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Annealing Behaviour of Helium Bubbles in Titanium Films by Thermal Desorption Spectroscopy and Positron Beam Analysis 被引量:2
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作者 刘超卓 周筑颖 +3 位作者 施立群 王宝义 郝小鹏 赵国庆 《Chinese Physics Letters》 SCIE CAS CSCD 2007年第8期2357-2360,共4页
Helium-containing Ti Glms are prepared using magnetron sputtering in the helium-argon atmosphere. Isochronal annealing at different temperatures for an hour is employed to reveal the behaviour of helium bubble growth.... Helium-containing Ti Glms are prepared using magnetron sputtering in the helium-argon atmosphere. Isochronal annealing at different temperatures for an hour is employed to reveal the behaviour of helium bubble growth. Ion beam analysis is used to measure the retained helium content. Helium can release largely when annealing above 970K. A thermal helium desorption spectroscopy system is constructed for assessment of the evolution of helium bubbles in the annealed samples by linear heating (OAK/s) from room temperature to 1500K. Also, Doppler broadening measurements of positron annihilation radiation spectrum are performed by using changeable energy positron beam. Bubble coarsening evolves gradually below 680K, migration and coalescence of small bubbles dominates in the range of 68-970 K, and the Ostwald ripening mechanism enlarges the bubbles with a massive release above 970K. 展开更多
关键词 coated conductor buffer layer self-epitaxy CEO2
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Development of scanning transmission ion microscopy computed tomography at Fudan microbeam line
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作者 LI Yongqiang HABCHI Claire +2 位作者 LIU Xue LIU Yiyang SHEN Hao 《Nuclear Science and Techniques》 SCIE CAS CSCD 2013年第4期5-8,共4页
The computed tomography was applied to setting STIM(Scanning Transmission Ion Microscopy) projections recorded at the Fudan Ion Beam Laboratory.In this work,in order to visualize the three-dimensional mass density dis... The computed tomography was applied to setting STIM(Scanning Transmission Ion Microscopy) projections recorded at the Fudan Ion Beam Laboratory.In this work,in order to visualize the three-dimensional mass density distribution in several specimens,example for a test structure of hollow gold cyliner was presented together with a detailed description of the developed system,including data reconstruction code(Tomorebuild 2) and image display software(AMIRA).Future development will allow the particle induced X-ray emission tomography for elemental analysis of micrometer-sized samples. 展开更多
关键词 计算机断层扫描 离子束 透射 线扫描 开发 微束 X射线发射 STIM
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Ion Beam Analysis of the Annealing Behavior of Helium in Ti Films
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作者 何志江 施立群 +3 位作者 刘超卓 张磊 鲁永芳 张斌 《Chinese Physics Letters》 SCIE CAS CSCD 2009年第4期74-77,共4页
We present a theoretical calculation finding that a spectrum from ion beam analysis will change at different stopping cross sections. This is more visible at a deeper place in the sample. Helium-contained Ti films ann... We present a theoretical calculation finding that a spectrum from ion beam analysis will change at different stopping cross sections. This is more visible at a deeper place in the sample. Helium-contained Ti films annealed at different temperatures are prepared to gain different stopping cross sections whereby the stopping cross section will change with the helium phase states and the pressure of helium bubbles. Then ion beam analysis is used to measure the concentration of helium. It is found that the concentration curve rises greatly after the sample is annealed at 673K which reflects the increasing size of the helium bubble. The results axe consistent with that of positron annihilation radiation spectra which are performed by using a changeable energy positron beam. 展开更多
关键词 gamma-ray bursts GAMMA-RAYS RELATIVITY
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Electron beam density imaging system at Beam study using a portable slit the Shanghai Electron Ion Trap
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作者 Yang Yang Lu Di +6 位作者 Pu Yun-Qing Yao Ke Chen Wei-Dong Xiao Jun Geng Zhi-Xian Roger Hutton Zou Ya-Ming 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第8期136-142,共7页
