Research on the interstellar medium and its interaction with the solar system constitutes a significant topic in planetary physics.As the Sun traverses the local interstellar cloud,interstellar neutrals penetrate the ...Research on the interstellar medium and its interaction with the solar system constitutes a significant topic in planetary physics.As the Sun traverses the local interstellar cloud,interstellar neutrals penetrate the heliosphere,forming the interstellar wind,and scattering solar extreme ultraviolet(EUV)emission lines.The intensity of the scattered radiation provides an indicator of the characteristic parameters of the interstellar wind,crucial for characterizing the heliosphere,the interstellar medium,and the evolution of the solar system.Meanwhile,a powerful method for studying stellar evolution is investigating the EUV emissions of stars.The only ongoing mission conducting an EUV full-sky survey is the relay satellite Queqiao-2.Due to the strong absorption of the interstellar medium at EUV wavelengths,modelling is essential to any study of these influences.In this study,we reviewed classical modelling methods for the density distribution of the interstellar helium atoms in the heliosphere,and the corresponding 58.4 nm radiation intensity.We established distinct density and intensity models for different orbital positions of Earth’s revolution.We found that when the Earth enters the helium focusing cone in the downwind region,both the helium density and the 58.4 nm radiation intensity increase rapidly,with the temperature effect being particularly important.The radiation intensity in the downwind direction can be 170 times that of the upwind direction.Some negligible factors were omitted for simplicity,such as the effects of the solar line width and Doppler shift.Our research can serve as an aid to the interpretation of the EUV observations in the full-sky survey conducted by Queqiao-2.展开更多
A fast-rising gas temperature is due to frequent collisions of the heavy particles in an atmosphericpressure dielectric barrier discharge.In this paper,a two-dimensional fluid model is applied to investigate the influ...A fast-rising gas temperature is due to frequent collisions of the heavy particles in an atmosphericpressure dielectric barrier discharge.In this paper,a two-dimensional fluid model is applied to investigate the influences of rising gas temperature on an atmospheric-pressure helium dielectric barrier discharge.With the increase in the gas temperature,it is found that:(1)a helium discharge can evolve from the discharge column to a homogeneous discharge;(2)the breakdown time is in advance and the gas breakdown voltage decreases;(3)the spatial distribution evolution of the electron density is similar to that of the helium atom density.The most significant discrepancy between them is that the electron densities are high at some positions where the helium atom densities are nevertheless low.Furthermore,the radial reduced electric fields are obtained under different gas temperatures.The physical reasons for the gas temperature effects are discussed.The simulation results provide a better understanding of the roles of the radial reduced electric field and the heavy particle.展开更多
Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method.To be specific,precise energy ...Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method.To be specific,precise energy eigenvalues of bound 1sns(~1S^e)(n=1-6)states and the resonance parameters i.e.positions and widths of^lS^e states due to 2sns(n=2-5)and 2pnp(n=2-5)configurations of confined helium below N=2 ionization threshold of He^+have been estimated.The two-parameter(Depth and Width)finite oscillator potential is used to represent the confining potential due to the quantum dot.It has been explicitly demonstrated that the electronic structural properties become sensitive functions of the dot size.It is observed from the calculations of ionization potential that the stability of an impurity ion within a quantum dot may be manipulated by varying the confinement parameters.A possibility of controlling the autoionization lifetime of doubly excited states of two-electron ions by tuning the width of the quantum cavity is also discussed here.展开更多
In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. T...In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized aJgorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.展开更多
The 1^10^＋ 1^1（-1）^＋and 1^1（2）^＋ states of the helium atom in the magnetic field regime between 0 and 100 a.u. are studied using a full configuration-interaction （CI） approach. The total energies, derivatives...The 1^10^＋ 1^1（-1）^＋and 1^1（2）^＋ states of the helium atom in the magnetic field regime between 0 and 100 a.u. are studied using a full configuration-interaction （CI） approach. The total energies, derivatives of the total energy with respect to the magnetic field and ionisation energies are calculated with Hylleraas-like functions in spherical coordinates in low to intermediate fields and Hylleraas Caussian functions in cylindrical coordinates in intermediate to high fields, respectively. In intermediate fields, the total energies and ionisation energies are determined in terms of Hermite interpolation, based on the results obtained with the two above-mentioned basis functions. Calculations show that the current method can produce lower total energies and larger ionisation energies, and make the two ionisation energy curves obtained with the two above-mentioned basis functions join smoothly in intermediate fields. Comparisons are also made with previous works.展开更多
