对任意算子，包括波色子和费米子， = C + B = B + B 对费米子，下面的公式很有用， = {A, B}C - B {A, C} = A{B,C} -B{A,C} 四个算子的计算如下 = A D + AC + BD + C D 但是对于费米子 = A{B,C}D - AC{B,D} + {A,C}BD - C{A,B}D 当然这些结果都可以用wick定理来做，但是对于简单的问题，上面的公式也有用。
第一颗原子弹爆炸当量的估算 费米对世界上第一颗原子弹的当量的估算，被传为美谈。 有人质疑费米是否作出过这种估算，认为是以讹传讹，下面给出比较可信的证据： http://www.nuclearfiles.org/menu/key-issues/nuclear-weapons/history/pre-cold-war/manhattan-project/trinity/index.htm http://www.nuclearfiles.org/menu/key-issues/nuclear-weapons/history/pre-cold-war/manhattan-project/trinity/eyewitness-enrico-fermi_1945-07-16.htm ” Trinity Test, July 16, 1945 Eyewitness Report by Enrico Fermi Observations During the Explosion at Trinity on July 16, 1945 On the morning of the 16th of July, I was stationed at the Base Camp at Trinity in a position about ten miles from the site of the explosion. The explosion took place at about 5:30 A.M. I had my face protected by a large board in which a piece of dark welding glass had been inserted. My first impression of the explosion was the very intense flash of light, and a sensation of heat on the parts of my body that were exposed. Although I did not look directly towards the object, I had the impression that suddenly the countryside became brighter than in full daylight. I subsequently looked in the direction of the explosion through the dark glass and could see something that looked like a conglomeration of flames that promptly started rising. After a few seconds the rising flames lost their brightness and appeared as a huge pillar of smoke with an expanded head like a gigantic mushroom that rose rapidly beyond the clouds probably to a height of 30,000 feet. After reaching its full height, the smoke stayed stationary for a while before the wind started dissipating it. About 40 seconds after the explosion the air blast reached me. I tried to estimate its strength by dropping from about six feet small pieces of paper before, during, and after the passage of the blast wave. Since, at the time, there was no wind I could observe very distinctly and actually measure the displacement of the pieces of paper that were in the process of falling while the blast was passing. The shift was about 2 1/2 meters, which, at the time, I estimated to correspond to the blast that would be produced by ten thousand tons of T.N.T. Source: U.S. National Archives, Record Group 227, OSRD-S1 Committee, Box 82 folder 6, Trinity. Transcription: Thank you Gene Dannen for transcribing this document. “ 下面是译言网的中文翻译，我借用一下： http://article.yeeyan.org/view/mjysci/121826 ” 译言网的中文翻译如下： “ 三位一体测试目击者报告 1945年7月16日 恩里科·费米 对位于三位一体试验场爆炸的观测 在7月16日的早晨，我被派驻在距爆炸现场10 英里的三位一体基地。 爆炸发生在上午大约5时 30分，我的面部由一块中间焊了黑玻璃的大板所保护。我的第一印象是爆炸形成了非常强烈的闪光，身体的暴露部分感到一股热浪袭来。虽然我并未直视爆炸点，但当时的印象是此处突然变得比白天还亮。接着我通过黑玻璃看向爆炸中心，可以看到一些火焰开始聚集，并立刻上升。几秒钟后上升的火焰亮度降低，烟的顶部扩大像一个巨大的蘑菇，很快就超越大概是3万英尺高空的云层。在达到其高度的极限时，烟柱维持了一段时间才开始被风吹散。 在爆炸发生后约40秒冲击波才到达我这里。我尝试通过这个方法估计其爆炸强度：在爆炸开始前，爆炸中，冲击波通过后分别在大约六英尺高撒落小纸片。因为在爆炸前，我清晰地观察到确实没有风造成飘落的纸片偏移。而冲击波到来时，纸片偏移了大约2.5米，当时，我就估计爆炸产生的TNT当量是10000吨。 资料来源：美国国家档案馆，记录组227，OSRD-S1委员会，82箱第6文件夹，“三位一体”。 抄本：感谢 Gene Dannen 抄写本文件。 “ 我不知道费米是怎么估算这一当量 － 10000吨 TNT － 的，所以我自己来估算了一下，方法如下，数据全部仅仅来自费米的原始报告： 1、费米距离爆心10英里，大约为16公里，则在此半径范围内，一千米高度的空气体积接近800立方千米，空气密度为1.29，则空气总质量约为10^12千克，即10亿吨。 2、纸片初始高度为2米左右，落地需要1秒钟，水平偏移了2.5米，即纸片水平速度约为2.5米每秒，将此速度粗略作为冲击波到达此处时候的速度。 3、假设原子弹爆炸时将这一范围内的空气全部加热为这一速度，则所需能量从动能公式计算出约为，3×10^12焦耳。 4、一千克TNT 的热值约为4*10^6焦耳，则上述的空气总能量约为 0.75 千吨的TNT 的能量，取整为一千吨TNT 当量。 5、考虑到前面计算空气体积的时候，是计算了一个厚度为一千米的圆饼而不是一个半径为16千米的半球， 如果按照半球计算，则体积会增加一个数量级，费米描述中就有（3万英尺）也是接近一万米的高度，但是空气密度随高度而减小，所以折中一下，取一个因子 5， 再考虑到冲击波只是原子弹爆炸释放能量的形式的一种，再取一个因子2。 6、这样，就正好得到了 一万吨 TNT 的 总当量。 很有意思的是， 我完成了上述估算以后，检索有没有其它的估算方法时，发现科学松鼠会上的一篇文章： http://songshuhui.net/archives/40461 费米问题，理科生的脑筋急转弯 Comments 候戏 发表于 2010-07-25 09:39 作者的方案是： ” 1）假设纸片做自由落体运动，初速度相当于气浪的速度，这个计算在初中物理习题中常见。 2）假设原子弹爆炸能量全部转化为空气的动能，爆炸之后，气浪形成球面向各个方向扩展，扩展到费米所在地时，球体内总的空气质量可以通过空气密度乘以球体体积算出来。 3）总能量等于气浪速度平方乘上空气质量。然后转换为 TNT当量单位 ，完成。 “ 思路和方法跟我完全一样。 难道就这么一条路？ 我反而郁闷了。 ^_^。。。。。。。。。。。。。。 顺便问问，编辑 MM 不给本文一朵 小红花吗 ？
