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銫元素 | 金屬銫具有高度的活性，並且非常容易自燃。除了在空氣中能夠自發燃燒以外，銫在很低溫度下就能夠與水發生爆炸性地反應，比鹼金屬中的其他元素更劇烈。銫可以在溫度低達 - 116℃的條件下與冰發生反應。由於其高度活性，該金屬被分類為危險性物質。銫通常在諸如礦物油等的乾燥的飽和烴中儲存和運輸。類似的，必須在惰性氣體的保護下處理銫，例如氬。然而，銫 - 水的爆炸威力通常比同樣量的鈉 - 水的威力小，這是由於銫在接觸到水的時候立即爆炸，使得聚集起氫氣的時間很少。銫可以儲存於真空密封的矽硼酸鹽玻璃製造的安瓿中。若銫的量超過 100 克，需要將銫放置在密封的不鏽鋼容器中運輸。
銫的化學性質與其他鹼金屬類似，但是更接近於元素週期表中其上面的元素銣的化學性質。由於銫是一種鹼金屬，可以預期其通常的化合價為 + 1。由於銫具有較高的原子量，並且比其他非放射性鹼金屬電正性更強，有一些較小的區別。銫是電正性最強的穩定化學元素。銫離子也比較大，並且與其他更輕的鹼金屬相比較軟。
### 化合物
銫化合物多數都含有 Cs+
離子，它能與很多種離子形成離子鍵。一個值得注意的例外是銫化物中含有 Cs−
。 其他例外還包括一些低氧化物（參見下面的氧化物章節）。
回到普通的銫化合物，Cs+ 的鹽通常是無色的，除非陰離子有顏色。 許多簡單的鹽具有潮解性，但比更輕的其他鹼金屬弱。銫的乙酸鹽、碳酸鹽、鹵化物、氧化物、硝酸鹽和硫酸鹽可溶於水。 複鹽通常溶解度較小，硫酸鋁銫溶解度較小的性質常用來從礦石中提純銫。與銻（例如 CsSbCl
4）、鉍、鎘、銅、鐵和鉛形成的復鹽通常溶解度很小。
氫氧化銫（CsOH）是一種具有強烈吸水性的強鹼。它能迅速腐蝕半導體材料（例如矽）的表面。 過去化學家曾認為 CsOH 是「最強的鹼」，因為大陽離子 Cs+ 與 OH-的相互作用很微弱。氫氧化銫確實是鹼性最強的阿倫尼烏斯鹼，但是許多無法存在於水溶液中的化合物的鹼性遠比 CsOH 強，例如正丁基鋰和氨基鈉。
銫與金的化學計量 1:1 的混合物加熱後可以反應形成黃色的金化銫。這裡的金陰離子表現為擬鹵素。該化合物能夠與水發生劇烈反應，生成氫氧化銫、金屬金以及氫氣。在液氨中，金化銫可以與銫特定的離子交換樹脂反應以產生四甲基金。類似的鉑化物，紅色的鉑化銫 Cs
2Pt 包含表現得像擬硫族的鉑陰離子。
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銫元素 | 與所有的金屬陽離子類似，Cs+ 與路易斯鹼在溶液中形成複合物。由於該粒子較大，Cs+ 通常的配位數大於 6，而較輕的鹼金屬陽離子的典型配位數為 6。這個趨勢在 CsCl 中很明顯，其配位數為 8。銫離子較高的配位數以及軟度（形成共價鍵的趨勢）是將其與其它陽離子分離的基礎，在實踐中用於對核廢料的整治，也就是將 137Cs+ 與大量的非放射性的 K+ 分離。
#### 鹵化物
氟化銫（CsF）是一種易潮解的白色固體，經常用於有機氟化學中作為氟陰離子的來源。氟化銫具有石鹽結構，也就是 Cs+ 和 F−以和氯化鈉中的 Na+ 和 Cl−相同的方式堆積成立方緊密堆積陣列。值得注意，銫和氟在所有已知的元素中分別具有最高和最低的電負性。
氯化銫以簡單立方晶系結晶。該結構包含以雙原子為基礎的立方晶格原胞，每個配位數都是 8，也被稱為氯化銫結構。氯原子位於立方的頂點上，而銫原子位於立方中央。該結構與溴化銫、碘化銫以及許多其它不包含銫離子的化合物相同。相反，大多數其它的鹼金屬鹵化物採用氯化鈉結構。採用氯化銫結構的原因是 Cs+ 的離子半徑為 174 pm，而 Cl−
的半徑為 181 pm。
#### 氧化物
銫可以和氧形成比其它鹼金屬更多的二元化合物。當銫在空氣中燃燒時，主要產生超氧化銫 CsO
2。氧化銫（Cs
2O）形成橙黃色的六方晶體，並且為僅有的反氯化鎘結構氧化物。它在 250℃時揮發，並且在溫度超過 400℃時分解為金屬銫和過氧化銫。除了超氧化物和臭氧化銫 CsO
3，，一些具有明亮的顏色的低氧化物也曾經被研究過，包括 Cs
7O、Cs
4O、Cs
11O
3、Cs
3O（暗綠色）、CsO、 Cs
3O
2 以及 Cs
7O
2。後者可以通過在真空中加熱以產生 Cs
2O。還存在與硫、硒以及銻的二元化合物。
### 同位素
銫一共有 39 種已知的同位素，其質量數（原子核中的核子數）在 112 至 151 之間。其中一些同位素在年老的恆星中由較輕的元素通過捕獲慢中子（S - 過程）合成，也可以在超新星爆發的過程 R - 過程中合成。然而，銫僅有唯一的穩定同位素，也就是具有 78 個中子的銫 - 133（133Cs）。儘管其原子核自旋量子數較大（7/2+），可以在其共振頻率 11.7 MHz 處對該同位素進行核磁共振的研究。 | [
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銫元素 | 銫 - 137 以 94.6% 的概率通過 β 衰變發射出 512keV 的電子衰變為鋇 - 137m（I=11/2-，t=2.55 分），隨後以 85.1% 的概率通過 662keV 的伽瑪衰變轉變為鋇 - 137。此外，銫 - 137 可以以 0.4% 的概率通過 beta 衰變直接轉變為鋇 - 137。
放射性同位素 135Cs 具有非常長的半衰期，大約 230 萬年，而 137Cs 和 134Cs 的半衰期分別為 30 年和 2 年。137Cs 通過 β 衰變轉變為分解為壽命很短的 137mBa，隨後轉變為非放射性的鋇，而 134Cs 直接轉變為 134Ba。具有質量數為 129、131、132 以及 136 的同位素的半衰期在一天和兩周之間，而大多數其它的同位素的半衰期僅數秒或者少於一秒。至少有 21 種亞穩核同質異能素，除了 134mCs（半衰期少於 3 小時），都很不穩定，並且半衰期僅數分鐘甚至更短。
同位素 135Cs 是鈾的長壽命裂變產物之一，可以在核反應爐中產生。然而，其裂變產物產量在大多數反應爐中都會比較少，這是由於其前體，135Xe 是極強的中子毒物，經常在衰變為 135Cs 之前嬗變為穩定的 136Xe。
由於銫 137 能夠 β 衰變為 137mBa，它是一種很強的伽瑪射線發射體。其半衰期使得它和 90Sr 一同成為中等壽命裂變產物。由於這兩種同位素，乏核燃料在經過數年的冷卻後仍在數百年內具有放射性。例如，137Cs 和 90Sr 一起成為了車諾比核事故之後其周圍區域內最大的放射源 。由於其較低的中子捕獲率，無法通過中子捕獲處理銫 - 137，所以必須讓它進行衰變。
幾乎所有的核分裂產生的銫都由開始富含中子的裂變產物的 β 衰變產生，例如各種碘的同位素以及氙的同位素 。由於碘和氙容易揮發，並且可以通過核燃料或者空氣擴散，輻射性的銫經常在遠離裂變地點的地方產生。自從 1945 年開始進行核試驗，銫 - 137 被釋放入大氣層並作為放射性塵埃落回地球表面。
### 存象
銫是一種相對比較稀有的元素，估計在地殼中的化學元素豐度約為 3ppm（百萬分之三）。銫在所有元素中豐度排第 45 名，而在所有金屬中豐度排第 36 名。儘管如此，銫的豐度要高於銻、鎘、錫以及鎢，並且比銀和汞的豐度高了兩個數量級，然而其豐度僅為銣的 3.3% | [
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銫元素 | 由於其離子半徑很大，銫是「不相容成分」之一。在分級結晶的過程中，銫在液相中濃縮，並且最後結晶。因此，銫的大礦床為在富集過程中形成的偉晶岩礦石。由於銫不像銣那樣可以將鉀置換出來，鹼蒸發鹽礦物天然氯化鉀（KCl）和光鹵石（KMgCl
3·6H
2O）中僅含 0.002% 的銫。所以銫僅能在若干種礦物質中找到。銫含量較豐富的礦物質包括綠柱石（Be
3Al
2(SiO
3)
6）和氟硼鉀石（(K,Cs)BF
4）。在密切相關的礦物質草莓紅綠柱石（Cs (Be2Li)Al2Si6O18）中 Cs
2O 的質量百分比可達 15%，而在稀有礦物硼銫鋁鈹石（(Cs,K)Al
4Be
4(B,Be)
12O
28）中可達 8.4%，在分布更廣的硼鋰鈹礦中含量較少。銫榴石 Cs(AlSi
2O
6) 是唯一的有經濟意義的銫礦石，在世界上某些地方的偉晶岩礦石中可以找到，並且它和有更重要的商業應用的鋰礦石
鋰雲母和透鋰長石共生。在偉晶岩礦石中，晶粒比較大並且容易與礦石其它部分分離，是採礦的高品質礦石。
世界上最重要的也是儲量最豐富的銫產地是位於加拿大馬尼托巴的伯尼克湖的堂科礦。估計其礦床中有 35 萬噸銫榴石礦石，占世界儲量的 2/3 儘管銫榴石中的銫的化學計量含量為 42.6%，來自該礦床的純淨銫榴石樣品中銫的含量僅約 34%，平均含量 24%。商業用銫榴石包含 19% 的銫。辛巴威的比基塔偉晶岩礦床生產透鋰長石，但是也有大量的銫榴石。納米比亞的卡里比布沙漠中也在開採大量的銫榴石。目前世界的年開採量為 5-10 噸，目前的儲量可供開採數千年。
## 生產
開採銫榴石是一種選別工藝，和其他大多數金屬採礦相比僅以小規模進行生產。首先將礦石擊碎，並且進行手工篩選，但是經常不做富集，然後將礦石粉碎。隨後主要通過三種方式將銫從銫榴石中提取出來：酸消解、鹼分解、以及直接還原。
在酸消解中，矽酸鹽銫榴石的岩石溶解在諸如鹽酸（HCl）、硫酸（H
2SO
4）、氫溴酸（HBr）或者氫氟酸（HF）中。採用鹽酸可以產生可溶解氯化物的混合物，而無法溶解的銫的氯化物復鹽以氯化銫銻（Cs
4SbCl
7）、氯碘化銫（Cs2ICl）或者氯化銫鈰（Cs
2(CeCl
6)）的形式沉澱出來。分離之後，將提純的沉澱復鹽分解，在水分蒸發後得到純的氯化銫。採用硫酸的消解的方法將得到無法溶解的復鹽銫礬（CsAl(SO
4)
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銫元素 | 2O）。銫礬與碳一起烘烤後將轉化為不溶於水的氧化鋁，得到的產物通過瀝濾得到硫酸銫（Cs
2SO
4）溶液。
將銫榴石與碳酸鈣和氯化鈣一同烘烤可以得到不易溶解的矽酸鹽和可溶解的氯化銫。通過用水瀝濾或者用氨水稀釋，可以得到稀釋的氯化銫溶液。該溶液可以通過蒸發以得到氯化銫或者轉變為銫礬或者碳酸銫。還可以在真空罐中使用鉀、鈉或者鈣對礦石直接還原以直接獲得金屬銫，但是該方法在經濟上不可行。
大多數以鹽的形式開採的銫直接轉化為用於諸如油井等應用的甲酸銫（HCOO−Cs+）。為了向發展中的市場供貨，卡博特公司在 1997 年在位於加拿大馬尼托巴的伯尼克湖附近的堂科礦建立了生產廠，年產甲酸銫溶液 1900m3。銫的主要小規模商用化合物為氯化銫以及硝酸銫。
此外，金屬銫可以通過從礦石中得到的提純化合物獲得。氯化銫以及其它鹵化銫可以在 700℃至 800℃的高溫下與鈣或者鋇一同加熱以將銫還原，然後通過蒸餾得到金屬銫。採用相同的方法，碳酸銫以及氫氧化銫等等可以通過使用鎂來還原。銫還可以通過電解熔融的氰化銫來得到。極純淨並且無氣體的銫可以通過以 390℃加熱疊氮化銫使其分解來得到，而疊氮化銫可以通過硫酸銫溶液和疊氮化鋇反映得到。在真空中，重鉻酸銫可以和鋯反應得到純淨的銫，而不產生其它氣體產物：
: Cs
2Cr
2O
7 + 2 Zr → 2 Cs + 2 ZrO
2+ Cr
2O
3。
2009 年純度為 99.8% 的銫（金屬含量）大約為每克 10 美元，但是其化合物便宜很多。
## 歷史
1860 年，羅伯特・威廉・本生和古斯塔夫・基爾霍夫在來自德國巴德迪爾克海姆的礦泉水中發現了銫。由於該元素在其發射光譜中明亮的藍色線，他們選擇了拉丁文中意為天藍色的單詞 _caesius_ 為其命名 。銫是第一種採用光譜學的方法發現的元素，與本生和基爾霍夫發明光譜儀相隔僅僅一年。 | [
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銫元素 | 為了獲得純淨的銫樣品，需要蒸發 44000 升水以得到 240 千克濃縮的鹽溶液。鹼土金屬或者以硫酸鹽的形式或者草酸鹽的形式沉澱，而溶液中僅僅剩下鹼金屬。在轉化為硝酸鹽並採用乙醇提取後，可以獲得不含鈉的混合物。該混合物中的鋰可以用碳酸銨沉澱出來。鉀、銣和銫可以與氯鉑酸形成不溶鹽，然而這些鹽在熱水中的溶解度有差別。這樣更不易溶於水的的銣和銫的六氯鉑酸鹽可以通過分級結晶的辦法獲得。在使用氫氣還原六氯鉑酸鹽之後，可以利用銣和銫的碳酸鹽在酒精中的溶解度差異分離開。該工藝可以從最初的 44000 升水中生產出 9.2 克氯化銣和 7.3 克氯化銫。
本生和基爾霍夫使用所獲得的氯化銫估計這種新元素的原子量為 123.35（目前接受的值為 132.9）。他們試圖使用電解熔融氯化銫的方法來生成銫單質，但是沒有獲得金屬物質，只獲得了一種藍色的各項同性的物質，"不論用肉眼還是在顯微鏡下" 都無法觀察到最細微的金屬物質的特徵。因此，他們認為它是低氯化物 Cs
2Cl。實際上他們獲得的可能是金屬銫和氯化銫的膠體混合物。使用水銀電極電解氯化銫的水溶液可以得到銫汞齊，在有水的條件下可以分解。純淨的銫單質最終由德國化學家卡爾・賽特貝格在跟隨凱庫勒和本生讀取博士學位的時候獲得。1882 年，他通過電解氰化銫獲得了金屬銫，而沒有出現氯化銫的問題。