In this work, a portable slit imaging system is developed to study both the electron beam diameter and the profile of the newly developed Shanghai Electron Beam Ion Trap (Shanghai EBIT). Images are detected by a cha... In this work, a portable slit imaging system is developed to study both the electron beam diameter and the profile of the newly developed Shanghai Electron Beam Ion Trap (Shanghai EBIT). Images are detected by a charge coupled device (CCD) sensitive to both X rays and longer wavelength photons (up to visible). Large scale ray tracings were conducted for correcting the image broadening effects caused by the finite slit width and the finite width of the CCD pixels. A numerical de-convolution method was developed to analyse and reconstruct the electron beam density distribution in the EBIT. As an example of the measured beam diameter and current density, the FWHM (full width at half maximum) diameter of the electron beam at 81 keV and 120 mA is found to be 76.2 μm and the density 2.00 × 10^3 A.cm-2, under a magnetic field of 3 T, including all corrections. 展开更多
关键词 electron beam density slit imaging de-convolution
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The present status of the Shanghai electron beam ion trap
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作者 GUO Pan-Lin HU Wei +11 位作者 GONG Pei-Rong LU Di HE Mian-Hong WU Shimin YAO Ke HUANG Min ZHANG Xue-Mei WANG Xin-Cheng ZHU Xi-Kai JIANG Di-Kui HUTTON R ZOU Ya-Ming 《Nuclear Science and Techniques》 SCIE CAS CSCD 2005年第6期335-337,共3页
In this report, an introduction to the structure of Shanghai EBIT, a brief description of the status ofShanghai EBIT project, and a short discussion of the first results of Shanghai EBIT are presented.
关键词 上海 电子束 原子物理学 电离
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Local Tuning of the Surface Potential in Silicon Carriers by Ion Beam Induced Intrinsic Defects
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作者 Daniel Blaschke Lars Rebohle +1 位作者 Ilona Skorupa Heidemarie Schmidt 《Advances in Materials Physics and Chemistry》 CAS 2022年第11期289-305,共17页
The immobilization of biomaterials on a carrier is the first step for many different applications in life science and medicine. The usage of surface-near electrostatic forces is one possible approach to guide the char... The immobilization of biomaterials on a carrier is the first step for many different applications in life science and medicine. The usage of surface-near electrostatic forces is one possible approach to guide the charged biomaterials to a specific location on the carrier. In this study, we investigate the effect of intrinsic defects on the surface potential of silicon carriers in the dark and under illumination by means of Kelvin probe force microscopy. The intrinsic defects were introduced into the carrier by local, stripe-patterned ion implantation of silicon ions with a fluence of 3 × 10<sup>13</sup> Si ions/cm<sup>2</sup> and 3 × 10<sup>15</sup> Si ions/cm<sup>2</sup> into a p-type silicon wafer with a dopant concentration of 9 × 10<sup>15</sup> B/cm<sup>3</sup>. The patterned implantation allows a direct comparison between the surface potential of the silicon host against the surface potential of implanted stripes. The depth of the implanted silicon ions in the target and the concentration of displaced silicon atoms was simulated using the Stopping and Range of Ions in Matter (SRIM) software. The low fluence implantation shows a negligible effect on the measured Kelvin bias in the dark, whereas the large fluence implantation leads to an increased Kelvin bias, i.e. to a smaller surface work function according to the contact potential difference model. Illumination causes a reduced surface band bending and surface potential in the non-implanted regions. The change of the Kelvin bias in the implanted regions under illumination provides insight into the mobility and lifetime of photo-generated electron-hole pairs. Finally, the effect of annealing on the intrinsic defect density is discussed and compared with atomic force microscopy measurements on the 2<sup>nd</sup> harmonic. In addition, by using the Baumgart, Helm, Schmidt interpretation of the measured Kelvin bias, the dopant concentration after implantation is estimated. 展开更多
关键词 Kelvin Probe Force Microscopy Surface Potential Intrinsic Defects SILICON Ion Implantation
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Rotating magnetic field inhibits Aβ protein aggregation and alleviates cognitive impairment in Alzheimer’s disease mice
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作者 Ruo-Wen Guo Wen-Jing Xie +5 位作者 Biao Yu Chao Song Xin-Miao Ji Xin-Yu Wang Mei Zhang Xin Zhang 《Zoological Research》 SCIE CSCD 2024年第4期924-936,共13页