We proposed a simple potential harmonic(PH) scheme for calculating the non\|relativistic radial correlation energies of atomic systems. The scheme was applied to the low\|lying \%n\%\+1\%S\%(\%n\%=1,2) and \%n\%\+3\%...We proposed a simple potential harmonic(PH) scheme for calculating the non\|relativistic radial correlation energies of atomic systems. The scheme was applied to the low\|lying \%n\%\+1\%S\%(\%n\%=1,2) and \%n\%\+3\%S\%(\%n\%=2,3) states of the helium atom. The results exhibit a very stable convergence characterization in both the angular and radial directions with PH and generalized Laguerre functions(GLF) respectively, even though the method is non\|variational one. The ninth significant figure of the non\|relativistic radial energy(NRE) calculated for the ground state exactly agrees with that of the most accurate literature data from the modified configuration interaction method. The convergent NRE′s for the excited states 2\+1\%S\%, 2\+3\%S\% and 3\+3\%S\% with the similar accuracy were also obtained.展开更多
We investigate the intensity effect of ultrashort assisting infrared laser pulse on the single-XUV-photon double ionization of helium atoms by solving full six-dimensional time-dependent Schrodinger equation with impl...We investigate the intensity effect of ultrashort assisting infrared laser pulse on the single-XUV-photon double ionization of helium atoms by solving full six-dimensional time-dependent Schrodinger equation with implement of finite element discrete variable representation.The studies of joint energy distributions and joint angular distributions of the two photoelectrons reveal the competition for ionized probabilities between the photoelectrons with odd parity and photoelectrons with even parity in single-XUV-photon double ionization process in the presence of weak infrared laser field,and such a competition can be modulated by changing the intensity of the weak assisting-IR laser pulses.The emission angles of the two photoelectrons can be adjusted by changing the laser parameters as well.We depict how the assisting-IR laser field enhances and/or enables the back-to-back and side-by-side emission of photoelectrons created in double ionization process.展开更多
The wave functions of the n1,3p (n=2, 3, 4) and the n 1,3D (n=3, 4, 5 ) low-lying states of the helium atom are expanded into the complete sets of the symmetrically adapted basis functions from hyperspherical harmonic...The wave functions of the n1,3p (n=2, 3, 4) and the n 1,3D (n=3, 4, 5 ) low-lying states of the helium atom are expanded into the complete sets of the symmetrically adapted basis functions from hyperspherical harmonic functions in the angle part and of generalized Laguerre functions in the radial part respectively, and are then augmented by the simplest type of Jastrow correlation factor to incorporate electron-nucleus cusp only. The excellent agreement between the present nonrelativistic eigen-energies and those from the sophisticated configuration interaction (CI) method for the examined states indicates that the hyperspherical harmonic method can also be applied to the P and the D excited states of the helium atom.展开更多
The helium atom confined by a non-impenetrable spherical box, i.e., a spherical Gaussian potential well which possesses finite height and range, is studied employing the exact diagonalization method. Total energies of...The helium atom confined by a non-impenetrable spherical box, i.e., a spherical Gaussian potential well which possesses finite height and range, is studied employing the exact diagonalization method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other： in general, the energies of the states decrease and the energy intervals between states increase with the reduction of the space dimensions.展开更多
The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function ...The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the energies of a spherical parabolic potential well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. We find also that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other. We find that the energy difference between states in a two-dimensional parabolic potential is also obviously larger than the corresponding levels for a spherical parabolic potential.展开更多
