Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S 2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduce...Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S 2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the （newly defined） space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated （at one-loop level） as the radiative correction on a bound electron staying in an off-mass-shell state^a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.展开更多
The Doppler-limited absorption spectra of ^14N and ^15N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging mol...The Doppler-limited absorption spectra of ^14N and ^15N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets （3s^4PJ→3p^4D^oJ, 3s^4PJ→3p^4P^oJ, 3s^2DJ→5s^2P^oJ, and 3p^2P^oJ→5s^2D^oJ） were measured and their J-dependent specific mass shifts were observed and discussed.展开更多
The mass-and field-shift parameters of the two 2s^(2)S_(1/2)→ 2p^(2)P_(1/2,3/2) transitions in the Li-like Ca ions are calculated by using multi-configuration Dirac-Hartree-Fock(MCDHF) and the relativistic configurat...The mass-and field-shift parameters of the two 2s^(2)S_(1/2)→ 2p^(2)P_(1/2,3/2) transitions in the Li-like Ca ions are calculated by using multi-configuration Dirac-Hartree-Fock(MCDHF) and the relativistic configuration interaction(RCI) methods with the inclusion of the transverse photon(Breit) interaction,vacuum polarization and self-energy corrections.In addition,the mass shift and field shift of these two transitions are calculated,where the field shift is calculated by using the evaluated value δ(r^(2)) obtained by [Atomic Data and Nuclear Data Tables 99 69(2013)].It is found that the mass shift of Li-like Ca ions is greater than the field shift.展开更多
The special mass shift coefficient and field parameter factor of four multiples,3s^4P→3p4P°,3s^4P→3p^4D°,3s^2D→5p^2D°,and 3s^2P→3p^2P°,of ^14N and ^15N were studied using the multi-configuratio...The special mass shift coefficient and field parameter factor of four multiples,3s^4P→3p4P°,3s^4P→3p^4D°,3s^2D→5p^2D°,and 3s^2P→3p^2P°,of ^14N and ^15N were studied using the multi-configuration Dirac-Hartree-Fock method and the relativistic configuration interaction approach.The normal mass shifts,special mass shifts,field shifts,and isotope shifts of N(I)were derived from the theoretical calculated normal mass shift parameter,special mass shift parameter and field parameter factor,and compared with the reported experimental measurements and theoretical results.展开更多
The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inv...The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.展开更多
Fixed-free single-walled carbon nanotubes (SWCNTs) have attracted a lot of interest in recent years due to their suitability for a wide range of applications, such as field emission and vacuum microelectronic devices,...Fixed-free single-walled carbon nanotubes (SWCNTs) have attracted a lot of interest in recent years due to their suitability for a wide range of applications, such as field emission and vacuum microelectronic devices, nanosensors, and nanoactuators. Based on a cantilever beam-bending model with a rigid mass at the free end and mode analysis, an analytical solution is developed in the present study to deal with the resonant frequency and mode shapes of a SWCNT- based mass sensor. The resonant frequency shift and mode shape of the fixed-free SWCNTs caused by the addition of a nanoscale particle to the beam tip are examined in order to explore the suitability of SWCNTs as a mass detector device. The simulation results reveal that the volume of the added particle has little effect on the first resonant frequency. In contrast, the second resonant frequency decreases with increasing the volume of the added particle. Furthermore, the resonant frequency shift of the first mode is very obvious for the amount of added mass, and the second resonant frequency decreases rapidly with increasing volume of added particle. Therefore, the first and second resonant frequencies can be used in the measurement of the mass of added particle and its volume, respectively.展开更多
Here we derive Newton’s and Einstein’s gravitational results for any mass less than or equal to a Planck mass. All of the new formulas presented in this paper give the same numerical output as the traditional formul...Here we derive Newton’s and Einstein’s gravitational results for any mass less than or equal to a Planck mass. All of the new formulas presented in this paper give the same numerical output as the traditional formulas. However, they have been rewritten in a way that gives a new perspective on the formulas when working with gravity at the level of the subatomic world. To rewrite the well-known formulas in this way could make it easier to understand the strengths and weaknesses in Newton’s and Einstein’s gravitation formulas at the subatomic scale, potentially opening them up for new important interpretations and extensions. For example, we suggest that the speed of gravity equal to that of light is actually embedded and hidden inside of Newton’s gravitational formula.展开更多
文摘Based on the accurate experimental data of energy-level differences in hydrogen-like atoms, especially the 1S 2S transitions of hydrogen and deuterium, the necessity of introducing a reduced Dirac equation with reduced mass as the substitution of original electron mass is stressed. Based on new cognition about the essence of special relativity, we provide a reasonable argument for the reduced Dirac equation to have two symmetries, the invariance under the （newly defined） space-time inversion and that under the pure space inversion, in a noninertial frame. By using the reduced Dirac equation and within the framework of quantum electrodynamics in covariant form, the Lamb shift can be evaluated （at one-loop level） as the radiative correction on a bound electron staying in an off-mass-shell state^a new approach eliminating the infrared divergence. Hence the whole calculation, though with limited accuracy, is simplified, getting rid of all divergences and free of ambiguity.
