Calculating the hadronic vacuum polarization and leading hadronic contribution to the muon

高二英语海洋科学单选题40题1. The dolphin is known for its intelligence and ____ swimming skills.A. excellentB. badC. commonD. poor答案：A。

本题考查形容词的词义。

“excellent”表示“优秀的，出色的”，海豚以其智力和出色的游泳技能而闻名，A 选项符合语境。

B 选项“bad”意为“坏的”，C 选项“common”意为“普通的”，D 选项“poor”意为“差的”，都不符合海豚游泳技能的特点。

2. The shark has sharp teeth to catch its ____.A. friendsB. enemiesC. foodD. partners答案：C。

本题考查名词词义。

鲨鱼锋利的牙齿是用来捕捉“食物”的，C 选项符合逻辑。

A 选项“friends”朋友，B 选项“enemies”敌人，D 选项“partners”伙伴，都不符合鲨鱼牙齿的用途。

3. The octopus can change its color to ____ from enemies.A. fightB. protectC. attackD. hide答案：D。

本题考查动词词义及搭配。

“hide from”表示“躲避”，章鱼能改变颜色来躲避敌人，D 选项符合。

A 选项“fight”战斗，B 选项“protect”保护，常用搭配为“protect...from...”，C 选项“attack”攻击，均不符合语境。

4. Whales are ____ animals and they live in groups.A. socialB. lonelyC. wildD. strange答案：A。

本题考查形容词词义。

“social”表示“群居的，社交的”，鲸鱼是群居动物，A 选项正确。

B 选项“lonely”孤独的，C 选项“wild”野生的，D 选项“strange”奇怪的，都不符合鲸鱼的生活习性。

托福阅读TPO21(试题+答案+译文)第一篇:GeothermalEnergy为了帮助大家备考托福阅读，提高成绩，下面小编给大家带来托福阅读TPO21(试题+答案+译文)第一篇:Geothermal Energy，希望大家喜欢！托福阅读原文【1】Earth's internal heat, fueled by radioactivity, provides the energy for plate tectonics and continental drift, mountain building, and earthquakes. It can also be harnessed to drive electric generators and heat homes. Geothermal energy becomes available in a practical form when underground heat is transferred by water that is heated as it passes through a subsurface region of hot rocks (a heat reservoir) that may be hundreds or thousands of feet deep. The water is usually naturally occurring groundwater that seeps down along fractures in the rock; less typically, the water is artificially introduced by being pumped down from the surface. The water is brought to the surface, as a liquid or steam, through holes drilled for the purpose.【2】By far the most abundant form of geothermal energy occurs at the relatively low temperatures of 80° to 180° centigrade. Water circulated through heat reservoirs in this temperature range is able to extract enough heat to warm residential, commercial, and industrial spaces. More than 20,000 apartments in France are now heated by warm underground water drawn from a heat reservoir in a geologic structure near Paris called the Paris Basin. Iceland sits on a volcanic structure known as the Mid-Atlantic Ridge. Reykjavik, the capital of Iceland, is entirely heated by geothermal energy derived from volcanicheat.【3】Geothermal reservoirs with temperatures above 180° centigrade are useful for generating electricity. They occur primarily in regions of recent volcanic activity as hot, dry rock; natural hot water; or natural steam. The latter two sources are limited to those few areas where surface water seeps down through underground faults or fractures to reach deep rocks heated by the recent activity of molten rock material. The world's largest supply of natural steam occurs at The Geysers, 120 kilometers north of San Francisco, California. In the 1990s enough electricity to meet about half the needs of San Francisco was being generated there. This facility was then in its third decade of production and was beginning to show signs of decline, perhaps because of over development. By the late 1990s some 70 geothermal electric-generating plants were in operation in California, Utah, Nevada, and Hawaii, generating enough power to supply about a million people. Eighteen countries now generate electricity using geothermal heat.【4】Extracting heat from very hot, dry rocks presents a more difficult problem: the rocks must be fractured to permit the circulation of water, and the water must be provided artificially. The rocks are fractured by water pumped down at very high pressures. Experiments are under way to develop technologies for exploiting this resource.【5】Like most other energy sources, geothermal energy presents some environmental problems. The surface of the ground can sink if hot groundwater is withdrawn without being replaced. In addition, water heated geothermally can contain salts and toxic materials dissolved from the hot rock. These waters present a disposal problem if they are not returned to theground from which they were removed.【6】The contribution of geothermal energy to the world's energy future is difficult to estimate. Geothermal energy is in a sense not renewable, because in most cases the heat would be drawn out of a reservoir much more rapidly than it would be replaced by the very slow geological processes by which heat flows through solid rock into a heat reservoir. However, in many places (for example, California, Hawaii, the Philippines, Japan, Mexico, the rift valleys of Africa)the resource is potentially so large that its future will depend on the economics of production. At present, we can make efficient use of only naturally occurring hot water or steam deposits. Although the potential is enormous, it is likely that in the near future geothermal energy can make important local contributions only where the resource is close to the user and the economics are favorable, as they are in California, New Zealand, and Iceland. Geothermal energy probably will not make large-scale contributions to the world energy budget until well into the twenty-first century, if ever.托福阅读试题1.According to the processes described in paragraph 1, what is the relationship between radioactivity and the steam produced by geothermal heat?A.Geothermally heated steam is produced when water is exposed to radioactivity deep underground.B.When water is introduced into holes drilled thousands of feet in the ground, it becomes radioactive and turns to steam.C.Radioactivity heats Earth's interior rock, which in turn can heat water to the point it becomes steam.D.When a reservoir of steam in subsurface rock is produced by radioactivity, it is said to be geothermally heated.2.The word "practical" in paragraph 1 is closest in meaning toable.B.plentiful.C.economical.D.familiar.3.The word "abundant" in paragraph 2 is closest in meaning toA.economical.B.familiar.C.plentiful.eful.4.According to paragraph 2, which of the following is true about heat reservoirs with a temperature in the range of 80°to 180° centigrade?A.They are under international control.B.They are more common than reservoirs that have a higher temperature.C.Few of them produce enough heat to warm large industrial spaces.D.They are used to generate electricity.5.According to paragraph 3, what is the connection between underground faults and naturally occurring steam?A.Underground faults enable the heat from molten-rock material to escape upward to regions where it can heat surface water enough to produce steam.B.Underground faults are created by steam that is produced in geothermal reservoirs deep inside Earth.C.Underground faults create spaces in which natural steam is sometimes trapped.D.Underground faults allow surface water to reach deep rocks that are hot enough to turn it into steam.6.In paragraph 3, why does the author mention that in the 1990s The Geysers was in its third decade of production?A.To provide the historical context of the geothermal production of electricity in the United States.B.To imply that The Geysers was the first geothermal site to be put into production in California.C.To help explain the signs of decline shown by The Geysers.D.To explain why 70 new geothermal sites were put into electricity production in the late 1990s.7.Which of the following can be inferred from paragraphs 2 and 3 about geothermal reservoirs?A.Volcanic heat is associated only with geothermal reservoirs that have a temperature over 180° centigrade.B.More countries produce power from geothermal reservoirs than use them for heating buildings.C.Most geothermal reservoirs are suitable for producing electricity.D.A higher geothermal reservoir temperature is needed to generate electricity than is needed to heat homes.8.According to paragraph 4, extracting heat from very hot, dry rocks is difficult in part becauseA.the underground rock must be fractured before heat can be removed from it.B.the water above the rock is under very high pressure.C.the rock breaks apart when water is pumped into it.D.the water circulated through the rock must be much cooler than the rock itself.9.The word "exploiting" in paragraph 4 is closest in meaningtoA.locating.B.increasing.C.making use of.D.estimating the size of.10.How is the problem that the surface may sink related to the problem that water heated geothermally may contain toxic materials?A.Both problems could be solved by returning groundwater that is removed from an underground heat reservoir back to the reservoir after heat is extracted from it.B.The problem of sinking is more difficult to solve than is the problem of toxic materials.nd at the surface sinks because the rock beneath the surface is weakened when salts and toxic materials are removed from it in the process of extracting geothermal energy.D.Both problems are caused by the fact that the hot groundwater in a heat reservoir dissolves the rock, which weakens the rock and makes the water toxic with salt.11.Which of the sentences below best expresses the essential information in the highlighted sentence in paragraph 6? Incorrect choices change the meaning in important ways or leave out essential information.A.Heat flows through solid rock very slowly, so it takes a very long time for geological processes to produce a reservoir of geothermal energy.B.Geothermal energy is not renewable because heat flows very slowly through solid rock into or out of a heat reservoir.C.The heat quickly removed from a heat reservoir is replaced so slowly by geological processes that geothermal energy is notpractically speaking, renewable.D.In most cases, heat travels into a heat reservoir so slowfy that it is a much quicker process to remove the heat from a reservoir than to replace it.12.In paragraph 6, the author implies that in California, Hawaii, the Philippines, Japan, Mexico, and the rift valleys of Africa the potential size of the geothermal resource is so large thatA.it might be economically worth developing these sites even though geothermal energy is not renewable.B.these sites will be the first geothermal energy sites to be developed with new technology.C.these sites are likely to make a large-scale contribution to the world energy budget in the twenty-first century.D.it does not matter whether they have naturally occurring deposits of hot water or steam.13. Look at the four squares [■] that indicate where the following sentence could be added to the passage. Where would the sentence best fit? Click on a square to add the sentence to the passage. In either case, the heated water will usually be under considerable pressure, and so may have a temperature that is well above its sea-level boiling point of 100° centigrade.Earth's internal heat, fueled by radioactivity, provides the energy for plate tectonics and continental drift, mountain building, and earthquakes. It can also be harnessed to drive electric generators and heat homes. Geothermal energy becomes available in a practical form when underground heat is transferred by water that is heated as it passes through a subsurface region of hot rocks (a heat reservoir) that may be hundreds or thousands of feet deep. ■【A】The water is usuallynaturally occurring groundwater that seeps down along fractures in the rock; less typically, the water is artificially introduced by being pumped down from the surface. ■【B】The water is brought to the surface, as a liquid or steam, through holes drilled for the purpose.■【C】By far the most abundant form of geothermal energy occurs at the relatively low temperatures of 80° to 180° centigrade. ■【D】Water circulated through heat reservoirs in this temperature range is able to extract enough heat to warm residential, commercial, and industrial spaces. More than 20,000 apartments in France are now heated by warm underground water drawn from a heat reservoir in a geologic structure near Paris called the Paris Basin. Iceland sits on a volcanic structure known as the Mid-Atlantic Ridge. Reykjavik, the capital of Iceland, is entirely heated by geothermal energy derived from volcanic heat.14. Directions: An introductory sentence for a brief summary of the passage is provided below. Complete the summary by selecting the THREE answer choices that express the most important ideas in the passage. Some sentences do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points.Heat reservoirs in the form of hot rock far beneath Earth's surface are a potential source of usable geothermal energy.A.Heat reservoirs with a temperature from 80° to 180° centigrade can be used, as in France and Iceland, to heat buildings.B.A number of countries now use geothermal reservoirs that contain water or steam above 180° centigrade to generate electricity.C.Most heat reservoirs with a temperature above 180° centigrade cannot be used for energy because they are usually too close to recent volcanic activity.D.The sinking of land above heat reservoirs and other environmental problems arise when water is pumped into a heat reservoir under high pressure.E.Experiments are under way to determine if geothermally heated waters could be used as a source of certain minerals that have been dissolved out of hot rocks deep within Earth.F.A number of issues, including how to extract heat from reservoirs that do not have a natural supply of water, will significantly limit the use of geothermal energy for the foreseeable future.托福阅读答案1.细节题，问radioactivity和steam的关系，所以找双关键词，分别定位至本段第一句和最后一句，第一句说radioactivity提供了地球的内热，最后一句说水变成蒸汽到达地表，水受热才能蒸汽，而这份热量是geothermal energy提供的，这就是二者的关系，所以答案是C。

