In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The...In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).展开更多
In this manuscript, the existence of periodic orbits of collision of the first kind has been discussed on the model of Autonomous Four-body Problem by the method of analytic continuation given by Giacaglia [1] and Bha...In this manuscript, the existence of periodic orbits of collision of the first kind has been discussed on the model of Autonomous Four-body Problem by the method of analytic continuation given by Giacaglia [1] and Bhatnagar [2] [3]. For the existence of periodic orbits, Duboshin’s criterion [4] has been satisfied and it has been confirmed by analyzing the Poincare surfaces of section (PSS) [5]. Also it has been shown that the case of collision given by Levi-Civita [6] [7] is conserved by the method analytic continuation. In all sections of this manuscript, equilateral triangular configuration given by Ceccaroni and Biggs [8] has been considered. In this model, third primary of L4 inferior mass (in comparison of the other primaries) is placed at the equilibrium point of the R3BP.展开更多
Stability for the notn-autonomous bicircular four-body model is analytically investigated in this study.The gowerning equation is derived from Newton's law of gravity.When the distance between the infnitesimal mas...Stability for the notn-autonomous bicircular four-body model is analytically investigated in this study.The gowerning equation is derived from Newton's law of gravity.When the distance between the infnitesimal mass and the third primary is expanded as Taylor expansions,the governing equation can be regarded 3 two parts:the unperturbed conservative system and the small periodically parametric excitations.The unperturbed system's natural frequency and paramettic frequency are analyzed for the posibility of principal parametric resonances.The method of multiple scales is applied directly to the governing equation.The stability conditions are obtained analytically for the principal pararmetric resonance.Numerical method demonstrates the efflciency of the analytical results.展开更多
Abstract:We study the four-body decays of neutral flavored mesons,including■,and■.These processes,which could be induced by a hypothetical doubly-charged scalar particle,do not conserve the lepton number.Assuming,as...Abstract:We study the four-body decays of neutral flavored mesons,including■,and■.These processes,which could be induced by a hypothetical doubly-charged scalar particle,do not conserve the lepton number.Assuming,as an example,that the mass of the doubly-charged particle is 1000 Ge V,and using the upper bounds of the couplings,we calculate the branching ratios of different channels.For■,and■,it is of the order of 10^(-30),10^(-32)–10^(-29),and 10^(-33)–10^(-28),respectively.Based on the experimental results for the■channels,we also find the upper limit for the quantity■.展开更多
Analytical formulae for the phase space factors and three-momenta of three-and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables.These formulae will...Analytical formulae for the phase space factors and three-momenta of three-and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables.These formulae will help experimental physicists to perform data analysis.As an example,we show how to use these formulae to distinguish the different mechanisms of the e+p→e+J/ψ+p process when searching the signals of P_(c) states in the energy region of the Electron-Ion collider at China(EicC).展开更多
A four-body distorted-wave approximation is applied for theoretical analysis of the fully differential cross sections（FDCS） for proton-impact single ionization of helium atoms in their ground states. The nine-dimens...A four-body distorted-wave approximation is applied for theoretical analysis of the fully differential cross sections（FDCS） for proton-impact single ionization of helium atoms in their ground states. The nine-dimensional integrals for the partial amplitudes are analytically reduced to closed-form expressions or some one-dimensional integrals which can be easily calculated numerically. Calculations are performed in the scattering and perpendicular planes. The influence of the target static electron correlations on the process is investigated using a number of different bound-state wave functions for the ground state of the helium targets. An illustrative computation is performed for 75-ke V proton–helium collisions and the obtained results are compared with experimental data and other theoretical predictions. Although for small momentum transfers, the comparison shows a reasonable agreement with experiments in the scattering and perpendicular planes, some significant discrepancies are still present at large momentum transfers in these planes. However, our results are compatible and for some cases, better than those of the other sophisticated calculations.展开更多
Fully differential cross sections （FDCS） are calculated within a four-body model for single ionization of helium by C6＋ impact at the incident energy of 100 MeV/a.u. （atomic unit）. The results are compared with e...Fully differential cross sections （FDCS） are calculated within a four-body model for single ionization of helium by C6＋ impact at the incident energy of 100 MeV/a.u. （atomic unit）. The results are compared with experimental data and other theoretical predictions. It is shown that our results are in very good agreement with experiment for three small momentum transfers in the scattering plane; however, some significant discrepancies are still present at the largest momentum transfer in both the scattering plane and the perpendicular plane. In actuality, the problem has not been explained by the theory during the last decade. Accordingly, the contributions of different scattering amplitudes to FDCS are analyzed. It is found that for the largest momentum transfer the cross section arising from a destructive interference of the three amplitudes is much smaller than the experimental data. However, the cross section due to the constructive interference of two scattering amplitudes between projectile-ionized electron interaction and projectile-passive electron interaction almost approaches the experimental data.展开更多
