Two-pion low-energy contribution to the muon g-2 with improved precision from analyticity and unitarity

The two-pion contribution from low energies to the muon magnetic moment anomaly, although small, has a large relative uncertainty since in this region the experimental data on the cross sections are neither sufficient nor precise enough. It is therefore of interest to see whether the precision can be improved by means of additional theoretical information on the pion electromagnetic form factor, which controls the leading-order contribution. In the present paper, we address this problem by exploiting analyticity and unitarity of the form factor in a parametrization-free approach that uses the phase in the elastic region, known with high precision from the Fermi-Watson theorem and Roy equations for pi pi elastic scattering as input. The formalism also includes experimental measurements on the modulus in the region 0.65-0.70 GeV, taken from the most recent e(+)e(-) ->pi(+)pi(-) experiments, and recent measurements of the form factor on the spacelike axis. By combining the results obtained with inputs from CMD2, SND, BABAR, and KLOE, we make the predictions a(mu)(pi pi,LO)2m(pi), 0.30 GeV] = (0.553 +/- 0.004) x 10(-10) and a(mu)(pi pi,LO)0.30 GeV; 0.63 GeV] = (133.083 +/- 0.837) x 10(-10). These are consistent with the other recent determinations and have slightly smaller errors.

Low tension strings on a cosmological singularity

It has recently been argued that the singularity of the Milne orbifold can be resolved in higher spin theories. In string theory scattering amplitudes, however, the Milne singularity gives rise to ultraviolet divergences that signal uncontrolled backreaction. Since string theory in the low tension limit is expected to be a higher spin theory (although precise proposals only exist in special cases), we investigate what happens to these scattering amplitudes in the low tension limit. We point out that the known problematic ultraviolet divergences disappear in this limit. In addition we systematically identify all divergences of the simplest 2-to-2 tree-level string scattering amplitude on the Milne orbifold, and argue that the divergences that survive in the low tension limit have sensible infrared interpretations.

Shock Tube Studies on Recombination Kinetics of Sodium Ion with Electron

The ionization kinetics of sodium diluted in argon is studied in a shock tube, in which the test gas mixture is ionized by a reflected shock wave and subsequently quenched by a strong rarefaction wave. A Langmuir electrostatic probe is used to monitor the variation of the ion number density at the reflection shock wave region. The working state of the probe is in the near fi-ee fall region and a correction for reduction of the probe current due to elastic scattering in the probe sheath is introduced. At the temperature range of 800 to 2600 K and in the ambience of argon gas, the three-body recombination rate coefficient of the sodium ion with electron is determined: 3.43 x 10(-14)T(-3.77) cm(6).s(-1).

Quantum Interference and Entanglement of Surface Plasmons

Surface plasma waves arise from the collective oscillations of billions of electrons at the surface of a metal in unison. The simplest way to quantize these waves is by direct analogy to electromagnetic fields in free space, with the surface plasmon, the quantum of the surface plasma wave, playing the same role as the photon. It follows that surface plasmons should exhibit all of the same quantum phenomena that photons do, including quantum interference and entanglement.

Unlike photons, however, surface plasmons suffer strong losses that arise from the scattering of free electrons from other electrons, phonons, and surfaces. Under some circumstances, these interactions might also cause “pure dephasing,” which entails a loss of coherence without absorption. Quantum descriptions of plasmons usually do not account for these effects explicitly, and sometimes ignore them altogether. In light of this extra microscopic complexity, it is necessary for experiments to test quantum models of surface plasmons.

In this thesis, I describe two such tests that my collaborators and I performed. The first was a plasmonic version of the Hong-Ou-Mandel experiment, in which we observed two-particle quantum interference between plasmons with a visibility of 93 ± 1%. This measurement confirms that surface plasmons faithfully reproduce this effect with the same visibility and mutual coherence time, to within measurement error, as in the photonic case.

The second experiment demonstrated path entanglement between surface plasmons with a visibility of 95 ± 2%, confirming that a path-entangled state can indeed survive without measurable decoherence. This measurement suggests that elastic scattering mechanisms of the type that might cause pure dephasing must have been weak enough not to significantly perturb the state of the metal under the experimental conditions we investigated.

These two experiments add quantum interference and path entanglement to a growing list of quantum phenomena that surface plasmons appear to exhibit just as clearly as photons, confirming the predictions of the simplest quantum models.