歷史上，銫的的最重要的用途是用於研究和開發，主要是用在化學和電子領域。20 世紀 20 年代用於無線電真空管之前，銫幾乎沒有任何應用。銫在真空管中起兩個作用，吸收製造完畢後剩餘的氧氣的吸氣劑以及可以起到增加加熱的陰極的導電性作用的塗層。一直到 20 世紀 50 年代，銫才開始被認為是高性能的工業金屬。無放射性的銫開始被用於光電池、光電倍增管、紅外光譜儀、多種有機反應的催化劑，閃爍計數器以及磁流體發電。
自從 1967 年，國際單位制基於銫的性質定義了其時間單位，也就是秒。國際單位制將一秒定義為不受外場干擾的銫 - 133 的原子基態的兩個超精細結構能級間躍遷所對應的輻射的 9,192,631,770 個周期的持續時間。
## 應用
### 石油探勘 | [
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銫元素 | 目前非放射性銫的最大的用途是石油提取工業中使用的基於甲酸銫的鑽井液。通過使氫氧化銫與甲酸反應製成的甲酸銫的水溶液（HCOO–Cs+）在 20 世紀 90 年代中期開始用於油井鑽井以及完井液。甲酸銫作為鑽井液的功能是潤滑鑽頭，將切下來的岩石帶至地表，並且在鑽井期間維持對地層的壓力。完井液的作用是在鑽井完成後生產前輔助控制硬體進駐，而甲酸銫在其中的作用是維持壓力。
甲酸銫鹽溶液的密度很高，達 2.3 g/cm3，再加上大多數銫化合物所具有的相對良性的性質，減少了鑽井液中有毒的高密度懸浮固體的需求。與其它許多高密度液體的成分不同，相對來說甲酸銫不會破壞環境。因此該技術具有很大的技術優勢、工程優勢以及環境優勢。甲酸銫鹽溶液可以與甲酸鉀、甲酸鈉混合以將液體的密度降低至水的密度（1.0 g/cm3）。此外，甲酸銫還可以生物降解以及回收，並且可以循環使用，考慮到其較高的價格（每桶 4000 美元），這一點非常重要。。鹼金屬的甲酸鹽可以安全的處理，而且不像他們所替代的高密度鹽溶液（如溴化鋅溶液）那樣具有腐蝕性，因此不會對生產底層或者井下的金屬造成損害。使用這些甲酸鹽也減少了清潔和處理的費用。
### 原子鐘
銫原子鐘觀察銫 - 133 原子在超精細結構之間躍遷產生的電磁輻射，並以此作為參考點。1955 年，第一個精確的銫原子鐘由路易斯・艾森在英國國家物理實驗室建成。在過去的半個多世紀中，人們不停的改進銫原子鐘，並且使用它作為標準時間和頻率測量的基準。這些鐘測量頻率的精度為 2-3×10-14，相當於時間測量的精度為每天 2 奈秒，或者 140 萬年 1 秒。目前最先進的銫原子鐘的精度超過了 10-15，這意味著從 6600 萬年前恐龍滅絕的時代起其誤差僅為 2 秒鐘，被認為是「人類目前所達到的最精確的單位實現」。
銫原子鐘也用於監控手機時間傳輸以及網際網路信息流的網絡中。
### 電力電子
銫蒸氣熱離子發電機是將熱能轉化為電能的低功率裝置。在雙電機真空管轉換器中，銫將在陰極聚集的空間電荷清除，並通過這種方式增強電流。
銫也因其具有光電發射的性質而重要，它可以將光能轉化為電流。由於諸如金屬化合物 K
2CsSb 等的銫基陰極發無線電子的電壓閾值較低，通常將銫用於光電池中。使用銫的光電發射裝置包括光學字符識別裝置、光電倍增管以及攝像管。儘管如此，鍺、銣、硒、矽、碲以及其他幾種元素可以替代銫作為光電發射材料。 | [
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銫元素 | 碘化銫（CsI）、溴化銫（CsBr）以及氟化銫（CsF）晶體可以用於閃爍計數器中的閃爍體。由於閃爍計數器適用於檢測伽瑪射線和 X 射線，它們廣泛的用於礦物勘探以及粒子物理學研究中。由於銫的原子量較大，可以提供較好的停止能力，因此可以提高檢測能力。銫化合物也提供了更快的響應速度（CsF）並且不易吸水（CsI）。
銫蒸氣用於許多普通磁強計中。銫也在分光光度法中作為內部標準使用。和其它鹼金屬類似，銫和氧的聯繫緊密，因此在真空管中銫被用作吸氣劑。銫還用於高能雷射、蒸氣輝光燈以及蒸氣整流器中。
### 離心液
由於其密度較高，氯化銫、硫化銫、以及三氟乙酸銫通常在分子生物學中用於密度梯度離心操作。該技術主要用於分離生物樣本中的病毒顆粒、細胞器以及核酸。
### 化學與醫學應用
銫在化學上的應用相對較少。銫的化合物通常用於增強若干化學品生產中的金屬 - 離子催化劑的作用，這些化學品包括丙烯酸、環氧乙烷、蒽醌、甲醇、鄰苯二甲酸酐、苯乙烯、甲基丙烯酸甲酯單體以及各種烯烴等等。銫化合物也用於在硫酸生產中將二氧化硫催化轉化為三氧化硫的過程中。
氟化銫在有機化學中被用作鹼或者氟離子的來源。銫鹽在合成環狀化合物、酯以及聚合等有機合成中有時用來替代鉀鹽或者鈉鹽。
### 核應用與同位素應用
銫 - 137 在工業應用中是一種非常常見的作為伽瑪射線發射源的同位素。其優勢在於它的半衰期大約 30 年，可以通過核燃料循環獲得，並且其最終產物鋇 - 137 是一種穩定的同位素。其較高的水溶性是其缺點，使得它無法用在用於食品和醫療用品的大型池式輻射器中。銫 - 137 已經被用在農業、癌症治療、食品消毒、污水污泥處理以及外科手術設備中。。銫的放射性同位素可以用在放射線療法中針對某些癌症治療，然而由於目前已經有了更好的替代品，且放射源中易溶於水的氯化銫可能造成大範圍污染，放療中逐漸不再採用銫放射源。在許多工業測量計中都採用了銫 - 137，包括濕度計、密度計、水平儀以及厚度計。測井設備中也會使用銫 - 137 來測量與岩層中的電子密度。 | [
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銫元素 | 銫 - 137 也用於水文學研究中。銫是核分裂反應的產物。自從大約 1945 年核試驗開始，一直到 20 世紀 80 年代中期，銫 137 被釋放進入大氣層，然後立即被吸收入水溶液中。那個時期的年度變化與土壤和沉積層有相關性。銫 - 134 以及含量更少的銫 - 135 也用於水文學研究作為核電工業中產生的銫的度量。這兩種同位素不像銫 - 133 或者銫 - 137 那樣常見，而且僅能通過人為過程產生。
### 其它應用
在早期的為長距離星際航行的太空飛行器推進器設計的離子推力器中使用銫和汞作為推進劑。在離子化方法中，需要通過與加載電壓的鎢電極接觸剝去推進劑的外層電子。考慮到銫對飛船部件的腐蝕作用，對離子推進器的研發轉向使用惰性氣體推進劑，例如氙。在地面測試中處理惰性氣體推進劑，並且其對飛船造成影響的可能性也更小。最終在 1998 年發射的試驗飛船深空 1 號中使用氙作為推進劑。儘管如此，已經建造的場發無線電子推進推力器仍然使用加速諸如銫等的金屬離子的簡單系統來形成推力。
在紅外照明彈中使用硝酸銫作為氧化劑和煙火著色劑來燃燒矽，例如 LUU-19 照明彈。這是因為硝酸銫的大部分輻射光都位於近紅外光譜中。銫也被用來減少 SR-71 黑鳥式偵察機的尾焰的雷達特徵。銫也經常和銣一起以碳酸鹽的形式加入玻璃以減少玻璃的導電性並且增加光纖與夜視設備的穩定性和持久性。氟化銫或者氟化鋁銫也用在以含鎂鋁合金釺焊的焊劑配方中。
## 健康以及安全危害
大多數人極少能碰到銫的化合物，但是由於銫的化學性質接近鉀，大多數化合物只有輕微的毒性。暴露在大量的銫化合物中會引起應急過度以及痙攣，但是由於在自然情況下不會遇到這樣大的劑量，銫並不是重要的化學環境污染物。在小鼠試驗中，氯化銫的半致死量（LD50）為每千克體重 2.3 克，與氯化鉀和氯化鈉的半致死量相近。
金屬銫是最活潑的元素之一，並且接觸水後會發生爆炸。銫接觸水後產生大量的熱，加熱了同時產生的氫氣並將其點燃，引起猛烈地爆炸。其它的鹼金屬也能發生相似的情況，但是銫和水的反應如此劇烈以至於可以和冷水反應。銫的自燃溫度為 - 116°C，因此銫極度容易自燃，並且在空氣中會發生爆炸性的燃燒，形成超氧化銫以及各種氧化物。超氧化銫是一種非常強的鹼，可以迅速的腐蝕玻璃。
由於人類的活動，生物圈中存在少量的銫的同位素銫 - 134 和銫 - 137，並且在不同地點放射強度也有所不同。 | [
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銫元素 | 放射性的銫不會像許多其它裂變產物（例如放射性碘和放射性鍶）那樣在人體內聚集。大約 10% 的吸收進人體的放射性銫會迅速通過汗和尿排出體外，而剩餘的 90% 其生物半衰期在 50 天至 150 天 放射性銫和鉀類似，傾向於在植物的組織中聚集，如水果和蔬菜。亦曾記錄放射性污染的森林中的蘑菇將銫聚集在其子實體中 。車諾比核事故之後，人們高度擔心銫 137 在湖水中聚集。使用狗進行的實驗表明每千克體重 3.8 毫居里的劑量（4.1 微克銫 - 137）會在三周內致死 較小劑量可能導致不育或者癌症。國際原子能機構以及其它機構警告諸如銫 - 137 的放射性材料可以用於放射性散布裝置（亦稱髒彈）中。
## 注釋
## 參考
## 參考資料
## 外部連結
* 元素銫在洛斯阿拉莫斯國家實驗室的介紹（英文）
* EnvironmentalChemistry.com —— 銫（英文）
* 元素銫在 _The Periodic Table of Videos_（諾丁漢大學）的介紹（英文）
* 元素銫在 Peter van der Krogt elements site 的介紹（英文）
* WebElements.com – 銫（英文） | [
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随机过程 | 在機率論中，**隨機過程**（英語：Stochastic process 或 Random process），又稱**隨機函數**（英語：Random function），是隨機變數的集合。若一隨機系統的樣本點是隨機函數，則稱此函數為樣本函數，這一隨機系統全部樣本函數的集合是一個**隨機過程**。實際應用中，樣本函數的一般定義在時間域或者空間域。隨機過程的實例如股票和匯率的波動、語音信號、視頻信號、體溫的變化，隨機運動如布朗運動、隨機徘徊等等。
## 定義
設 $(\Omega ,{\mathcal {F}},P)$ 為一機率空間，另設集合 $T$ 為一指標集合。如果對於所有 $t\in T$ ，均有一隨機變數 $\xi _{t}(\omega )$ 定義於機率空間 $(\Omega ,{\mathcal {F}},P)$ ，則集合 $\{\xi _{t}(\omega )|t\in T\}$ 為一隨機過程。
通常，指標集合 $T$ 代表時間，以實數或整數表示。以實數形式表示時，隨機過程稱為連續隨機過程；以整數表示時，則為離散隨機過程。隨機過程中的參數 $\omega $ 只為分辨同類隨機過程中的不同實例，如在上文下中不構成誤會，通常略去。例如表達單次元布朗運動時，常以 $W_{t}$ 表達，但若考慮兩同時進行布朗運動的粒子，則會分別以 $W_{t}(1)$ 和 $W_{t}(2)$ （或作 $W_{1}(t)$ 和 $W_{2}(t)$ ）表示。
## 歷史
為了了解金融市場和研究布朗運動，在 19 世紀後期人們開始研究隨機過程。第一個用數學語言描述布朗運動的是數學家 Thorvald N. Thiele。 他在 1880 年發表了第一篇關於布朗運動的文章。隨後，在 1900 年， Louis Bachelier 的博士論文「投機理論」 提出了股票和期權市場的隨機分析。阿爾伯特・愛因斯坦（在他 1905 年的一篇論文中）和瑪麗安・一維 Smoluchowski（1906 年）從物理界的角度出發，把它作為了一種間接證明了原子和分子的存在。他們所描述的布朗運動方程式在 1908 年被讓・佩蘭核實。
從愛因斯坦的文章的摘錄描述了隨機模型的基本原理：
"它必須明確假定每個單個顆粒執行的運動是獨立於所有其他的粒子的運動；它也將被認為是 1 的動作和相同的顆粒在不同的時間間隔是獨立的過程，只要這些的時間間隔不是非常小" | [
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随机过程 | " 我們引入一時間間隔 $\tau $ 蛋白考慮，相對來說這是非常小的，但是我們可觀察到的時間間隔，仍然過大，在兩個連續時間間隔 $\tau $ 蛋白，由粒子所執行的動作可以被認為是作為彼此獨立的事件 "。
## 架構
在機率論的測量理論中，需要解決一個問題。如何構造一個 Σ- 代數的所有功能空間的衡量子集，然後把它有限化。為了解決這個問題，採用了 Kolmogorov 擴展方法。
* Kolmogorov 擴展方法過程：
假定所有函數 f 的空間機率測度： $f:X\to Y$ 存在，那麼它可以被用來指定有限維隨機變數 $f(x_{1}),\dots ,f(x_{n})$ . 的聯合機率分布。現在從這個 n 維機率分布，我們可以推斷出第（n - 1）維邊際機率為 $f(x_{1}),\dots ,f(x_{n-1})$ 。但是需要注意的是兼容性狀態，即這種邊際機率分布是在相同的類作為 1 從完全成熟的隨機過程衍生。例如，如果該隨機過程是一個 Wiener 過程（在這種情況下，邊際是指數類的所有高斯分布），但不是在一般對所有的隨機過程。這種方程式稱為查普曼 - 洛夫方程式。
科摩哥洛夫擴展定理保證了隨機過程的有限維機率分布滿足查普曼 - 科摩哥洛夫的兼容性條件的存在..