高二英语海洋科学单选题40题1. There are many kinds of fish in the ocean. The ______ is one of them.A. sharkB. elephantC. tigerD. monkey答案：A。

本题考查海洋生物名词。

选项B“elephant”是大象，生活在陆地；选项C“tiger”是老虎，生活在陆地；选项D“monkey”是猴子，生活在陆地。

只有选项A“shark”鲨鱼是海洋生物。

2. The ______ can change its color to protect itself.A. dolphinB. starfishC. chameleonD. whale答案：B。

此题考查海洋生物特性。

选项A“dolphin”海豚不能变色；选项C“chameleon”变色龙，但它不是海洋生物；选项D“whale”鲸鱼也不能变色。

而选项B“starfish”海星可以改变颜色来保护自己。

3. Which of the following is NOT a marine mammal?A. SealB. JellyfishC. WalrusD. Orca答案：B。

本题考查海洋哺乳动物。

选项A“Seal”海豹、选项C“Walrus”海象、选项D“Orca”虎鲸都是海洋哺乳动物，而选项B“Jellyfish”水母是腔肠动物，不是哺乳动物。

4. The ______ has a hard shell and moves slowly.A. crabB. birdC. catD. rabbit答案：A。

本题围绕海洋生物的特征。

选项B“bird”鸟、选项C“cat”猫、选项D“rabbit”兔子都不是海洋生物，且没有硬壳。

而选项A“crab”螃蟹有硬壳且移动缓慢，是海洋生物。

5. Among these marine creatures, the ______ is known for its beautiful shape.A. sea urchinB. horseC. pigD. duck答案：A。

2019年1⽉5⽇托福阅读考试真题及答案
1⽉5⽇新⼀期的托福考试已经顺利完成，相信⼤家对真题及其答案⾮常感兴趣，接下来就和店铺⼀起看看2019年1⽉5⽇托福阅读考试真题及答案。

Passage One
学科分类：地质类
题⽬：全球⽓候的形成
内容回忆：科学家通过研究北冰洋冰架核，通过研究⽕⼭，判断过去全球⽓候
词汇题：
1. relatively = comparatively
2. episode = occurrence
3. amplify = strength
Passage Two
学科分类：⽣物类
题⽬：⽕在植物⽣长中的作⽤
内容回忆：⽕对于植物有益处也有害处，益处是可以把腐殖质燃烧，让他快速
变成植物可以⽤的营养。

后⾯举例说明美国黄⽯国家公园在 1988
年着⽕，让部分之前消失的物种重新出现
词汇题：
1. completely = entirely
2. uniform = same
3. magnitude= size
4. readily=easily
Passage Three
学科分类：天⽂
题⽬：地球海洋的形成
内容回忆：海洋的形成，通过研究地球轨道 orbit 运动，太阳活动的变化去猜
测海洋的形成，最终得出结论地球海洋形成是慢慢演变的
词汇题：
1. extreme = intense
2. collide= mix together
3. in retrospect=reconsider the past。

极地科考英语语态练习40题1. The ice samples in the polar region are often ______ for scientific research.A. studiedB. being studiedC. studiedD. to be studied答案：A。

本题考查一般现在时的被动语态。

选项A“studied”是一般现在时的被动语态形式，表示“被研究”，符合句子语境。

选项B“being studied”是现在进行时的被动语态，表示“正在被研究”，此处没有正在进行的意思。

选项C 重复了选项A。

选项D“to be studied”是不定式的被动形式，表示“将要被研究”，与句子的时态不符。

2. The temperature in the polar areas ______ every day.A. is measuredB. measuresC. is measuringD. has measured答案：A。

此题考查一般现在时的被动语态。

选项A“is measured”是被动语态，“温度被测量”，符合题意。

选项B“measures”是主动形式，温度不能主动测量。

选项C“is measuring”是现在进行时，不符合语境。

选项D“has measured”是现在完成时，也不符合句子的时态要求。

3. The polar bears' living conditions ______ by scientists.A. are observedB. observeC. is observedD. observes答案：A。

本题考查一般现在时的被动语态。

主语“living conditions”是复数，所以要用“are observed”，表示“被观察”。

选项B 和D 是主动形式，不符合句子意思。

选项C“is observed”用于主语是单数的情况。

4. The data about the polar climate ______ carefully.A. is collectedB. are collectedC. collectsD. collected答案：A。

小学上册英语第4单元真题试卷英语试题一、综合题(本题有100小题，每小题1分，共100分.每小题不选、错误，均不给分)1.The ______ can live a long time.2. A silverfish is a type of ________________ (昆虫).3.I have a _______ (surprise) for you.4.Catalysts can significantly speed up reaction rates without being _____ in the process.5.In a reversible reaction, reactants can form products and _____ can reform the reactants.6.In spring, the _____ blooms beautifully.7.What is the name of the ocean located on the east coast of the United States?A. Atlantic OceanB. Pacific OceanC. Indian OceanD. Arctic OceanA8.The Earth's core is primarily made up of ______ and nickel.9.I can ______ (展示) my talents.10.The chemical formula for copper(II) sulfate is _____.11.My dad teaches me to be __________ (负责任的) in my actions.12.What do you call a person who repairs cars?A. MechanicB. ElectricianC. PlumberD. PainterA13.My favorite ________ is pink.14.The antelope grazes on the _____ grass.15.The __________ is a famous landmark in Paris.16.My _____ (叔叔) works at a zoo and takes care of the animals. 我叔叔在动物园工作，照顾动物。