The four-body model has been used to calculate the fully differential cross-sections （FDCS） for the single ionization of helium by 100 MeV/amu Ca^＋ impact in geometries. By comparing with experimental data and othe...The four-body model has been used to calculate the fully differential cross-sections （FDCS） for the single ionization of helium by 100 MeV/amu Ca^＋ impact in geometries. By comparing with experimental data and other theories, we find the results of four-body model are in very good agreement in the scattering plane, but poor agreement out of the scattering plane. Accordingly, the contributions of different scattering amplitudes to FDCS are analyzed. It is found that the cross sections due to the interference of the scattering amplitudes between projectile-target nucleus interaction and projectile-ejected electron interaction almost tend to experimental results around the recoil region in geometries. In particular in the perpendicular plane, the cross section originating from interference of the scattering amplitudes between projectile-target nucleus and projectile-ejected electron interactions yields an experimental double-peak structure in the angular distribution. However, this feature could not be presented by the interference of the three amplitudes. Thus, the failure of the fourbody model predicting the feature in this geometry may be attributed to an inappropriate weighting of the three amplitudes.展开更多
A four-body distorted wave approximation is presented for theoretical investigations of the single ionization of groundstate helium atoms by fully stripped carbon ions at impact energies of 2 MeV/amu and 100 MeV/amu. ...A four-body distorted wave approximation is presented for theoretical investigations of the single ionization of groundstate helium atoms by fully stripped carbon ions at impact energies of 2 MeV/amu and 100 MeV/amu. The nine-dimensional integrals for the partial quantum-mechanical transition amplitudes of the specified reaction are reduced to some analytical expressions or one-dimensional integrals over real variables. Fully differential cross sections（FDCSs） are calculated and compared with their experimental values as well as the results obtained from other theories. Despite the simplicity and quickness of the proposed quadrature, the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other complicated theories.展开更多
The four-body Coulomb–Born distorted wave approximation is applied to investigate the integral as well as projectile angular-differential cross sections for single-electron capture in the collision of energetic singl...The four-body Coulomb–Born distorted wave approximation is applied to investigate the integral as well as projectile angular-differential cross sections for single-electron capture in the collision of energetic singly positive charged helium ions with helium atoms in their ground states. The formalism satisfies the correct boundary conditions. The influence of the dynamic electron correlations on the cross sections is studied by considering the inter electronic interactions in the complete perturbation potentials in post form. Also, the sensitivity of the cross sections to the static electronic correlations is studied by using the single-zeta and the highly correlated Byron–Joachain wave functions to describe the initial bound state of the active electrons. The obtained results for the energy range of 40–5000 ke V/amu are reported and compared with other three- and four-body theoretical data and available experimental measurements. The comparison leads us to discuss the validity of the applied approach and survey the interaction effects on the cross sections by recognizing the electron–electron interaction. Particularly, for differential cross sections, the comparison of the present four-body method with the experiment shows that the agreement is not as good as that for its three-body version.展开更多
The present paper deals with the existence of periodic orbits in the Circular Restricted Four-Body Problem (CR4BP) in two-dimensional co-ordinate system when the second primary is a triaxial rigid body and the third p...The present paper deals with the existence of periodic orbits in the Circular Restricted Four-Body Problem (CR4BP) in two-dimensional co-ordinate system when the second primary is a triaxial rigid body and the third primary of inferior mass (in comparison of the other primaries) is placed at triangular libration point L4 of the Circular Restricted Three-Body Problem (CR3BP). With the help of generating solutions, we formed a basis for the existence of periodic orbits, then an analytical approach given by Hassan et al. [1], was applied to our model of equilateral triangular configuration. It is found that in general solution also;the character of periodic orbits is conserved. For verification of the existence of periodic orbits, we have applied the criterion of Duboshin [2] and found satisfied.展开更多
文摘In this work, the Hamiltonian of the four-body problem is considered under the effects of solar radiation pressure. The equations of motion of the infinitesimal body are obtained in the Hamiltonian canonical form. The libration points and the corresponding Jacobi constants are obtained with different values of the solar radiation pressure coefficient. The motion and its stability about each point are studied. A family of periodic orbits under the effects of the gravitational forces of the primaries and the solar radiation pressure are obtained depending on the pure numerical method. This purpose is applied to the Sun-Earth-Moon-Space craft system, and the results obtained are in a good agreement with the previous work such as (Kumari and Papadouris, 2013).