* 分離性
回想一下，在洛夫公理化中存在對於機率問題有還是沒有的不確定性。科摩哥洛夫擴展首先聲明是可衡量的功能，其中有限多個坐標 $[f(x_{1}),\dots ,f(x_{n})]$ 被限制在 $Y_{n}$ 中可測量的子集所有集合。如果一個是 / 否有關的問題都可以通過觀察至多有限多個坐標的值回答，那麼它有一個機率的答案。
在測度理論，如果我們有一個可數無限集合測集，所有的人都那麼的聯合和交集是可測集。對於我們而言，這意味著是 / 否依賴於可數個坐標的問題有一個機率的答案。
## 過濾
給定一個機率空間 $(\Omega ,{\mathcal {F}},P)$ , 過濾是一個弱增長對 σ- 代數 在 $\Omega $ , $\{{\mathcal {F}}_{t},t\in T\}$ 集合一些全序集 T, 上界由 ${\mathcal {F}}$ 決定。即對於 _s_,_t_ $\in T$ 且 _s_ < _t_, 有 | [
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随机过程 | : ${\mathcal {F}}_{s}\subseteq {\mathcal {F}}_{t}\subseteq {\mathcal {F}}$
### 自然過濾
給定一個隨機過程 $X=\{X_{t}:t\in T\}$ 。在這個過程中，需要過濾這裡的 ${\mathcal {F}}_{t}$ . 這個通過 $X_{s}$ 和時間 _s_ = _t_ 產生。舉個例子， ${\mathcal {F}}_{t}=\sigma (\{X_{s}^{-1}(A):s\leq t,A\in \Sigma \})$ 一個隨機過程總是適應其自然過濾。
## 相關條目
* 隨機控制
## 參考文獻
## 外部連結
* An 8 foot tall Probability Machine (named Sir Francis) comparing stock market returns to the randomness of the beans dropping through the quincunx pattern. （頁面存檔備份，存於網際網路檔案館） from Index Funds Advisors IFA.com （頁面存檔備份，存於網際網路檔案館）
* Stochastic Processes used in Quantitative Finance, sitmo.com
* Addressing Risk and Uncertainty | [
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催乳激素抑制激素 | **多巴胺**（英語：**dopamine** 或 **DA**，擷取自 **2-(3,4-dihydroxyphenyl)ethylamine**），或稱 **2-(3,4 - 二羥基苯基) 乙胺**，化學式：C6H3(OH)2-CH2-CH2-NH2）是一種重要的神經傳遞質，可影響一個人的情緒。
多巴胺是兒茶酚胺和苯乙胺類的，一種在腦和身體中扮演幾個重要作用的有機化合物，它是一種胺，通常在人的腦和腎臟中合成，由其前體的左旋多巴除去羧基合成。在大腦中多巴胺作為神經傳遞質，透過神經元釋放一種化學物質將訊號發送到其它神經細胞。大腦包括幾個不同的多巴胺通路，其中一個起著獎勵–激勵行為的主要作用。大多數類型的獎勵增加多巴胺在腦中的濃度，並且許多成癮藥物增加多巴胺神經元活動。其他的腦多巴胺用來參與運動控制和控制各種激素的釋放。
神經系統以外，在身體的幾個部分多巴胺作為局部化學信使的功能。在血管中它抑制正腎上腺素的釋放，並作為血管擴張劑（在正常濃度下）；在腎臟中它增加鈉和尿的排泄；在胰臟中它減少胰島素生產；在消化系統中它減少胃腸蠕動和保護腸黏膜；並在免疫系統中它減少淋巴球的活性。血管除外，多巴胺在這些外圍系統局部合成，在鄰近該釋放它的細胞旁發揮其作用。
幾個重要的神經系統疾病與多巴胺系統的功能障礙有關，而使用一些改變多巴胺作用的關鍵藥物來治療他們。帕金森氏症一種退行性狀況引起身體震顫和運動障礙，是透過中腦中稱為黑質區的分泌神經元分泌多巴胺不足所引起。其代謝前體 L-DOPA 可以工業製造，其純銷售形式為左旋多巴是最廣泛使用的治療方法。有證據表明思覺失調症涉及多巴胺活性水平的改變，大多數經常使用的抗精神病藥物具有降低多巴胺活動的主要效果。類似多巴胺拮抗劑藥物，也有一些是最有效抗嘔吐藥物。不寧腿綜合徵與注意力不足過動症與多巴胺活性降低有關。高劑量多巴胺興奮劑可以上癮，但也有一些使用較低劑量治療過動症。多巴胺本身可製造成靜脈注射的藥物：雖然不能從血液到達腦部，其週邊作用使其對心臟衰竭或休克的治療是有用的，尤其是對新生嬰兒。
* * *
## 簡介
多巴胺是一種用來幫助細胞傳送脈衝的化學物質，是神經傳導物質的一種。這種傳導物質主要負責大腦的情慾，感覺，將興奮及開心的訊息傳遞。與上癮有關。
愛情的感覺對應到生化層次，和腦裡產生大量多巴胺起的作用有關。
吸菸和吸毒都可以增加多巴胺的分泌，使上癮者感到開心及興奮。多巴胺傳遞開心、興奮情緒的這功能，醫學上被用來治療抑鬱症。 | [
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催乳激素抑制激素 | **多巴胺不足**或失調則會令人失去控制肌肉的能力、或是導致注意力無法集中。失去控制肌肉能力，在嚴重時會導致手腳不自主地顫動、乃至罹患帕金森氏症。
當我們積極做某事時，腦中會非常活躍的分泌出大量多巴胺。它是一種使人類引起慾望的大腦神經傳遞質。
極端情形如亨丁頓舞蹈症，是多巴胺分泌過多而導致的疾病，患者的四肢和軀幹會如舞蹈般不由自主地抽動，造成日常行動不便，疾病發展到晚期，病人的生活將無法自理，失去行動能力，無法說話，容易噎到，甚至無法進食。
多巴胺最常被使用的形式為鹽酸鹽，為白色或類白色有光澤的結晶，無臭，味微苦。露置空氣中及遇光後色漸變深。在水中易溶，在無水乙醇中微溶，在氯仿或乙醚中極微溶解。熔點 243℃-249℃（分解）。
多巴胺在人體的功能可分為神經系統內與神經系統外兩個部分。
多巴胺在腦的功能中，在運動控制、動機、喚醒、認知、獎勵的功能上扮演重要角色，還與一些更基礎的功能相關，例如哺乳、性慾、噁心。多巴胺類的神經元在人腦中的含量約有 400,000 個，其實是相對的少，並且只有在少數區域存在，但是卻投射到很多腦區，並能引起有很強大的功用。這些神經元最早在 1964 年由 Annica Dahlström 和 Kjell Fuxe 標繪出來，並給予這些區域 A 開頭的名字。在他們的模型中，A1-A7 區包含正腎上腺素，A8-A14 則包含多巴胺。以下是他們辨認出來包含多巴胺的區域：
* 黑質是中腦中一小塊形成基底核的區域，其中多巴胺神經元多在黑質的緻密部（A8）和其周遭（A9）被發現，和運動控制相關，若有失去大部分此區域的多巴胺神經元，會導致帕金森氏症。
* 腹側被蓋區（A10）則是另一塊屬於中腦的區域，是人腦中最多多巴胺神經元的地方，但實際上此區域仍然是非常的小。此區域的多巴胺神經元投射到伏核、前額葉皮質等其他區域，主要和獎勵、動機的功能相關。
* 下視丘後葉也有一些多巴胺神經元（A11），投射到脊髓，但功能並不是很清楚。
* 弓形核（A12）和腦室旁核（A14）都在下視丘，這些多巴胺神經元投射到腦垂腺前葉，透過中央聯合的循環組織，抑制催乳激素釋放細胞分泌催乳激素。通常說到這裡的調控時，多巴胺時常被稱為催乳素抑制因子、抑制催乳激素賀爾蒙、催乳激素抑制素。
* 一樣是在下視丘，不定區（A13）的多巴胺神經元則參與性腺激素釋放激素的控制。 | [
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催乳激素抑制激素 | * 還有多巴胺神經元位在視網膜，被稱為無軸突細胞，在日光的刺激下會活化，釋放多巴胺致細胞外受質中，相對的，在夜晚就會沈寂下來。這些視網膜中的多巴胺能夠抑制桿細胞而提升錐細胞的功能，最後產生對顏色敏感、並增加對比的效果，而其代價是在光線昏暗時便會降低其敏感度。
在神經系統外，在週邊，多巴胺也在侷限的區域透過外分泌或旁分泌產生功能：
* 首先是免疫系統，尤其是淋巴球，能夠製造並分泌多巴胺，其功能主要是抑制淋巴球的活性，但此系統的功能為何還不是很清楚。
* 腎的小管細胞能分泌多巴胺，且腎有許多細胞能表現多種多巴胺受器，多巴胺在此能增加腎的灌流、提高絲球體的過濾，並增加鈉離子的排泄。當腎部的多巴胺功能缺失時（可能肇因於高血壓或基因的問題），會導致鈉離子的排泄減少，造成高血壓。
* 胰臟也可以分泌多巴胺（外分泌），其功能可能與保護腸道的黏膜和降低嘗胃道蠕動相關，但還並不是很確定。
* 胰臟的胰島也和多巴胺相關，有證據顯示胰島的 β 細胞製造胰島素時，也會製造多巴胺受器，這些受器受到多巴胺作用的結果是降低胰島素的釋放，但這些多巴胺的來源還沒有釐清的很清楚。
## 結構
多巴胺分子由兒茶酚結構 (一個苯環與兩個羥基側基) 經由乙基鏈連接一個胺基的。因此多巴胺可能是最簡單的兒茶酚胺類家族，包括神經傳遞質正腎上腺素和腎上腺素。存在一個苯環與胺連接，使得它取代的苯乙胺家族，其中包括大量的精神藥物。
類似大多數胺，多巴胺是一種有機鹼。在酸性環境中，通常質子化。質子化形式是高度水溶性相對穩定的，但它是能夠被氧化，如果暴露於氧或其它氧化劑。在鹼性環境，多巴胺不會質子化。在這種游離鹼形式，它是更少水溶性，也比較反應性高。因為質子化形式增加穩定性和水溶性的，多巴胺提供化學或藥物使用的鹽酸多巴胺–即創建了鹽酸鹽，當多巴胺與鹽酸結合。在乾燥形式時鹽酸多巴胺是一種精細無色粉末！
## 生物化學
多巴胺是腦內極其重要的神經傳遞質，因為其作用特點又被稱作**快樂物質**。多巴胺屬於單胺類物質中的兒茶酚胺類，合成順序依次為酪胺酸 - 左旋多巴 - 多巴胺 - 正腎上腺素最後透過單胺氧化酶和兒茶酚胺氧位甲基移位酶酶解失活。合成腦內的 3/4 的 DA 細胞體位於中腦前部或者中腦。黑質包含了靈長類腦 DA 神經元的主要部分，黑質又可分為緻密部和網狀部。黑質 DA 神經元的主要投射部位尾核殼核伏隔核。大腦皮層是另一個主要投射部位。
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催乳激素抑制激素 | 目前共發現五種多巴胺受體，分為 D1 樣（D1 D5）D2 樣（D2 D3 D4 ）。DA 受體都隸屬於 G 蛋白偶聯受體的超級家族。
### 釋放與降解
DA 的釋放是一種量子釋放，胞裂外排（exocytosis）。動作電位到達神經末梢時候，突觸前膜通透性發生改變，Ca 離子進入細胞，促進囊泡附著於前膜，繼而形成小孔。由於嗜絡蛋白的收縮，將囊泡內容物排出。DA 的降解分為兩類，一種是酶解，另一種是再攝取。DA 及單胺類在神經末梢中再攝取占總排出量的四分之三，突觸間隙的 DA 可以被前膜，後膜，非神經組織攝取。先是通過細胞膜進入胞漿，這一階段由 NA-K-ATP 供能。第二步是囊泡攝取，這一步由 Mg-ATP 供能。酶解部分由單胺氧化酶和兒茶酚胺氧位甲基移位酶酶解失活。
## 主要多巴胺通道
* 中腦皮層通路（mesocortical system）
* 中腦邊緣系統通道（mesolimbic system）
* 黑質紋狀體徑路（nigrostriatal system）
* 結節漏斗徑路（tuberoinfundibular system）
獎賞機制，多巴胺的獎賞通路，各種成癮物質均由位於中腦邊緣皮質的通路發生作用：
1. 腹側被蓋核
2. 伏隔核
3. 前額葉皮層
作用於此通路，促進多巴胺的釋放使機體產生欣快感，停用後的戒斷反應等等。D1D2 受體均參與自我給藥行為。
## 多巴胺與思覺失調症
引發精神醫學的革命性進展的藥物是氯丙嗪，它主要透過阻斷邊緣系統的 D2 受體發揮抗精神疾病作用。此後類似的藥物不斷被研發。
經典的思覺失調症的多巴胺假說：思覺失調症是由於多巴胺功能亢進造成的，一度在學術界占據壟斷地位，直到目前為止所有的思覺失調症假說都不能與多巴胺無關。
隨著第二代抗精神病藥物如氯氮平、利培酮的問世，其特點是對 D2 受體的低阻斷效果，更多的是對 5-HT，NE 受體的阻斷，調節麩胺酸多種受體發揮作用，對經典的多巴胺假說提出了質疑。
傳統的抗精神病藥物阻斷中腦邊緣系統 D2 受體發揮抗精神病作用，但是同時阻斷了多巴胺在結節漏斗徑路的 D2 受體，導致泌乳素分泌增多。傳統的抗精神病藥物亦阻斷了黑質紋狀體的 D2 受體，引發錐體外症候群如肌肉張力上升，類帕金森氏症。臨床上多採用苯海索、金剛烷胺、溴隱亭對抗以上不良反應。
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] |
催乳激素抑制激素 | 多巴胺最早是在 1910 年由喬治・巴格和詹姆斯・尤恩在英國倫敦惠康實驗室合成。於 1957 年凱瑟琳・蒙塔古首先在人的大腦中鑑定出多巴胺。它被命名為多巴胺，因為它是一種單胺，其前體是 3,4 - 二羥基苯丙胺酸（左旋多巴胺）。在 1958 年阿爾維德・卡爾森在瑞典國家心臟研究所化學藥理學實驗室中最早認識到多巴胺作為神經傳遞質的功能。卡爾森被授予 2000 年諾貝爾生理學或醫學獎，其表明多巴胺不僅是正腎上腺素和腎上腺素的前體，而且自身也是神經傳遞質。
## 參考文獻
### 引用
### 來源
**書籍**
## 參見
## 外部連結
* U.S. National Library of Medicine: Drug Information Portal - Dopamine
* Dopamine: analyte monograph - The Association for Clinical Biochemistry and Laboratory Medicine
* Biochemistry of Parkinson's Disease（英文） | [
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] |
数 | **數**（number）是一個用作計數、標記或用作量度的抽象概念，是用以比較同質性或同屬性物件等級的簡單符號記錄形式（或稱度量）。因此，「數」是「量」的抽象化，數是用來界定某物件的量與一單位量的關係；用集合的概念來說，數是相似的類所構成的集合，其由各種物件中抽象而得，例如 5 個人、5 公升、5 小時等相似的類（所有 5 個量的物件）所構成的集合，用 5 表示之。
