We report in this paper the ground-state energy 2s2 1S and total energies of doubly excited states 2p2 1D, 3d2 1D, 4f2 1I of the Helium isoelectronic sequence from H- to Ca18+. Calculations are performed using the Mod...We report in this paper the ground-state energy 2s2 1S and total energies of doubly excited states 2p2 1D, 3d2 1D, 4f2 1I of the Helium isoelectronic sequence from H- to Ca18+. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) in the framework of a variational procedure. The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function [1] combining with Hylleraas-type wave function [2]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This first proposed MAOT variational procedure, leads to accurate results in good agreement as well as with available other theoretical results than experimental data. In the present work, a new correlated wave function is presented to express analytically the total energies for the 2s2 1S ground state and each doubly 2p2 1D, 3d2 1D, 4f2 1I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2) systems.展开更多
The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series ...The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO_(2) and a longitudinal 3k antiferromagnetic(AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT +U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT +U approaches to this system is made.展开更多
We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We obser...We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.展开更多
A time dependent Hamiltonian associated to the impact parameter model for the scattering of a light particle and two heavy ones is considered. Existence and non degeneracy of the ground state is shown.
The classical frustrated antiferromagnetic J_1–J_2 model is considered in a description of the classical spin wave for a vector spin system. Its ground state(GS) spin ordering is analyzed by minimizing its energy. Ou...The classical frustrated antiferromagnetic J_1–J_2 model is considered in a description of the classical spin wave for a vector spin system. Its ground state(GS) spin ordering is analyzed by minimizing its energy. Our analytical derivations show that all the spins in the GS phase must lie in planes that are parallel to each other. When applying the derived formulations to concrete lattices such as the square and simple cubic lattices, we find that in the large J_2 region, a large continuous GS degeneracy concluded by a qualitative analysis is lifted, and collinear striped ordering is selected as the GS phase.展开更多
The potential energy function of nitrogen dioxide with the C2v symmetry in the ground state is represented using the simplified Sorbie-Murrell many-body expansion function in terms of the symmetry of NO2. Using the po...The potential energy function of nitrogen dioxide with the C2v symmetry in the ground state is represented using the simplified Sorbie-Murrell many-body expansion function in terms of the symmetry of NO2. Using the potential energy function, some potential energy surfaces of NO2(C2v, X^-^2A1), such as the bond stretching contour plot for a fixed equilibrium geometry angle θ and contour for O moving around N-O (R1), in which R1 is fixed at the equilibrium bond length, are depicted. The potential energy surfaces are analysed. Moreover, the equilibrium parameters for NO2 with the C2v, Cs and Dsn symmetries, such as equilibrium geometry structures and energies, are calculated by the ab initio (CBS-Q) method.展开更多
Starting from Wigner’s definition of the function named now after him we systematically develop different representation of this quasiprobability with emphasis on symmetric representations concerning the canonical va...Starting from Wigner’s definition of the function named now after him we systematically develop different representation of this quasiprobability with emphasis on symmetric representations concerning the canonical variables (q,p) of phase space and using the known relation to the parity operator. One of the representations is by means of the Laguerre 2D polynomials which is particularly effective in quantum optics. For the coherent states we show that their Fourier transforms are again coherent states. We calculate the Wigner quasiprobability to the eigenstates of a particle in a square well with infinitely high impenetrable walls which is not smooth in the spatial coordinate and vanishes outside the wall boundaries. It is not well suited for the calculation of expectation values. A great place takes on the calculation of the Wigner quasiprobability for coherent phase states in quantum optics which is essentially new. We show that an unorthodox entire function plays there a role in most formulae which makes all calculations difficult. The Wigner quasiprobability for coherent phase states is calculated and graphically represented but due to the involved unorthodox function it may be considered only as illustration and is not suited for the calculation of expectation values. By another approach via the number representation of the states and using the recently developed summation formula by means of Generalized Eulerian numbers it becomes possible to calculate in approximations with good convergence the basic expectation values, in particular, the basic uncertainties which are additionally represented in graphics. Both considered examples, the square well and the coherent phase states, belong to systems with SU (1,1) symmetry with the same index K=1/2 of unitary irreducible representations.展开更多