The vacuum Regge Trajectory in conventional field theory

The effect on the scattering amplitude of the existence of a pole in the angular momentum plane near J = 1 in the channel with the quantum numbers of the vacuum is calculated. This is then compared with a fourth order calculation of the scattering of neutral vector mesons from a fermion pair field in the limit of large momentum transfer. The presence of the third double spectral function in the perturbation amplitude complicates the identification of pole trajectory parameters, and the limitations of previous methods of treating this are discussed. A gauge invariant scheme for extracting the contribution of the vacuum trajectory is presented which gives agreement with unitarity predictions, but further calculations must be done to determine the position and slope of the trajectory at s = 0. The residual portion of the amplitude is compared with the Gribov singularity.

Experimental study study of antiproton-proton annihilation into a pair of charged Pi-Mesons or K-Mesons for incident antiproton mementa in the range from 0.72 GeV/c to 2.62 GeV/c

The cross sections for the two antiproton-proton annihilation-in-flight modes,

ˉp + p → π⁺ + π^-

ˉp + p → k⁺ + k^-

were measured for fifteen laboratory antiproton beam momenta ranging from 0.72 to 2.62 GeV/c. No magnets were used to determine the charges in the final state. As a result, the angular distributions were obtained in the form [dσ/dΩ (Θ_C.M.) + dσ/dΩ (π – Θ_C.M.)] for 45 ≲ Θ_C.M. ≲ 135°.

A hodoscope-counter system was used to discriminate against events with final states having more than two particles and antiproton-proton elastic scattering events. One spark chamber was used to record the track of each of the two charged final particles. A total of about 40,000 pictures were taken. The events were analyzed by measuring the laboratory angle of the track in each chamber. The value of the square of the mass of the final particles was calculated for each event assuming the reaction

ˉp + p → a pair of particles with equal masses.

About 20,000 events were found to be either annihilation into π ^±-pair or k ^±-pair events. The two different charged meson pair modes were also distinctly separated.

The average differential cross section of ˉp + p → π⁺ + π^- varied from ~ 25 µb/sr at antiproton beam momentum 0.72 GeV/c (total energy in center-of-mass system, √s = 2.0 GeV) to ~ 2 µb/sr at beam momentum 2.62 GeV/c (√s = 2.64 GeV). The most striking feature in the angular distribution was a peak at Θ_C.M. = 90° (cos Θ_C.M. = 0) which increased with √s and reached a maximum at √s ~ 2.1 GeV (beam momentum ~ 1.1 GeV/c). Then it diminished and seemed to disappear completely at √s ~ 2.5 GeV (beam momentum ~ 2.13 GeV/c). A valley in the angular distribution occurred at cos Θ_C.M. ≈ 0.4. The differential cross section then increased as cos Θ_C.M. approached 1.

The average differential cross section for ˉp + p → k⁺ + k^- was about one third of that of the π^±-pair mode throughout the energy range of this experiment. At the lower energies, the angular distribution, unlike that of the π^±-pair mode, was quite isotropic. However, a peak at Θ_C.M. = 90° seemed to develop at √s ~ 2.37 GeV (antiproton beam momentum ~ 1.82 GeV/c). No observable change was seen at that energy in the π^±-pair cross section.

The possible connection of these features with the observed meson resonances at 2.2 GeV and 2.38 GeV, and its implications, were discussed.

Elimination of parity doublets in Regge amplitudes

In Part I, the common belief that fermions lying on linear trajectories must have opposite-parity partners is shown to be false. Reggeization of a sequence of positive-parity fermion resonance is carried out in the Van Hove model. As a consequence of the absence of negative-parity states, the partial-wave amplitudes must have a fixed cut in the J plane. This fixed cut, in conjunction with the moving Regge pole, provides a new parametrization for fermion-exchange reactions, which is in qualitative agreement with the data.

In Part II, the spin structure of three particle vertices is determined from the quark model. Using these SU(6)_W vertices in the Van Hove model, we derive a Reggeized scattering amplitude. In addition to Regge poles there are necessarily fixed Regge cuts in both fermion and boson exchange amplitudes. These fixed cuts are similar to those found in Part I, and may be viewed as a consequence of the absence of parity doubled quarks. The magnitudes of the pole and cut terms in an entire class of SU(6) related reactions are determined by their magnitudes in a single reaction. As an example we explain the observed presence or absence of wrong-signature nonsense dips in a class of reactions involving vector meson exchange.