代表「數」的一系列符號，包括數字、運算符號等統稱為記數系統。在日常生活中，數通常出現在在標記（如公路、電話和門牌號碼）、序列的指標（序列號）和代碼（ISBN）上。在數學裡，數的定義延伸至包含如如分數、負數、無理數、超越數及複數等抽象化的概念。
起初人們只覺得某部分的數是數，後來隨著需要，逐步將數的概念擴大；例如畢達哥拉斯認為，數必須能用整數和整數的比表達的，後來發現無理數無法這樣表達，引起第一次數學危機，但人們漸漸接受無理數的存在，令數的概念得到擴展。
數的算術運算（如加減乘除）在抽象代數這一數學分支內被廣義化成抽象數字系統，如群、環和體等。
## 數的類別
數可以被分類為數系的集合內。對於以符號表示數的不同方式，則請看記數系統。
### 自然數
最常用的數為**自然數**，有些人指**正整數**，有些人則指**非負整數**。前者多在數論中被使用，而在集合論和電腦科學中則多使用後者的定義。
在十進位數字系統裡，自然數的標記符號為 0 至 9 等十個數字，將以十為基數的進位制使用在大於九的數上。
因此，大於九的數會有兩個或兩以上的位數。表示所有自然數的集合為ℕ $\mathbb {N} \ $ 。
### 整數
**負整數**是小於 0 的整數，通常在其前面加上一負號 (−)，來表示其為正整數的對立。
例如，若一個正整數是用來表示距一定點 0 右邊多少的距離，則一個負整數即表示距此定點 0 左邊多少的距離。
相似地，若一正整數表示一銀行存款，則一負整數即表示一銀行提款。
負整數、正整數和零三者即合稱為整數ℤ、 $\mathbb {Z} \ $ （德語 _Zahl_ 的縮寫）。
### 有理數 | [
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数 | 有理數是指可以被表示成整數分子 ( ${\mathit {m}}$ ) 和非零整數分母 ( ${\mathit {n}}$ ) 的分數的數，即 ${\tfrac {m}{n}}$ ，其代表 1 被分做相同的 ${\mathit {n}}$ 份，再取 ${\mathit {m}}$ 份後的量。兩個不同分數可能會對應到相同的有理數，如： ${\tfrac {-10}{-20}}={\tfrac {2}{4}}={\tfrac {1}{2}}$ 。若 ${\mathit {m}}$ 的絕對值大於 ${\mathit {n}}$ 的絕對值時，其分數的絕對值會大於 1。分數可以是正的、負的、或零。所有分數所組成的集合包含有整數，因為每一個整數都可以寫成分母為 1 的分數。有理數的符號為ℚ， $\mathbb {Q} $ （_quotient_ <中文：商> 的縮寫）。
### 實數
不嚴謹地說，實數可以和一連續的直線數線視為同一事物。
所有的有理數都是實數，實數也包含無理數，
所有實數可以分成正數、零和負數。
實數可以被其數學性質獨特地描繪出：它是唯一的一個完備全序體。
但它不是個代數閉域。
十進位數是另一種能表示數的方式。
在以十為底的數字系統內，數可以被寫成一連串的數字，
且在個位數右邊加上句號（小數點）（在美國和英國等地）或逗號（在歐洲大陸），負實數則在再前面加上一個負號。以十進位標記的有理數，其位數會一直重複或中斷（雖然其後面可以加上任意數量的零），而 0 是唯一不能以重複位數定義的實數。例如，分數 ${\frac {5}{4}}$ 能夠寫做中斷位數的十進位數 1.25，也能寫做重複位數的十進位數 1.24999...（無限的 9）。
分數 ${\frac {1}{3}}$ 只能夠寫做 0.3333...（無限的 3）。
所有重複與中斷的十進位數定義了能被寫成分數的有理數。
而不像重複與中斷的十進位數一般，非重複且非中斷的十進位數代表**無理數**，不能被寫成分數的數。
例如，著名的數學常數， $\pi $ （圓周率）和 ${\sqrt {2}}$ 都是無理數，表示成十進位數 0.101001000100001... 的實數也是無理數，因為其表示不會重複，也不會中斷。
**實數**由所有能被十進位數表示的數所組成，不論其為有理數或無理數。
另外，實數也可以分為代數數和超越數，
其中超越數一定是無理數且有理數一定是代數數，其他則不一定。 | [
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数 | 實數的符號為 $\mathbb {R} \ $ ℝ(Real 的縮寫)。
實數可以被用來表示量度，而且對應至數線上的點。
當量度只可能精準至某一程度時，使用實數來表示量度總是會有一些誤差。
這一問題通常以取定一適當位數的有效數字來處理。
### 複數
移動到更多層次的抽象化時，實數可以被延伸至**複數** $\mathbb {C} $ 。
歷史上，此數的誕生源自於如何將負 1 取平方根的問題。
從這一問題，一個新的數被發現了：-1 的平方根。
此數被標記為 **i**，由萊昂哈德・歐拉介紹出的符號。
複數包含了所有有 $a+bi$ 形式的數，其中 $a$ 和 $b$ 是實數。
當 $a$ 為零時， $a+bi$ 被稱為虛數。
相同地，當 $b$ 為零時， $a+bi$ 為實數，因為它沒有虛數部份。
一個 $a$ 和 $b$ 為整數的複數稱為高斯整數。
複數是個代數閉域，即任一複數係數的多項式都能有解。
複數也可以對應至複數平面上的點。
上述就提到的各個數系，每個都是下一個數系的子集。
以符號來表示的話，即為 $\mathbb {N} \subset \mathbb {Z} \subset \mathbb {Q} \subset \mathbb {R} \subset \mathbb {C} $ 。
### 其他類型
Superreal, 超實數和超現實數加上無限小和無限大兩種數來延伸實數，但依然是體。
* 四元數
* 八元數
* 十六元數
* P 進數
## 表示方式
* 分數
* 小數
* 科學記數法
* 數字系統
* 進位制
## 記數系統
數和以符號來表示數的記數系統不同。
五可以表示成十進位數 5 和羅馬數字 V。
記數系統在歷史上的重要發展是進位制的發展，
如現今的十進位制，可以用來表示極大的數。
而羅馬數字則需要額外的符號來表示較大的數。**記數系統**是指用何種方式來記錄數的系統，可以是符號形式，也可以是實物形式。
無論符號記數還是實物記數，
如今都抽象成了數碼的有序左右排列形式，並且認定左面的數碼是右面數碼的 N 倍（N 是一個大於 1 的自然數），這就是 N 進位記數法，簡稱為 **N 進位**。N＝2、3、4、5、8、10、16、... 的進位，就分別稱為二進位、三進位、四進位、五進位、八進位、十進位、十六進位、... 各種進位數之間可以轉化。
例如二進位的 10111 和十進位的 23 可以相互轉化。 | [
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数 | 人們熟悉十進位，目前電子機器記數使用二進位，將來出現四進位的量子態記數方式也未必可知。
記數系統中使用的占位符號叫數碼，N 進位的數碼所代表的數從 0 到 N-1，分別用 0、1、2、... 、@來記，其中 @代表的數是 N-1，是最大數碼。
例如十六進位使用的數碼是 0、1、2、3、4、5、6、7、8、9、A、B、C、D、E、F，十六進位的最大數碼 @就是「F」。
用數碼左右排列的數如果認定某數碼間的位置有一個小數點，就可以表示具有小數部分的數。
小數點左移一位，該數就縮小 N 倍，相反則該數擴大 N 倍。
人們習慣用「-」放在數碼排列的最左面來表示負數，例如十進位的 - 675.76。
機器表示正負數一般不用「+」、「-」，而使用**限位數**的方法。限位數就是數碼位數固定的數。
例如，3 位十進位數共有 1000 個，只能是 000～999，不可能出現其他的表示。
如果認定某位置有小數點，這 1000 個數就可以表示具有小數部分的數。
限位數可以不用「+」、「-」就可以表示正負數，方法是將所有能表示出來的數按著大小分為對稱的兩部分，
對稱的規則是「表示的兩整數之和是數的總數」，
較大的那個對稱數就表示較小那個對稱數的相反數。
這種規定之下，3 位十進位數的 501～999 就可以認定是負數 - 499～-1，由於 500 自身對稱，去掉二義性，
規定 500 就表示是「-500」，這就是**對稱制**（類似 2 補數表示法）。對稱制中偶進位的負數會比正數多一個，
因而表數正負數的區間不對稱，但 N 是奇數時，表數區間是對稱的。對稱制適合機器數值計算。
## 歷史
### 整數的歷史
#### 第一個數
數的第一次使用可回溯到大約西元前三萬年前，
當計數符號被舊石器時代的人使用的時期。
現今所知最早的一個例子在南非的一個洞穴內。[1] 此一系統沒有進位制的概念（如現今所用的十進位制），這使得它表示大數的能力受到了限制。
現今所知最早有進位制的系統則是美索不達米亞的六十進位制（約西元前 3400 年），
而最早的十進位制在西元前 3100 年的埃及。[2] （頁面存檔備份，存於網際網路檔案館）
#### 0 的歷史
把零當成數來使用和其在進位制中當占位標記不同。
許多的古印度人使用梵文 _Shunya_ 來指_虛無_這一概念，
而在數學文章內，這一詞則常被拿來指零這一數。 | [
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数 | [3] 波你尼（Pāṇini，西元前 5 世紀）在其以梵文寫形式文法的書－八章書（Ashtadhyayi）裡，使用了無效（零）算子。
文獻顯示古希臘似乎不確定零做成一個數的地位：
他們問自己 "無物如何變成有物"，因而導致有趣的哲學問題。
在中世紀時，零和真空的性質和存在甚至成了宗教上的爭論。
埃利亞人芝諾的悖論很大一部份便依靠在對零不確定的解釋上。（古希臘人甚至懷疑過 1 是否是一個數。）
墨西哥中南部奧爾梅克文明晚期的人民已在新大陸上開始使用真正的零，
其時間可能是在西元前 4 世紀，但較肯定的是在西元前 40 年，它變成了瑪雅數字和瑪雅曆的一部份，
但完全沒有影響到舊大陸的記數系統。
西元 130 年時，托勒密被喜帕恰斯和巴比倫人在六十進位制裡使用了零的符號（小圓圈加上一長上標線）所影響，將其使用在希臘數字上。因為它只是單獨使用，而非做為一占位符，希臘的零是舊大陸第一個做為書寫使用的真正的零。而在之後的拜占庭抄本上，希臘的零才演變成了希臘字母 Ο（另外它也有 70 的意思）。
另一真正的零在西元 525 年被使用在以羅馬數字編製的表格上（狄奧尼修斯・伊希格斯是現知第一位使用者），但當時是使用意思為_無物_的一個名詞 _nulla_，而非一個符號。當除法把零視為餘數時，則使用另一意思也是_無物_的詞 _nihil_。中世紀的零被所有中世紀計算復活節的計算家們使用著。其首字母 N 的單獨使用是在西元 725 年由聖比德或其同僚在羅字數字的表格上使用，一個真正的零的符號。
零的一個早期書寫使用是於西元 628 年由婆羅摩笈多（寫於宇宙的開始（Brāhmasphuṭasiddhānta））所使用的。他把零視為一個數，並討論包含零的運算，包括除法。在同一時期（西元七世紀），其概念已很清楚地傳到了柬埔寨，後來顯示其觀念的文書更傳到了中國和伊斯蘭世界。
#### 負數的歷史
負數的抽象概念早在西元前 100 年至 50 年間就被確認過了。中國的九章算術裡就提到尋找圖形面積的方法：以紅色棒子來標記正數，黑色來標記負數。這是負數在東方最早被提及的記錄。而西方的第一次論述則是在西元三世紀的希臘，丟番圖在其著作 _Arithhmetica_ 裡提及一個和 $4x+20=0$ （其解為負數）相等的方程，且說這個方程會給出荒謬的解答。 | [
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数 | 在西元七世紀間，負數在印度被用來表示負債。丟番圖先前的論述被印度數學家婆羅摩笈多在宇宙的開始中討論的更詳盡，他使用負數來產生公式解，到現在還依然被使用著。但到了西元 12 世紀的印度，婆什迦羅第二在得出一元二次方程的負根之後，卻還說這一負值「在此例不被採用，因為它不適合；人們不會同意有負根的。」
大多數的歐洲數學家直到西元十七世紀仍不接受負數的概念，雖然斐波那契允許負數在金融問題上被解釋為負債，後來又允許視為損失。負數在歐洲的第一次被使用是在西元十五世紀被尼古拉斯・丘凱所使用的。他把負號加上數的右上方（冪的位置）上來表示負數，但也說這些負數是「荒謬的數」。亞諾用 $(-1):1=1:(-1)$ 這個比例式來反對引進負數這個概念，在這個比例式中，大數比小數等於小數比大數。
十七世紀，數學家沃利斯主張負數會大於無限，而且一般的實作應該忽略任何由題目導出的負數，因為它們是無意義的。
### 有理數、無理數和實數的歷史
#### 有理數的歷史
有理數的概念，相信起源於史前時期。就連古埃及的數學手稿中已經出現了將一般的分數轉換成古埃及分數的方法。古希臘和古印度數學家也將有理數理論的研究作為一般數論研究的一部分。 其中最有名的是公元前 300 年左右的歐幾里得的幾何原本。在古印度手稿中與此最為相關的則是研究數論的 Sthananga Sutra。
小數的概念與十進位記號有緊密的關係；它們似乎是串聯地發展的。 比如說，在印度耆那教的箴言集就提到了 $\pi $ 和 2 的算術平方根。
### 複數
最早但短暫論及負數平方根的是在西元一世紀希臘數學家和發明家希羅的工作中，當他在思考一金字塔可能的平截頭體體積時。複數在西元十六世紀開始變得很顯著，因為義大利數學家（見塔塔利亞和卡爾達諾）所發現三次及四次多項式的公式解。這一公式很快就被知道，而即使只注意實數解的部份，有時也會有需要操作負數平方根的時候。 | [
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数 | 這使人感到雙倍的不安，因為當時連負數都不被認為是很牢固的了。虛（imaginary）這一詞因此在 1637 年被笛卡爾創造出來，並且帶有些許貶義（參考虛數中討論複數真實性的部份）。更令人困惑的來源是等式 ${\sqrt {-1}}^{2}={\sqrt {-1}}{\sqrt {-1}}=-1$ 似乎任性地不和代數恆等式 ${\sqrt {a}}{\sqrt {b}}={\sqrt {ab}}$ 相合，而這一代數恆等式卻是在 $a$ 和 $b$ 都是正數時成立，而且也在 $a$ 和 $b$ 一正一負時可以被使用在複數計算上。這一恆等式（和另一相關的恆等式 ${\frac {1}{\sqrt {a}}}={\sqrt {\frac {1}{a}}}$ ）在 $a$ 和 $b$ 皆為負數時的錯誤使用甚至使得萊昂哈德・歐拉感到迷惑。這一困難最終導致他使用一特別的符號 $i$ 來取代 ${\sqrt {-1}}$ 來警惕此一錯誤。