We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonometh...We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonomethyl)-naphthalene-2-ol and 1-pyrenecarboxaldehyde. Especially, the density functional theory(DFT) and time-dependent density functional theory(TDDFT) methods for HNP monomer are introduced. Moreover, the "our own n-layered integrated molecular orbital and molecular mechanics"(ONIOM) method(TDDFT:universal force field(UFF)) is used to reveal the aggregation-induced emission(AIE) effect on the ESIPT process for HNP in crystal. Our results confirm that the ESIPT process happens upon the photoexcitation for the HNP monomer and HNP in crystal, which is distinctly monitored by the optimized geometric structures and the potential energy curves. In addition, the results of potential energy curves reveal that the ESIPT process in HNP will be promoted by the AIE effect. Furthermore, the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) for the HNP monomer and HNP in crystal have been calculated. The calculation demonstrates that the electron density decrease of proton donor caused by excitation promotes the ESIPT process. In addition, we find that the variation of atomic dipole moment corrected Hirshfeld population(ADCH) charge for proton acceptor induced by the AIE effect facilitates the ESIPT process. The results will be expected to deepen the understanding of ESIPT dynamics for luminophore under the AIE effect and provide insight into future design of high-efficient AIE compounds.展开更多
The ambiguity of the structure of ^(12)Be especially in the configuration of Be ground state has attracted a lot of attention recently.We notice that the nuclear reaction cross section or at low energy region is sensi...The ambiguity of the structure of ^(12)Be especially in the configuration of Be ground state has attracted a lot of attention recently.We notice that the nuclear reaction cross section or at low energy region is sensitive to the surface structure of ^(12)Be,which is greatly impacted by the ground state configuration of ^(12)Be especially by the occupancy probability of the s orbital component.By using existed interaction cross section data of ^(12)Be on C at 790 MeV/nucleon and Glauber model,the upper limit of the s orbital occupation probability of ^(12)Be ground state is roughly determined to be about 56%with Single Particle Model calculations.This demonstrates that the method is very promising to determine the s orbital component of ^(12)Be with proper nuclear-matter density distribution calculations for different orbitals of ^(12)Be ground state.Hence we bring forward to determine the s orbital component of ^(12)Be by measuring the ctr of ^(12)Be on C and Al at several tens of MeV/nucleon.In this paper,the feasibility and detailed experimental scheme of the ctr measurement are carefully studied.The precision of the s orbital occupation probability of ^(12)Be ground state is expected to achieve 9%by using the proposed 2%ctr data.展开更多
We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,th...We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.展开更多
In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,w...In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].展开更多
We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under som...We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.展开更多
In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger...In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.展开更多
The geometries, vibrational frequencies and bind energies are reported for the ground states of CaC 2H + 2, CaC 2D + 2 and CaC 2H + 4. CaC 2H + 2 and CaC 2H + 4 equilibrium geometries have C 2v symmetry with the metal...The geometries, vibrational frequencies and bind energies are reported for the ground states of CaC 2H + 2, CaC 2D + 2 and CaC 2H + 4. CaC 2H + 2 and CaC 2H + 4 equilibrium geometries have C 2v symmetry with the metal ion lying in the perpendicular bisector of the C-C bond. The ground state in both CaC 2H + 2 and CaC 2H + 4 molecules ia a 2A 1 state and the binding in the ground state is mainly electrostatic. For both CaC 2H + 2 and CaC 2H + 4 the ligand is only slightly distorted from its free ligand structure, the C-C distance has hardly increased and there is only a very small bending of the H atom away from the Ca atom. This is consistent with the electrostatic nature of the bonding. Two different approaches-Hartree-Fock(HF) and density functional theory methods(DFT)-are used and basis sets here used is 6-311+G(3df,2p). The DFT results are in good agreement with experiments, namely, DFT methods provide the benefits that some more expensive ab initio methods can do, but at essentially HF cost. So it is important to include electron correlation for accurate results in this study.展开更多