2023年1月浙江高考英语阅读B篇解析(笔记版)2023年1月浙江高考英语阅读B篇解析(笔记版)2023年1月的浙江高考英语阅读B篇是一个重要的考试部分。

在本文中，我们将对该篇阅读材料进行详细解析和分析，帮助考生更好地理解文中的内容，并为他们在考试中取得更好的成绩提供指导。

首先，让我们对阅读材料进行整体概述。

该篇文章主要谈论了气候变化对海洋中的生物多样性和海洋生态系统的影响。

文章列举了一些具体的例子和数据，旨在向读者展示气候变化是如何对海洋生态系统造成负面影响的。

接下来，我们将逐段对文章内容进行解析。

第一段是文章的引言部分，旨在向读者介绍本文的主题。

该段落提到了气候变化对地球的重要性，并简要概述了气候变化对海洋生物和生态系统的影响。

此处，作者通过引用科学家的观点来支持他们的论述，使文章更有说服力。

接着，第二段详细讨论了气候变化对海洋温度的影响。

文章指出，随着地球变暖，海洋温度上升，这对海洋生物的生存环境带来了很大的威胁。

为了支持这个论点，作者引用了一项研究，并分享了相关数据。

这些具体的信息有助于读者更好地理解气候变化对海洋生态系统的负面影响。

在第三段，文章转向讨论气候变化对海洋酸化的影响。

作者解释了二氧化碳的排放是造成海洋酸化的主要原因，并指出这一现象对海洋生物的生存造成了严重的威胁。

为了支持这一观点，作者引用了另外一项研究，并提供了相关的事实和数据。

这些信息加强了文章的可信度。

随后的一段具体讨论了气候变化对海洋生物多样性的影响。

文章指出，气候变化导致的环境变化对海洋生态系统中的物种多样性产生了负面影响。

为了支持这一说法，作者引用了一些案例研究，并提供了适当的例证。

这些具体的例子有助于读者更好地理解气候变化对海洋生物多样性的威胁。

最后一段是文章的结论部分，总结了文章的主要观点。

作者再次强调了气候变化对海洋生态系统的危害，并呼吁人们采取积极的行动来减缓气候变化的影响。

这一段提供了一个有力的结论，强调读者应对气候变化负责，并呼吁他们行动起来。

1月24日托福阅读真题
第一篇：火星上的水
【文章解析】：
第一段：综述火星的大气特征，与地球形成对比，提出在这种气候条件下液态水不易在表面形成。

第二段：通过各种探测手段对火星表面地质特征(沉淀，水道)的研究得出结论：火星上确实存在液态水。

第三段：液态水的存在证明，火星上很可能存在生命迹象。

第四段：然而对于火星上生命迹象的研究存在很多的难题。

第二篇：二战后欧洲经济
文章解析：
第一段：综述二战后各国经济的发展。

(此段中出现很多细节性的对比数据，考查考生对杂乱的细节信息的收集与梳理能力)
第二段：战后经济发展的原因：马歇尔计划对欧洲经济发展的巨大推动作用，但是经济支援停止后，经济发展也陷入停滞。

第三段：战后经济发展的原因：政府在欧洲经济发展中起到的作用：支持私有化经济，维持经济的稳定性。

第四段：政府间的合作也对推动了经济的发展。

第五段：美国对于欧洲的经济援助停止后，当地的经济发展也陷入停滞，究其原因是没有有技术的工人操作现代化的机械。

第三篇：罗马的文化入侵
文章解析：
文章关注罗马文明在文化方面对于其他区域的影响。

首先，拉丁语被广泛推崇，人们认为学习语言不仅是为了日常交流，更重要的是可以成为更好的人(当时
人们对于罗马文化的推崇可见一斑)，语言的广泛传播的同时更推动了罗马文化和政治方面的深入影响。

接下来阐述罗马建筑的影响，罗马在征服属地之后，影响当地的建筑风格，随后当地的建筑越来越罗马风。

建筑除了装饰更重要的作用是用于政治和宗教聚会。

随后记叙罗马民主意识的发展和传播。

新东方：5月16日托福阅读真题新东方：2015年5月16日托福阅读真题第一篇考生回忆：测定星球与宇宙的年龄。

先说了尝试测定地球的年龄。

但是发现地球上面的地质特征不太靠谱，因为会持续受到风吹雨打的地质腐蚀，所以人们想到了去测定陨石(meteorites)来替代，然后说陨石按照主要是石头、主要是铁还是两者兼具可以分开三个类别。

然后根据一些研究得出来的结论是地球和月球的年龄都是46亿年(4.6 billion years)。

所以最后得出来的结论是太阳的年龄也差不多，进而整个太阳系的年龄也差不多。

后面又讲了测定宇宙的年龄。

用的是红移(redshift)技术，通过“宇宙大爆炸理论+多普勒效应”可以最终测出宇宙年龄。

第二篇考生回忆：动物传播(Animal Dispersal)。

先说了动物传播所需要付出的代价/成本(cost)，除了肌肉(muscle)与能量(energy)的成本外，还会让自己暴露在捕猎者(predator)的危险之下。

那么既然有如此大得代价，为什么还要传播呢?(当然是回报更大)。

后面又说了不同性别的动物，其传播行为的特征不一样。

比如作为雄性(male)的动物，通常会比雌性(female)要迁徙得更远，雌性则守护领地。

有两个理论尝试解释这种现象。

第一种理论是说这样可以避免近亲繁殖(inbreeding)而导致的基因疾病(genetic disease)而导致后代无法繁殖。

另外一个理论的时有研究认为这种现象是因为雄性在求交配的时候会与同类竞争打架，而打输的雄性就被驱赶出族群，远离驻地。

这样的研究不适用于松鼠(squirrel)，但是却适合于狮子(lion)。

第三篇考生回忆：美索不达美亚平原文明崛起的成因探究。

传统理论认为是外因(invasion)，新的理论认为是内因。

例如，贸易的发达，举了农业的橄榄油(olive)作为例子。

这种农产品由于不会和其他作物争夺资源和劳动力，所以很适合大力生产。

其次，农业发展导致的人口增长也是文明崛起的主要原因。

高二科学发现英语阅读理解30题1<背景文章>Isaac Newton is one of the most renowned scientists in history. His discovery of the law of universal gravitation revolutionized the field of physics. Newton was born in 1642. In his early years, he showed great interest in mathematics and science.One day, while Newton was sitting under an apple tree, an apple fell on his head. This simple event led him to think deeply about the forces acting on objects. He began to wonder why apples always fall downwards and not in any other direction. This led him to formulate the idea of gravity.Newton's law of universal gravitation states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This law not only explained the motion of celestial bodies but also had a profound impact on the development of science and technology.The discovery of universal gravitation had a significant impact on later generations. It provided a foundation for modern physics and helped scientists understand the workings of the universe. It also inspired many other scientific discoveries and advancements.Newton's work was not only limited to the discovery of gravity. He also made significant contributions to mathematics, optics, and mechanics. His book "Philosophiae Naturalis Principia Mathematica" is considered one of the most important scientific works of all time.Newton's discovery of universal gravitation was a result of his deep thinking, curiosity, and perseverance. His work has inspired generations of scientists and continues to be studied and admired today.1. Newton was born in ___.A. 1640B. 1642C. 1644D. 1646答案：B。