觀看十八世紀時亞伯拉罕・棣莫弗和萊昂哈德・歐拉的工作。棣莫弗於西元 1730 年完成了以他為名的著名公式，棣莫弗定理：
: $(\cos \theta +i\sin \theta )^{n}=\cos n\theta +i\sin n\theta \,$
而歐拉則在西元 1748 元完成複數分析中的歐拉公式：
: $\cos \theta +i\sin \theta =e^{i\theta }.\,$
複數的存在在西元 1799 年由卡斯帕爾・韋塞爾提出了幾何解釋之前都沒有被完全地接受，這一解釋在幾年後被高斯重新發現並普及，結果使複數理論得到了顯要的擴張。複數圖像表示的概念早在 1685 年便在沃利斯的 _De Algebra tractatus_ 一書中提及。
也是在 1799 年，高斯提出了第一個廣為人接受的代數基本定理證明，表示任一複數係數多項都有完全的複數解。複數理論被廣泛地接受，奧古斯丁・路易・柯西和尼爾斯・阿貝爾的工作也佔了很大的功勞，尤其是後者，他是第一個大膽成功使用複數的人。 | [
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数 | 高斯研究過高斯整數（ $a+bi$ 中的 $a$ 和 $b$ 是整數或有理數）。而其學生費迪南・艾森斯坦則研究過 $a+b\omega $ 中的 ω 是 $x^{3}-1=0$ 複數根的類型。其他種類的複數還有由較大 $k$ 值的單位根 $x^{k}-1=0$ 推出的類型。其普遍化大部份歸功於恩斯特・庫默爾的工作，他也引進了理想數的概念，它在 1893 年被菲利克斯・克萊因表示成幾何實體。域的一般理論由埃瓦裡斯特・伽羅瓦創造出來，他主要在研究由多項式方程 $F(x)=0$ 產生出來的體。
西元 1850 年，皮瑟成功地把極點（pole）和分支點（branch point）區別出來，而且引起了數學奇點的概念，這一概念最終導致出了黎曼球的概念。
## 參考
## 參見
* 數線
* 數表
* №
**不同文化的數字**
* 阿拉伯數字
* 巴比倫數字
* 古埃及數字
* 希臘數字
* 羅馬數字
* 希伯來數字 | [
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弱作用力 | **弱交互作用**（又稱**弱力**或**弱核力**）是自然的四種基本力中的一種，其餘三種為強交互作用、電磁力和引力。次原子粒子的放射性衰變就是由它引起的，恆星中一種叫氫融合的過程也是由它啟動的。弱交互作用會影響所有的費米子，即所有自旋為半奇數的粒子。
在粒子物理學的標準模型中，弱交互作用的理論指出，它是由 W 及 Z 玻色子的交換（即發射及吸收）所引起的，由於弱力是由玻色子的發射（或吸收）所造成的，所以它是一種非接觸力。這種發射中最有名的是 β 衰變，它是放射性的一種表現。重的粒子性質不穩定，由於 Z 及 W 玻色子比質子或中子重得多，所以弱交互作用的作用距離非常短。這種交互作用叫做「弱」，是因為 β 衰變發生的機率比強交互作用低很多，表示它的一般強度比電磁及強交互作用弱好幾個數量級。大部份粒子在一段時間後，都會通過弱交互作用衰變。弱交互作用有一種獨一無二的特性 —— 那就是夸克味變 —— 其他交互作用做不到這一點。另外，它還會破壞宇稱對稱及 CP 對稱。夸克的味變使得夸克能夠在六種「味」之間互換。
弱力最早的描述是在 1930 年代，是四費米子接觸交互作用的費米理論：接觸指的是沒有作用距離（即完全靠物理接觸）。但是現在最好是用有作用距離的場來描述它，儘管那個距離很短。在 1968 年，電磁與弱交互作用統一，它們是同一種力的兩個表徵，現在叫電弱交互作用。
弱交互作用在粒子的 β 衰變中最為明顯，在由氫生產重氫和氦的過程中（恆星熱核反應的能量來源）也很明顯。放射性碳定年法用的就是這樣的衰變，此時碳 - 14 通過弱交互作用衰變成氮 - 14。它也可以造出輻射冷光，常見於超重氫照明；也造就 β 放射這個應用領域（把 β 射線的電子當電流用）。
## 性質
弱交互作用有如下的數項特點：
1. 唯一能夠改變夸克味的交互作用。
2. 唯一能令宇稱不守恆的交互作用。因此它也是唯一違反 CP 對稱的交互作用。
3. 由具質量的規範玻色子所介導的交互作用。這一不尋常的特點可由標準模型的希格斯機制得出。 | [
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弱作用力 | 由於弱交互作用載體粒子（W 及 Z 玻色子）質量很大（約 90 GeV/c2），所以他們的壽命很短：平均壽命約為 3 × 10-25 秒。弱交互作用的耦合常數（交互作用強度的一個指標）介乎 10−7 與 10−6 之間，而相比下，強交互作用的耦合常數約為 1，故就強度而言，弱交互作用是弱的。弱交互作用的作用距離很短（約為 10−17–10−16m）。在大約 10−18 米的距離下，弱交互作用的強度與電磁大約一致；但在大約 3×10−17 的距離下，弱交互作用比電磁弱一萬倍。
在標準模型中，弱交互作用會影響所有費米子，還有希格斯玻色子；弱交互作用是除引力交互作用外唯一一種對微中子有效的交互作用。弱交互作用並不產生束縛態（它也不需要束縛能），而重力、電磁力和強核力則分別會在天文、原子、原子核的尺度下產生束縛態。
它最明顯的過程是由第一項特點所造成的：味變。比方說，一個中子比一個質子（中子的核子拍檔）重，但它不能在沒有變味（種類）的情況下衰變成質子，它兩個「下夸克」中的一個需要變成「上夸克」。由於強交互作用和電磁交互作用都不允許味變，所以它一定要用**弱交互作用**；沒有弱交互作用的話：夸克的特性，如奇異及魅（與同名的夸克相關），會在所有交互作用下守恆。因為弱衰變的關係，所以所有介子都不穩定。在 β 衰變這個過程下，中子裏面的「下夸克」，會發射出一個虛
W−
玻色子，它隨即衰變成一電子及一反電微中子。
由於玻色子的大質量，所以弱衰變相對於強或電磁衰變，可能性是比較低的，因此發生得比較慢。例如，一個中性 π 介子在通過電磁衰變時，壽命約為 10-16 秒；而一個帶電 π 介子的通過弱核力衰變時，壽命約為 10-8 秒，是前者的一億倍。相比下，一個自由中子（通過弱交互作用衰變）的壽命約為 15 分鐘。
### 弱同位旋與弱超荷
弱同位旋（T3）是所有粒子都擁有的一種性質（量子數），決定了粒子在弱交互作用下該如何反應。對於弱交互作用來說，弱同位旋的作用跟電磁交互作用中的電荷，或者是強交互作用中的色荷一樣。所有費米子的弱同位旋均為 +1⁄2 或 -1⁄2，例如上夸克的弱同位旋為 +1⁄2，而下夸克的弱同位旋則為 -1⁄2。另一方面，在弱衰變的前後，夸克的 T3 永遠是不一樣的。也就是說，T3 = +1⁄2 的上型夸克（上、粲 (魅) 及頂），在弱衰變後必須變為 T3 = −1⁄2 的下型夸克（下、奇及底），反之亦然。 | [
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] |
弱作用力 | 弱同位旋是守恆的：反應產物的弱同位旋總和，等於反應物的弱同位旋總和。例如，一左手
π+
介子，弱同位旋為 + 1，一般衰變成一
ν
μ（+1⁄2）及一
μ+
（+1⁄2，因為是右手反粒子）。
在電弱理論中，粒子有一種新的性質，稱為弱超荷。它的數值由粒子的電荷及弱同位旋決定：
: $\qquad Y_{W}=2(Q-T_{3})$ ，
其中 _YW_ 為粒子的弱超荷，_Q_ 為電荷（以基本電荷為單位）及 _T3_ 為弱同位旋。弱超荷是 U (1) 部份生成元的規範群。
### 對稱破缺
長久以來，人們以為自然定律在鏡像反射後會維持不變，鏡像反射等同把所有空間軸反轉。也就是說在鏡中看實驗，跟把實驗設備轉成鏡像方向後看實驗，兩者的實驗結果會是一樣的。這條所謂的定律叫宇稱守恆，古典重力、電磁及強交互作用都遵守這條定律；它被假定為一條萬物通用的定律。然而，在 1950 年代中期，楊振寧與李政道提出弱交互作用可能會破壞這一條定律。吳健雄與同事於 1957 年發現了弱交互作用的宇稱不守恆，為楊振寧與李政道帶來了 1957 年的諾貝爾物理學獎。
儘管以前用費米理論就能描述弱交互作用，但是在發現宇稱不守恆及重整化理論後，弱交互作用需要一種新的描述手法。在 1957 年羅伯特・馬沙克與喬治・蘇達尚，及稍後理察・費曼與默里・蓋爾曼，提出弱交互作用的 **V−A**（向量 V 減軸向量 A 或左手性）拉格朗日量。在這套理論中，弱交互作用只作用於左手粒子（或右手反粒子）。由於左手粒子的鏡像反射是右手粒子，所以這解釋了宇稱的最大破壞。有趣的是，由於 **V−A** 開發時還未有發現 Z 玻色子，所以理論並沒有包括進入中性流交互作用的右手場。 | [
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弱作用力 | 然而，該理論允許複合對稱 **CP** 守恆。**CP** 由兩部份組成，宇稱 **P**（左右互換）及電荷共軛 **C**（把粒子換成反粒子）。1964 年的一個發現完全出乎物理學家的意料，詹姆斯・克羅寧與瓦爾・菲奇以 K 介子衰變，為弱交互作用下 CP 對稱破缺提供了明確的證據，二人因此獲得 1980 年的諾貝爾物理學獎。小林誠與益川敏英於 1972 年指出，弱交互作用的 CP 破壞，需要兩代以上的粒子，因此這項發現實際上預測第三代粒子的存在，而這個預測在 2008 年為他們帶來半個諾貝爾物理學獎。跟宇稱不守恆不一樣，CP 破壞的發生機率並不高，但是它仍是解答宇宙間物質反物質失衡的一大關鍵；它因此成了安德烈・薩哈羅夫的重子產生過程三大條件之一。
## 交互作用類型
弱交互作用共有兩種。第一種叫「載荷流交互作用」，因為負責傳遞它的粒子帶電荷（
W+
或
W−
），β 衰變就是由它所引起的。第二種叫「中性流交互作用」，因為負責傳遞它的粒子，Z 玻色子，是中性的（不帶電荷）。
### 載荷流交互作用
在其中一種載荷流交互作用中，一帶電荷的輕子（例如電子或緲子，電荷為−1）可以吸收一
W+
玻色子（電荷為 + 1），然後轉化成對應的微中子（電荷為 0），而微中子（電子、μ 及 τ）的類型（代）跟交互作用前的輕子一致，例如：
: $\mu ^{-}+W^{+}\to \nu _{\mu }$
同樣地，一下型夸克（電荷為−1⁄3）可以通過發射一
W−
玻色子，或吸收一
W+
玻色子，來轉化成一上型夸克（電荷為 +2⁄3）。更準確地，下型夸克變成了上型夸克的量子疊加態：也就是說，它有著轉化成三種上型夸克中任何一種的可能性，可能性的大小由 CKM 矩陣所描述。相反地，一上型夸克可以發射一
W+
玻色子，或吸收一
W−
玻色子，然後轉化成一下型夸克：
: $d\to u+W^{-}$
: $d+W^{+}\to u$
: $c\to s+W^{+}$
: $c+W^{-}\to s$
由於 W 玻色子很不穩定，所以它壽命很短，很快就發生衰變。例如：
: $W^{-}\to e^{-}+{\bar {\nu }}_{e}~$
: $W^{+}\to e^{+}+\nu _{e}~$
W 玻色子可以衰變成其他產物，可能性不一。
在中子所謂的 β 衰變中（見上圖），中子內的一下夸克，發射出一虛 | [
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弱作用力 | W−
玻色子，並因此轉化成一上夸克，中子亦因此轉化成質子。由於過程中的能量（即下夸克與上夸克間的質量差），
W−
只能轉化成一電子及一反電微中子。在夸克的層次，過程可由下式所述：
: $d\to u+e^{-}+{\bar {\nu }}_{e}~$
### 中性流交互作用
在中性流交互作用中，一夸克或一輕子（例如一電子或緲子）發射或吸收一中性 Z 玻色子。例如：
: $e^{-}\to e^{-}+Z^{0}$
跟 W 玻色子一樣，Z 玻色子也會迅速衰變，例如：
: $Z^{0}\to b+{\bar {b}}$
## 電弱理論
在粒子物理學的標準模型描述中，弱交互作用與電磁交互作用是同一種交互作用的不同方面，叫電弱交互作用，這套理論在 1968 年發表，開發者為謝爾登・格拉肖、阿卜杜勒・薩拉姆與史蒂文・溫伯格。他們的研究在 1979 年獲得了諾貝爾物理學獎的肯定。希格斯機制解釋了三種大質量玻色子（弱交互作用的三種載體）的存在，還有電磁交互作用的無質量光子。
根據電弱理論，在能量非常高的時候，宇宙共有四種無質量的規範玻色子場，它們跟光子類似，還有一個複向量希格斯場雙重態。然而在能量低的時候，規範對稱會出現自發破缺，變成電磁交互作用的 **U**(1) 對稱（其中一個希格斯場有了真空期望值）。雖然這種對稱破缺會產生三種無質量玻色子，但是它們會與三股光子類場融合，這樣希格斯機制會為它們帶來質量。這三股場就成為了弱交互作用的
W+
、
W−
及 Z 玻色子，而第四股規範場則繼續保持無質量，也就是電磁交互作用的光子。
雖然這套理論作出好幾個預測，包括在 Z 及 W 玻色子發現前預測到它們的質量，但是希格斯玻色子本身仍未被發現。歐洲核子研究組織轄下的大型強子對撞機，它其中一項主要任務，就是要生產出希格斯玻色子。
2013 年 3 月 14 日，歐洲核子研究組織發佈新聞稿，正式宣布探測到新的粒子，即希格斯玻色子。
## 參考資料
### 註釋
### 大眾書籍
* Oerter, R. The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Plume. 2006. ISBN 9780132366786. | [
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] |
弱作用力 | * Schumm, B.A. Deep Down Things: The Breathtaking Beauty of Particle Physics. Johns Hopkins University Press. 2004. ISBN 0-8018-7971-X.