紧邻芝加哥大学学生公寓，离知名的费米研究所不远的地方，有一小小的广场。广场上竖立一个怪怪的雕塑。尽管每天从雕塑的另一边上下班，时不时看到有人照像留念，可从来没有想过那是一尊什么雕像?直到前几天才知道那是纪念一项影响深远，改变历史的重要科学实验。大家猜猜是什么实验？给大家点提示：与著名物理学家费米有关，与核武器有关。 谜底揭开： 是为了纪念1942年12月2日，费米(Enrico Fermi)领导的研究小组在芝加哥大学体育馆旧址第一次成功实现了自限制链式核反应试验（self-sustaining nuclear chain reaction），从而开启了可人为控制核能量释放的新时代。 雕塑的主题：核能量（Nuclear Energy），是在1967年，这一重要事件刚好25年的时候，为纪念人类利用核能量而建立，由艺术家Henry Moore创作。看起来像人的骷髅，或原子弹爆炸的蘑菇云，不过雕塑家告诉他的一位朋友说：环绕四周看看，透过那些开放的空间，你也许觉得置身于教堂之中。（To some, it suggests the shape of the human skull or the atomic mushroom cloud. Henry Moore told a friend, however, that he hoped those viewing it would go around it, looking out through the open spaces, and that they may have a feeling of being in a cathedral.）。不过说实话，我没有能够完全理解最后一句话隐含的意义。 The First Pile http://www.atomicarchive.com/History/firstpile/firstpile_01.shtml On December 2, 1942, man first initiated a self-sustaining nuclear chain reaction, and controlled it. Beneath the West Stands of Stagg Field , Chicago, late in the afternoon of that day, a small group of scientists witnessed the advent of a new era in science. History was made in what had been a squash-rackets court. Precisely at 3:25 p.m. , Chicago time, scientist George Weil withdrew the cadmium-plated control rod and by his action man unleashed and controlled the energy of the atom. As those who witnessed the experiment became aware of what had happened, smiles spread over their faces and a quiet ripple of applause could be hear. It was a tribute to Enrico Fermi , Nobel Prize winner, to whom, more than to any other person, the success of the experiment was due. Fermi, born in Rome, Italy, on September 29, 1901, had been working with uranium for many years. In 1934 he bombarded uranium with neutrons and produced what appeared to be element 93 (uranium is element 92) and element 94. However, after closer examination it seemed as if nature had gone wild; several other elements were present, but none could be fitted into the periodic table near uranium where Fermi knew they should have fitted if they had been the transuranic elements 92 and 94. It was not until five years later that anyone, Fermi included, realized he had actually caused fission of the uranium and that these unexplained elements belonged back in the middle part of the periodic table. Fermi was awarded the Nobel Prize in 1938 for his work on transuranic elements. He and his family went to Sweden to receive the prize. The Italian Fascist press severely criticized him for not wearing a Fascist uniform and failing to give the Fascist salute when he received the award. The Fermis never returned to Italy. From Sweden, having taken most of his personal possessions with him, Fermi proceeded to London and thence to America where he has remained ever since . The modern Italian explorer of the unknown was in Chicago that cold December day in 1942. An outsider looking into the squash court where Fermi was working would have been greeted by a strange sight. In the center of the 30- by 60-foot room, shrouded on all but one side by a gray balloon cloth envelope, was a pile of black bricks and wooden timbers, square at the bottom and a flattened sphere on top. Up to half of its height, its sides were straight. The top half was domed, like a beehive. During the construction of this crude appearing but complex pile (the name which has since been applied to all such devices) the standing joke among the scientists working on it was: If people could see what we're doing with a million-and-a-half of their dollars, they'd