托福考试 复习托福阅读TPO19(试题+答案+译文)第3篇:Discovering the Ice Ages托福阅读原文【1】In the middle of the nineteenth century, Louis Agassiz, one of the first scientists to study glaciers, immigrated to the United States from Switzerland and became a professor at Harvard University, where he continued his studies in geology and other sciences. For his research, Agassiz visited many places in the northern parts of Europe and North America, from the mountains of Scandinavia and New England to the rolling hills of the American Midwest. In all these diverse regions, Agassiz saw signs of glacial erosion and sedimentation. In flat plains country, he saw moraines (accumulations of earth and loose rock that form at the edges of glaciers) that reminded him of the terminal moraines found at the end of valley glaciers in the Alps. The heterogeneous material of the drift (sand, clay, and rocks deposited there) convinced him of its glacial origin.【2】The areas covered by this material were so vast that the ice that deposited it must have been a continental glacier larger than Greenland or Antarctica. Eventually, Agassiz and others convinced geologists and the general public that a great continental glaciation had extended thepolar ice caps far into regions that now enjoy temperate climates. For the first time, people began to talk about ice ages. It was also apparent that the glaciation occurred in the relatively recent past because the drift was soft, like freshly deposited sediment. We now know the age of the glaciation accurately from radiometric dating of the carbon-14 in logs buried in the drift. The drift of the last glaciation was deposited during one of the most recent epochs of geologic time, the Pleistocene, which lasted from 1.8 million to 10,000 years ago. Along the east coast of the United States, the southernmost advance of this ice is recorded by the enormous sand and drift deposits of the terminal moraines that form Long Island and Cape Cod.【3】It soon became clear that there were multiple glacial ages during the Pleistocene, with warmer interglacial intervals between them. As geologists mapped glacial deposits in the late nineteenth century, they became aware that there were several layers of drift, the lower ones corresponding to earlier ice ages. Between the older layers of glacial material were well-developed soils containing fossils of warm-climate plants. These soils were evidence that the glaciers retreated as the climate warmed. By the early part of the twentieth century, scientists believed that four distinct glaciations had affected North America and Europe during the Pleistocene epoch.【4】This idea was modified in the late twentieth century, when geologistsand oceanographers examining oceanic sediment found fossil evidence of warming and cooling of the oceans. Ocean sediments presented a much more complete geologic record of the Pleistocene than continental glacial deposits did. The fossils buried in Pleistocene and earlier ocean sediments were of foraminifera—small, single-celled marine organisms that secrete shells of calcium carbonate, or calcite. These shells differ in their proportion of ordinary oxygen (oxygen-16) and the heavy oxygen isotope (oxygen-18). The ratio of oxygen-16 to oxygen-18 found in the calcite of a foraminifer's shell depends on the temperature of the water in which the organism lived. Different ratios in the shells preserved in various layers of sediment reveal the temperature changes in the oceans during the Pleistocene epoch.【5】Isotopic analysis of shells allowed geologists to measure another glacial effect. They could trace the growth and shrinkage of continental glaciers, even in parts of the ocean where there may have been no great change in temperature—around the equator, for example. The oxygen isotope ratio of the ocean changes as a great deal of water is withdrawn from it by evaporation and is precipitated as snow to form glacial ice. During glaciations, the lighter oxygen-16 has a greater tendency to evaporate from the ocean surface than the heavier oxygen-18 does. Thus, more of the heavy isotope is left behind in the ocean and absorbed by marine organisms. From this analysis of marine sediments, geologistshave learned that there were many shorter, more regular cycles of glaciation and deglaciation than geologists had recognized from the glacial drift of the continents alone.托福阅读试题1.The word “accumulations” in the passage (paragraph 1) is closest in meaning toA.signs.B.pieces.C.types.D.deposits.2.The word “heterogeneous” in the passage (paragraph 1) is closest in meaning toA.remaining.B.varied.C.familiar.yered.3.According to paragraph 1, what persuaded Louis Agassiz that glaciation in the past had been widespread?A.Geologic differences between mountain valleys and flat plains.B.The presence of similar glacial material in many different regions.C.Geologic research on mountain glaciers in the Alps.D.Evidence of regional differences in the drift caused by glacial erosion.4.The word “enjoy” in the passage (paragraph 2) is closest in meaning toA.experience.B.resemble.C.expect.D.dominate.5.It can be inferred from paragraph 2 that Agassiz and other geologists of his time were not able to determineA.which geographic regions had been covered with ice sheets in the last ice age.B.the exact dates at which drifts had been deposited during the last ice age.C.the exact composition of the drifts laid during the last ice age.D.how far south along the east coast of the United States the ice had advanced during the last ice age.6.According to paragraph 3, what did geologists conclude as a result of finding well-developed soils containing warm-climate plant fossils between layers of glacial drift?A.There had been only one warm period before the Pleistocene epoch.B.There had been multiple periods of mild weather between ice ages.C.Several glacial periods occurred after the Pleistocene epoch.D.Some earlier epochs were warmer than the Pleistocene.7.According to paragraph 3 and 4, scientists modified their theory about the exact number of glaciations because of evidence obtained fromA.ocean sediments.B.interglacial soils.C.glacial deposits.D.air samples.8.The word “reveal” in the passage (paragraph 4) is closest in meaning toA.result from.B.vary with.C.show.D.preserve.9.According to paragraph 4, scientists use foraminifera shells to learn about Pleistocene ocean conditions byA.measuring the amount of calcium carbonate present in the shells.B.determining the proportion of shell in each layer of sediment.paring shells deposited during the Pleistocene with those buried earlier.D.calculating the relative quantity of two oxygen isotopes in the calcite.10.It can be inferred from paragraph 5 that foraminifera fossil shellscontaining calcite with high percentages of oxygen-16 were deposited at times whenA.polar ice extended as far as equatorial regions of land and sea.B.extensive glaciation was not occurring.C.there were no great increases in ocean temperature.D.there was heavy snowfall on continental glaciers.11.In paragraph 5, why does the author include the information that the “oxygen isotope r atio of the ocean changes as a great deal of water is withdrawn from it by evaporation and is precipitated as snow to form glacial ice”?A.To explain how scientists were able to calculate how frequently the continental ice sheets expanded and contracted.B.To explain how scientists have determined that there was no great change in ocean temperatures at the equator during past glaciations.C.To provide evidence that oxygen-16 has a greater tendency to evaporate than does oxygen-18 .D.To suggest that equatorial marine organisms absorb more heavy isotopes than do marine organisms elsewhere.12.According to paragraph 5, when did scientists begin to realize that more than one ice age had occurred?A.In the mid nineteenth century.B.In the late nineteenth century.C.In the early twentieth century.D.In the late twentieth century.13. Look at the four squares [■] that indicate where the following sentence could be added to the passage. Where would the sentence best fit ? In his view, there could be no other explanation for the composition of such drift.Paragraph 1: In the middle of the nineteenth century, Louis Agassiz, one of the first scientists to study glaciers, immigrated to the United States from Switzerland and became a professor at Harvard University, where he continued his studies in geology and other sciences. For his research, Agassiz visited many places in the northern parts of Europe and North America, from the mountains of Scandinavia and New England to the rolling hills of the American Midwest. ■【A】In all these diverse regions, Agassiz saw signs of glacial erosion and sedimentation. ■【B】In flat plains country, he saw moraines (accumulations of earth and loose rock that form at the edges of glaciers) that reminded him of the terminal moraines found at the end of valley glaciers in the Alps. ■【C】The heterogeneous material of the drift (sand, clay, and rocks deposited there) convinced him of its glacial origin. ■【D】14. Directions: An introductory sentence for a brief summary of the passage is provided below. Complete the summary by selecting the THREE answer choices that express the most important ideas in thepassage. Some sentences do not belong in the summary because they express ideas that are not presented in the passage or are minor ideas in the passage. This question is worth 2 points.Louis Agassiz was the first to note signs of glacial erosion and sedimentation in diverse regions of Europe and North America.A.Evidence of a pattern of glacier-like deposits eventually convinced most geologists that an enormous continental glacier had extended into the temperate zone.B.Glacial research showed that many layers of ice were deposited, with each new period of glaciation extending farther south than the one before.C.Isotopic analysis of marine sediments showed that periods of glaciation and deglaciation were more frequent, shorter, and more cyclic than previously thought.D.Nineteenth-century geologists came to accept the idea that the areas covered by polar ice had reached as far as the equator, a far larger area than Agassiz had thought.E.Nineteenth-century geologists studying the layers of drift concluded that during the Pleistocene epoch, several glaciations had occurred with warm periods between them.F.Research involving foraminifera fossil shells show that ocean temperatures in the Northern Hemisphere varied greatly during the mostextensive periods of glaciation.托福阅读答案1.回到原文“accumulations of earth and loose rock …”文中的意思是指的泥土的积累，形成叫moraines的物质，而泥土的积累其实就可以看做是沉淀，比如三角洲就是泥土的积累或者说是沉淀出来的，所以选D。

2022年考研考博-考博英语-河北农业大学考试全真模拟易错、难点剖析AB卷（带答案）一.综合题(共15题)1.单选题The theory of plate tectonics describes the motions of the lithosphere, the comparatively rigid outer layer of the Earth that includes all the crust and part of the underlying mantle. The lithosphere is divided into a few dozen plates of various sizes and shapes, in general the plates are in motion with respect to one another. A mid-ocean ridge is a boundary between plates where new lithospheric material is injected from below. AS the plates diverge from a mid-ocean ridge they slide on a more yielding layer at the base of the lithosphere.Since the size of the Earth is essentially constant, new lithosphere can be created at the mid-ocean ridges only if an equal amount of lithospheric material is consumed elsewhere. The site of this destruction is another kind of plate boundary: a subduction zone. There one plate dives under the edge of another and is reincorporated into the mantle. Both kinds of plate boundary are associated with fault systems, earthquakes and volcanism, but the kinds of geologic activity observed at the two boundaries are quite different.The idea of sea-food spreading actually preceded the theory of plate tectonics. In its original version, in the early 1960’s, it described the creation and destruction of the ocean floor, but it did not specify rigid lithospheric plates. The hypothesis was substantiated soon afterward by the discovery that periodic reversals of the Earth’s magnetic field are recorded in the oceanic crust. As magma rises under the mid-ocean ridge, ferromagnetic minerals in the magma become magnetized in the direction of the geomagnetic field. When the magma cooks and solidifies, the direction and the polarity of the field are preserved in the magnetized volcanic rock. Reversals of the field give rise to a series of magnetic stripes running parallel to the axis of the rift. The oceanic crust thus serves as a magnetic tape recording of the history of the geomagnetic field that can be dated independently the width of the stripes indicates the rate of the sea-floor spreading.1. What is the main topic of the passage?2. According to the passage, there are approximately how many lithospheric plates?3. Which of the following is true about tectonic plates?4. According to the passage, which of the following statements about the lithosphere is LEAST likely to be true?5. What does the author imply about the periodic reversal of the Earth’s magnetic field?问题1选项A.Magnetic field reversal.B.The formation of magma.C.The location of mid-ocean ridges.D.Plate tectonic theory.问题2选项A.Six.B.Twelve.C.Twenty-four or more.D.One thousand nine hundred.问题3选项A.They are moving in relationship to one other.B.They have unchanging borders.C.They are located far beneath the lithosphere.D.They have the same shape.问题4选项A.It is a relatively inflexible layer of the Earth.B.It is made up entirely of volcanic ash.C.It includes the crust and some of the mantle of the Earth.D.It is divided into plates of various shapes and sizes.问题5选项A.It is inexplicable.B.It supports the hypothesis of sea-floor spreading.C.It was discovery before the 1960’s.D.It indicates the amount of magma present.【答案】第1题:D第2题:C第3题:A第4题:B第5题:B【解析】1.主旨大意题。