### 科學書籍
* Bromley, D.A. Gauge Theory of Weak Interactions. Springer. 2000. ISBN 3-540-67672-4.
* Coughlan, G.D.; Dodd, J.E.; Gripaios, B.M. The Ideas of Particle Physics: An Introduction for Scientists 3rd. Cambridge University Press. 2006. ISBN 978-0521677752.
* Cottingham, W.N.; Greenwood, D.A. An introduction to nuclear physics 2. Cambridge University Press. 2001: 30 [2011-07-29]. ISBN9780521657334. （原始內容存檔於 2015-02-02）.
* Griffiths, D.J. Introduction to Elementary Particles. John Wiley & Sons. 1987. ISBN 0-471-60386-4.
* Kane, G.L. Modern Elementary Particle Physics. Perseus Books. 1987. ISBN 0-201-11749-5.
* Perkins, D.H. Introduction to High Energy Physics. Cambridge University Press. 2000. ISBN 0-521-62196-8. | [
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固態電子 | **固態電子元件**（英語：**Solid-state electronics**）是指那些完全使用固體電子材料、並利用束縛於其內電子或者其他載子導電的電路元件。這一概念經常用來與早期的技術如真空管等作比較。並且，「固態」一詞還特別地將電子 - 機械綜合設備，例如繼電器、開關和硬碟，和其他具有活動件的設備排除開外。雖然固態電子元件材料包括結晶體、多晶體、無定形體，並且包括導體、絕緣體和半導體，固態電子元件還是以結晶半導體為主。
通常的固態元件包括電晶體、微處理器晶片以及動態隨機存取存儲器（Dynamic random-access memory (DRAM)）等。動態隨機存取存儲器在計算機及其相關產品中應用廣泛，而且最近的固態硬碟有取代傳統機械旋轉式硬碟的趨勢。固態電子元件的行為涉及了大量的電磁學、量子力學過程。固態電子元件的概念在 1950 年代和 1960 年代開始變得流行，那段時間業界經歷了真空管到半導體二極體和之後的電晶體的技術轉變。後來，積體電路（integrated circuit (IC)）、發光二極體（light-emitting diode (LED)）以及液晶顯示器（liquid-crystal display (LCD)）等成為了固態電子設備研究的新成果。
## 概要
在固態電子元件中，電流被約束在固態物質之中，並設計特定的方式讓它關斷或者方法。可以通過兩種方式理解電流：一種是傳統的帶有負電荷電子，另一種是帶有正電荷的電洞（electron holes）。在有的半導體中，電流主要是流動的電子，而在另一類半導體中，電流主要是流動的電洞。上述兩種電流的組成成分都被成為「載子」。
對於數據存儲設備，固態元件比傳統的硬碟等更快、更可靠，但是在現階段通常更昂貴。雖然固態元件的價格不斷在下降，磁碟、磁帶以及光碟也不斷在改善其性能價格比，這一市場的競爭依然激烈。
第一個固態電子元件可以追溯到 1930 年代用在無線電接收器中的檢波器。一個外表類似鬍鬚的導線被放置並與固態材料（例如鍺）接觸，從而通過接觸結效應（contact junction effect）探測無線電訊號。不過，固態電子元件的蓬勃發展還是要到之後 1947 年電晶體的發明之後。日後的大部分科技產品都與它直接關係。 | [
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] |
固態電子 | 在 1960 年代和 1970 年代，用電晶體代替了笨重，易碎，耗能的真空管，這不僅在技術上而且在人們的生活習慣上都掀起了一場革命，這使得第一個真正的便攜式消費電子產品成為可能，例如電晶體收音機，盒式磁帶播放機，對講機對講機和石英手錶，以及第一批實用的計算機和手機。
固態電子設備的示例包括微處理器晶片，LED 燈，太陽能電池，相機中使用的電荷耦合元件（CCD）圖像傳感器和半導體雷射器。
## 相關條目
* 半導體
* PN 接面
* 固態硬碟
## 參考文獻
## 延伸閱讀
* Netbook Trends and Solid-State Technology Forecast (PDF). pricegrabber.com. : 7 [2009-01-28]. （原始內容 (PDF) 存檔於 2009-02-26）.
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热学 | **熱學**又稱**熱物理學**，是研究熱現象（即與溫度有關的物理現象）的科學。
熱學一般分為熱力學和統計力學兩部分，前者是建立在實驗基礎上的宏觀理論，後者是建立在量子力學和數理統計學上的微觀理論。
## 研究史
熱學是從 18 世紀末才發展起來，主要是研究功與熱之間的能量轉換。在此功會被定義為力與位移的內積；而熱則定義為在熱力系統邊界中，由溫度之差所造成的能量傳遞。
## 定律
* 熱力學第零定律
* 倘兩個熱力學系統均與第三個系統處於熱平衡狀態，此三個系統，也必互相處於熱平衡。
* 熱力學第一定律
* 也即能量不滅定律
* 熱力學第二定律
* 熱不可能從低溫狀態轉變到高溫狀態，而沒有外力影響。
* 熱力學第三定律
* 當一個系統趨近於絕對溫度零度時（即攝氏 - 273.15 度），系統的熵變化率乃零。
## 參見
* 熱力學
* 熱能 | [
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強子 | **強子**（英語：hadron）是粒子物理學中一種由夸克或反夸克通過強作用力綑綁在一起的複合粒子。
強子主要分為以下兩大類：
* 重子：由三個夸克或三個反夸克組成，自旋總是半整數；也就是說，它們是費米子。例如，組成原子核的質子和中子都是重子。
* 介子：由一個夸克和一個反夸克組成，自旋是整數；也就是說，它們是玻色子。例如，
π
介子可以是
π0
、
π+
、
π−
，每一種都分別帶有不同的電荷。
π0
介子是由上夸克與反上夸克組成，或由下夸克與反下夸克組成。
π+
介子是由上夸克與反下夸克組成。
π−
介子是由下夸克與反上夸克組成。
另外，還有一些比較稀有的奇異強子：
* Z(4430)：由 Belle 實驗發現的一種介子共振，質量為 4430 MeV。這個粒子內含的夸克為
c
c
d
u
，因此可以候選為由四個夸克組成的四夸克。2014 年，大型強子對撞機底夸克（Large Hadron Collider beauty，LHCb）實驗團隊發現與確認 Z (4430) 粒子存在。
* 由四個夸克與一個反夸克組成的五夸克可能會存在，但是至今為止，尚未有實驗證據確切地證實存在，不過 2015 年七月的新數據分析可能證實它的存在。
在所有強子之中，只有質子是穩定的，束縛於原子核內的中子也是穩定的，其它種類的強子在普通狀況都是不穩定的。自由中子會進行衰變，半衰期約為 880 秒。在實驗方面，強子物理學研究通常會將質子或像鉛一類的重元素原子核碰撞在一起，然後分析產生的粒子射叢。
## 詞源
在 1962 年國際高能物理大會的全體會議裏，列夫・奧肯發表演講提議創建術語「hadron」，
> 儘管這篇報告論述的是弱交互作用，我們會時常談到感受強交互作用的粒子。這些粒子不只給出很多科學問題，它們也造成了一個術語問題。重點是「感受強交互作用的粒子」是一個很笨拙的術語，它並沒有使自己形成一個形容詞。因此，例如，衰變為感受強交互作用的粒子被稱為「非輕子的行為」。這定義並不精確，因為「非輕子的行為」可能指稱的是「光子的行為」。在這篇報告裏，我將稱呼「感受強交互作用的粒子」為強子，其對應衰變為強子的行為（希臘語「ἁδρός」表示為「大」、「重」的意思，而「λεπτός」表示為「小」、「輕」的意思）。我希望這術語會在未來被證明使用很方便。 — 列夫・奧肯，1962 年
>
>
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強子 | 根據夸克模型，強子的性質主要是決定於其價夸克，例如，質子是由兩個上夸克與一個下夸克所組成；上夸克的電荷為 +2⁄3，下夸克的電荷為−1⁄3，所以，質子的電荷為 + 1。
每一個夸克都帶有色荷，這色荷可以為紅色，綠色或藍色，而強子的色荷必需為零，即強子的顏色必需為「無色」或「白色」，這是因為一種稱為夸克禁閉的物理現象。最簡單達成這目標的方法有兩種：
* 組成重子的三個夸克必須帶有不同的色荷。
* 組成介子的一個夸克與一個反夸克必須帶有相反的顏色，例如，假若夸克帶有紅色，則反夸克必須帶有反紅色。
更進一步分析，強子並不只是由兩個或三個夸克組成，這是因為強交互作用的能量，即傳遞強交互作用的膠子可能會擁有足夠能量 $E$ 來產生共振，而這共振是由帶質量夸克所組成的：
: $E>mc^{2}$ ；
其中， $m$ 是夸克的質量。
因此，數量比率為 1:1 的虛夸克與虛反夸克，形成了大多數帶質量粒子在強子內部。兩個或三個價夸克是額外多餘部分。由於虛夸克不是穩定的波包（量子），而是非規律的暫時性現象，辨識哪個夸克是實夸克，哪個夸克是虛夸克，這動作並不具有實際意義，只有額外多餘部分才可從外部觀察得到。
如同所有次原子粒子，每個強子都被分派一個量子數對應於龐加萊群的表示：JPC(m)；其中，J 是自旋量子數，P 是內秉宇稱，C 是正反共軛（電荷共軛），m 是粒子質量。注意到強子的大部分質量不是由價夸克所貢獻，而是因為質能等價，大部分質量是從強相對作用的能量所貢獻的。強子也帶有味量子數，例如，同位旋、奇異數、頂數、底數、粲數等等。所有夸克都帶有一種加性的守恆量子數，稱為重子數 B；夸克的重子數為 +1⁄3，反夸克的重子數為−1⁄3，因此，重子的重子數為 1，介子的重子數為 0。
強子的激發態稱為「共振」；每一個基態強子都可能對應於幾個激發態。在粒子物理實驗裏，可能會觀察到幾百個共振；通過強相對作用，它們很快地會衰變，大約在 10−24 秒內。
在某些相態裏，強子可能會消逝無蹤，例如，在非常高溫與高壓狀況，除非有足夠多風味的夸克，量子色動力學的理論預測，夸克與膠子會逃出強子的禁閉，因為能量越高，強相對作用的耦合越弱，這性質稱為漸近自由，已被實驗證實在 1 GeV 與 1 TeV 能量區間成立。
## 重子
重子是由三個夸克組成，是自旋為 1⁄2 費米子。每一個夸克的重子數為 1⁄3，所以，重子的重子數為 1。最為人知的重子是質子與中子。 | [
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強子 | 物理學者假設，除了三個夸克以外，還擁有一對夸克與反夸克的奇異重子存在。這種重子稱為五夸克，處於五夸克態。2000 年代曾提出幾個候選五夸克，但是更深入研究發現它們並不存在。這結果不排除未來可能找到五夸克的可能性，只是排除了這些候選五夸克。
每一種重子都有其對應的反重子，假設將重子裏的每一個夸克用其反夸克取代，則可得到這反重子。例如，質子是由兩個上夸克與一個下夸克組成，它的反粒子是反質子，是由兩個反上夸克與一個反下夸克組成。
## 介子
介子是由夸克 - 反夸克對組成的強子。介子是自旋為整數的玻色子，擁有偶數個夸克。介子的重子數為零。在粒子物理學實驗裏常見的介子有
π
介子、
K
介子等等。在原子核裏，
K
介子通過核力也扮演了捆綁核子的角色。
原則而言，幾個夸克 - 反夸克對組成的介子可能存在。由兩對組成的假想介子稱為四夸克，處於四夸克態。2000 年代曾提出幾個候選四夸克，但是它們是否存在仍極具爭議。另外，還有一些假想的奇異介子是在夸克模型的分類以外，這包括膠球與混介子（被激發態膠子綑綁組成的介子）
## 參閱
* 大型強子對撞機
* 粒子列表
* 強子化
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张量场 | 在數學，物理和工程上，**張量場**（tensor field）是一個的非常一般化的幾何變數的概念。它被用在微分幾何和流形的理論中，在代數幾何中，在廣義相對論中，在材料的應力和應變的分析中，和在物理科學和工程的無數應用中。它是向量場和純量場的想法的一般化，而向量場可以視為「從點到點變化的向量」。
物理學中場的一種。假如一個空間中的每一點的屬性都可以以一個張量來代表的話，那麼這個場就是一個張量場。最常見的張量場有廣義相對論的應力能張量場（Stress-energy tensor field）。