We carry out quantum scattering dynamics and quasi-classical trajectory(QCT)calculations for the O+H2+reactive collision in the ground(1^2A')and first excited(1^2A')potential energy surface.We calculate the re...We carry out quantum scattering dynamics and quasi-classical trajectory(QCT)calculations for the O+H2+reactive collision in the ground(1^2A')and first excited(1^2A')potential energy surface.We calculate the reaction probabilities of O+H2^+(v=0,j=0)→OH^++H and O+H2^+(v=0,j=0)→OH+H^+reaction for total angular momentum J=0.The results calculated by QCT are consistent with those from quantum mechanical wave packet.Using the QCT method,we generate in the center-of-mass frame the product state-resolved integral cross-sections(ICSs);two commonly used generalized polarization-dependent differential cross-sections(PDDCSs),(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt);and three angular distributions of the product rotational vectors,P(θr),P(φr),and P(θr,φr).We discuss the influence on the scalar and vector properties of the potential energy surface,the collision energy,and the isotope mass.Since there are deep potential wells in these two potential energy surfaces,their kinetic characteristics are similar to each other and the isotopic effect is not obvious.However,the well depths and configurations of the two potential energy surfaces are different,so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.展开更多
After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in gene...After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in general form. Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities. The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics. A large set of these states do not belong to sub- or to super-Poissonian states but are also not Poissonian states. We illustrate in examples their photon distributions. This shows that the notions of sub- and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of squeezing and the disentanglement of their operators. Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.展开更多
In this paper the results of dynamic NMR studies on ethylmethylamino-tertiary-butyl-phenylborane (EMABPB) with or without light are reported. The NMR data were recorded on a Bruker 400 MHz NMR equipped with our custom...In this paper the results of dynamic NMR studies on ethylmethylamino-tertiary-butyl-phenylborane (EMABPB) with or without light are reported. The NMR data were recorded on a Bruker 400 MHz NMR equipped with our custom-made optical probe and with our custom-made 450 watts (W) monochromatic light sources. The molecular photochemistry including twisted intramolecular charge-transfer-excited-state (TICT) of the EMABPB in several solvents has been investigated. These results indicate that the aminoborane demonstrates multiple configurations in CD3Cl and CD2Cl2 resulting in the shifts of the signals of the alkyl groups on the nitrogen and boron. This indicates that there are some time-dependent changes at constant temperature over the irradiation interval. At ﹣60°C and the presence of light (λ = 265 nm), we observed a large change in the populations of the two sites, and this by itself indicates a modification in the rotation around the boron nitrogen bond in the excited state. By considering the existence of the TICT state, many important energy technologies may be developed with higher efficiency by controlling the back-electron transfer processes.展开更多
The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari...The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 151-154, 2012, has been removed from this site.展开更多
文摘We report in this paper the ground-state energy 2s2 1S and total energies of doubly excited states 2p2 1D, 3d2 1D, 4f2 1I of the Helium isoelectronic sequence from H- to Ca18+. Calculations are performed using the Modified Atomic Orbital Theory (MAOT) in the framework of a variational procedure. The purpose of this study required a mathematical development of the Hamiltonian applied to Slater-type wave function [1] combining with Hylleraas-type wave function [2]. The study leads to analytical expressions which are carried out under special MAXIMA computational program. This first proposed MAOT variational procedure, leads to accurate results in good agreement as well as with available other theoretical results than experimental data. In the present work, a new correlated wave function is presented to express analytically the total energies for the 2s2 1S ground state and each doubly 2p2 1D, 3d2 1D, 4f2 1I excited states in the He-like systems.The present accurate data may be a useful guideline for future experimental and theoretical studies in the (nl2) systems.
基金supported by National Natural Science Foundation of China, (Grant No. 12104034)。
文摘The magnetic states of the strongly correlated system plutonium dioxide(PuO_(2)) are studied based on the density functional theory(DFT) plus Hubbard U(DFT +U) method with spin–orbit coupling(SOC) included. A series of typical magnetic structures including the multiple-k types are simulated and compared in the aspect of atomic structure and total energy. We test LDA, PBE, and SCAN exchange–correlation functionals on PuO_(2) and a longitudinal 3k antiferromagnetic(AFM) ground state is theoretically determined. This magnetic structure has been identified to be the most stable one by the former computational work using the hybrid functional. Our DFT +U + SOC calculations for the longitudinal 3k AFM ground state suggest a direct gap which is in good agreement with the experimental value. In addition, a genetic algorithm is employed and proved to be effective in predicting magnetic ground state of PuO2. Finally, a comparison between the results of two extensively used DFT +U approaches to this system is made.