350 keV He^(+) ions were injected into laser powder bed fusion(LPBF)-processed 304L stainless steel and traditional rolled 304L stainless steel with a flux of 1×10^(17) ions/cm^(2) at room temperature,followed by...350 keV He^(+) ions were injected into laser powder bed fusion(LPBF)-processed 304L stainless steel and traditional rolled 304L stainless steel with a flux of 1×10^(17) ions/cm^(2) at room temperature,followed by annealing at 750℃ for 10,100,and 300 h,respectively.The results showed that material swelling due to helium bubble coarsening was almost not observed in either the LPBF or rolled samples after 10 h of annealing duration.Rapid coarsening and swelling of bubbles occurred in the rolled samples,but only moderate bubble growth occurred in the LPBF sample after annealing for 100 h.After annealing for 300 h,the helium bubbles in both samples tended to grow steadily.For 10 h of annealing,the irradiated samples were in a disequilibrium state,and the apparent activation energy(E^(act))calculated by the Arrhenius model determined that helium atoms tended to diffuse through the displacement mechanism,and helium bubbles grew under the migration and coalescence(MC)mechanism.With annealing times over 100 h,the high-density dislocations and nano-oxide particles in the LPBF sample still had a strong trapping effect on the movement and growth of helium bubbles.After annealing for 300 h,the cellular subgrains in the LPBF sample decomposed,and the nano-oxide particles had no trapping effect on the helium bubbles.At this time,the dislocation structure played a primary role in suppressing the growth of helium bubbles,and the radiation resistance of the LPBF sample remained superior to that of the rolled samples.展开更多
We demonstrate via first-principle calculations based on the density functional theory that the magnetic moment of a helium atom under a given magnetic field has a positive correlation with the electric dipole moment ...We demonstrate via first-principle calculations based on the density functional theory that the magnetic moment of a helium atom under a given magnetic field has a positive correlation with the electric dipole moment when an external electric field is applied to the system.Our calculation shows that the enhancement of the magnetic moment is significant due to the reduction of the triplet-singlet splitting.We argue that this finding can be generalized to organic molecules,especially to macromolecules where the structure induced an electric dipole moment which may give rise to significantly enhanced responses to the external magnetic field.These results suggest that considerable magnetic responses prevail,particularly in bio-molecules without an inversion center.展开更多
The original intention of the author’s preoccupation with the quantum-me-chanical behaviour of simple atoms and molecules such as Hydrogen and He-lium was,on the one hand,the elegant simplicity of Niels Bohr’s atom ...The original intention of the author’s preoccupation with the quantum-me-chanical behaviour of simple atoms and molecules such as Hydrogen and He-lium was,on the one hand,the elegant simplicity of Niels Bohr’s atom model for Hydrogen,describing the metastable states of the excited electrons by pla-nar concentric electron orbits,and,on the other hand,the hardly intelligible wave mechanical approach of Heisenberg,Schrödinger and others,describing mainly atoms with multiple electrons by three-dimensional orbitals which were characterized by probabilities of presence.Thereby the question arose whether it would be possible to find alternative atom models with well-defined electron trajectories.Therein,Louis de Broglie’s thesis of the wavy nature of electron motion implicating standing waves would have to be implemented.Nevertheless,as reviewed in the introduction,the orthodox three-dimensional concept influenced the own thinking in such a way that three-dimensional constellations for the electronic excited states were conceived.The break-through was achieved for the electronic ground state in the form of the spin-orbit coupling where the spin acts as a perpetuum mobile,inducing the orbital angular momentum h/2π.Furthermore,the insight was gained that a circu-larly rotating electron intrinsically corresponds to a harmonic oscillator,thus fulfilling the condition of a standing wave.Based on this concept,a double planar model was established for the H2-molecule which could be empirically verified by X-ray data from literature.However,for the two electrons contain-ing Helium a 2D-array seemed impossible since the Pauli-principle seemed to be violated.After a long stepwise succession of 3D-attempts which turned out to be impossible—not least since eccentric forces are not possible in such a system—the here presented 2D-version for Helium was found,composed by two imaginary orthogonal electron orbits.It will enable in a subsequent pub-lication the quantum mechanical interpretation of the thermal-radiative be-haviour of Helium which was reported in the author’s publication nine years ago.展开更多
The matrix elements of the correlation function between symmetric potential harmonics were first simplified into the analytical summation of the grand angular momentum. The correlation-function potential-harmonic and ...The matrix elements of the correlation function between symmetric potential harmonics were first simplified into the analytical summation of the grand angular momentum. The correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF) proposed by us recently was then applied to directly solve the Schrodinger equation for n3S(n=2-5) excited states of the helium atom. With only 12 PHs, the convergent eigenenergies of 23S, 33S, 43S and 53S states were 2.17427, 2.06849, 2.03644, 2.02257 Eh, respectively. The errors only were 0.00096, 0.00020, 0.00007, 0.00005 Eh, when compared with the exact Hylleraas variational results respectively.展开更多
基金supported by the National Key R&D Program of China(2021YFA0718600)the National Natural Science Foundation of China(42441809).