一、选择题1. 下列哪个数是偶数？A. 3B. 5C. 8D. 102. 下列哪个图形是正方形？A. 正三角形B. 长方形C. 正五边形D. 梯形3. 下列哪个国家位于欧洲？A. 中国B. 美国C. 法国D. 日本4. 下列哪个季节是夏季？A. 春季B. 夏季C. 秋季D. 冬季5. 下列哪个单位是长度单位？A. 千克B. 米C. 秒D. 摄氏度二、填空题1. 2 + 3 = _______2. 5 × 4 = _______3. 7 2 = _______4. 8 ÷ 2 = _______5. 3 × 5 + 2 = _______三、判断题1. 2 × 2 = 4 （）2. 5 × 5 = 25 （）3. 8 ÷ 2 = 4 （）4. 7 3 = 4 （）5. 6 × 6 = 36 （）四、应用题1. 小明有10个苹果，他吃掉了3个，还剩下多少个苹果？2. 小红有20元，她买了5本书，每本书5元，她还剩下多少钱？3. 一辆汽车每小时行驶60千米，行驶2小时后，汽车行驶了多少千米？4. 一桶水有5升，小明喝掉了3升，还剩下多少升水？5. 小华有30个气球，他送给朋友10个，还剩下多少个气球？五、简答题1. 请简述圆的性质。

2. 请简述平行四边形的性质。

3. 请简述长方形的性质。

4. 请简述正方形的性质。

5. 请简述三角形的性质。

六、计算题1. 123 + 4562. 789 3213. 456 × 784. 321 ÷ 125. 12.5 ×6.3七、几何题1. 画一个直径为8厘米的圆。

2. 画一个边长为6厘米的正方形。

3. 画一个底边为4厘米，高为5厘米的三角形。

4. 画一个长为10厘米，宽为5厘米的长方形。

5. 画一个对角线相等的菱形。

八、代数题1. 解方程：2x + 3 = 112. 解方程：5x 2 = 183. 解方程：3x + 4 = 2x + 104. 解方程：4x 3 = 2(x + 1)5. 解方程：x^2 5x + 6 = 0九、应用题1. 一辆汽车以每小时80千米的速度行驶，行驶了4小时后，汽车行驶了多少千米？2. 一桶油重20千克，每次倒出5千克，倒出几次后，油桶里还剩多少千克？3. 一块长方形菜地，长为20米，宽为15米，这块菜地的面积是多少平方米？4. 一个班级有40名学生，其中有男生25名，女生多少名？5. 一辆火车以每小时100千米的速度行驶，行驶了5小时后，火车行驶了多少千米？十、英语题1. What is the capital of France?2. How many days are in a week?3. What is the opposite of "hot"?4. What is the plural form of "cat"?5. What is the past tense of "do"?十一、物理题1. What is the unit of force?2. What is the formula for calculating work?3. What is the speed of light in a vacuum?4. What is the law of conservation of energy?5. What is the difference between mass and weight?十二、历史题1. Who was the first president of the United States?2. What year did World War II begin?3. What was the main cause of the French Revolution?4. Who was the first woman to fly solo across the Atlantic Ocean?5. What was the significance of the Great Wall of China?十三、化学题1. What is the chemical symbol for oxygen?2. What is the formula for water?3. What is the process called when atoms gain or lose electrons?4. What is the pH scale used to measure?十四、生物题1. What is the function of the mitochondria in a cell?2. List the three domains of life.3. What is photosynthesis?4. What is the difference between a plant and an animal cell?5. What is the process of digestion?十五、地理题1. What is the largest continent on Earth?2. What is the deepest ocean on Earth?3. What is the capital city of Brazil?4. What is the significance of the Amazon Rainforest?5. What is the main cause of desertification?十六、数学题1. Solve for x: 3x 5 = 142. Simplify: (x^2 4) / (x + 2)3. Find the perimeter of a rectangle with a length of 12 units and a width of 5 units.4. Solve for y: 2y + 6 = 3y 25. Find the area of a circle with a radius of 7 units.十七、逻辑题1. If it is raining, then the ground is wet. The groundis wet. What can be concluded?2. All cats have fur. Some dogs have fur. Can we conclude that all dogs have fur?3. If a number is divisible 3, then it is also divisible 6. Is the number 18 divisible 3?4. If all birds can fly, and a penguin is a bird, then what can we conclude about penguins?5. If it is not morning, then it is either afternoon or evening. It is not morning. What time of day is it?十八、物理实验题1. Describe the steps to measure the speed of sound.2. What is the purpose of a calorimeter in an experiment?3. How would you set up an experiment to test the effect of gravity on falling objects?4. Describe the procedure for conducting an experiment to determine the density of a substance.5. What safety precautions should be taken when conducting a chemical experiment?十九、文学题1. Who wrote "To Kill a Mockingbird"?2. What is the theme of Shakespeare's "Romeo and Juliet"?3. Describe the setting of "The Great Gats" F. Scott Fitzgerald.4. What is the significance of the red rose in "Wuthering Heights" Emily Brontë?5. What is the main character's quest in "The Lord of the Rings" J.R.R. Tolkien?二十、艺术题1. What is the difference between an oil painting and an acrylic painting?2. Describe the technique of chiaroscuro in art.3. What is the role of the conductor in an orchestra?4. What are the four elements of music?5. What is the difference between a symphony and an opera?二十一、经济学题1. What is the difference between microeconomics and macroeconomics?2. Define the term "supply and demand."3. What is the role of central banks in an economy?4. Explain the concept of inflation.5. What are the three types of economic systems?二十二、心理学题1. Define the term "learning theory."2. What is the difference between cognitive and behavioral therapy?3. Explain the concept of the "fight or flight" response.4. What is the role of the prefrontal cortex in decisionmaking?5. Define the term "sensation" in psychology.二十三、社会学题1. What is the difference between social structure and social institutions?2. Define the term "social capital."3. What is the role of social norms in society?4. Explain the concept of social stratification.5. What is the difference between ethnicity and race?二十四、计算机科学题1. What is the difference between a binary tree and a binary search tree?2. Define the term "algorithm."4. Explain the concept of objectoriented programming.5. What is the difference between a stack and a queue?二十五、天文学题1. What is the difference between a planet and a star?2. Define the term "black hole."3. What is the speed of light in a vacuum?4. Explain the theory of relativity.5. What is the significance of the Hubble Space Telescope?二十六、哲学题1. Define the term "existentialism."2. What is the difference between metaphysics and epistemology?3. Explain the concept of "the self" in philosophy.4. What is the role of ethics in philosophy?5. Define the term "ontology."二十七、法律题1. What is the difference between a civil law and a criminal law?2. Define the term "due process."3. What is the role of the Supreme Court in the United States?4. Explain the concept of "precedent" in law.5. What is the difference between a tort and a contract?二十八、体育题1. What is the primary objective in basketball?2. Define the term "dribbling" in soccer.3. What is the difference between a forward pass and a lateral pass in American football?4. Explain the scoring system in tennis.答案一、选择题1. C2. B3. C4. B5. B二、填空题1. 52. 203. 54. 45. 23三、判断题1. √2. √3. √4. ×5. √四、应用题1. 7个苹果2. 5元3. 160千米4. 2升5. 20个气球五、简答题1. 圆的性质包括：所有点到圆心的距离相等，圆周角定理，圆内接四边形的对角互补等。

高一英语地球科学单选题50题1. In a science research on the Earth, the part of the Earth that is closest to the surface and consists of solid rocks is called _.A. mantleB. crustC. coreD. magma答案：B。

解析：“crust”指的是地壳，是地球最接近表面且由坚硬岩石组成的部分。

“mantle”是地幔，位于地壳之下；“core”是地核，是地球的中心部分；“magma”是岩浆，并非最接近地球表面的部分，所以正确答案是B。

2. Scientists believe that the _ is mainly composed of iron and nickel.A. crustB. mantleC. outer coreD. lithosphere答案：C。

解析：外核（outer core）主要由铁和镍组成。

地壳（crust）主要是岩石组成；地幔（mantle）成分与外核不同；岩石圈（lithosphere）包含地壳和上地幔顶部，其成分不是主要为铁和镍，所以C正确。

3. During the popular science lecture, it was mentioned that the _ is a semi - fluid layer between the crust and the core.A. magmaC. inner coreD. asthenosphere答案：B。