基金the National Key R&D Program of China(Grant No.2017YFA0304401)the Technical Innovation Program of Hubei Province(Grant No.2018AAA045)the National Natural Science Foundation of China(Grant No.11904387)。
文摘We report on electromagnetically induced transparency cooling of ^(40)Ca^(+)to sympathetically cool the threedimensional secular modes of motion in a ^(40)Ca^(+)–^(27)Al^(+)two-ion pair near the ground state.We observe simultaneous ground state cooling across all radial modes and axial modes of a ^(40)Ca^(+)–^(27)Al^(+)ion pair,occupying a broader cooling range in frequency space over 3 MHz.The cooling time is observed to be less than 1 ms.The mean phonon number and heating rates of all motional modes are measured.This study is not only an important step for reducing the secular motion time-dilation shift uncertainty and uptime ratio of ^(27)Al^(+)optical clock,but also essential for high-fidelity quantum simulations and quantum information processors using trapped ions.
文摘A time dependent Hamiltonian associated to the impact parameter model for the scattering of a light particle and two heavy ones is considered. Existence and non degeneracy of the ground state is shown.
基金Supported by the National Natural Science Foundation of China under Grant No 11774002
文摘The classical frustrated antiferromagnetic J_1–J_2 model is considered in a description of the classical spin wave for a vector spin system. Its ground state(GS) spin ordering is analyzed by minimizing its energy. Our analytical derivations show that all the spins in the GS phase must lie in planes that are parallel to each other. When applying the derived formulations to concrete lattices such as the square and simple cubic lattices, we find that in the large J_2 region, a large continuous GS degeneracy concluded by a qualitative analysis is lifted, and collinear striped ordering is selected as the GS phase.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10376021 and 10676025, and the Scientific Research Fund of Sichuan Provincial Education Department (2006A131).
文摘The potential energy function of nitrogen dioxide with the C2v symmetry in the ground state is represented using the simplified Sorbie-Murrell many-body expansion function in terms of the symmetry of NO2. Using the potential energy function, some potential energy surfaces of NO2(C2v, X^-^2A1), such as the bond stretching contour plot for a fixed equilibrium geometry angle θ and contour for O moving around N-O (R1), in which R1 is fixed at the equilibrium bond length, are depicted. The potential energy surfaces are analysed. Moreover, the equilibrium parameters for NO2 with the C2v, Cs and Dsn symmetries, such as equilibrium geometry structures and energies, are calculated by the ab initio (CBS-Q) method.
文摘Starting from Wigner’s definition of the function named now after him we systematically develop different representation of this quasiprobability with emphasis on symmetric representations concerning the canonical variables (q,p) of phase space and using the known relation to the parity operator. One of the representations is by means of the Laguerre 2D polynomials which is particularly effective in quantum optics. For the coherent states we show that their Fourier transforms are again coherent states. We calculate the Wigner quasiprobability to the eigenstates of a particle in a square well with infinitely high impenetrable walls which is not smooth in the spatial coordinate and vanishes outside the wall boundaries. It is not well suited for the calculation of expectation values. A great place takes on the calculation of the Wigner quasiprobability for coherent phase states in quantum optics which is essentially new. We show that an unorthodox entire function plays there a role in most formulae which makes all calculations difficult. The Wigner quasiprobability for coherent phase states is calculated and graphically represented but due to the involved unorthodox function it may be considered only as illustration and is not suited for the calculation of expectation values. By another approach via the number representation of the states and using the recently developed summation formula by means of Generalized Eulerian numbers it becomes possible to calculate in approximations with good convergence the basic expectation values, in particular, the basic uncertainties which are additionally represented in graphics. Both considered examples, the square well and the coherent phase states, belong to systems with SU (1,1) symmetry with the same index K=1/2 of unitary irreducible representations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11574115 and 11704146)
文摘We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonomethyl)-naphthalene-2-ol and 1-pyrenecarboxaldehyde. Especially, the density functional theory(DFT) and time-dependent density functional theory(TDDFT) methods for HNP monomer are introduced. Moreover, the "our own n-layered integrated molecular orbital and molecular mechanics"(ONIOM) method(TDDFT:universal force field(UFF)) is used to reveal the aggregation-induced emission(AIE) effect on the ESIPT process for HNP in crystal. Our results confirm that the ESIPT process happens upon the photoexcitation for the HNP monomer and HNP in crystal, which is distinctly monitored by the optimized geometric structures and the potential energy curves. In addition, the results of potential energy curves reveal that the ESIPT process in HNP will be promoted by the AIE effect. Furthermore, the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) for the HNP monomer and HNP in crystal have been calculated. The calculation demonstrates that the electron density decrease of proton donor caused by excitation promotes the ESIPT process. In addition, we find that the variation of atomic dipole moment corrected Hirshfeld population(ADCH) charge for proton acceptor induced by the AIE effect facilitates the ESIPT process. The results will be expected to deepen the understanding of ESIPT dynamics for luminophore under the AIE effect and provide insight into future design of high-efficient AIE compounds.