Amyloid beta(Aβ)monomers aggregate to form fibrils and amyloid plaques,which are critical mechanisms in the pathogenesis of Alzheimer’s disease(AD).Given the important role of Aβ1-42 aggregation in plaque formation... Amyloid beta(Aβ)monomers aggregate to form fibrils and amyloid plaques,which are critical mechanisms in the pathogenesis of Alzheimer’s disease(AD).Given the important role of Aβ1-42 aggregation in plaque formation,leading to brain lesions and cognitive impairment,numerous studies have aimed to reduce Aβaggregation and slow AD progression.The diphenylalanine(FF)sequence is critical for amyloid aggregation,and magnetic fields can affect peptide alignment due to the diamagnetic anisotropy of aromatic rings.In this study,we examined the effects of a moderate-intensity rotating magnetic field(RMF)on Aβaggregation and AD pathogenesis.Results indicated that the RMF directly inhibited Aβamyloid fibril formation and reduced Aβ-induced cytotoxicity in neural cells in vitro.Using the AD mouse model APP/PS1,RMF restored motor abilities to healthy control levels and significantly alleviated cognitive impairments,including exploration and spatial and non-spatial memory abilities.Tissue examinations demonstrated that RMF reduced amyloid plaque accumulation,attenuated microglial activation,and reduced oxidative stress in the APP/PS1 mouse brain.These findings suggest that RMF holds considerable potential as a non-invasive,high-penetration physical approach for AD treatment. 展开更多
关键词 lzheimer’s disease Rotating magnetic field Amyloid-β Cognitive function Alzheimer’s disease animal models
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Polydispersity effects on the magnetization of diluted ferrofluids:a lognormal analysis 被引量:2
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作者 王旭飞 施立群 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第10期534-540,共7页
Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lo... Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lognormal dispersion, it first performs reduced calculations without material parameters. From the results, it is extrapolated that for the ferrofluid of lognormal polydispersion, in comparison with the corresponding monodispersion, the saturation magnetization is enhanced higher by the particle size distribution. It also indicates that in an equivalent magnetic field, the lognormally polydispersed ferrofluid is magnetically saturated faster than the corresponding monodispersion. Along the theoretical extrapolations, the polydispersity effects are evaluated for a typical ferrofluid of magnetite, with a dispersity of σ = 0.20. The results indicate that the lognormal polydispersity leads to a slight increase of the saturation magnetization, but a noticeable increase of the speed to reach the saturation value in an equivalent magnetic field. 展开更多
关键词 FERROFLUID polydispersity effects lognormal distribution
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The Effect of Current Density on CN_(x) Crystal Grain Growth in Electrochemical Deposition 被引量:2
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作者 YU Wei-Feng CAO Rong-Gen +2 位作者 TIAN Yu WANG Jian-Zhong NING Xi-Jing 《Chinese Physics Letters》 SCIE CAS CSCD 2011年第2期228-230,共3页
The effect of charge current density on the growth of CN_(χ)films by electrolysis of a methanol-urea solution is investigated experimentally.It is seen that the C-C_(3)N_(4) phase grains in the films are about 200-30... The effect of charge current density on the growth of CN_(χ)films by electrolysis of a methanol-urea solution is investigated experimentally.It is seen that the C-C_(3)N_(4) phase grains in the films are about 200-300 nm for a density of 55 mA/cm^(2)and dendrite growth takes place with grains as large as 7μm formed when density is about 70 m A/cm^(2). 展开更多
关键词 CRYSTAL ELECTROCHEMICAL METHANOL
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KLn Dielectronic Recombination Process of B- Through He-like Cu Ions 被引量:1
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作者 高迎辉 张雪梅 +3 位作者 孟凡昌 陈卫东 陈重阳 邹亚明 《Chinese Physics Letters》 SCIE CAS CSCD 2008年第3期930-933,共4页
