导出E=mc^2和m=m0/√1-v^2/c^2的一种方案

借助光子导出了E=mc^2和m=m0/√1-v^2/c^2。     

导出E=mc2和m=m0/1-v2√c2的一种方案

借助光子导出了E=mc2和m=(m0)/(1-v2/c2).     

对=2～(1/2)的一种定性说明

给出一种对公式=2～(1/2)的定性说明.     

关于=2～(1/2)的一个简易证明

在普通物理热学教学当中,碰到有气体分子平均相对速率u= 2 V的关系式,这个关系式在普通物理教科书中一般不作证明。现介绍一种不超出大学一年级学生知识范围的一种简易证明方法如下。 气体分子由于热运动,对于个别分子来讲它的运动是具有偶然性的。由这些分子组成的整个系统的运动服从统计规律。但在这个系统中两个分子的碰撞却依然服从力学规律。我们认为分子之间的碰撞是弹性的,分子的质量是m。在发生碰撞前两分子的速度为Vi和Vj,碰撞之后的速度为Vi和Vj,碰前Vi和 Vj的夹角为 a,碰后 Vi和 Vj的夹角为(01 02),其中 01是 V’t与 VJ的夹…     

(AlB2)m (m=1~6) 团簇的几何结构和电子性质

采用密度泛函理论(DFT)中的B3LYP方法得到了(AlB2)m团簇的平衡几何结构. 计算并分析了基态掺杂团簇的平均结合能、电离势、能隙和前线分子轨道. 结果表明：掺杂团簇(AlB2)m (m=1~6)整体上具有较高化学活性,(AlB2)5团簇具有金属特征. Al原子总是向团簇外围扩散并且以配位数较少的方式与主团簇结合,团簇表现出以AlB2分子为基元生长的迹象. B-Al键长大于B-B键长. 电荷总是从Al原子转移到B原子. (AlB2)m团簇中B原子的2p轨道在成键中起主要作用,并使(AlB2)m团簇趋于形成离域π键.     

Eu_mSi_n(m=1～2,n=1～8)团簇结构和性质的密度泛函理论研究

在密度泛函理论的框架下,采用广义梯度近似（GGA）研究了Eu₂Si_n（n=1～7）团簇的基态几何结构,系统计算了平均结合能E_b、二阶能量差分△₂E、最高占据轨道（HOMO）与最低未占据轨道（LUMO）之间的能隙,并与已有的EuSi_n（n=2～8）团簇相关数据作对比分析.研究表明:单Eu原子比双Eu原子掺杂的Si团簇具有更高的稳定性,EuSi₃、EuSi₆、Eu₂Si₄团簇较相应邻近团簇结构稳定;Eu_mSi_n（m=1～2,n=l～8）团簇的能隙随着团簇总原子数的增加呈现振荡变化,态密度分析得到能隙振荡变化的原因是S原子的s轨道与Eu原子的p轨道发生了杂化.     

气体分子运动速度=2~(1/2)v关系式的简易推导方法

对 u =2 v式给出了适合工科普通物理教学的简易推导方法     

193T1超形变带K=1/2的可能性

分析了脱耦合项对于原子核转动惯量的重要影响.总结了奇质量核K=1/2带转动惯量变化规律的新特点.在此基础上讨论了¹⁹³T1中3条新的超形变带的内部结构.目前尚无足够证据能够确认它们都是K=1/2带.     

第一性原理对Al_mSi_n(m=1,2;n=1～6)团簇结构与性质的研究

本文运用第一性原理对Al_mSi_n（m=1,2;n=1～6）团簇的结构与性质进行了研究.在BLYP的水平上进行了结构优化和频率分析,得到了团簇的最低能量结构.同时计算和讨论了A1_msi_n团簇的束缚能、总能的二阶能量差分和分裂能以及费米能随原子数的变化.研究结果表明:Al_mSi_n团簇在m+n<4时的几何结构是平面结构,从4个原子开始转为空间的立体结构;除AlSi₃和Al₂Si₂团簇外,Al_mSi_n（m=1,2;n=1～6）团簇的束缚能随原子数增加而减小;分析A1_mSi_n（m=1,2;n=1～6）团簇的二阶能量差分和分裂能发现:在m+n=3,5时,团簇都出现较稳定的结构.     