必須注意到很多不嚴格的稱為「張量」的數學結構實際上是「張量場」，定義在流形上的場在流形的每點定義一個張量。
## 幾何式介紹
向量場的幾何直覺就是在某個區域的每一點指定一個帶有長度和方向的「箭頭」（也就是在這區域的每一點指定了一個向量）。彎曲空間的向量場的例子有在地球表面的水平風速的氣象圖。
張量場的一般想法綜合更豐富的幾何訊息 — 例如在度量張量的情況就是點到點變化的橢球 — 以及我們不需要把概念建立在曲面的特定映射方式上的思想。它應該獨立於緯度和經度存在，或任何我們用以引入數字坐標的特定的 ' 繪圖映射 '。
## 向量叢解釋
當代的張量場思想的數學表達把它分為兩步的概念。
首先有向量叢的想法，實際上就是「依賴於參數的向量空間」— 參數就是一個流形。例如：依角度變化的一維向量空間可以看起來像默比烏斯帶也可以像圓柱。給定 _M_ 上的向量叢 _V_，相應的場的概念稱為叢的一個「截面」：隨著 m 在 _M_ 上改變，在 _m_ 點的向量空間 _V_m 上的向量 _vm_ 的一個選擇。
因為張量積概念和任何基的選擇無關，在 _M_ 上的兩個向量叢的乘積是常規做法。從切線束（切空間的叢）開始，在張量的無分量處理中的整個機制可以一種常規的方式照搬歸來 — , 而且也是坐標無關的，就像在簡介中提到的一樣。
最後，我們給出**張量場**的一個定義，也就是作為某個張量叢的一個截面。因為所有東西都是用內在的方式去做的。
## 應用
例如，曲率張量用在微分幾何中而應力能張量在物理和工程上很重要。這兩個都和愛因斯坦的廣義相對論理論相關。工程上，很多背景流形經常是歐幾里得三維空間張量場賦予流形的任意給定點一個空間
: $V\otimes ...\otimes V\otimes V^{*}\otimes ...\otimes V^{*}$
中的張量。 | [
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张量场 | 其中 _V_ 是切空間而 _V_\* 是餘切空間，參看切線束和餘切叢。
## 記號
張量場的記號和張量空間的極相近，有時會混淆。所以，切線束 _TM_=_T_（_M_）有時寫作
: $T_{0}^{1}(M)=T(M)=TM$
以強調切線束是流形 M 的（1,0）型張量場的空間。不要和看起來非常相近的記號
: $T_{0}^{1}(V)$
搞混。在後一種情況，我們有一個張量空間，而在前一種情況我們有對流形每點有定義的張量空間。
手寫體字母有時用於表示光滑的張量場。所以
: ${\mathcal {T}}_{n}^{m}(M)$
是 _M_ 上的無限可微分張量場的（_m_,_n_）型張量叢的截面集。一個張量場是該集的一個元素。
## 張量微積分
在理論物理和其他領域，用張量場表達的微分方程式提供了表達本質上是幾何的（由張量的本質保證）並在傳統上和微積分相關的關係的一種極為通用的方式。表述這樣的方程式需要一種新的概念，稱為協變導數。這個概念用於表述張量場沿著一個向量場的變化。最初的絕對微積分後來被稱為張量微積分，導致了聯絡這個幾何概念被分離出來。
## 通過一個線叢的扭轉
張量場的一個推廣是加入一個額外的 _M_ 上的線叢 _L_。若 _W_ 是 _V_ 和 _L_ 的張量積叢，則 _W_ 是一個同樣維度的向量空間叢。這使得我們能夠定義**張量密度**，一個 ' 扭轉 ' 類型的張量場。張量密度是當 _L_ 是「流形的密度」叢（也就是餘切叢的行列式叢）時的特殊情況（嚴格來講，需要使用轉移函數的絕對值 — 這對可定向流形來說沒有什麼區別）。
密度叢 _L_ 的一個特點（再次假設可定向）是，_L_s 對於一個實數 _s_ 是可以定義的；這可以從取嚴格正值的轉換函數得到。這意味著，例如，我們可以取「半密度」，當 _s_ = ½。一般來講，我們可以取 _W_ 的截面，_V_ 和 _L_s 的張量積，並考慮比重 _s_ 的**張量密度場**（tensor density fields）。
半密度用於在流形上定義積分算子和幾何量子化（geometric quantization）這樣的領域。
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张量场 | 當 _M_ 是一個歐幾里得空間是，而所有的場都在用 _M_ 的向量平移下不變時，我們回到了張量場和位於原點的一個張量同義的情況。這沒有什麼害處，還經常在應用中採用。用在張量密度上，這確實有區別。密度叢不能嚴格的定義在一點；所以現在張量的數學處理的一個局限就是張量密度要用一種迂迴的方式來定義。
## 閉餘鍵和連鎖律
作為張量概念的高級解釋，可以把連鎖律在多變數的情況進行解釋，作為在坐標轉換時的應用，也作為張量場中的張量本身的一致性的要求。
抽象的講，我們可以把連鎖律作為一個 1 - 閉餘鍵。這給了用內在的方式定義切線束所需要的一致性。其他張量的向量叢有相應的閉餘鍵，可以從把張量構造的泛函屬性用到連鎖律本身得到；這就是為什麼它們也是內在的概念。
通常所說的處理張量的經典方法試圖對此反向解讀 — 所以是一種啟發式的，後驗（_post hoc_）的方法而非真正基本的方法。隱含的定義張量如何在坐標轉換下變化是閉餘鍵所表達的那種自洽。張量密度的構造是一個閉餘鍵級別上的扭轉。幾何學家從不懷疑張量「量」的幾何本質；這種下降論證抽象的證明了整個理論的正確性。
## 參看
* jet 叢
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未解決的physics問題 | 有一些重要但**尚未解決的物理問題**。其中包括理論性的，即現時理論未能夠給予觀測到的物理現象或實驗結果令人滿意的解釋；還有實驗性的，即能夠周密測試某先進理論或深入研究某物理現象的實驗，不過現時現地很難建造或完成。
## 純理論方面的問題
這裏列出的基礎理論問題或理論構想缺乏實驗證明。在這些問題之間，可能有強烈的相互關聯。例如，額外維度或超對稱可能有辦法解釋級列問題。物理學者認為，完整無瑕的量子重力理論應該能夠解釋大多數列出的問題（除了穩定島問題以外）。
### 量子重力、物理宇宙學、廣義相對論
**真空災變**
: 從航海家探測衛星測量到的數據所推斷出的真空能量密度上限為 1014 GeV/m3，而從量子場論估算出的零點能量密度卻為 10121 GeV/m3，兩個數值竟然相差了 107 個數量級。物理史上從未見到這麼大的差距，很多物理學者認為這是當今物理理論的重大瑕疵。
**量子重力**
: 如何整合量子力學和廣義相對論成為完整一致的理論（或許是一種嶄新的量子場論）？時空的基本本質是否是連續的，還是離散的？這完整一致的理論是否涉及由一種假定的重力子所傳遞的作用力，還是從時空離散結構衍生的產物（迴圈量子重力理論的理論）？在超小尺度、超大尺度或其它極端案例，廣義相對論的預測與量子重力理論有甚麼差異？
**黑洞、黑洞資訊悖論、黑洞輻射**
: 理論預期的黑洞熱輻射現象是否屬實？此種輻射是否帶有關於黑洞內部結構的資訊，如同規範 - 重力二元性所建議，還是不然，如同史蒂芬・霍金的原本計算？若為不然，則黑洞能夠蒸發乾淨，注意到量子力學並沒有給出摧毀資訊的機制，那麼，儲存於黑洞的資訊又會怎麼樣？是否黑洞蒸發到某一程度就會自動停止，只剩下殘餘黑洞？根據無毛定理，黑洞只有三種屬性：質量、電荷量、角動量；除此以外，沒有任何內部結構。這定理是否正確？為何尚未找出探勘黑洞內部的方法？
**額外維度**
: 大自然是否擁有多於四個時空維度。假若答案為「是」，則到底有多少時空維度？維度是不是宇宙的基本屬性，還是其它物理定律的合理結果？物理實驗能否觀測到更高維度的證據？
**宇宙暴脹**
: 宇宙暴脹理論是否正確？若為正確，這段時期所發生事件的細節為何？這造成暴脹的假定暴脹場到底為何？假若暴脹在過去某一時間曾經發生，有否有可能藉著量子力學漲落的暴脹機制，繼續自我維持暴脹，因此在宇宙某超遠處，這暴脹仍舊正在進行中？
**多重宇宙** | [
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未解決的physics問題 | : 是否有足夠的物理理論基礎來支持期待其它宇宙的存在，雖然這些宇宙從根本而言是無法觀測到的？例如，量子力學的多世界是否存在？在這些宇宙裏，在高能量狀況，由於使用別種方式破壞物理力的明顯對稱，所造成的物理定律是否會迥然不同。使用人擇原理來消解全局宇宙困境是否正確？
**宇宙審查假說**
: 黑洞內部有一個奇異點。通常在這奇異點的外圍有一層事件視界，速度最快的光波也無法逃離到事件視界之外。裸奇異點是缺乏事件視界的奇異點。由於沒有事件視界隔離，物理學者可以觀測到裸奇異點的物理行為。但是，至今為止，物理學者尚未觀測到裸奇異點的蛛絲馬跡。物理學者懷疑，從實際物理的初始條件是否能形成裸奇異點？羅傑・彭羅斯提出的宇宙審查假說表明，這是不可能的事。但是，物理學者還不能證明這假設的任何版本為正確無誤。
**時序保護猜想**
: 在廣義相對論的愛因斯坦場方程式的某些解答中，會出現有封閉類時曲線，即粒子移動於時空的世界線為封閉迴路，從初始點移動經過一段路程後，又會返回初始點。封閉類時曲線意味著一種時間旅行，能夠返回過去的時間旅行。史蒂芬・霍金的時序保護猜想表明，強烈地不允許任何除了微觀尺度以外的時間旅行。結合廣義相對論與量子力學在一起的量子重力理論，能否排除封閉類時曲線的可能性？
**時間箭頭**
: 物理學在微觀的層次幾乎完全是時間對稱的。這意味著，假設將時間流逝的方向倒轉，則原本物理定律仍然會保持為正確。但是在巨觀層次，時間存在著明顯的流逝方向。時間箭頭就是用於描述這種不對稱的現象。由於時間演進和時間反演而產生的不同物理現象，它們給出的關於時間屬性的資料為何？
: 根據 CPT 對稱理論，從 CP 破壞的證實可以立即斷言時間是無法反演的。因此，時間對稱性不成立，時間箭頭可以建立起來。但是，這方法並不是直接地，而是間接地證實時間對稱性不成立。測量基本粒子的內稟電偶極矩實驗可以更強烈、更直接地證實這性質。假設基本粒子擁有內稟電偶極矩，則宇稱對稱性和時間對稱性都會被破壞。更詳盡細節，請查閱基本粒子的電偶極矩。對於各種粒子的電偶極矩，現在最準確的實驗測值為
: 中子
: $|p_{n}|<2.9\times 10^{-26}\ e\ \mathrm {cm} \ (90\%C.L.)$ 、
: : 電子
: $|p_{e}|<1.6\times 10^{-27}\ e\ \mathrm {cm} \ (90\%C.L.)$ 、
: : 水銀 | [
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] |
未解決的physics問題 | : $|p_{Hg}|<3.1\times 10^{-29}\ e\ \mathrm {cm} \ (95\%C.L.)$ 。
: 另外一個衍生的問題是，為什麼 CP 破壞只有在某些弱交互作用的衰變中才能觀測得到，例如 K 介子衰變，而在其它交互作用都觀測不到？
**定域性原理與非定域現象**
: 定域性原理表明，物體只會被其緊鄰周遭環境事物影響。1935 年，阿爾伯特・愛因斯坦等發表 EPR 弔詭，認為量子力學的基礎理論，因為違背了定域性原理，可能不完備。三十年之後，約翰・貝爾提出反駁，主張 [定域隱變數理論不能複製量子力學的所有預測。在量子力學裏，是否會出現非定域現象？假設非定域現象存在，這是否只局限於貝爾不等式被違背所顯露出的量子糾纏；資訊、能量或物質能否能以非定域方式的傳播？在哪種狀況可以觀測到非定域現象？非定域現象的存在與否，對於時空的基本結構，有甚麼含意？非定域現象與量子糾纏有甚麼關聯？如何藉著非定域現象來說明量子力學基礎性質的正確詮釋？
**宇宙的終極命運**
: 根據天文觀測和宇宙學理論，可以對可觀測宇宙未來的演化作出預言。宇宙最終是否走向熱寂、大崩墜、大撕裂、大反彈，還是按照多重宇宙論的論述，可能存在很多各種各樣的宇宙，新的宇宙可能正在誕生，同時老舊的宇宙可能正在湮滅，但整個平行宇宙永遠不會完全終結？
### 高能物理學／粒子物理學
**希格斯機制**
: 希格斯玻色子的分支比是否符合標準模型？是否只有一種希格斯玻色子？
**級列問題**
: 為什麼重力是那麼的微弱？只有當質量在普朗克尺度時，大約為 1019 GeV，超大於電弱尺度，246 GeV，電弱理論描述的物理行為所涉及的能量），重力才會顯得強勁。為什麼這尺度的相差會有如天壤之別？是甚麼物理過程使得電弱尺度的物理量，例如希格斯粒子的質量，無法獲得普朗克尺度數量級的量子修正？請問這是因為超對稱、額外維度，還是人擇的精細調節？
**磁單極子**
: 在最初宇宙、高能量的時期，粒子有否帶有磁荷？若有，則為何現在那麼難偵測到它們？現在有沒有任何磁單極子仍舊存在？（保羅・狄拉克指出，某種磁單極子的存在可以解釋電荷量子化）。