Anisotropic spin transport in two-terminal mesoscopic rings: Rashba and Dresselhaus spin-orbit interactions

We theoretically investigate the spin transport in two-terminal mesoscopic rings in the presence of both the Rashba spin-orbit interaction (RSOI) and the Dresselhaus spin-orbit interaction (DSOI). We find that the interplay between the RSOI and DSOI breaks the original cylindric symmetry of the mesoscopic rings and consequently leads to the anisotropic spin transport, i.e., the conductance is sensitive to the positions of the incoming and outgoing leads. The anisotropic spin transport can survive even in the presence of disorder caused by impurity elastic scattering in a realistic system.

Microscopic Three-Body Force Effect on Nucleon-Nucleon Cross Sections in Symmetric Nuclear Matter

We provide a microscopic calculation of neutron-proton and proton-proton cross sections in symmetric nuclear matter at various densities, using the Brueckner-Hartee-Fock approximation scheme with the Argonne V-14 potential including the contribution of microscopic three-body force. We investigate separately the effects of three-body force on the effective mass and on the scattering amplitude. In the present calculation, the rearrangement contribution of three-body force is considered, which will reduce the neutron and proton effective mass, and depress the amplitude of cross section. The effect of three body force is shown to be repulsive, especially in high densities and large momenta, which will suppress the cross section markedly.

Exotic behaviour of angular dispersion of weakly bound nucleus F-17 at small angles

The differential cross sections of F-17 and O-17 elastic scattering products on Pb-208 have been measured at the Radioactive Ion Beam Line at Lanzhou (RIBLL). Two angular dispersion plots of ln(d sigma/d theta) versus theta 2 are obtained from the angular distribution of the elastic scattering differential cross sections. The angular dispersion plot exhibits a clear turning point for F-17 in the range of small scattering angles 6 degrees-20 degrees due to its exotic structure, but for O-17, the turning point is not observed in the same angular range. The experimental results have been compared with previous data of other groups. Systematical analysis on the available data supports the above conclusion that there is an exotic behaviour of the angular dispersion plot of weakly bound nuclei with halo or skin structure as compared with that of the ordinary nuclei near stable line. Therefore the turning point of the angular dispersion plot appears at small angle for weakly bound nuclei with halo or skin structure, and can be used as a new probe to investigate the halo and skin phenomena of weakly bound nuclei.

Study of unbound nuclei N-11 resonance energy level

The excitation functions of elastic scattering proton which were measured with inverse kinematics of elastic resonance scattering reactions in GANIL and MSU have been fitted by the multi-energy level R-matrix theory. The final result shows that the new energy levels order for nucleus N-11 should be 1/2(+), 1/2(-), 5/2(+), 3/2(+), 3/2(-), 5/2(+), 7/2(-), which is consistent with the experimental results of Be-11 (the mirror nucleus of N-11) and the theoretical calculation of N-11 with GCM theory.

Evidence of strong projectile-target-core interaction in single ionization of neon by electron impact

The momentum distributions of recoil ions were measured in the single ionization of neon by electron impact at incident energies between 80 and 2300 eV. It was found that there are a noticeable number of recoil ions carrying large momenta, and the relative contributions of these ions becomes more pronounced with the further decrease of incident electron energy. These observed behaviors indicate that there is a strong projectile-target-core interaction in the single-ionization reaction. By comparing our results with those of electron-neon elastic scattering, we concluded that the elastic scattering of the projectile electron on the target core plays an important role at low and intermediate collision energies.