解析：地幔（mantle）是位于地壳和地核之间的半流体层。

岩浆（magma）是存在于地幔上部等部分的熔融物质，不完全等同于地幔；内核对 inner core）不是地壳和地核之间的层；软流圈asthenosphere）是地幔中的一部分，不如地幔这个概念全面，所以答案是B。

a r X i v :p h y s i c s /0507019v 1 [p h y s i c s .a t o m -p h ] 4 J u l 2005Lamb Shift of Muonic Deuterium and Hydrogen E.BorieForschungszentrum Karlsruhe,Institut f¨u r Hochleistungsimpuls and Mikrowellentechnik (IHM),Hermann-von-Helmholtzplatz 1,76344Eggenstein-Leopoldshafen,Germany Abstract My previous calculations of the Lamb shift in muonic hydrogen are reviewed and compared with other work.In addition,numerical results for muonic deuterium are presented.Introduction The energy levels of muonic atoms are very sensitive to effects of quantum electrodynamics (QED),nuclear structure,and recoil,since the muon is about 206times heavier than the electron [1].A number of theoretical analyses of the Lamb shift (the 2p-2s transition)in light muonic atoms have been published [2,3,4,5,6,15,7,9,16],most recently in view of a proposed measurement of the Lamb shift im muonic hydrogen [8].The present paper repeats the independent recalculation of some of the most important effects [3]and extends the numerical calculations to the case of muonic deuterium,including effects that were not considered previously [10].Muonic deuterium is in many ways similar to muonic hydrogen,but there are some differences.In addition to the different mass the deuteron has spin 1and both magnetic and quadrupole moments.In the numerical calculations the fundamental constants from CODATA 2002([11]):α−1, c ,m µ,m e ,m u =137.0359991,197.32697MeV ·fm,105.658369MeV,0.5109989MeV,931.5050MeV,respectively Also,the following properties of the proton and deuteron were used:m p =938.272MeV/c 2,R p =0.875±0.007fm (other recent values are discussed below)and µp =2.79285µN .Also,m d =1875.613MeV/c 2,R d =2.139±0.003fm and µd =0.85744µN =0.307012µp .([11])The deuteron has spin 1and thus has both magnetic and quadrupole moments.The quadrupole moment of the deuteron is taken to be Q =0.2860(15)fm 2[12,13,14].Vacuum PolarizationThe most important QED effect for muonic atoms is the virtual production and anni-hilation of a single e +e −pair It has as a consequence an effective interaction of order αZαwhich is usually called the Uehling potential ([17,18].This interaction describes the most important modification of Coulomb’s law.Numerically it is so important that it should not be treated using perturbation theory;instead the Uehling potential should be added to the nuclear electrostatic potential before solving the Dirac equation.However,a perturbative treatment is also useful in the case of very light atoms,such as hydrogen.However,unlike some other authors,we prefer to use relativistic(Dirac)wave functions to describe the muonic orbit.Since these contributions have been extensively discussed in the literature[1,2,3,4](among others),there is no need to go into detail here.The results,calculated as the expectation value of the Uehling potential using point-Coulomb Dirac wave functions with reduced mass are,for muonic deuterium:R d=2.139fm2p1/2−2s1/22p3/2−2s1/2227.6577227.66351.66622 1.66626point nucleus2p1/2−2s1/22p3/2−2s1/2 Uehling205.0199205.0250Kaellen-Sabry 1.50807 1.50811The effect offinite proton size calculated here can be parametrized as-0.0109 r2 .How-ever higher iterations can change these results.The contribution due to two and three iterations have been calculated by[4]and[23],respectively,giving a total of0.151meV. An additional higher iteration includingfinite size and vacuum polarization is given in ref.[4](equations(66)and(67))and ref.[2](equations(264)and(268)).These amount to -0.0164 r2 .The best way to calculate this would be an accurate numerical solution of the Dirac equation in the combined Coulomb-plus Uehling potential.The mixed muon-electron vacuum polarization correction([21,2])is0.00007meV for hydrogen and0.00008meV for deuterium.The Wichmann-Kroll contribution was calculated using the parametrization for the potential given in[1].The result obtained for hydrogen is-0.00103meV,consistent with that given in[2].For deuterium,the contribution is-0.00111meV.The equivalent potential for the virtual Delbr¨u ck effect was recomputed from the Fourier transform given in[22]and[1].The resulting potential was checked by reproducing previously calculated results for the2s-2p transition in muonic Helium,and the3d-2p transitions in muonic Mg and Si.The result for hydrogen is+(0.00135±0.00015)meV, and for deuterium it is+(0.00147±0.00016)meV.As in the case of muonic helium, this contribution very nearly cancels the Wichmann-Kroll contribution.The contribution corresponding to three photons to the muon and one to the proton should be analogous to the light by light contribution to the muon anomalous moment;to my knowledge, the corresponding contribution to the muon form factor has never been calculated.It will be comparable to the other light by light contributions.This graph was included in contributions to the muon’s anomalous magnetic moment;the contribution to the muon form factor is one of the most significant unknown corrections.The sixth order vacuum polarization corrections to the Lamb shift in muonic hydrogen have been calculated by Kinoshita and Nio[23].Theirresultforthe 2p-2stransition(in hydrogen)is ∆E (6)=0.120045·(αZ )2·m rα3αZm r 2 r 3 (2)+(αZ )2(F REL +m 2r F NR ) (1)where r 2 is the mean square radius of the proton.For muonic hydrogen,the coef-ficient of r 2 is 5.1975(meV fm −2),giving an energy shift (for the leading term)of (3.979±0.076)meV if the proton rms radius is 0.875fm.Other values of the proton radius that have been reported recently in the literature are 0.880fm [25]and (0.895±0.018fm)[26].The second term in Eq.(1)contributes -0.0232meV for a dipole form factor and -0.0212meV for a Gaussian form factor.The parameters were fitted to the proton rms radius.This can be written as -0.0347 r 2 3/2or -0.0317 r 2 3/2.This differs slightly from the value given by Pachucki [5].The model dependence introduces an uncertainty about ±0.002meV.The remaining terms contribute 0.00046meV.This estimate includes all of the terms given in [24],while other authors [5]give only some of them.Clearly theneglected terms are not negligible.There is also a contribution of-3·10−6meV to the binding energy of the2p1/2-level,and a recoil correction of0.013meV to the binding energy of the2s-level.Pachucki[5]has estimated a correction similar to the second term(proportional to r3 (2))in Eq.(1).Since the logarithmic terms in the two-photon correction withoutfinite size(see below)also seem to be suspect,this correction requires further investigation. In particular,the parametrization of the form factors used in any calculation should reproduce the correct proton radius.For muonic deuterium,the main contribution amounts to-6.0732 r2 =-(27.787±0.078)meV.Depending on the model,the term proportional to r3 (2)gives a contribution of0.382meV or0.417meV.As mentioned previously,thefinite-size contributions to vacuum polarization in muonic hydrogen can be parametrized as−0.0109 r2 −0.0164 r2 ,giving a total of−0.0273 r2 or-0.0209(6)meV if the proton radius is0.875fm.For deuterium.only the contribution corresponding to thefirst term of the sum(−0.0129 r2 )has been calculated.The contribution due to nuclear polarization(in hydrogen)has been calculated by Rosenfelder[29]to be0.017±0.004meV,and by Pachuki[5]to be0.012±0.002meV. Other calculations[30,31]give intermediate values(0.013meV and0.016meV,respec-tively).The value appearing in table2is an average of the three most recent values,with the largest quoted uncertainty,which is probably underestimated.Relativistic RecoilAs is well-known,the center-of-mass motion can be separated exactly from the relative motion only in the nonrelativistic limit.Relativistic corrections have been studied by many authors,and will not be reviewed here.The relativistic recoil corrections summa-rized in[1]include the effect offinite nuclear size to leading order in mµ/m N properly.Up to now this method has been used to treat recoil corrections to vacuum polarization only in the context of extensive numerical calculations that include the