong>Abstract</strong> Based on the multi-configuration Dirac–Hartree–Fock method and using the GRASPVU package, a theoretical investigation was performed to study the lifetimes of hyperfine levels of the first excited level 3d<sup>9</sup>4s <sup>3</sup>D<sub>3</sub> in Ni-like ions (<em>Z</em> = 72–79) for all stable isotopes with nuclear spin. Comparisons between hyperfine-induced electric quadrupole transition rates and the pure magnetic octupole transition rates show that the extra electric quadrupole transition channel caused by the nuclear magnetic dipole and electric quadrupole hyperfine interaction is important for most hyperfine levels in each individual ion. Lifetimes of most hyperfine levels are sensitive to this extra decay channel. Extreme cases are found in <sup>181</sup>Ta, <sup>185</sup>Re and <sup>187</sup>Re, where lifetimes of some hyperfine levels are shortened by more than an order of magnitude.
DOI: 10.6084/m9.figshare.1012022
title: Table of numerical values for the magnetic field direction and laser directions/polarizations leading to spin-independent lattices along <em>z</em> and <em>y</em>, and a spin-dependent lattice along <em>x</em> in the required configuration

description: <b>Table B1.</b> Table of numerical values for the magnetic field direction and laser directions/polarizations leading to spin-independent lattices along <em>z</em> and <em>y</em>, and a spin-dependent lattice along <em>x</em> in the required configuration. <strong>Abstract</strong> We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunnelling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular field and for a uniform gas, the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation, we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally, we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular, we discuss how to prepare and detect a given Majorana edge state.
DOI: 10.6084/m9.figshare.1012022.v1
title: Table of numerical values for the magnetic field direction and laser directions/polarizations leading to spin-independent lattices along <em>z</em> and <em>y</em>, and a spin-dependent lattice along <em>x</em> in the required configuration

description: <b>Table B1.</b> Table of numerical values for the magnetic field direction and laser directions/polarizations leading to spin-independent lattices along <em>z</em> and <em>y</em>, and a spin-dependent lattice along <em>x</em> in the required configuration. <strong>Abstract</strong> We propose an experimental implementation of a topological superfluid with ultracold fermionic atoms. An optical superlattice is used to juxtapose a 1D gas of fermionic atoms and a 2D conventional superfluid of condensed Feshbach molecules. The latter acts as a Cooper pair reservoir and effectively induces a superfluid gap in the 1D system. Combined with a spin-dependent optical lattice along the 1D tube and laser-induced atom tunnelling, we obtain a topological superfluid phase. In the regime of weak couplings to the molecular field and for a uniform gas, the atomic system is equivalent to Kitaev's model of a p-wave superfluid. Using a numerical calculation, we show that the topological superfluidity is robust beyond the perturbative limit and in the presence of a harmonic trap. Finally, we describe how to investigate some physical properties of the Majorana fermions located at the topological superfluid boundaries. In particular, we discuss how to prepare and detect a given Majorana edge state.
DOI: 10.6084/m9.figshare.1011988
title: The table represents the condition on the order parameters ψ<sub><em>A</em></sub>, ψ<sub><em>B</em></sub> and ψ<sub><em>C</em></sub> and occupation densities ρ<sub><em>A</em></sub>, ρ<sub><em>B</em></sub> and ρ<sub><em>C</em></sub> that characterize the different compressible and insulating phases

description: <b>Table 2.</b> The table represents the condition on the order parameters ψ<sub><em>A</em></sub>, ψ<sub><em>B</em></sub> and ψ<sub><em>C</em></sub> and occupation densities ρ<sub><em>A</em></sub>, ρ<sub><em>B</em></sub> and ρ<sub><em>C</em></sub> that characterize the different compressible and insulating phases. The last two columns enumerate static structure factor, <em>S</em><sub><strong>q</strong></sub>(<strong>q = π, π</strong>) and the SF stiffness, α<sub><em>s</em></sub> for different phases. <strong>Abstract</strong> We investigate the phase diagram of interacting bosons in a tripartite lattice in two dimensions. An analytic computation of the phase diagram in the parameter space defined by the on-site boson–boson repulsion parameter and the chemical potential is done via a second-order strong coupling perturbation theory on the extended Bose–Hubbard model, which is hence supplemented by numerical mean-field calculations. Interesting results emerge in the form of exotic density ordered phases with one-third, two-third and unity filling of bosons per trimer. The pattern repeats as the chemical potential is increased. Further regions of supersolid and superfluid phases are noted in the numerical study of the mean-field model where the phase diagram shows a transition from compressible to insulating phases.
DOI: 10.6084/m9.figshare.1011987
title: The range of μ in terms of on-site interaction, <em>U</em> and nearest-neighbour exchange <em>V</em> for different incompressible phases

description: <b>Table 1.</b> The range of μ in terms of on-site interaction, <em>U</em> and nearest-neighbour exchange <em>V</em> for different incompressible phases. The discussion is restricted until the MI (2) lobe. <strong>Abstract</strong> We investigate the phase diagram of interacting bosons in a tripartite lattice in two dimensions. An analytic computation of the phase diagram in the parameter space defined by the on-site boson–boson repulsion parameter and the chemical potential is done via a second-order strong coupling perturbation theory on the extended Bose–Hubbard model, which is hence supplemented by numerical mean-field calculations. Interesting results emerge in the form of exotic density ordered phases with one-third, two-third and unity filling of bosons per trimer. The pattern repeats as the chemical potential is increased. Further regions of supersolid and superfluid phases are noted in the numerical study of the mean-field model where the phase diagram shows a transition from compressible to insulating phases.
DOI: 10.6084/m9.figshare.1011988.v1
title: The table represents the condition on the order parameters ψ<sub><em>A</em></sub>, ψ<sub><em>B</em></sub> and ψ<sub><em>C</em></sub> and occupation densities ρ<sub><em>A</em></sub>, ρ<sub><em>B</em></sub> and ρ<sub><em>C</em></sub> that characterize the different compressible and insulating phases

description: <b>Table 2.</b> The table represents the condition on the order parameters ψ<sub><em>A</em></sub>, ψ<sub><em>B</em></sub> and ψ<sub><em>C</em></sub> and occupation densities ρ<sub><em>A</em></sub>, ρ<sub><em>B</em></sub> and ρ<sub><em>C</em></sub> that characterize the different compressible and insulating phases. The last two columns enumerate static structure factor, <em>S</em><sub><strong>q</strong></sub>(<strong>q = π, π</strong>) and the SF stiffness, α<sub><em>s</em></sub> for different phases. <strong>Abstract</strong> We investigate the phase diagram of interacting bosons in a tripartite lattice in two dimensions. An analytic computation of the phase diagram in the parameter space defined by the on-site boson–boson repulsion parameter and the chemical potential is done via a second-order strong coupling perturbation theory on the extended Bose–Hubbard model, which is hence supplemented by numerical mean-field calculations. Interesting results emerge in the form of exotic density ordered phases with one-third, two-third and unity filling of bosons per trimer. The pattern repeats as the chemical potential is increased. Further regions of supersolid and superfluid phases are noted in the numerical study of the mean-field model where the phase diagram shows a transition from compressible to insulating phases.