文摘In this manuscript, the existence of periodic orbits of collision of the first kind has been discussed on the model of Autonomous Four-body Problem by the method of analytic continuation given by Giacaglia [1] and Bhatnagar [2] [3]. For the existence of periodic orbits, Duboshin’s criterion [4] has been satisfied and it has been confirmed by analyzing the Poincare surfaces of section (PSS) [5]. Also it has been shown that the case of collision given by Levi-Civita [6] [7] is conserved by the method analytic continuation. In all sections of this manuscript, equilateral triangular configuration given by Ceccaroni and Biggs [8] has been considered. In this model, third primary of L4 inferior mass (in comparison of the other primaries) is placed at the equilibrium point of the R3BP.
基金The authors gratefully acknowledge the support of the National Natural Science Foundation of China through Grant Nos.11402007,11772009,and 11672007.
文摘Stability for the notn-autonomous bicircular four-body model is analytically investigated in this study.The gowerning equation is derived from Newton's law of gravity.When the distance between the infnitesimal mass and the third primary is expanded as Taylor expansions,the governing equation can be regarded 3 two parts:the unperturbed conservative system and the small periodically parametric excitations.The unperturbed system's natural frequency and paramettic frequency are analyzed for the posibility of principal parametric resonances.The method of multiple scales is applied directly to the governing equation.The stability conditions are obtained analytically for the principal pararmetric resonance.Numerical method demonstrates the efflciency of the analytical results.
基金Supported by National Natural Science Foundation of China(11405037,11575048,11505039)
文摘Abstract:We study the four-body decays of neutral flavored mesons,including■,and■.These processes,which could be induced by a hypothetical doubly-charged scalar particle,do not conserve the lepton number.Assuming,as an example,that the mass of the doubly-charged particle is 1000 Ge V,and using the upper bounds of the couplings,we calculate the branching ratios of different channels.For■,and■,it is of the order of 10^(-30),10^(-32)–10^(-29),and 10^(-33)–10^(-28),respectively.Based on the experimental results for the■channels,we also find the upper limit for the quantity■.
基金Supported by the Fundamental Research Funds for the Central Universitiesthe National Key R&D Program of China (2020YFA0406400)the Key Research Program of the Chinese Academy of Sciences (XDPB15)。
文摘Analytical formulae for the phase space factors and three-momenta of three-and four-body final states are derived for all sets of independent kinematic variables containing invariant mass variables.These formulae will help experimental physicists to perform data analysis.As an example,we show how to use these formulae to distinguish the different mechanisms of the e+p→e+J/ψ+p process when searching the signals of P_(c) states in the energy region of the Electron-Ion collider at China(EicC).
文摘A four-body distorted-wave approximation is applied for theoretical analysis of the fully differential cross sections（FDCS） for proton-impact single ionization of helium atoms in their ground states. The nine-dimensional integrals for the partial amplitudes are analytically reduced to closed-form expressions or some one-dimensional integrals which can be easily calculated numerically. Calculations are performed in the scattering and perpendicular planes. The influence of the target static electron correlations on the process is investigated using a number of different bound-state wave functions for the ground state of the helium targets. An illustrative computation is performed for 75-ke V proton–helium collisions and the obtained results are compared with experimental data and other theoretical predictions. Although for small momentum transfers, the comparison shows a reasonable agreement with experiments in the scattering and perpendicular planes, some significant discrepancies are still present at large momentum transfers in these planes. However, our results are compatible and for some cases, better than those of the other sophisticated calculations.