文摘Research on the interstellar medium and its interaction with the solar system constitutes a significant topic in planetary physics.As the Sun traverses the local interstellar cloud,interstellar neutrals penetrate the heliosphere,forming the interstellar wind,and scattering solar extreme ultraviolet(EUV)emission lines.The intensity of the scattered radiation provides an indicator of the characteristic parameters of the interstellar wind,crucial for characterizing the heliosphere,the interstellar medium,and the evolution of the solar system.Meanwhile,a powerful method for studying stellar evolution is investigating the EUV emissions of stars.The only ongoing mission conducting an EUV full-sky survey is the relay satellite Queqiao-2.Due to the strong absorption of the interstellar medium at EUV wavelengths,modelling is essential to any study of these influences.In this study,we reviewed classical modelling methods for the density distribution of the interstellar helium atoms in the heliosphere,and the corresponding 58.4 nm radiation intensity.We established distinct density and intensity models for different orbital positions of Earth’s revolution.We found that when the Earth enters the helium focusing cone in the downwind region,both the helium density and the 58.4 nm radiation intensity increase rapidly,with the temperature effect being particularly important.The radiation intensity in the downwind direction can be 170 times that of the upwind direction.Some negligible factors were omitted for simplicity,such as the effects of the solar line width and Doppler shift.Our research can serve as an aid to the interpretation of the EUV observations in the full-sky survey conducted by Queqiao-2.
基金supported by the Liaoning Provincial Department of Education Fund(No.LJ2020008)。
文摘A fast-rising gas temperature is due to frequent collisions of the heavy particles in an atmosphericpressure dielectric barrier discharge.In this paper,a two-dimensional fluid model is applied to investigate the influences of rising gas temperature on an atmospheric-pressure helium dielectric barrier discharge.With the increase in the gas temperature,it is found that:(1)a helium discharge can evolve from the discharge column to a homogeneous discharge;(2)the breakdown time is in advance and the gas breakdown voltage decreases;(3)the spatial distribution evolution of the electron density is similar to that of the helium atom density.The most significant discrepancy between them is that the electron densities are high at some positions where the helium atom densities are nevertheless low.Furthermore,the radial reduced electric fields are obtained under different gas temperatures.The physical reasons for the gas temperature effects are discussed.The simulation results provide a better understanding of the roles of the radial reduced electric field and the heavy particle.
基金Financial Support under Grant No.37(3)/14/27/2014-BRNS from the Department of Atomic Energy,BRNS,Government of IndiaFinancial Support under Grant No.PSW-160/14-15(ERO)from University Grants Commission,Government of India
文摘Bound and resonance states of helium atom have been investigated inside a quantum dot by using explicitly correlated Hylleraas type basis set within the framework of stabilization method.To be specific,precise energy eigenvalues of bound 1sns(~1S^e)(n=1-6)states and the resonance parameters i.e.positions and widths of^lS^e states due to 2sns(n=2-5)and 2pnp(n=2-5)configurations of confined helium below N=2 ionization threshold of He^+have been estimated.The two-parameter(Depth and Width)finite oscillator potential is used to represent the confining potential due to the quantum dot.It has been explicitly demonstrated that the electronic structural properties become sensitive functions of the dot size.It is observed from the calculations of ionization potential that the stability of an impurity ion within a quantum dot may be manipulated by varying the confinement parameters.A possibility of controlling the autoionization lifetime of doubly excited states of two-electron ions by tuning the width of the quantum cavity is also discussed here.
基金The project supported by National Natural Science Foundation of China under Grant No. 10147207, the Natural Science Foundation of Chongqing Science and Technology Committee under Grant No. 2005BB8267, and the Fundamental Research Foundation of Chongqing Education Committee under Grant No. KJ060813
文摘In this paper,the ground state wave function of four parameters is developed and expression of the ground state level is derived for the helium atom when the radial Schrodinger equation of the helium atom is solved. The ground energy is respectively computed by the optimized aJgorithms of Matlab 7.0 and the Monte Carlo methods. Furthermore, the ground state wave function is obtained. Compared with the experiment value and the value with the variation calculus in reference, the results of this paper show that in the four-parameter scheme, not only the calculations become more simplified and precise, but also the radial wave function of the helium atom meets the space symmetry automatically in ground state.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10874133)
文摘The 1^10^＋ 1^1（-1）^＋and 1^1（2）^＋ states of the helium atom in the magnetic field regime between 0 and 100 a.u. are studied using a full configuration-interaction （CI） approach. The total energies, derivatives of the total energy with respect to the magnetic field and ionisation energies are calculated with Hylleraas-like functions in spherical coordinates in low to intermediate fields and Hylleraas Caussian functions in cylindrical coordinates in intermediate to high fields, respectively. In intermediate fields, the total energies and ionisation energies are determined in terms of Hermite interpolation, based on the results obtained with the two above-mentioned basis functions. Calculations show that the current method can produce lower total energies and larger ionisation energies, and make the two ionisation energy curves obtained with the two above-mentioned basis functions join smoothly in intermediate fields. Comparisons are also made with previous works.
