卢瑟福散射公式的几何证明方法

给出两种比较简单的推导卢瑟福散射公式的几何方法:利用圆锥曲线的基本知识并结合参数的物理意义得出卢瑟福公式.     

α粒子散射截面新解

原子的核式结构模型可通过α粒子的散射得到证实。α粒子的散射理论是原子物理教学的重要内容。但因卢瑟福散射公式需利用理论力学的知识方能推导，导致该部分内容在普通物理教学中只能简单介绍而无法深入展开。本文介绍了一种适用于普通物理教学的求解α粒子散射截面的新方法。     

《从零学相对论》连载(22)

正8.5.3牛顿引力论对星光偏角的推导[选读]索尔德纳在1801年推导星光偏角公式时,光速的有限性已被证实.只要承认光的微粒说并默认光微粒(即现在的光子)在引力场中的表现与普通质点的唯一不同就是以光速运动,就不难用牛顿引力论推出偏角公式.此式的推导方法很多,现在介绍一种"借他山之石"的简便方法.首先考虑质量为m的普通质点在太阳附近飞过时因受太阳引力而出现的偏角.这种情况与卢瑟福1911年研究的α粒子散射类似,因此可以借用其     

多次散射等过程对卢瑟福散射实验的影响

在卢瑟福散射实验中,多次散射等因素会影响模型的验证结果．通过角分布的卷积研究多次散射过程,采用卢瑟福散射角分布与小角度散射的角分布函数的卷积来近似描述多次散射的影响,并提出使用小角度散射数据与卢瑟福散射截面卷积的模型来描述大角度数据的方法．实验结果表明：与卢瑟福散射公式相比,卷积模型与实验数据符合得更好．     

用不变速度推导卢瑟福散射公式

通过横向速度变换得到两种不变速度，由此推出卢瑟福散射公式。     

弱源—表面镀膜式α散射实验

一、引言α粒子散射实验是原子物理学发展中极为重要的早期实验之一。1910年卢瑟福(E.Rutherford)、盖革(H.Geiger)和马斯顿(E.Marsden)等用α粒子射击重金属箔,结果,粒子被分别散射到不同方向上,并发生了大角度散射,由此诞生了卢瑟福的原子行星模型。随着量子理论的发展,现在对原子结构有了进一步的认识。但在非相对论量子力学中,散射截面的计算与经典的卢瑟福公式相同。因     

导出卢瑟福公式的简易方法

卢瑟福公式在《理论力学》教材中一般是从比耐公式出发导出来的,过程比较复杂.现介绍一个用动量矩(角动量)守恒律来导出卢瑟福公式,方法比较简单.-a质点运动的性质 把一个a质点射入原子中,因为a质点带电荷2e,原子核带正电荷2e,(Z为原子的原子序数)它们相互作用遵循库仑定律斥力:又因原子核的质量一般比a质点的质量大许多倍,故近似的可以认为原子核不动,所以a质点运动的性质,是在平方反比斥力的有心力的作用下的运动问题.a质点的轨道是双曲线的一支,这时力心(原子核)在轨道凸的一边.二示意图说明 如图:o代表原子核(力心)的位置,设a质点在力…     

非水平直圆管中黏性流体层流流量公式的推导及实验验证

通过牛顿粘滞定律和修正后的伯努利方程对非水平直圆管中黏性流体作层流运动时的流量公式进行了推导。指出将泊肃叶公式中的压强视作广义压强,则文中的推导公式与泊肃叶公式完全一致。说明泊肃叶公式可以用来求解非水平直圆管中黏性流体作层流运动时的流量。本文通过实验验证了推导公式。     

巧推经典和相对论多普勒效应公式

无论是经典多普勒效应公式还是相对论多普勒效应公式,在大学物理教材中都可以找到其具体的推导方法,而且每种多普勒效应公式的推导方法都不止一种．但是这些推导方法均较为繁琐．笔者在实际教学过程中发现,通过建模,可以对两种多普勒效应公式进行非常巧妙的推导,特别是对于相对论多普勒效应公式,推导过程显得尤其简洁．     

等离子体中电子弹性散射截面及电导率计算

本文研究了近理想等离子体中的电子弹性散射过程.利用Debye-Hückel模型考虑等离子体环境对电子与离子间相互作用的屏蔽效应.结合分波法计算了不同Debye长度情况下,电子与不同核电荷数离子散射的分波相移和微分散射截面.研究了散射波函数、分波相移和微分截面随等离子体屏蔽参数的变化规律.最后,基于Spitzer公式, 初步讨论了分波法计算的等离子体的电导率与卢瑟福公式计算的电导率之间的区别.     

Guided-Wave Two-Dimensional Acousto-Optic Scanner Using Proton-Exchanged Lithium Niobate Waveguide

Two-dimensional scanning of a 0.6328 mum guided-light beam has been realized using noncolinear acousto-optic (AO) coplanar Bragg diffraction together with colinear AO guided-mode to substrate radiation-mode conversion in a Z-cut Xpropagation LiNbO3 proton-exchanged (PE) waveguide. The two surface acoustic (SAW) waves utilized are at the center frequencies of 500 and 200 MHz, propagating in the Y and X axes, respectively. Two-dimensional scanning of approximately 720 resolvable light beam spots, namely, 18 40 (horizontal vertical) scanning, has been demonstrated using a light beam of 1.0 mm aperture. The total number of resolvable beam spots can be greatly increased from 720 by simply utilizing SAW transducers of larger bandwidth and a light beam of greater aperture. It should also be possible to significantly increase the diffraction efficiency from 3 % by optimizing the parameters of the PE waveguide and the SAWs.     