基金supported by the National Natural Science Foundation of China(Grant No.11274215)the Natural Science Foundation of Shanxi Province,China(Grants Nos.20051008 and 2010011009)the Technology Project of Shanxi Provincial Education Department,China(Grant No.20111011)
文摘Fully differential cross sections （FDCS） are calculated within a four-body model for single ionization of helium by C6＋ impact at the incident energy of 100 MeV/a.u. （atomic unit）. The results are compared with experimental data and other theoretical predictions. It is shown that our results are in very good agreement with experiment for three small momentum transfers in the scattering plane; however, some significant discrepancies are still present at the largest momentum transfer in both the scattering plane and the perpendicular plane. In actuality, the problem has not been explained by the theory during the last decade. Accordingly, the contributions of different scattering amplitudes to FDCS are analyzed. It is found that for the largest momentum transfer the cross section arising from a destructive interference of the three amplitudes is much smaller than the experimental data. However, the cross section due to the constructive interference of two scattering amplitudes between projectile-ionized electron interaction and projectile-passive electron interaction almost approaches the experimental data.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.11274215）, the Natural Science Foundation of Shanxi Province, China （No.20051008 and No.2010011009）, and the Technology Project of Shanxi Provincial Education Department, China （No.20111011）.
文摘The four-body model has been used to calculate the fully differential cross-sections （FDCS） for the single ionization of helium by 100 MeV/amu Ca^＋ impact in geometries. By comparing with experimental data and other theories, we find the results of four-body model are in very good agreement in the scattering plane, but poor agreement out of the scattering plane. Accordingly, the contributions of different scattering amplitudes to FDCS are analyzed. It is found that the cross sections due to the interference of the scattering amplitudes between projectile-target nucleus interaction and projectile-ejected electron interaction almost tend to experimental results around the recoil region in geometries. In particular in the perpendicular plane, the cross section originating from interference of the scattering amplitudes between projectile-target nucleus and projectile-ejected electron interactions yields an experimental double-peak structure in the angular distribution. However, this feature could not be presented by the interference of the three amplitudes. Thus, the failure of the fourbody model predicting the feature in this geometry may be attributed to an inappropriate weighting of the three amplitudes.
基金the office of graduate studies at the University of Isfahan for their support and research facilities
文摘A four-body distorted wave approximation is presented for theoretical investigations of the single ionization of groundstate helium atoms by fully stripped carbon ions at impact energies of 2 MeV/amu and 100 MeV/amu. The nine-dimensional integrals for the partial quantum-mechanical transition amplitudes of the specified reaction are reduced to some analytical expressions or one-dimensional integrals over real variables. Fully differential cross sections（FDCSs） are calculated and compared with their experimental values as well as the results obtained from other theories. Despite the simplicity and quickness of the proposed quadrature, the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other complicated theories.
文摘The four-body Coulomb–Born distorted wave approximation is applied to investigate the integral as well as projectile angular-differential cross sections for single-electron capture in the collision of energetic singly positive charged helium ions with helium atoms in their ground states. The formalism satisfies the correct boundary conditions. The influence of the dynamic electron correlations on the cross sections is studied by considering the inter electronic interactions in the complete perturbation potentials in post form. Also, the sensitivity of the cross sections to the static electronic correlations is studied by using the single-zeta and the highly correlated Byron–Joachain wave functions to describe the initial bound state of the active electrons. The obtained results for the energy range of 40–5000 ke V/amu are reported and compared with other three- and four-body theoretical data and available experimental measurements. The comparison leads us to discuss the validity of the applied approach and survey the interaction effects on the cross sections by recognizing the electron–electron interaction. Particularly, for differential cross sections, the comparison of the present four-body method with the experiment shows that the agreement is not as good as that for its three-body version.
文摘The present paper deals with the existence of periodic orbits in the Circular Restricted Four-Body Problem (CR4BP) in two-dimensional co-ordinate system when the second primary is a triaxial rigid body and the third primary of inferior mass (in comparison of the other primaries) is placed at triangular libration point L4 of the Circular Restricted Three-Body Problem (CR3BP). With the help of generating solutions, we formed a basis for the existence of periodic orbits, then an analytical approach given by Hassan et al. [1], was applied to our model of equilateral triangular configuration. It is found that in general solution also;the character of periodic orbits is conserved. For verification of the existence of periodic orbits, we have applied the criterion of Duboshin [2] and found satisfied.