17F和18Ne与质子弹性散射研究

论文讲述了采用逆运动学方法用放射性核束~(17)F和~(18)Ne与质子弹性散射的实验准备、设汁方法、实验情况、实验数据处理过程、理论分析处理和得到的结果。弹性散射测量核敞射的角分布，对位置探测器有很高的要求。在实验的准备阶段，为了对放射性核束的准确定位，研制了位置分辨为lITlm的高位团置分辨的PPAC。山于质予的穿透能力很强，在半导体硅探测器中的能损很小，实验前，刘。测量反冲质子的探测器PSSD在低能量沉积下的工作情况进行了测试，满足质f位置和I能量测量的要求。实验采用初级束流强度约为80nA能量为45Mev／A的~(20)Ne轰击lmm厚的~9Be，反应产物经过500μm厚的Wedge~(27)Al，通过次级束流线的筛选，得到~(17)F和~(18)Ne和少量的~(16)O束流，其能量分别为17.7Mev／A、16.1Mev／A和14.3Mev／A。然后轰击60μm厚的(CH_2)_n靶。用次级束流线装置的两个焦点处的塑料闪烁体测量放射性核束的时间Tl和T2，根据飞行时间差在相同的磁场条件下来鉴别粒子和得到放射性核束的能量。用靶前的两个PPAC和靶后的一个PPAC来确定放射性核束的入射方向、反应点和出射方向，反冲质子的位置由分布于各实验室系角区的五个PSSD来测定。实验数据处理时，根据放射性核束经过基本相同的飞行路径和磁场条件，用T1和T2测到的飞行时间差来确定放射性核束的能量。将入射到PPAC上的弹核粒子位置，经对宏观几何位置矫正后，来确定弹核粒子的入射方向、反应点位置和出射方向。将PSSD测量到的位置谱经与沉积能量相关的修正因子对位置修正后，确定反冲核在PSSD上的几何位置点，跟PPAC测量确定的靶上的反应点位置结合，确定反冲核的出射方向。测量得到的位置经过空间关系换算，由测量到的弹核入射方向、反应点位置和反冲核出射方向，得到弹性散射的实验室系散射角。累计所有测到的事件得到初始的反冲核实验测量角分布。采用逐个事件的方法，用一事先产生的一系列点组成的数据库模拟探测器边界，事件的几何探测效率进行归一化，得到实际的实验室系散射角分布。用弹核出射角度随反冲核的出射角度的运动学关系鉴别来自靶中的H和C的散射事件。将实验室系角分布转换到质心系下后，再根据弹核粒子数、单位面积靶核数和测量到的事件数，得到实验测量的质的弹性散射微分截面。实验得到的微分截面数据采用零程相互作用的扭曲波玻恩近似理论计算程序DWUCK4序进行光学势拟合计算，选用较准确描述奇异核性质的CH89参数化的光学势为初始的光学势参数，对光学势参数的组成成分进行敏感性分析后，确定参数搜索的顺序，用跟各参数相关联的自动参数搜索程序ABOD进行分析处理。进行光学模型的理论拟合计算时，将计算结果和实验值进行比较，拟合实验数据，求得光学势参数。参数拟合佳度用残差平方和检验(χ~2检验)。得到~(17)F和~(18)Ne与质子弹性散射的光学势参数。根据得到的光学势参数进行折叠模型分析。得到了，1)~(17)F和~(18)Ne实势相互作用均方根半径分别为，_(rF)~(1/2) = 3．239(fm)，_(r_Ne)~(1/2) = 3.317 (fm)。跟相对论平均场计算结果比较分析表明，~(17)F的核物质半径为2.95±0.03fm，~(18)Ne的核物质半径为3.07±0.03fm,~(17)F和~(18)Ne表面的密度要比相对论平均场理论预言的值要大。2)~(17)F和~(18)Ne的自旋轨道耦合相互作用主要作用于核表面区域，这是因为位于核外层的价质子的影响。

The eigenphase formulation of fine-structure transition cross sections

The eigenphase formulation of Blatt and Biedenharn is applied to fine-structure transitions in *P atoms colliding with ‘S perturbers. Consideration is given to the limit of weak spin-orbit interaction. If the eigenphases are equal to the phaseshifts for elastic scattering by the molecular potentials then the expression for the total cross section reduces to the expression derived in the elastic approximation. However, a numerical comparison for the Li(2p ’P) + He(’S) system shows that the elastic molecular phaseshifts are not good approximations to the eigenphases. Hence the elastic approximation cannot be reliable.

Electron/positron collisions with positronium

We report results for e(+/-)-Ps(Is) scattering in the energy range up to 80 eV calculated in 9-state and 30-state coupled pseudostate approximations. Cross-sections are presented for elastic scattering, ortho-para conversion, discrete excitation, ionization and total scattering. Resonances associated with the Ps(n = 2) threshold are also examined and their positions and widths determined. Very good agreement is obtained with the variational calculations of Ward et al. [J. Phys. B 20 (1987) 127] below 5.1 eV. (C) 2004 Elsevier B.V. All rights reserved.