Effect ofγ-radiation on the spectral luminescence characteristics of impure cadmium tungstate crystals

Results of a study of the effect of γ-radiation on the spectral luminescence properties of cadmium tungstate crystals doped with silver, bismuth, and molybdenum cations are presented. Spectral characteristics of the nondnnnoped crystals are briefly described. Absorption and photo and X-ray luminescence spectra of the crystals taken before and after exposure to γ-radiation (5.5·10⁴ Gy) are compared. It is found that the spectral characteristics of the crystals doped with silver, bismuth, and molybdenum cations do not change markedly after the exposure. The relation between the type of impurity-induced defects, individual characteristics of the impurity cations, and the character of the effect of γ-radiation on the spectral luminescence properties of impure crystals is analyzed (preliminarily). Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 55–60, January–February, 1997.     

Femtosecond Transform-Limited Pulse Generation by Compensating for the Linear Chirp of SPM Spectra in Dispersion Shifted Fibers

A simple technique of pulse compression, based on the linear chirp compensation of self-phase modulation (SPM) spectra in dispersion shifted fibers, is demonstrated. The optimization procedure is carried out, for a short span of a single-mode fiber, using a parabolic law, which describes the behavior of the squared output pulse width versus the pump peak power in the case of Gaussian pulses. The experimental results give a minimum pulse duration of 233 fs, which is in good agreement with the model. Shorter and coherent pulses, down to 90 fs, have been obtained by inserting an interference filter at the optical output.     

Sorting of bending magnets for the SSRF booster

The Shanghai Synchrotron Radiation Facility(SSRF)booster ring,a full energy injector for the storage ring,is deigned to accelerate the electron beam energy from 150MeV to 3.5GeV that demands high extraction efficiency at the extraction energy with low beam loss rate when electrons are ramping.Closed orbit distortion(COD)caused by bending magnet field uniformity errors which affects the machine performance harmfully could be effectively reduced by bending magnet location sorting.Considering the affections of random errors in measurement,both ideal sorting and realistic sorting are studied based on measured bending magnet field uniformity errors and one reasonable combination of bending magnets which can reduce the horizontal COD by a factor of 5is given as the final installation sequence of the booster bending magnets in this paper.     

Measurement of nonlinear coefficient of optical fiber based on small chirped soliton transmission

We measure the waveform and phase curves of short optical pulses before and after transmission over different lengths of fibers by use of the pulse analyzer with the frequency-resolved optical gating (FROG),and numerically simulate pulse evolution under the experimental conditions.The nonlinear coefficient of the fiber is given by comparing the experimental results with the numerical ones.Difference between the experiment and numerical simulation is analyzed.     

Resonance scattering of canonical elastic shells in absorbing fluid medium

Resonance scattering of elastic spherical shell and cylindrical shell while the surrounding fluid medium has absorption is studied. The normal mode solution derived using exact elastic theory and the separation of variables is still applicable. However, the scattering form function has to be modified for the absorbing medium, otherwise the unreasonable result would be obtained. The backscattering form function in the absorbing medium is redefined, and the form function of elastic spherical and cylindrical shell with vacuum or solid matter filled is calculated in various absorption conditions. The results show that the absorption of surrounding fluid leads to notable attenuation of the coincidence resonances in the mid-frequency, but it has a little influence on the low-frequency resonance scattering induced by the filler inside the shell.     

Single-beam self-referenced phase-sensitive surface plasmon resonance sensor with high detection resolution

A versatile and low-cost single-beam self-referenced phase-sensitive surface plasmon resonance(SPR)sensing system with ultra-high resolution performance is presented.The system exhibits a root-mean-square phase fluctuation of ±0.0028.over a period of 45 min.i.e.a resolution of±5.2×10-9 refractive index units.The enhanced performance has been achieved through the incorporation of three design elements:a true single-beam configuration enabling complete self-referencing so that only the phase change associated with SPR gets detected,a differential measurement scheme to eliminate spurious signals not related to the sensor response,and the elimination of retardation drifts by incorporating temperature stabilization in the liquid crystal phase modulato .Our design should bring the detection sensitivity of non-labeling SPR biosensing closer to that achievable by conventional fluorescence-based techniques.     

Influences of SiO2 protective layers and annealing on the laser-induced damage threshold of Ta2O5 films

Ta2O5 films are prepared on BK7 substrates with conventional electron beam evaporation deposition.The effects of SiO2 protective layers and annealing on the laser-induced damage threshold (LIDT) of the films are investigated.The results show that SiO2 protective layers exert little influence on the electric field intensity(EFI)distribution,microstructure and microdefect density but increase the absorption slightly.Annealing iS effective on decreasing the microdefect density and the absorption of the films.Both SiO2 protective layers and annealing are beneficial to the damage resistance of the films and the latter is more effective to improve the LIDT.Moreover,the maximal LIDT of Ta2O5 films is achieved by the combination of SiO2 protective layers and annealing.     

A stereo matching algorithm using multi-peak candidate matches and geometric constraints

Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correla- tion coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.