文摘The Doppler-limited absorption spectra of ^14N and ^15N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets （3s^4PJ→3p^4D^oJ, 3s^4PJ→3p^4P^oJ, 3s^2DJ→5s^2P^oJ, and 3p^2P^oJ→5s^2D^oJ） were measured and their J-dependent specific mass shifts were observed and discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.11864036)the Funds for Creative Research Groups of Gansu Province,China(Grant No.20JR5RA541)。
文摘The mass-and field-shift parameters of the two 2s^(2)S_(1/2)→ 2p^(2)P_(1/2,3/2) transitions in the Li-like Ca ions are calculated by using multi-configuration Dirac-Hartree-Fock(MCDHF) and the relativistic configuration interaction(RCI) methods with the inclusion of the transverse photon(Breit) interaction,vacuum polarization and self-energy corrections.In addition,the mass shift and field shift of these two transitions are calculated,where the field shift is calculated by using the evaluated value δ(r^(2)) obtained by [Atomic Data and Nuclear Data Tables 99 69(2013)].It is found that the mass shift of Li-like Ca ions is greater than the field shift.
基金supported by the National Natural Science Foundation of China(No.11674096,No.11874151,and No.11834003)Shanghai Pujiang Talents Plan(No.18PJ1403100).
文摘The special mass shift coefficient and field parameter factor of four multiples,3s^4P→3p4P°,3s^4P→3p^4D°,3s^2D→5p^2D°,and 3s^2P→3p^2P°,of ^14N and ^15N were studied using the multi-configuration Dirac-Hartree-Fock method and the relativistic configuration interaction approach.The normal mass shifts,special mass shifts,field shifts,and isotope shifts of N(I)were derived from the theoretical calculated normal mass shift parameter,special mass shift parameter and field parameter factor,and compared with the reported experimental measurements and theoretical results.
基金Project supported by the National Natural Science Foundation of China(Nos.11272127 and51425006)the Research Fund for the Doctoral Program of Higher Education of China(No.20130142110022)the Grant from the Impact and Safety of Coastal Engineering Initiative Program of Zhejiang Provincial Government at Ningbo University(No.zj1213)
文摘The dynamic characteristics of a quartz crystal resonator（QCR） in thicknessshear modes（TSM） with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction（surface shear force）, thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.
文摘Fixed-free single-walled carbon nanotubes (SWCNTs) have attracted a lot of interest in recent years due to their suitability for a wide range of applications, such as field emission and vacuum microelectronic devices, nanosensors, and nanoactuators. Based on a cantilever beam-bending model with a rigid mass at the free end and mode analysis, an analytical solution is developed in the present study to deal with the resonant frequency and mode shapes of a SWCNT- based mass sensor. The resonant frequency shift and mode shape of the fixed-free SWCNTs caused by the addition of a nanoscale particle to the beam tip are examined in order to explore the suitability of SWCNTs as a mass detector device. The simulation results reveal that the volume of the added particle has little effect on the first resonant frequency. In contrast, the second resonant frequency decreases with increasing the volume of the added particle. Furthermore, the resonant frequency shift of the first mode is very obvious for the amount of added mass, and the second resonant frequency decreases rapidly with increasing volume of added particle. Therefore, the first and second resonant frequencies can be used in the measurement of the mass of added particle and its volume, respectively.
文摘Here we derive Newton’s and Einstein’s gravitational results for any mass less than or equal to a Planck mass. All of the new formulas presented in this paper give the same numerical output as the traditional formulas. However, they have been rewritten in a way that gives a new perspective on the formulas when working with gravity at the level of the subatomic world. To rewrite the well-known formulas in this way could make it easier to understand the strengths and weaknesses in Newton’s and Einstein’s gravitation formulas at the subatomic scale, potentially opening them up for new important interpretations and extensions. For example, we suggest that the speed of gravity equal to that of light is actually embedded and hidden inside of Newton’s gravitational formula.