基金Supported by the National Natural Science Foundation of China(No. 2 970 30 0 3)
文摘We proposed a simple potential harmonic(PH) scheme for calculating the non\|relativistic radial correlation energies of atomic systems. The scheme was applied to the low\|lying \%n\%\+1\%S\%(\%n\%=1,2) and \%n\%\+3\%S\%(\%n\%=2,3) states of the helium atom. The results exhibit a very stable convergence characterization in both the angular and radial directions with PH and generalized Laguerre functions(GLF) respectively, even though the method is non\|variational one. The ninth significant figure of the non\|relativistic radial energy(NRE) calculated for the ground state exactly agrees with that of the most accurate literature data from the modified configuration interaction method. The convergent NRE′s for the excited states 2\+1\%S\%, 2\+3\%S\% and 3\+3\%S\% with the similar accuracy were also obtained.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11774131 and 91850114).
文摘We investigate the intensity effect of ultrashort assisting infrared laser pulse on the single-XUV-photon double ionization of helium atoms by solving full six-dimensional time-dependent Schrodinger equation with implement of finite element discrete variable representation.The studies of joint energy distributions and joint angular distributions of the two photoelectrons reveal the competition for ionized probabilities between the photoelectrons with odd parity and photoelectrons with even parity in single-XUV-photon double ionization process in the presence of weak infrared laser field,and such a competition can be modulated by changing the intensity of the weak assisting-IR laser pulses.The emission angles of the two photoelectrons can be adjusted by changing the laser parameters as well.We depict how the assisting-IR laser field enhances and/or enables the back-to-back and side-by-side emission of photoelectrons created in double ionization process.
基金Supported by the National Natural Science Foundation of China(No. 29703003).
文摘The wave functions of the n1,3p (n=2, 3, 4) and the n 1,3D (n=3, 4, 5 ) low-lying states of the helium atom are expanded into the complete sets of the symmetrically adapted basis functions from hyperspherical harmonic functions in the angle part and of generalized Laguerre functions in the radial part respectively, and are then augmented by the simplest type of Jastrow correlation factor to incorporate electron-nucleus cusp only. The excellent agreement between the present nonrelativistic eigen-energies and those from the sophisticated configuration interaction (CI) method for the examined states indicates that the hyperspherical harmonic method can also be applied to the P and the D excited states of the helium atom.
基金The project supported by National Natural Science Foundation of China under Grant No.10475021
文摘The helium atom confined by a non-impenetrable spherical box, i.e., a spherical Gaussian potential well which possesses finite height and range, is studied employing the exact diagonalization method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other： in general, the energies of the states decrease and the energy intervals between states increase with the reduction of the space dimensions.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475021 and the Natural Science Foundation of Guangdong Province under Grant No. 04009519
文摘The helium atom confined by a spherical parabolic potential well is studied employing the adiabatic hyperspherical approach method. Total energies of the ground and three low-excited states are obtained as a function of the confined potential radii. We find that the energies of a spherical parabolic potential well are in good agreement with those of an impenetrable spherical box for the larger confined potential radius. We find also that the confinement may cause accidental degeneracies between levels with different low-excited states and the inversion of the energy values. The results for the three-dimensional spherical potential well and the two-dimensional disc-like potential well are compared with each other. We find that the energy difference between states in a two-dimensional parabolic potential is also obviously larger than the corresponding levels for a spherical parabolic potential.
基金supported by the National Natural Science Foundation of China(Nos.U22B2067 and 52073176).