吡啶-水团簇(C_5H_5N)_n(H_2O)_m(n=1～2,m=1～4)结构和红外光谱的理论研究

利用密度泛函理论,在B3LYP/6-311++G(d,p)基组水平上对吡啶-水团簇(C5H5N)n(H2O)m(n=1~2,m=1~4)的可能构型进行全优化,得到了团簇的稳定结构;计算结果显示,在吡啶和水的二聚体中,稳定构型只有一种,没有发现通过π氢键(O—H…π)作用形成的团簇结构。为了研究各团簇结构的稳定性,在相同的基组水平上计算得到了各团簇构型的总能量和结合能,结果显示,对于团簇(C5H5N)n(H2O)4(n=1~2),团簇中的水分子形成四元环的结构要比形成三元环的结构稳定。对团簇的最高占据轨道与最低空轨道之间的能隙分析发现,团簇C5H5N(H2O)4的最低能量结构具有较高的稳定性,可能具有幻数结构;最后,分析讨论了吡啶-水团簇的红外振动光谱,对较强的谱峰进行了指认。     

Bestimmung des (631)K=1/2, I=1/2-Zustandes im U 239

Theγ-ray spectrometer at the DR 3-reactor at Risø was used to investigate the low energyγ-lines of U 239 which are emitted during neutron-capture in U 238. Very closely lying lines have been found between 500 and 650 keV. The big intensity of the 133 keV line and the lack of other transitions of appropriate energy and intensity point out that this line corresponds to the hinderedE 2-transition from the (631)I=1/2⁺ level to the (622)I=5/2⁺ groundstate. A suggestion was made for the decay possibility of the octupole states at 700 keV found by N.Fiebiger.     

Polarization switching in a ring cavity with resonantly drivenJ=1/2 toJ=1/2 atoms

We have solved within the mean field limit for the steady state behaviour of a gas ofJ=1/2 toJ=1/2 model atoms in a ring cavity excited by an incident laser field of arbitrary polarization. Results are presented for the case of zero applied magnetic field and exact resonance between the laser frequency, the atomic transition and a cavity resonance (pure absorptive case). We find that the behaviour of the polarization switching between ⁺ and ^– outputs depends on the values of the upper and lower state collisional relaxation rates, expressed via a single parameter . The case of linearly polarized input is of particular interest since optical bistability is found to occur for 2, being pre-empted by polarization switching for >2. The results are discussed in terms of an atomic feedback mechanism coupling the ⁺ and ^– modes.     

s~(1/2)=355GeV附近的R值测量

利用北京谱仪 (BES)在s=3.5 5GeV附近获取的总积分亮度约为 5 pb-1的实验数据 ,测量了e e-湮没强子产生截面与 μ子对产生截面的比值 (即R值 ) .其测量误差比其它实验组已发表的此能区的测量误差减小约 5 0 % .     

Der Zerfall des122Xe (T 1/2=20,l h) und des122J (T 1/2=3,6min)

Theγ spectra emitted in the decay of¹²²Xe and¹²²I have been investigated using Ge(Li) detectors and a Ge(Li)-NaI coincidence apparatus. 14γ transitions with energies between 61.8 and 416.9 keV have been identified in the decay of¹²²Xe, 44 transitions between 564.0 and 3,291.0 keV in the decay of¹²²I. Level schemes having 7 excited levels for¹²²I and 21 excited levels for¹²²Te are proposed.     