基金Supported by the National Natural Science Foundation of China(No.11179018 and 11305238)the Instrument Developing Project of the Chinese Academy of Sciences(No.YZ201246)
文摘The ambiguity of the structure of ^(12)Be especially in the configuration of Be ground state has attracted a lot of attention recently.We notice that the nuclear reaction cross section or at low energy region is sensitive to the surface structure of ^(12)Be,which is greatly impacted by the ground state configuration of ^(12)Be especially by the occupancy probability of the s orbital component.By using existed interaction cross section data of ^(12)Be on C at 790 MeV/nucleon and Glauber model,the upper limit of the s orbital occupation probability of ^(12)Be ground state is roughly determined to be about 56%with Single Particle Model calculations.This demonstrates that the method is very promising to determine the s orbital component of ^(12)Be with proper nuclear-matter density distribution calculations for different orbitals of ^(12)Be ground state.Hence we bring forward to determine the s orbital component of ^(12)Be by measuring the ctr of ^(12)Be on C and Al at several tens of MeV/nucleon.In this paper,the feasibility and detailed experimental scheme of the ctr measurement are carefully studied.The precision of the s orbital occupation probability of ^(12)Be ground state is expected to achieve 9%by using the proposed 2%ctr data.
基金supported by NSFC(12075102 and 11971212)the Fundamental Research Funds for the Central Universities(lzujbky-2020-pd01)。
文摘We study the ground states of attractive binary Bose-Einstein condensates with N particles,which are trapped in the steep potential wellsλV(x)inℝ2.We show that there exists a positive number N*such that if N>N*,the system admits no ground state for anyλ>0.Moreover,there exist two positive numbers,M*andλ*(N),such that if N<M*,then for anyλ>λ*(N),the system admits at least one ground state.Asλ→∞,for any fixed N<M*,we give a detailed description for the limit behavior of both positive and semi-trivial ground states.
基金Supported by the National Natural Science Foundation of China (11971393).
文摘In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].
基金supported by National Natural Science Foundation of China(11971202)Outstanding Young foundation of Jiangsu Province(BK20200042)。
文摘We study the Choquard equation-Δu+V(x)u-b(x)∫R3|u(y)|2/|x-y|dyu,x∈R3,where V(x)=V1(x),b(x)=b1(x)for x1>0 and V(x)=V2(x),b(x)=b2(x)for x1<0,and V1,V2,b1and b2are periodic in each coordinate direction.Under some suitable assumptions,we prove the existence of a ground state solution of the equation.Additionally,we find some sufficient conditions to guarantee the existence and nonexistence of a ground state solution of the equation.
文摘In this paper, we study the following Schrödinger-Kirchhoff equation where V(x) ≥ 0 and vanishes on an open set of R<sup>2</sup> and f has critical exponential growth. By using a version of Trudinger-Moser inequality and variational methods, we obtain the existence of ground state solutions for this problem.