think we are crazy. If they knew why we are doing it, they'd know we are. In relation to the fabulous atomic bomb program, of which the Chicago Pile experiment was a key part, the successful result reported on December 2nd formed one more piece for the jigsaw puzzle which was atomic energy. Confirmation of the chain reactor studies was an inspiration to the leaders of the bomb project, and reassuring at the same time, because the Army's Manhattan Engineer District had moved ahead on many fronts. Contract negotiations were under way to build production-scale chain reactors, land had been acquired at Oak Ridge, Tennessee, and millions of dollars had been obligated. Three years before the December 2nd experiment, it had been discovered that when an atom of uranium was bombarded by neutrons, the uranium atom sometimes was split, or fissioned. Later, it had been found that when an atom of uranium fissioned, additional neutrons were emitted and became available for further reaction with other uranium atoms. These facts implied the possibility of a chain reaction, similar in certain respects to the reaction which is the source of the sun's energy. The facts further indicated that if a sufficient quantity of uranium could be brought together under the proper conditions, a self-sustaining chain reaction would result. This quantity of uranium necessary for a chain reaction under given conditions is known as the critical mass, or more commonly, the critical size of the particular pile. For three years the problem of a self-sustaining chain reaction had been assiduously studied. Nearly a year after Pearl Harbor, a pile of critical size was finally constructed. It worked. A self-sustaining nuclear chain reaction was a reality. Nuclear Energy Henry Moore, sculptor On December 2, 1942, man achieved here the first self-sustaining chain reaction and thereby initiated the controlled release of nuclear energy. Chicago Pile No. 1 ( CP-1 ) was constructed in a makeshift laboratory under the grandstand of Stagg Field Stadium at The University of Chicago. In 1965, the site was designated a registered national historic landmark. The sculpture was dedicated in 1967 on the 25th anniversary of the first controlled generation of nuclear power, an experiment by Enrico Fermi and his colleagues. The sculpture, provided by the Trustees of the B.F.Ferguson Monument Fund of the Art Institute of Chicago , is on the east side of Ellis Avenue between 56th and 57th Streets ( map ). The sculpture Nuclear Energy was unveiled at 3:36 p.m. on December 2, 1967, precisely a quarter-century after scientists at the University of Chicago achieved the first controlled self-sustaining nuclear chain reaction, initiating the atomic age. The 12-foot bronze sculpture stands on the site of the University's old Stagg Field, where the experiment took place under the leadership of Enrico Fermi. To some, it suggests the shape of the human skull or the atomic mushroom cloud. Henry Moore told a friend, however, that he hoped those viewing it would go around it, looking out through the open spaces, and that they may have a feeling of being in a cathedral. adapted from The Nuclear Chain Reaction--Forty Years Later, edited by Robert G. Sachs, 1984. The First Reactor tells the story of Chicago Pile 1 and the first controlled, self-sustaining nuclear chain reaction. It contains The First Pile by Corbin Allardice and Edward Trapnell, postwar recollections of Enrico and Laura Fermi, many photographs, and a list of suggested references. The First Reactor is available in PDF format (free download: Adobe Acrobat Reader ) or may be requested from the Office of Nuclear Energy, Science and Technology of the U.S. Department of Energy .
标签: 费米