Uehling potential in the complete potential,as described in[1].They can be included explicitly,as a perturbation correction to point-Coulomb values.Recall that(to leading order in1/m N), the energy levels are given byE=E r−B202mNh(r)+2B0P1(r) (2)where E r is the energy level calculated using the reduced mass and B0is the unperturbed binding energy.Alsoh(r)=−P1(r)(P1(r)+13rQ2(r)[P1(r)+Q4(r)/r3](3)HereP1(r)=4παZ ∞r r′ρ(r′)dr′=−V(r)−rV′(r)(4)Q2(r)=4παZ r0r′2ρ(r′)dr′=r2V′(r)Q4(r)=4παZ r0r′4ρ(r′)dr′An effective charge densityρV P for vacuum polarization can be derived from the Fourier transform of the Uehling potential.Recall that(for a point nucleus)V Uehl(r)=−αZ3π·χ1(2m e r)=−(αZ)2αz2·1+1π ∞0q2·j0(qr)3π·∞1dz(z2−1)1/22z2 2q2+4m2e z2dq =23π(2m e)χ0(2m e r)Q2(r)=αZ 1+2α3π ∞1dz(z2−1)1/22z2· 2q2+4m2e z2(6qr−(qr)3)cos(qr)+(3(qr)2−6)sin(qr)(deuterium).To obtain the full relativistic and recoil corrections,one must add thedifference between the expectation values of the Uehling potential calculated with rel-ativistic and nonrelativistic wave functions,giving a total correction of0.0166meV formuonic hydrogen.This is in quite good agreement with the correction of.0169meVcalculated by Veitia and Pachucki[33].The treatment presented here has the advantage of avoiding second order perturbation theory.For deuterium,one obtains a total correctionof0.0179meV.The review by Eides et al.[2]gives a better version of the two photon recoil(Eq.136)than was available for the review by Borie and G.Rinker[1].Evaluating this expressionfor muonic hydrogen gives a contribution of-0.04497meV to the2p-2s transition in hydrogen and-0.02656meV in deuterium.Higher order radiative recoil corrections givean additional contribution(in hydrogen)of-0.0096meV[2].However,some of thecontributions to the expressions given in[2]involve logarithms of the mass ratio mµ/m N. Logarithms can only arise in integrations in the region from mµto m N;in this regionthe effect of the nuclear form factor should not be neglected.Pachucki[4]has estimated afinite size correction to this of about0.02meV,which seems to be similar to the termproportional to r3 (2)given in Eq.(1)as calculated in the externalfield approximation by Friar[24].This two-photon correction requires further investigation.In particular, the parametrization of the form factors used in any calculation should reproduce thecorrect proton radius.Also the relationship among the different contributions needs to be specified more clearly.An additional recoil correction for states withℓ=0has been given by[34](see also[2]).It is∆E n,ℓ,j=(αZ)4·m3rκ(2ℓ+1) (6)When evaluated for the2p-states of muonic hydrogen,onefinds a contribution to the 2p-2s transition energy of0.0575meV for the2p1/2state and-0.0287meV for the2p3/2 state in hydrogen(0.0168meV for the2p1/2state and-0.0084meV for the2p3/2state in deuterium)Afinal point about recoil corrections is that in the case of light muonic atoms,the mass ratio mµ/m N is considerably larger than the usual perturbation expansion parameterαZ. Contributions of higher order in the mass ratio could be significant.Muon Lamb ShiftFor the calculation of muon self-energy and vacuum polarization,the lowest order(one-loop approximation)contribution is well-known,at least in perturbation theory.Including also muon vacuum polarization(0.0168meV)and an extra term of order(Zα)5as given in[2]:which contributes-0.00443meV,onefinds a contribution of-0.66788meV for the 2s1/2−2p1/2transition and-0.65031meV for the2s1/2−2p3/2transition.For deuterium, the corresponding contributions are given by-0.77462meV for the2s1/2−2p1/2transi-tion and-0.75512meV for the2s1/2−2p3/2transition.The second order calculation indeuterium includes muonic vacuum polarization(0.01968meV);the extra term of order (Zα)5as given in[2],contributes-0.00518meV.These results,and the higher order corrections[1,21]can be summarized asTransition2p1/2−2s1/22p3/2−2s1/2m2µ· ∇2V m2µF′1(0)+aµ2m2µ 2dr L· σµwhere F2(0)=aµ;the higher order contributions(fourth and sixth)can be taken from the well-known theory of the muon’s anomalous magnetic moment:F2(0)=aµ=α/2π+0.7658(α/π)2+24.05(α/π)3.The fourth order contribution to F′1(0)is0.46994(α/π)2+2.21656(α/π)2=2.68650(α/π)2[1].The sixth order contributions to F′1(0)that involve electron vacuum polarization loops(especially the light-by-light graph) might contribute at an experimentally significant level,but have not been calculated.Summary of contributions for muonic hydrogenUsing the fundamental constants from the CODATA2002([11])onefinds the transition energies in meV in table2.Here the main vacuum polarization contributions are given for a point nucleus,using the Dirac equation with reduced mass.Some uncertainties have been increased from the values given by the authors,as discussed in the text.Thefinite size corrections for hydrogen up to order(αZ)5can be parametrized as 5.1975 r2 +0.0109 r2 +0.0164 r2 +0.0347 r3 (2).The various contributions are dis-cussed in the text.Contribution Value(meV)Uncertainty(meV)recoil[2](eq136)-0.04497recoil,higher order[2]-0.0096recoil,finite size[24]0.0130.001recoil correction to VP[1]-0.0042additional recoil[34]0.0575nuclear size(R p=0.875fm)0.007fmmain correction[24]-3.9790.076order(αZ)5[24]0.02320.002order(αZ)6[24]-0.0005correction to VP-0.0083polarization0.0150.004parametrized as6.0732 r2 +0.0129 r2 +0.0409 r3 (2),although not all contributions to the effect of finite size on the vacuum polarization correction are included.Contribution Value(meV)Uncertainty(meV)recoil[2](eq136)-0.02656recoil,higher order[2]?recoil,finite size[24]0.0190.003recoil correction to VP[1]-0.0048additional recoil[34]0.0168nuclear size(R d=2.139fm)0.003fmmain correction[24]-27.7870.078order(αZ)5[24]0.04000.018order(αZ)6[24]-0.0045correction to VP-0.0592polarization?Hydrogen Deuterium Dirac8.415648.86430Uehling(VP)0.00500.00575K¨a llen-Sabry 0.000040.00005Recoil (Eq.(6))-0.0862-0.02522m µ1dr1+a µm µ L · s 1(7)This can be rearranged to give the well-known form for spin 1/2particles with an anomalous magnetic moment,namely−1dr ·1+a µ+(a µ+1/2)m N /m µm N m µ+12m 2r −12m 21dr 1+κ2/Z m 2 L · s 2Usually one writes Z +κ2m p where µ2is the magnetic moment of the nucleus in units of nuclear magnetons (µN =e/2m p ).A value of µd =0.85744µN =0.307012µp corresponds to κd =0.714.V s 1,s 2=2(1+a µ)µ2r dV 3∇2V s 1· s 2V Q=−αQ 1dr 3 s2·ˆr s2·ˆr− s2· s2with Q in units of1/m22.Thequadrupolemomentof thedeuteronis taken to beQ=0.2860(15)fm2[12,13,14].In other units,onefinds Q=25.84/m2d=7.345×10−6MeV−2.Note that V L,s1describes thefine structure,while the hyperfine structure is described(in perturbation theory)by the expectation values of V L,s2,V s1,s2,and V Q(where appli-cable).The Uehling potential has to be included in the potential V(r).For states withℓ>0 in light atoms,and neglecting the effect offinite nuclear size,we may take1dr =αZ3π ∞1(z2−1)1/22z2·(1+2m e rz)·e−2m e rz dz (8)which is obtained from the Uehling potential[17,18]by differentiation.Then,assuming that it is sufficient to use nonrelativistic point Coulomb wave functions for the2p state, onefinds 1r3 2p·(1+ε2p)whereε2p=2αz2·1+1(1+az)2+2az4mµm N 1dr 2p·(1+κ) 2(1+x p)δjj′(F(F+1)−11/4)+6ˆjˆj′(C F1(1+aµ)−2(1+x)) ℓF112j ℓF112j′ (10) whereˆj=√2m p(1+κp)=0.09245represents a recoil correction due to Thomas precession[7,34,35].The correction due to vacuum polarization(Eq.