文摘The geometries, vibrational frequencies and bind energies are reported for the ground states of CaC 2H + 2, CaC 2D + 2 and CaC 2H + 4. CaC 2H + 2 and CaC 2H + 4 equilibrium geometries have C 2v symmetry with the metal ion lying in the perpendicular bisector of the C-C bond. The ground state in both CaC 2H + 2 and CaC 2H + 4 molecules ia a 2A 1 state and the binding in the ground state is mainly electrostatic. For both CaC 2H + 2 and CaC 2H + 4 the ligand is only slightly distorted from its free ligand structure, the C-C distance has hardly increased and there is only a very small bending of the H atom away from the Ca atom. This is consistent with the electrostatic nature of the bonding. Two different approaches-Hartree-Fock(HF) and density functional theory methods(DFT)-are used and basis sets here used is 6-311+G(3df,2p). The DFT results are in good agreement with experiments, namely, DFT methods provide the benefits that some more expensive ab initio methods can do, but at essentially HF cost. So it is important to include electron correlation for accurate results in this study.
基金Project supported by the National Natural Science Foundation of China(Grant No.11504206)the Shandong Jiaotong University PhD Research Start-up Fund,China.
文摘We carry out quantum scattering dynamics and quasi-classical trajectory(QCT)calculations for the O+H2+reactive collision in the ground(1^2A')and first excited(1^2A')potential energy surface.We calculate the reaction probabilities of O+H2^+(v=0,j=0)→OH^++H and O+H2^+(v=0,j=0)→OH+H^+reaction for total angular momentum J=0.The results calculated by QCT are consistent with those from quantum mechanical wave packet.Using the QCT method,we generate in the center-of-mass frame the product state-resolved integral cross-sections(ICSs);two commonly used generalized polarization-dependent differential cross-sections(PDDCSs),(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt);and three angular distributions of the product rotational vectors,P(θr),P(φr),and P(θr,φr).We discuss the influence on the scalar and vector properties of the potential energy surface,the collision energy,and the isotope mass.Since there are deep potential wells in these two potential energy surfaces,their kinetic characteristics are similar to each other and the isotopic effect is not obvious.However,the well depths and configurations of the two potential energy surfaces are different,so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.
基金This work has been supported by the National Natural Science Foundation of China under Grant No. 10471051, and also by the Key Project of Chinese National Programs for Fundamental Research and Development(973 program) through Grant No. 2004CB318000, and also by the Fundamental Research Funds for the Central Universities under Grant No. M2009027.
文摘After developing the concept of displaced squeezed vacuum states in the non-unitary approach and establishing the connection to the unitary approach we calculate their quasiprobabilities and expectation values in general form. Then we consider the displacement of the squeezed vacuum states and calculate their photon statistics and their quasiprobabilities. The expectation values of the displaced states are related to the expectation values of the undisplaced states and are calculated for some simplest cases which are sufficient to discuss their categorization as sub-Poissonian and super-Poissonian statistics. A large set of these states do not belong to sub- or to super-Poissonian states but are also not Poissonian states. We illustrate in examples their photon distributions. This shows that the notions of sub- and of super-Poissonian statistics and their use for the definition of nonclassicality of states are problematic. In Appendix A we present the most important relations for SU (1,1) treatment of squeezing and the disentanglement of their operators. Some initial members of sequences of expectation values for squeezed vacuum states are collected in Appendix E.
文摘In this paper the results of dynamic NMR studies on ethylmethylamino-tertiary-butyl-phenylborane (EMABPB) with or without light are reported. The NMR data were recorded on a Bruker 400 MHz NMR equipped with our custom-made optical probe and with our custom-made 450 watts (W) monochromatic light sources. The molecular photochemistry including twisted intramolecular charge-transfer-excited-state (TICT) of the EMABPB in several solvents has been investigated. These results indicate that the aminoborane demonstrates multiple configurations in CD3Cl and CD2Cl2 resulting in the shifts of the signals of the alkyl groups on the nitrogen and boron. This indicates that there are some time-dependent changes at constant temperature over the irradiation interval. At ﹣60°C and the presence of light (λ = 265 nm), we observed a large change in the populations of the two sites, and this by itself indicates a modification in the rotation around the boron nitrogen bond in the excited state. By considering the existence of the TICT state, many important energy technologies may be developed with higher efficiency by controlling the back-electron transfer processes.
文摘The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 151-154, 2012, has been removed from this site.