古今中外妙证勾股

勾股定理有许多种证法,1940年统计,国内外对勾股定理的证法达365种,迄今为止,已达500余种.兹仅撷取了如下几种,旨在激起同学们“善于探索创新,归纳总结实践”,创造出更多更好的证法.     

290 AMeV 12C诱发乳胶核反应末态粒子多重数关联

对290 AMeV 12C诱发乳胶核反应末态粒子间的多重数关联进行了研究。实验结果表明:黑径迹粒子、灰径迹粒子、重电离粒子多重数之间存在较强的关联,而且黑径迹粒子和重电离粒子多重数有饱和的趋势,这些特征与高能区实验结果一致;簇射粒子与其他粒子间的关联性较弱,这一特征与高能区实验结果不同,主要归因于弹核能量较低、簇射粒子产额较小;黑径迹粒子、灰径迹粒子在前后半球的平均多重数随靶核的增大而增加;实验结果可用基于碰撞几何的旁观体-反应体模型及级联蒸发模型来解释。We have investigated the multiplicity correlation of particles produced in 12C-emulsion interactions at 290 AMeV. It is found that there is a strong correlation between black track particle, grey track particle and heavily ionized track particle, and finally black track particles and heavily ionized track particles tend to saturation, which is the same as the experimental results observed at high energies. The multiplicity correlation between shower particle and other particles is weaker, which is different from the experimental results observed at high energies. This discriminating character can be explained by the lower energy of projectile. The productivity of shower particle is lower at intermediate energies compared to that at high energies. The forward-backward averaged multiplicity of black track particle and grey track particle increases with the increasing target size.     

波包宽度对弹核碎裂反应截面的影响

运用改进的量子分子动力学(ImQMD)模型嫁接GEMINI统计衰变模型对波包宽度与弹核碎裂反应截面之间的关系进行了理论分析,分析了不同的波包宽度对400 AMeV 36Ar+C,20Ne与C,Al,Cu,Sn弹核碎裂反应截面的影响,分析了同位素36Ar,40Ar与Al反应在不同的波包宽度下的同位素分布。分析结果表明:波包宽度的选择影响着弹核碎裂的反应截面,并且与核反应体系有关。当σ2_r = 2 fm2时的计算结果与实验结果一致;而σ_r =(0.88+0.09 A1/3) fm的计算结果与体系有很大的关系,对弹核碎裂的反应截面影响明显。不的波包宽度对丰中子核40Ar的弹核碎裂反应截面的影响要小于对36Ar的弹核碎裂反应截面的影响,而且随体系分布的波包宽度计算的同位素要比σ2_r =2 fm2时计算的同位素多。The relations between wave packet width and projectile fragmentation cross sections are studied in theory by using the improved quantum molecular dynamics (ImQMD) and GEMINI models. The effect of different wave packet width for projectile fragmentation cross sections is analyzed for the reaction 36Ar on C, 20Ne on C, Al, Cu, Sn at 400 AMeV, the isotope distributions with different wave packet width are studied for reactions 36Ar, 40Ar on Al. The results show that the projectile fragmentation cross sections are affected by the choice of the wave packet width, and are related to the system of nuclear reaction. The calculation results of σ2_r =2 fm2are in agreement with the experimental results, but the results of σ_r = (0.88+0.09A1/3) fm have a strong relation with reaction system and the projectile fragmentation cross sections are affected obviously. The influence of wave packet width for 40Ar projectile fragmentation cross sections is smaller than that for 36Ar.Moreover isotope distributions with system-size-dependent wave packet width are larger than with σ2_r =2 fm2.     

Evidence of self-affine multiplicity fluctuation of particle production in 84Kr--emulsion interactions at 1.7 A GeV

Self-affine multiplicity fluctuation is investigated by using the two-dimensional factorial moment methodology and the concept of the Hurst exponent (H). Investigation on the experimental data of compound particles and target fragments emitted in 84 Kr-AgBr interactions at 1.7 A GeV reveals that the best power law behaviours are exhibited at H=0.7 and 0.6 respectively, and the data for shower particles produced in 84 Kr-emulsion interactions at 1.7 A GeV indicate that the best power law behaviour occurs at H=0.6, all of which show the self-affine multiplicity fluctuation patterns. The multifractality and the non-thermal phase transition occurring during producing the compound particles, the target fragments, and the shower particles in the 84 Kr-AgBr interaction and the 84 Kr-emulsion interaction are also discussed. The multifractality is observed during producing compound particles, target fragments, and shower particles. In the target fragment production, an evidence of non-thermal phase transition is observed, but in the shower particle production and the compound particle production, no evidence of non-thermal phase transition is observed.     

Evidence of self-affine multiplicity fluctuation of target residues in ^84Kr-AgBr interactions at 1.7 AGeV

Self-affine multiplicity scaling is investigated in the framework of a two-dimensional factorial moment methodology using the concept of the Hurst exponent （H）. Analyzing the experimental data of target evaporated fragments emitted in ^84Kr-AgBr interactions at 1.7 AGeV revealed that the best power law behavior is exhibited for H = 0.3 indicating a self-arlene multiplicity fluctuation pattern. A signal of multifractality is also observed from knowledge of the anomalous fractal dimension dq extracted from the intermittency exponent aq of the anisotropic phase space scenario.     

Self-affine Multiplicity Fluctuation of Slow Particles in 16O-AgBr Collisions at 3.7 A GeV

We study the slow particles in 160-AgBr collisions at 3.7A GeV in nuclear emulsion with the method of twodimensional factorial moments using the Hurst exponent. Our investigation reveals the power law behaviour, exhibited in self-affine analysis, better than that in self-similar analysis. This work shows a clear evidence of self-affine target fragmentation.     

中高能重离子诱发乳胶核反应慢粒子产生(英文)

对150 AMeV 4He,290 AMeV 12C,400 AMeV 12C,400 AMeV 20Ne及500 AMeV 56Fe诱发乳胶不同靶核反应靶核碎片多重数分布及关联进行了研究。结果表明,黑径迹粒子、灰径迹粒子及重电离粒子平均多重数随靶核大小的增加而增加,不同靶核碎片多重数之间存在线性关联。这些实验结果均可以依据核-核碰撞几何模型及级联蒸发模型来解释。     

60 A GeV?16 O诱发乳胶核反应慢粒子产生研究

对60AGeV^16O诱发乳胶核反应靶核碎片多重数分布及其关联进行了实验研究,并与FRITOF1．7加级联机制模型和DIUNUC2．0模型计算结果进行了比较／。     

60A GeV16O诱发乳胶核反应慢粒子产生研究

对60AGeV ¹⁶O诱发乳胶核反应靶核碎片多重数分布及其关联进行了实验研究,并与FRITOF1.7加级联机制模型和DTUNUC 2.0模型计算结果进行了比较.     

Production of helium projectile fragments in {16O－emulsion interactions at 4.5 A GeV/c

The measurements of partial production cross sections of the multiple helium projectile fragments emitted at 4.5 A GeV/c {}^{16}O－Em interactions are reported. We have studied the production rate of helium projectile fragments due to fragmentation of {}^{16}O ions and compared it with that obtained from different projectiles at various energies. The dependence of on the mass number of the incident beams is formulated. The multiplicity distributions of the helium fragments produced in {}^{16}O－Em interactions at different energies exhibit Koba－Nielson－Olesen (KNO) scaling. The correlation of helium projectile fragments and target fragments is also investigated and it is found that the average of target fragments is increased with the decrease of the number of helium fragments in peripheral interactions.