(9))should be applied to the HFS shifts of the2p-states.As has been known for a long time[7,16,4,35],the states with total angular momentum F=1are a superposition of the states with j=1/2and j=3/2.Let thefine structure splitting be denoted byδ=E2p3/2−E2p1/2=8.352meV,and letβp=(αZ)4m3r1/21/2(β′/8)(2+x p+aµ)[−δF,0+1/3δF,1]3/23/2δ+(β′/4)(4+5x d−aµ)[−1/12δF,1+1/20δF,2]3/21/2(β′/24)(1+2x p−aµ)[√Then for the2p-level with j=j′=1/2and F=0,the energy shift is given by −(β′/8)(2+x p+aµ)=-5.971meV,and for the2p-level with j=j′=3/2and F=2, the energy shift is given byδ+(β′/80)(4+5x p−aµ)=9.6243meV.For the2p-levels with F=1the corresponding matrix has to be diagonalized.The resulting numerical values for the eigenvalues are(∆±R)/2=1.846meV and6.376meV, where∆=δ−β′(x p−aµ)/16R2=[δ−β′(1+7x p/8+aµ/8)/6]2+(β′)2(1+2x p−aµ)2/288Hyperfine structure of the2p-state in muonic deuteriumFor the2p state,the matrix elements of the magnetic hyperfine structure have been given by Brodsky and Parsons[35].For hydrogen they are the same as those calculated above. Here the Uehling potential will be included in the expectation value of1dras discussed above.LetβD=16(1+κd)(αZm r/n)3ℓ(ℓ+1)(2ℓ+1)=(1+κd)1/21/2(βD/6)(2+x d+aµ)[−δF,1/2+1/2δF,3/2]3/23/2δ+(βD/4)(4+5x d−aµ)[−1/6δF,1/2−1/15δF,3/2+1/10δF,5/2] 3/21/2(βD/48)(1+2x d−aµ)[√5δF,3/2]where x d=(m2µ/m d m r)(κd/(1+κd))=0.0248.For the evaluation of the contributions of the quadrupole HFS,letǫQ=αQ 1drFor a point Coulomb potential,and the2p-state,ǫQ=αQ(Zαm r)3/24=0.43243meV. The quadrupole interaction results in energy shifts ofj j′Energy2δF,1/2−1/√As mentioned before,the Uehling potential has to be included in the potential V(r). For states withℓ>0in light atoms,this can be taken into account by multiplyingβD andǫQ by(1+ε2p)whereε2p is given by Eq.(9).With a numerical value ofε2p=0.000391 for muonic deuterium,the value ofǫQ is increased to0.43440meV and the value ofβD is increased toβ′D=4.0922meV.Then for the2p-level with j=j′=3/2and F=5/2,the energy shift is given by δ+ǫQ/5+(β′D/40)(4+5x d−aµ)=9.373meV.For the2p-levels with F=1/2and F=3/2,the corresponding matrices have to be diagonalized.The resulting numerical values for the eigenvalues are,for F=1/2,-1.3834meV and8.5974meV;for F=3/2they are0.6856meV and 8.2410meV.Hyperfine structure of the2s-state:in an ns state with j=1/2isThe expectation value of V s1s22µ2α(αZ)3m3r∆E ns==3n3mµm2·(1+κ2)·(1+aµ)=(8/n3)βp·(1+aµ)=(8/n3)×22.8332meV (see,for example[2],Eq.(271,277)).The numerical value was calculated for hydrogen. For deuterium,with s2=1,the corresponding hyperfine splitting is2(αZ)4m3r∆E ns=As was shown in[7,2],the energy shift of the2s-state in muonic hydrogen is given by:∆E2s=β·(1+aµ)·(1+εV P+εvertex+εBreit+εF S,rec)·[δF1−3δF0]/4(11) The corrections due to QED effects,nuclear size and recoil are analogous for muonic deuterium.The QED corrections have been discussed by Borie[3,7,16](see also[38]),and are given in Appendix2.The correction due tofinite size and recoil have been given in[4]as-0.145meV,while a value of-0.152meV is given in[42].Ref.[4]also gives a correction as calculated by Zemach([40])equal to-0.183meV,but claims that this correction does not treat recoil properly.The Zemach correction is equal toεZem=−2αZm r r (2)where r (2)is given in[7,24,41].Using the value r (2)=1.086±0.012fm from[41], givesεZem=−0.00702,and a contribution of of-0.1742meV to the hyperfine splitting of the2s state.Including this,but not other recoil corrections to the hyperfine structure of the2s-state gives a total splitting of22.7806meV.Additional higher order corrections calculated in Ref.[42]amount to a total of-0.0003meV and are not included here.It would be very desirable to understand the reasons for the discrepancy between references[4]and[42]in the calculations of this effect.Also,since the Zemach radius seems to be sensitive to details of the electric and magnetic charge distributions[41], evaluations performed with a dipole-type form factor may not be good enough.This point requires further invesigation.For muonic deuterium,the coefficient of r (2)is-0.007398fm−1,giving,withr (2)=2.593±0.016fm from[41],εZem=−0.01918±0.00012.The total hyperfine splitting of the2s-state of muonic deuterium,including all correc-tions,is3∆E2s=Transition Energy shift in meV2p1/2−2s1/2 2.6552p3/2−2s1/212.6364p1/2−2s1/2 4.7244p3/2−2s1/212.2802p1/2−4s1/2-3.4032p3/2−4s1/2 6.5784p1/2−4s1/2-1.3346p3/2−4s1/2 6.2226p3/2−4s1/27.354Table6:Fine-and hyperfine contributions to the Lamb shift in muonic deuterium.Tables5and6give the contributions to the transition energies due tofine and hyperfine structure.Summary of contributions and ConclusionsThe most important contributions to the Lamb shift in muonic hydrogen,including hyperfine structure,have been independently recalculated.A new calculation of some terms that were omitted in the most recent literature,such as the virtual Delbr¨u ck effect [22]and an alternative calculation of the relativistic recoil correction have been presented.Numerically the results given in table2add up to a total correction of (206.032(6)-5.225 r2 +0.0347 r2 3/2)meV=202.055±0.12meV.(for the value of the proton radius from[11]).As is well known,most of the uncertainty arises from the uncertainty in the proton radius.Numerical results were also given for muonic deuterium.The total correction is (228.573(6)-6.086 r2 +0.0409 r2 3/2)meV=200.767±0.09meV.The complete depen-dence on the deuteron radius is uncertain since contributions from iteration of the 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)+Q 4(r )/r 3]where P 1,Q 2,and Q 4are defined in Eq.(4).Keeping only the Coulomb and Uehling potentials,one findsP 1(r )=−αZ 2α3π[χ1(2m e r )+(2m e r )χ0(2m e r )] Q 4(r )=αZ 2αz 21+1π ∞01q dqwhere χn (x )is defined in [1].Since vacuum polarization is assumed to be a relatively small correction to the Coulomb potential,it will be sufficient to approximate Q 2(r )by αZ/r .After some algebra,one can reduce the expectation values to single integrals:P 1(r ) =2m e αZ 2αz· 1+1(1+az )5δℓ0+1r P 1(r ) =−(αZ )3m r m e 2αz· 1+12(1+az )4δℓ0+1Finally,αZ 62αz 2· 1+1az 2+azaz ln(1+az ) +3(az )2+2az −14(1+az )4 δℓ0+1−3az −2(az )23n 3m µm 2s 2·(1+a µ)[F (F +1)−s 2(s 2+1)−3/4]As was shown in[7,2],theenergy shift of the 2s-state has to be multiplied by:1+εV P +εvertex +εBreit +εF S,recHere ([38])εvertex =2α(αZ )4 =−1.36·10−4and ([2],Eq.(277))εBreit =17(αZ )23π2 ∞0r 2drR ns (r )z 2· 1+14m 2e [z 2+(q/2m e )2](12)One can do two of the integrals analytically and obtains for the2s-state(with a=2m e/(αZm r) and sinh(φ)=q/(2m e)=K/a)εV P1=4α(1+K2)2F(φ)G M(αZm r K)dK 2−7(1+K2)2 (13)where F(φ)is known from the Fourier transform of the Uehling potential(given as U2(q)in Ref.[1])and is given byF(φ)=1αU2(q)with sinh(φ)=q/2m e.The other contribution,as discussed by[38,39]arises from the fact that the lower energy hyperfine state,being more tightly bound,has a higher probability of being in a region where vacuum polarization is large.This results in an additional energy shift of2 V Uehl(r)ψ2s(r)δMψ2s(r)d3rFollowing Ref.[38]with y=(αZm r/2)·r,one hasδMψ2s(r)=2mµ∆νFψ2s(0) 24−13π2 ∞0dK2−17(1+K2)3−241+K2 2−7(1+K2)2+tan−1(K)2(1+K2)+20(1+K2)3 (14)Sternheim[39]denotes the two contributions byδM andδE,respectively.An alternative exres-sion,obtained by assuming a point nucleus,using Eq.(131)from[1]for the Uehling potential, and doing the integrations in a different order,isεV P2=16αz2·1+1(1+az)2· az1+az+232(1+az)3+ln(1+az)· 1−22(1+az)2 dz(15)with a=2m e/(αZm red).Both methods give the same result.In the case of ordinary hydrogen,each of these contributes3α2/8=1.997·10−5.The accuracy of the numerical integration was checked by reproducing these results.One can thus expect that muonic vacuum polarization will contribute3α2/4≃4·10−5,as in the case of normal hydrogen. This amounts to an energy shift of0.0009meV in muonic hydrogen and0.0002meV in muonic deuterium.Contributions due to the weak interaction or hadronic vacuum polarization should be even smaller.For muonic hydrogen,one obtainsεV P1=0.00211andεV P2=0.00325for a point nucleus.Including the effect of the proton size(with G E(q)=G M(q)as a dipole form factor)reduces these numbers to0.00206and0.00321,respectively.For the case of muonic deu-terium,the corresponding numbers areεV P1=0.00218(0.00207)andεV P2=0.00337(0.00326), respectively.The contribution to the hyperfine splitting of the2s-state of hydrogen is then 0.0470meV+0.0733meV=0.1203meV(0.1212meV if muonic vacuum polarization is included). The combined Breit and vertex corrections reduce this value to0.1207meV.(0.1226meV if the proton form factors are not taken into account).The contribution to the hyperfine structure from the two loop diagrams[19]can be calculated by replacing U2(αZm r K)=(α/3π)F(φ)by U4(αZm r K)(as given in[1,6])in equations13and 14.The resulting contributions are1.64·10−5and2.46·10−5(for deuterium1.69·10−5and 2.54·10−5),respectively,giving a total shift of0.0009meV in muonic hydrogen and0.0002meV in muonic deuterium.21。