The KLn dielectronic recombination processes of trapped highly charged B-like through He-like Cu ions are studied theoretically, and the theoretical results are used to analyse our previous experimental data at Heidel... The KLn dielectronic recombination processes of trapped highly charged B-like through He-like Cu ions are studied theoretically, and the theoretical results are used to analyse our previous experimental data at Heidelberg electron beam ion trap (EBIT). The theoretical resonant positions agree with the experimental resonant positions to a precision of 0.4%, in comparison with the resonant positions of those highest peaks between theory and experiment. The experimental spectra are then fitted using a formula with the theoretical resonant energies and strengths, the result shows good overall agreement between theory and experiment over a wide electron energy range. The distribution of highly charged states is obtained from the fitting parameters. 展开更多
关键词 RATE COEFFICIENTS ISOSEQUENCES TRAP FE CA MG NI AR SI
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Time-Resolved Measurements of the Adsorption/Desorption of Rb Atoms on Octadecyltrichlorosilane Coated Surfaces 被引量:1
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作者 廖康佳 王美玲 +1 位作者 张贵迎 赵凯锋 《Chinese Physics Letters》 SCIE CAS CSCD 2015年第7期121-123,共3页
We carry out the first time-resolved measurement of Rb atoms desorbing from octadecyltrichlorosilane coated sur- faces by polarizing the atoms near the surface using an evanescent wave pump pulse and watching the subs... We carry out the first time-resolved measurement of Rb atoms desorbing from octadecyltrichlorosilane coated sur- faces by polarizing the atoms near the surface using an evanescent wave pump pulse and watching the subsequent intensity change of another evanescent wave probe beam, and find the mean adsorption (dwell) time to be about 400ns at a cell body temperature of 112℃. The adsorption energy is found to be 0.19eV from the surface tem- perature dependence of the adsorption time. This method can be extended to study the adsorption/desorption process of other alkali atoms on other surfaces of transparent substrates with an ultimate time resolution limited by the flight time of atoms in the evanescent wave which is of the order of nanoseconds. 展开更多
关键词 Time-Resolved Measurements of the Adsorption/Desorption of Rb Atoms on Octadecyltrichlorosilane Coated Surfaces RB OTS
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Pair Production in an Intense Laser Pulse: The Effect of Pulse Length 被引量:1
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作者 REN Na WANG Jia-Xiang +1 位作者 LI An-Kang WANG Ping-Xiao 《Chinese Physics Letters》 SCIE CAS CSCD 2012年第7期47-50,共4页
Production of positron-electron (e^(+) e^(-) ) pairs in an intense laser pulse is investigated by solving the Dirac equation with analytical and numerical methods.We observe that the probability of the pair production... Production of positron-electron (e^(+) e^(-) ) pairs in an intense laser pulse is investigated by solving the Dirac equation with analytical and numerical methods.We observe that the probability of the pair production will firstly decrease slowly as the pulse length T becomes shortened.Then it will increase until T is reduced to the Compton time Tc =(h)/(mec) ≈ 1.29 × 10^(-21)s and finally decrease exponentially to zero.Hence,for a prominent pair production,we not only require that the electric field strength should be higher than the Schwinger critical value Ecr =m^(2)c^(3)/(e(h)) ≈ 1.32 × 10^(16) V/cm,but also that the pulse duration T should be larger than Tc.The latter is shown to be related to momentum requirement for the transition.For fields with different pulse lengths,the phase and chirp influences upon the pair production are also explored. 展开更多
关键词 TRANSITION PULSE slowly
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P-Type Nitrogen-Doped ZnO Films Prepared by In-Situ Thermal Oxidation of Zn_3N_2 Films
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作者 靳玉平 张斌 +1 位作者 王建中 施立群 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第5期119-122,共4页
P-type nitrogen-doped ZnO films are prepared successfully by in-situ thermal oxidation of Zn3N2 films. The prepared films are characterized by x-ray diffraction, non-Rutherford back.scattering (non-RBS) spectroscopy... P-type nitrogen-doped ZnO films are prepared successfully by in-situ thermal oxidation of Zn3N2 films. The prepared films are characterized by x-ray diffraction, non-Rutherford back.scattering (non-RBS) spectroscopy, x- ray photoelectron spectroscopy, and photoluminescence spectrum. The results show that the Zn3N1 films start to transform to ZnO at 400℃ and the total nitrogen content decreases with the increasing annealing temperature. The p-type fihns are achieved at 500℃ with a low resistivity of 6.33Ω.cm and a high hole concentration of +8.82 × 10^17 cm-3, as well as a low level of carbon contamination, indicating that the substitutional nitrogen (No) is an effective acceptor in the ZnO:N film. The photoluminescence spectra show clear UV emissions and also indicate the presence of oxygen vacancy (Vo) defects in the ZnO:N films. The p-type doping mechanism is briefly discussed. 展开更多