Intensity of cross-peaks in hyscore spectra of S = 1/2, I = 1/2 spin systems

The cross-peak intensity for a S = 1/2, I = 1/2 spin system in two-dimensional HYSCORE spectra of single-crystals and powders is analyzed. There is a fundamental difference between these two cases. For single crystals, the cross-peak intensity is distributed between the two (+, +) and (+, -) quadrants of the hyperfine sublevel correlation (HYSCORE) spectrum by the ratio c(2):s(2) (C. Gemperle, G. Aebli, A. Schweiger, and R. R. Ernst, J. Magn. Reson. 88, 241 (1990)). However, for powder spectra another factor becomes dominant and governs cross-peak intensities in the two quadrants. This factor is the phase interference between modulation from different orientations of the paramagnetic species. This can lead to essentially complete disappearance of the cross-peak in one of the two (+, +) or (+, -) quadrants. In the (+, +) quadrant, cross-peaks oriented parallel to the main (positive) diagonal of the HYSCORE spectrum are suppressed, while the opposite is true in the (+, -) quadrant where cross-peaks nearly perpendicular to the main (negative) diagonal of HYSCORE spectra are suppressed. Analytical expressions are derived for the cross-peak intensity profiles in powder HYSCORE spectra for both axial and nonaxial hyperfine interactions (HFI). The intensity is a product of two terms, one depending only on experimental parameter (tau) and the other only on the spin Hamiltonian. This separation provides a rapid way to choose tau for maximum cross-peak intensity in a region of interest in the spectrum. For axial HFI, the Hamiltonian-dependent term has only one maximum and decreases to zero at the canonical orientations. For nonaxial HFI, this term produces three separate ridges which outline the whole powder lineshape. These three ridges have the majority of the intensity in the HYSCORE spectrum. The intensity profile of each ridge resembles that observed for axial HFI. Each ridge defines two principal values of the HFI similar to the ridges from an axial HFI.     

Intensity of Cross-Peaks in Hyscore Spectra of S = 1/2, I = 1/2 Spin Systems

The cross-peak intensity for a S = 1/2, I = 1/2 spin system in two-dimensional HYSCORE spectra of single-crystals and powders is analyzed. There is a fundamental difference between these two cases. For single crystals, the cross-peak intensity is distributed between the two (+, +) and (+, −) quadrants of the hyperfine sublevel correlation (HYSCORE) spectrum by the ratio c²:s² (C. Gemperle, G. Aebli, A. Schweiger, and R. R. Ernst, J. Magn. Reson. 88, 241 (1990)). However, for powder spectra another factor becomes dominant and governs cross-peak intensities in the two quadrants. This factor is the phase interference between modulation from different orientations of the paramagnetic species. This can lead to essentially complete disappearance of the cross-peak in one of the two (+, +) or (+, −) quadrants. In the (+, +) quadrant, cross-peaks oriented parallel to the main (positive) diagonal of the HYSCORE spectrum are suppressed, while the opposite is true in the (+, −) quadrant where cross-peaks nearly perpendicular to the main (negative) diagonal of HYSCORE spectra are suppressed. Analytical expressions are derived for the cross-peak intensity profiles in powder HYSCORE spectra for both axial and nonaxial hyperfine interactions (HFI). The intensity is a product of two terms, one depending only on experimental parameter (τ) and the other only on the spin Hamiltonian. This separation provides a rapid way to choose τ for maximum cross-peak intensity in a region of interest in the spectrum. For axial HFI, the Hamiltonian-dependent term has only one maximum and decreases to zero at the canonical orientations. For nonaxial HFI, this term produces three separate ridges which outline the whole powder lineshape. These three ridges have the majority of the intensity in the HYSCORE spectrum. The intensity profile of each ridge resembles that observed for axial HFI. Each ridge defines two principal values of the HFI similar to the ridges from an axial HFI.     

Instantons and the DeltaI = 1/2 rule

The instanton-induced interaction leads to a significant enhancement of the Ao weak amplitude determining the DeltaI = 1/2 rule, through the contribution of operators with dimension d = 9, as we show in the weak K--> pi(pi) decay.     

N=1/2 Wess-Zumino model is renormalizable

The Wess-Zumino model on N=1/2 nonanticommutative superspace, which contains the dimension-6 term F3, is shown to be renormalizable to all orders in perturbation theory, upon adding F and F2 terms to the original Lagrangian. The renormalizability is possible, even with this higher-dimension operator, because the Lagrangian is not Hermitian. Such deformed field theories arise naturally in string theory with a graviphoton background.