In the previous paper by one of us (hereafter paper I), the author considered Rydberg states of the muonic-electronic helium atom or helium-like ion and used the fact that the muon motion occurs much more rapidly than...In the previous paper by one of us (hereafter paper I), the author considered Rydberg states of the muonic-electronic helium atom or helium-like ion and used the fact that the muon motion occurs much more rapidly than the electron motion. Assuming that the muon and nucleus orbits are circular, he applied the analytical method based on separating rapid and slow subsystems. He showed that the electron moves in an effective potential that is mathematically equivalent to the potential of a satellite orbiting an oblate planet like the Earth. He also showed that the “unperturbed” elliptical orbit of the electron engages in two precessions simultaneously: the precession of the electron orbit in the plane of the orbit and the precession of the orbital plane of the electron around the axis perpendicular to the plane of the muon and nuclear orbits. The problem remained whether or not the allowance for the ellipticity of the orbit could significantly change the results. In the present paper, we address this problem: we study how the allowance for a relatively low eccentricity ε of the muon and nucleus orbits affects the motion of the electron. We derive an additional, ε-dependent term in the effective potential for the motion of the electron. We show analytically that in the particular case of the planar geometry (where the electron orbit is in the plane of the muon and nucleus orbits), it leads to an additional contribution to the frequency of the precession of the electron orbit. We demonstrate that this additional, ε-depen- dent contribution to the precession frequency of the electron orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Therefore, the results of our paper seem to be important not only qualitatively, but also quantitatively.展开更多
We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework ...We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework of a variational approach. The critical values of the screening parameters for the ground states of the systems under consideration are reported for which the three-body systems are stable, while all the possible fragments are unbound;that is, it shows windows for Borromean binding.展开更多
Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character...Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model.However,limiting their ability to serve in this role,recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton,pion,kaon,and deuteron.In the context of radius measurement using electron+hadron elastic scattering,the past decade has shown that reliable extraction requires minimisation of bias associated with practitioner-dependent choices of data fitting functions.Different answers to that challenge have been offered;and this perspective describes the statistical Schlessinger point method(SPM),in unifying applications to proton,pion,kaon,and deuteron radii.Grounded in analytic function theory,independent of assumptions about underlying dynamics,free from practitioner-induced bias,and applicable in the same form to diverse systems and observables,the SPM returns an objective expression of the information contained in any data under consideration.Its robust nature and versatility make it suitable for use in many branches of experiment and theory.展开更多
文摘In the previous paper by one of us (hereafter paper I), the author considered Rydberg states of the muonic-electronic helium atom or helium-like ion and used the fact that the muon motion occurs much more rapidly than the electron motion. Assuming that the muon and nucleus orbits are circular, he applied the analytical method based on separating rapid and slow subsystems. He showed that the electron moves in an effective potential that is mathematically equivalent to the potential of a satellite orbiting an oblate planet like the Earth. He also showed that the “unperturbed” elliptical orbit of the electron engages in two precessions simultaneously: the precession of the electron orbit in the plane of the orbit and the precession of the orbital plane of the electron around the axis perpendicular to the plane of the muon and nuclear orbits. The problem remained whether or not the allowance for the ellipticity of the orbit could significantly change the results. In the present paper, we address this problem: we study how the allowance for a relatively low eccentricity ε of the muon and nucleus orbits affects the motion of the electron. We derive an additional, ε-dependent term in the effective potential for the motion of the electron. We show analytically that in the particular case of the planar geometry (where the electron orbit is in the plane of the muon and nucleus orbits), it leads to an additional contribution to the frequency of the precession of the electron orbit. We demonstrate that this additional, ε-depen- dent contribution to the precession frequency of the electron orbit can reach the same order of magnitude as the primary, ε-independent contribution to the precession frequency. Therefore, the results of our paper seem to be important not only qualitatively, but also quantitatively.
基金Supported by the National Natural Science Foundation of China under Grant No.11304086the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province of China under Grant No.UNPYSCT-2015019the Natural Science Foundation for Distinguished Young Scholars in Heilongjiang University under Grant No.JCL201503
文摘We have carried out calculations to search Borromean windows(BWs) for 11 different three-body systems interacting with screened Coulomb(Yukawa-type) potentials using Hylleraas-type wave functions within the framework of a variational approach. The critical values of the screening parameters for the ground states of the systems under consideration are reported for which the three-body systems are stable, while all the possible fragments are unbound;that is, it shows windows for Borromean binding.
基金Supported by the National Natural Science Foundation of China(12135007)Natural Science Foundation of Jiangsu Province(BK20220122)STRONG-2020"The strong interaction at the frontier of knowledge:fundamental research and applications"which received funding from the European Union's Horizon 2020 research and innovation programme(824093)。
文摘Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model.However,limiting their ability to serve in this role,recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton,pion,kaon,and deuteron.In the context of radius measurement using electron+hadron elastic scattering,the past decade has shown that reliable extraction requires minimisation of bias associated with practitioner-dependent choices of data fitting functions.Different answers to that challenge have been offered;and this perspective describes the statistical Schlessinger point method(SPM),in unifying applications to proton,pion,kaon,and deuteron radii.Grounded in analytic function theory,independent of assumptions about underlying dynamics,free from practitioner-induced bias,and applicable in the same form to diverse systems and observables,the SPM returns an objective expression of the information contained in any data under consideration.Its robust nature and versatility make it suitable for use in many branches of experiment and theory.