关键词 ZnO in or as In P-Type Nitrogen-Doped ZnO Films Prepared by In-Situ Thermal Oxidation of Zn3N2 Films of by
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The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin
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作者 卜庆阳 李增花 Hans-Josef Schulze 《Chinese Physics Letters》 SCIE CAS CSCD 2016年第3期20-23,共4页
The equation of state for nuclear matter is presented within the Brueckner Hartree-Fock (BHF) scheme, by using the realistic Argonne VI8 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nu... The equation of state for nuclear matter is presented within the Brueckner Hartree-Fock (BHF) scheme, by using the realistic Argonne VI8 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces. It is then applied to calculate the properties of finite nuclei within a simple liquid-drop model, and we compare the calculated volume, surface, and Coulomb parameters with the empirical ones from the liquid drop model. Nuclear density distributions and charge radii in good agreement with the experimental data are obtained~ and we predict the neutron skin thickness of various nuclei. 展开更多
关键词 for on of The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin BHF IS been EOS that
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A K-CELL injection system for SH-PermEBIT
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作者 韩川 赵瑞峰 +2 位作者 施展 Roger Hutton 路迪 《Nuclear Science and Techniques》 SCIE CAS CSCD 2014年第4期21-23,共3页
In this paper,we report a newly developed Knudsen Cell injection system for SH-PermEBIT.This technique can overcome disadvantages of introducing organometallic gases and wired probes into EBIT and provide steady conti... In this paper,we report a newly developed Knudsen Cell injection system for SH-PermEBIT.This technique can overcome disadvantages of introducing organometallic gases and wired probes into EBIT and provide steady continuous injection.A specially designed vacuum line is used to ensure that the Knudsen Cell satisfies the vacuum level of SH-permEBIT.Using this system we successfully injected ytterbium into the SH-permEBIT and recorded a spectrum in the visible wavelength region. 展开更多
关键词 喷射系统 注射系统 EBIT 有机气体 波长范围 真空度 可见光 细胞
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Resonance Excitation Rate Coefficient of Ni-Like Tantalum
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作者 沈天明 陈重阳 +1 位作者 王炎森 顾明峰 《Chinese Physics Letters》 SCIE CAS CSCD 2007年第4期925-928,共4页
The ab initio calculations of electron-impact resonant excitation rate coefficients from the ground level to 54 fine-structure levels of 3d94l (1 = s, p, d, f) configurations of Ni-like tantalum ion are performed by... The ab initio calculations of electron-impact resonant excitation rate coefficients from the ground level to 54 fine-structure levels of 3d94l (1 = s, p, d, f) configurations of Ni-like tantalum ion are performed by using a fully relativistic distorted-wave approximation. The configuration-interaction effects are taken into account. The decays to autoionizing levels possibly followed by autoionization cascades are also included in the calculation. The contributions from doubly-excited intermediate states of Cu-like 31^17n′l′n′l″ (n′ = 4, 5; n″ = 5 - 15) are calculated explicitly, and the contributions from high Rydberg states (n″〉 15) are taken into account by using n-3 scaling law. The present results should be more accurate than the existent calculations. 展开更多
关键词 RECOMBINATION RATE COEFFICIENTS DIELECTRONIC RECOMBINATION COLLISIONSTRENGTHS IONS CONFIGURATIONS ISOSEQUENCES FE CA MG AR
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Scanning transmission ion microscopy on Fudan SPM facility
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作者 LI Yongqiang SATOH Takahiro +3 位作者 SHEN Hao ZHENG Yi LI Xinyi LIU Bo 《Nuclear Science and Techniques》 SCIE CAS CSCD 2011年第5期282-286,共5页