文摘350 keV He^(+) ions were injected into laser powder bed fusion(LPBF)-processed 304L stainless steel and traditional rolled 304L stainless steel with a flux of 1×10^(17) ions/cm^(2) at room temperature,followed by annealing at 750℃ for 10,100,and 300 h,respectively.The results showed that material swelling due to helium bubble coarsening was almost not observed in either the LPBF or rolled samples after 10 h of annealing duration.Rapid coarsening and swelling of bubbles occurred in the rolled samples,but only moderate bubble growth occurred in the LPBF sample after annealing for 100 h.After annealing for 300 h,the helium bubbles in both samples tended to grow steadily.For 10 h of annealing,the irradiated samples were in a disequilibrium state,and the apparent activation energy(E^(act))calculated by the Arrhenius model determined that helium atoms tended to diffuse through the displacement mechanism,and helium bubbles grew under the migration and coalescence(MC)mechanism.With annealing times over 100 h,the high-density dislocations and nano-oxide particles in the LPBF sample still had a strong trapping effect on the movement and growth of helium bubbles.After annealing for 300 h,the cellular subgrains in the LPBF sample decomposed,and the nano-oxide particles had no trapping effect on the helium bubbles.At this time,the dislocation structure played a primary role in suppressing the growth of helium bubbles,and the radiation resistance of the LPBF sample remained superior to that of the rolled samples.
基金supported by the National Natural Science Foundation of China(11974366)the Fundamental Research Funds for the Central Universities.
文摘We demonstrate via first-principle calculations based on the density functional theory that the magnetic moment of a helium atom under a given magnetic field has a positive correlation with the electric dipole moment when an external electric field is applied to the system.Our calculation shows that the enhancement of the magnetic moment is significant due to the reduction of the triplet-singlet splitting.We argue that this finding can be generalized to organic molecules,especially to macromolecules where the structure induced an electric dipole moment which may give rise to significantly enhanced responses to the external magnetic field.These results suggest that considerable magnetic responses prevail,particularly in bio-molecules without an inversion center.
文摘The original intention of the author’s preoccupation with the quantum-me-chanical behaviour of simple atoms and molecules such as Hydrogen and He-lium was,on the one hand,the elegant simplicity of Niels Bohr’s atom model for Hydrogen,describing the metastable states of the excited electrons by pla-nar concentric electron orbits,and,on the other hand,the hardly intelligible wave mechanical approach of Heisenberg,Schrödinger and others,describing mainly atoms with multiple electrons by three-dimensional orbitals which were characterized by probabilities of presence.Thereby the question arose whether it would be possible to find alternative atom models with well-defined electron trajectories.Therein,Louis de Broglie’s thesis of the wavy nature of electron motion implicating standing waves would have to be implemented.Nevertheless,as reviewed in the introduction,the orthodox three-dimensional concept influenced the own thinking in such a way that three-dimensional constellations for the electronic excited states were conceived.The break-through was achieved for the electronic ground state in the form of the spin-orbit coupling where the spin acts as a perpetuum mobile,inducing the orbital angular momentum h/2π.Furthermore,the insight was gained that a circu-larly rotating electron intrinsically corresponds to a harmonic oscillator,thus fulfilling the condition of a standing wave.Based on this concept,a double planar model was established for the H2-molecule which could be empirically verified by X-ray data from literature.However,for the two electrons contain-ing Helium a 2D-array seemed impossible since the Pauli-principle seemed to be violated.After a long stepwise succession of 3D-attempts which turned out to be impossible—not least since eccentric forces are not possible in such a system—the here presented 2D-version for Helium was found,composed by two imaginary orthogonal electron orbits.It will enable in a subsequent pub-lication the quantum mechanical interpretation of the thermal-radiative be-haviour of Helium which was reported in the author’s publication nine years ago.
基金Project supported by the National Natural Science Foundation of China and by the Natural Science Foundation for Youth of Shandong University.
文摘The matrix elements of the correlation function between symmetric potential harmonics were first simplified into the analytical summation of the grand angular momentum. The correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF) proposed by us recently was then applied to directly solve the Schrodinger equation for n3S(n=2-5) excited states of the helium atom. With only 12 PHs, the convergent eigenenergies of 23S, 33S, 43S and 53S states were 2.17427, 2.06849, 2.03644, 2.02257 Eh, respectively. The errors only were 0.00096, 0.00020, 0.00007, 0.00005 Eh, when compared with the exact Hylleraas variational results respectively.