In this paper,we report a novel measurement system based on the development of Fudan Scanning Proton Microscopy(SPM) facility.By using Si-PIN diode(Hamamatsu S1223-01) detector,scanning transmission ion microscopy(STI... In this paper,we report a novel measurement system based on the development of Fudan Scanning Proton Microscopy(SPM) facility.By using Si-PIN diode(Hamamatsu S1223-01) detector,scanning transmission ion microscopy(STIM) measurement system has been set up.It can provide density and structural images with high probing efficiency and non-destruction by utilizing the energy loss of high energy(MeV) and focused ions penetrating through a thin sample.STIM measurement is able to map the density distribution of organic elements which mostly compose biology materials,such information can not be detected by using conventional Be-windowed Si(Li) X-ray detector in Particle Induced X-ray Emission(PIXE) technique.The spatial resolution capability of STIM is higher than PIXE technique at same accelerator status.As a result of STIM measurement,Paramecium attached on the top of Kapton tube was measured by STIM. 展开更多
关键词 显微镜 SPM 离子 扫描 复旦大学 设施 测量系统 传输
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Simple statistical model for predicting thermal atom diffusion on crystal surfaces
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作者 于卫锋 林正喆 宁西京 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第11期458-462,共5页
A simple model based on the statistics of single atoms is developed to predict the diffusion rate of thermal atoms in (or on) bulk materials without empirical parameters. Compared with vast classical molecular-dynam... A simple model based on the statistics of single atoms is developed to predict the diffusion rate of thermal atoms in (or on) bulk materials without empirical parameters. Compared with vast classical molecular-dynamics simulations for predicting the self-diffusion rate of Pt, Cu, and Ar adatoms on crystal surfaces, the model is proved to be much more accurate than the Arrhenius law and the transition state theory. Applying this model, the theoretical predictions agree well with the experimental values in the presented paper about the self-diffusion of Pt (Cu) adatoms on the surfaces. 展开更多
关键词 adatoms diffusion Arrhenius law transition state theory molecular dynamics simulations
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Effect of an upward magnetic field on nanosized sulfide precipitation in ultra-low carbon steel
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作者 Kang-jia Duan Ling Zhang +3 位作者 Xi-zhi Yuan Shan-shan Han Yu Liu Qing-song Huang 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2015年第7期714-720,共7页
An induction levitation melting (ILM) refining process is performed to remove most microsized inclusions in ultra-low carbon steel (UCS). Nanosized, spheroid shaped sulfide precipitates remain dispersed in the UCS... An induction levitation melting (ILM) refining process is performed to remove most microsized inclusions in ultra-low carbon steel (UCS). Nanosized, spheroid shaped sulfide precipitates remain dispersed in the UCS. During the ILM process, the UCS is molten and is rotated under an upward magnetic field. With the addition of Ti additives, the spinning molten steel under the upward magnetic field ejects particles because of resultant centrifugal, floating, and magnetic forces. Magnetic force plays a key role in removing sub-micrometer-sized particles, composed of porous aluminum titanate enwrapping alumina nuclei. Consequently, sulfide precipitates with sizes less than 50 nan remain dispersed in the steel matrix. These findings open a path to the fabrication of clean steel or steel bearing only a nanosized strengthen- ing phase. 展开更多
关键词 ultra-low carbon steel magnetic field sulfide precipitation induction levitation TITANIUM
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Calculation of photon angular distribution and polarization for radiative recombination for high-charged hydrogen-like ions
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作者 沈天明 陈重阳 王炎森 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第4期1008-1013,共6页
In this paper a systematic study is carried out on the angular distribution and polarization of photons emitted following radiative recombination of H-like ions by a non-relativistic dipole approximation. In order to ... In this paper a systematic study is carried out on the angular distribution and polarization of photons emitted following radiative recombination of H-like ions by a non-relativistic dipole approximation. In order to incorporate the screening effect due to inner-shell electrons, a distorted wave approazh is used. The dependences of the calculated angular distribution and polarization on the reduced energy and nuclear charge are fitted by the corresponding empirical formulas respectively. 展开更多
关键词 radiative recombination angular distribution POLARIZATION fit formula
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