**質子衰變與大統一理論** | [
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未解決的physics問題 | : 怎樣能夠將量子場論的三種不同的基本交互作用，即強交互作用、弱交互作用和電磁交互作用，統一成為單獨一種交互作用？至今為止，一些常見的主流大統一模型為 SO (10) 模型、喬吉 - 格拉肖模型等等。由於這些模型預測的新粒子的質量為大統一尺度數量級，大大地超過碰撞實驗的可能範圍，所以，物理學者無法做實驗直接觀測到這些新粒子。因此，物理學者必需使用間接方法，例如，質子衰變實驗、基本粒子電偶極矩實驗、微中子屬性實驗、磁單極子偵測實驗等等。注意到質子為質量最輕的重子，質子是否為絕對的穩定？倘若不是，質子的半衰期為何？日本的超級神岡偵測器並沒有確切地偵測到任何質子衰變事件。從實驗得到的數據，質子的壽命被設定為超過 1033 年。
**超對稱**
: 時空超對稱是否實現於大自然？假若是，超對稱破壞的機制為何？超對稱是否能夠穩定電弱尺度，避免大幅度量子修正？最輕的超對稱粒子是否為暗物質的組成成分之一？
**第四代夸克與輕子**
: 由於共同提出卡比博 - 小林 - 益川矩陣來解釋 CP 破壞的現象，並且給出了標準模型會允許多達三代夸克與輕子存在的原因，小林誠與益川敏英因此榮獲 2008 年諾貝爾物理學獎。這理論並沒有限制最多只能有三代。那麼，有否可能找到第四代夸克或輕子？是否能夠構想出解釋不同代粒子之間質量差異的理論，一種關於湯川耦合的理論？
**反物質**
: 在宇宙中，為什麼偵測實驗結果顯示，物質比反物質多很多？大爆炸應該製造出同樣數量的粒子與反粒子，而粒子會和反粒子湮滅產生光子。因此宇宙應該充滿了光子，而不會有很多物質存在。但是，宇宙現在的狀況並不是這樣。在大霹靂發生之後，一定有某些物理定律不平等地作用於物質與反物質。請問這些物理定律為何？在最初宇宙是否有某些作用力存在，但是後來隨著宇宙演化，這些作用力已消失無蹤？
### 核子物理學
**量子色動力學**
: 強交互作用物質有哪些相態？在宇宙中，這些相態的角色為何？核子的內部結構為何？量子色動力學對於強交互作用物質的屬性方面的預測為何？哪種機制主掌了夸克和膠子的變遷為 π 介子與核子？是甚麼機製造成了量子色動力學的重要特色：夸克禁閉與漸近自由？怎樣將量子色動力學與廣義相對論合併為一個完整理論？
**核子天文物理學**
: 中子星和稠密核物質的物理性質為何？描述宇宙中各種元素的核合成過程？驅動恆星與星際爆炸的核子反應為何？
**原子核**
: 核力如何將質子與中子結合為穩定原子核？
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] |
未解決的physics問題 | : 有些化學元素的原子核，其質子和中子的數目恰巧為幻數數目，核物理學家推測這些化學元素特別穩定。這理論稱為穩定島理論。鑑於這理論，最沉重的穩定或介穩定原子核為何？
### 其它
**量子混沌**
: 對應原理表明，古典力學是量子力學的古典極限。量子混沌理論試圖在量子力學與古典力學之間建立一座橋梁。怎樣以量子力學來表述古典的混沌動力系統？量子力學與古典混沌之間的關係為何？
**量子力學的對應極限**
: 量子理論的描述怎樣成為做實驗所觀查到的大自然實在，這包括量子態疊加、波函數塌縮、量子去相干等等？換句話說，這是一種測量問題，造成波函數塌縮為確定態的量子測量所倚賴的機制為何？
**物理資訊**
: 除了黑洞或波函數塌縮以外，還有哪些物理現象，不可挽回地湮滅了關於其先前所處狀態的資訊？
**萬有理論**
: 又稱為「終極理論」，萬有理論試圖解釋與聯結所有已知的物理現象，並且預測在原則上可行的任何實驗的結果。但是，構築這理論所遇到最困難的問題是，怎樣將廣義相對論與量子力學統一為單一理論？
**基礎物理常數**
: 能夠解釋所有基礎物理常數的理論為何？基礎物理常數是否會隨著時間的演進而改變？
**規範場論**
: 於 2000 年，克雷數學研究所發表七大千禧年大獎難題，其中一道題目為楊 - 米爾斯存在性與質量間隙。這是理論物理中規範場論的一道基礎問題。楊 - 米爾斯理論是一種規範場論。獲勝者必須嚴格證明楊－米爾斯場論存在（即需符合構造性量子場論的標準），亦要證明質量間隙，即此理論所預測質量最輕的粒子，其質量為正值。
## 缺乏清楚科學解釋的經驗現象
### 物理宇宙學
**宇宙的存在**
: 形成宇宙或多重宇宙的物質、能量、時空、基本作用力，它們的物質源頭為何？能否設計出可行的實驗來證實多重宇宙存在。
**重子不對稱性**
: 為什麼在可觀測宇宙中，重子的數量比反重子多很多？
**宇宙學常數問題** | [
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] |
未解決的physics問題 | : 根據廣義相對論，宇宙真空裏蘊藏的能量會產生引力場，真空能量密度 $\rho _{vac}$ 與宇宙學常數 $\Lambda $ 之間的關係為 $\rho _{vac}c^{2}=\Lambda c^{4}/8\pi G$ 。怎樣計算真空能量密度是物理學尚未解決的一個大問題。最簡單算法總和所有已知量子場貢獻出的零點能，但這理論結果超過天文觀測值 120 個數量級，被驚歎為「物理史上最差勁的理論預測」！為什麼從真空能量密度計算出的宇宙學常數，會與天文觀測值相差這麼大？這問題稱為宇宙學常數問題。到底是甚麼物理機制抵銷這超大數值？解決這問題可能要用到量子引力理論。
**暗物質**
: 無法用電磁輻射偵測，而是從作用於可見物質與背景輻射的重力效應連帶推斷出來的物質，稱為暗物質。物理學者尚不清楚甚麼是暗物質的基本成分？是否與超對稱有關？歸因於暗物質的天文現象，實際上是否是重力的延伸？
**暗能量**
: 暗能量是一種充溢於整個空間的能量的假定形式。暗能量傾向於增加宇宙膨脹速度。最近完成的關於超過 20 萬座星系的調查，似乎確定了暗能量的存在。但是，物理學者仍舊無法精確地描述與解釋暗能量的物理性質。暗能量主要有兩種模型：宇宙學常數模型與第五元素模型。每一種模型都有其強點與弱點，尚未有任何實驗結果令人信服地顯示哪一種模型為正確模型，也可能都不夠正確。
**宇宙巧合問題**
: 為什麼恰巧就在這時候，宇宙的暗能量密度與物質密度幾乎等值？這問題稱為「宇宙巧合問題」。
: 如右圖所示，物質密度 $\rho _{m}$ 與宇宙標度因子 $a$ 的三次方成反比：
: $\rho _{m}\approx 1/a^{3}$ ，
: 而暗能量密度 $\rho _{*}$ 與宇宙標度因子的關係式為
: $\rho _{*}\approx 1/a^{k}$ ;
: 其中， $k$ 是依暗能量的本質而定的常數，必需小於 3。
: 假設暗能量是宇宙學常數或真空零點能，則 $k=0$ ，暗能量密度 $\rho _{*}$ 為常數，那麼，這種萬年不遇的巧合實在令人費解。難道暗能量密度是某種純量場，或許暗能量與物質會發生某種耦合，從而造成暗能量密度與物質密度幾乎等值？
**熵 (時間箭頭)**
: 宇宙最初是處於一個高度有序的狀態，一個低熵狀態。為甚麼會出現這麼高度有序的狀態，從而造成過去與未來的區別，以及熱力學第二定律？
**宇宙視界問題** | [
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未解決的physics問題 | : 為什麼大霹靂理論對於夜晚天空的各向異性的預測值似乎大於觀測數據，而遙遠的宇宙卻顯得那麼均勻？宇宙暴脹理論已廣泛地被天文學者接受為解答，但仍舊可能有其它解答，例如，光速可變理論。
**宇宙微波背景輻射的各向異性的黃道定向**
: 微波天空在距離一百三十億光年以外的某些大型特徵，似乎跟太陽系的運動與定向有所關聯。這是否為系統誤差、觀測結果被定域效應汙染，還是哥白尼原則未經解釋的破壞？
**宇宙的形狀**
: 宇宙共動空間的 3 - 流形，又稱為「宇宙的形狀」，是甚麼樣子？現時，天文學者仍舊不清楚宇宙的曲率與拓撲，天文學者只知道，以可觀測尺度衡量，曲率接近於零。宇宙暴脹假設建議，宇宙的形狀可能無法測量，但是，於 2003 年，尚皮耶・盧敏內等與其他研究團隊建議，宇宙的形狀可能為龐加萊同調球面。經過威爾金森微波各向異性探測器三年觀測得到的數據確認了這模型的一些預測，但是，這模型的正確性尚未得到廣泛支持。
### 高能物理學／粒子物理學
**電弱對稱破缺**
: 到底是甚麼機制打破了電弱規範對稱，從而賦予 W 及 Z 玻色子質量？是標準模型的簡單希格斯機制嗎，還是根據藝彩理論的點子，是大自然用一種類似強作用力的新規範作用力來破壞了電弱規範對稱？物理學者希望能夠用大型強子對撞機做實驗核對藝彩理論。
**微中子質量**
: 究竟是甚麼機制賦予微中子質量？任何粒子，假若其反粒子就是自己，則稱此粒子為馬約拉那粒子。微中子是否為馬約拉那粒子？如果微中子滿足馬約拉納方程式，我們便有機會觀察到不放出微中子的雙重 β 衰變。有沒有可能會是因為微中子的特殊屬性，從而使得微中子無法與一個正常粒子發生碰撞而互相湮滅？目前有許多實驗試圖去驗證微中子是否為馬約拉納粒子。
**微中子超光速異常**
: OPERA (實驗)，是一個檢驗微中子振盪現象的實驗。於 2011 年 9 月，歐洲核子研究組織（CERN）與 OPERA 共同宣布，從它們合作測量到的微中子飛行時間數據，它們發現緲微中子以超光速運動。請問這是做錯實驗獲得的結果，還是狹義相對論的確切瑕疵？2012 年 2 月 22 日，科學新聞網頁雜誌 Science Insider 報告，從全球定位系統接收器到電腦之間的光纖纜線，由於與電腦的積體電路卡連接不良，造成了 60 奈秒延遲。將連接維修後，這問題不再發生。這實驗失誤似乎可以解釋微中子的超光速異常。但是，仍舊必需做實驗拿到更多數據來檢驗這假說。 | [
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未解決的physics問題 | **基本粒子的慣性質量與重力質量比率**
: 根據廣義相對論的等效原理，對於所有基本粒子，慣性質量與重力質量比率為 1 。但是，對於很多粒子，並沒有任何實驗確認這論點。特別而言，物理學者很想知道，具有某巨觀質量的反物質，其重量為何？
**質子自旋危機**
: 質子是自旋為 1/2 的費米子，但是，於 1988 年，歐洲緲子共同研究團隊發現，質子的三個主要價夸克只貢獻出總自旋的 20-30%。自旋的其它部分是甚麼機制貢獻出的，是由膠子，還是由持續不斷地生成與湮滅中的海夸克對偶所貢獻出的？
**質子尺寸之謎**
: 質子真實的電荷半徑為何？
**量子色動力學的非微擾方法**
: 在涉及到描述原子核的能量尺度範圍，量子色動力學的方程式無法解析，雖然格點量子色動力學貌似可以給出在這極限的解答。那麼， 量子色動力學怎樣描述核子與核子內部組構的物理現象呢？
**夸克禁閉**
: 為什麼所有實驗，都只能觀測到從夸克或膠子建成的粒子，像介子或重子，而無法觀測到自由存在的夸克或膠子？這現象是怎樣從量子色動力學裏面出現？
**強 CP 問題與軸子**
: 為什麼強交互作用對於宇稱與電荷共軛 charge conjugation 運算具有不變性？1977 年提出的皮塞 - 奎恩理論（Peccei–Quinn theory）是否為這問題的正確解答？
**假想的粒子**
: 超對稱理論與其它廣為人知的理論預測了很多假想粒子，其中，哪些假想粒子真正存在於大自然？
### 天文學、天文物理學
**吸積盤噴流**
: 為什麼環繞著某些像活躍星系核一類的星體的吸積盤，會沿著其旋轉軸噴出相對論性噴流？天文學者認為這些噴流有很多用途，從除去正在形成的恆星的角動量，到將活躍星系核內部重新離子化。但是，天文學者仍舊不清楚吸積盤噴流的初始由來。
**準週期性震盪**
: 有些像白矮星、中子星、黑洞一類的緻密星，其吸積盤的內部邊緣在某頻率附近會忽隱忽現地發射出 X 射線，這現象稱為「準週期性震盪」。可以從星體的功率譜的峰點找到震盪痕跡。物理學者不知道為什麼會出現準週期性震盪？為什麼這些震盪的頻率與中心物體的質量成正比？有時候，在功率譜會出現多個峰點。為甚麼對於不同的星體，這些峰點的頻率比率會不一樣。
**日冕加熱問題** | [
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未解決的physics問題 | : 為什麼太陽的日冕（大氣層）溫度（1 至 3 百萬 K）超高於表面溫度（6000K）？對於這問題，過去幾十年，物理學者提出了很多理論，但只有兩個理論可能最為正確：波動加熱理論與 en 磁重聯理論 magnetic reconnection theory。磁重聯理論的缺陷是，為什麼觀測到的磁重聯效應比較理論預測快過很多數量級？美國國家航空暨太空總署的太陽偵測加級器任務預定於 2015 年啟航，準備勘測太陽的日冕加熱狀況。
**瀰漫星際帶**
: 是甚麼物質造成了在天文線譜裏觀測到的多條星際吸收線？請問這些物質是否為分子物質？假若是分子物質，到底是哪些分子物質，它們是怎樣形成的？
**伽瑪射線爆發**
: 從遙遠的星系突然發生的超大能量爆炸，其所伴隨的快閃伽瑪射線，稱為「伽瑪射線爆發」，是宇宙最明亮的電磁事件，通常持續時間在 0.01-1000 秒。物理學者不清楚為甚麼會發生這種短時段、高強度的猝爆？於 2008 年，美國國家航空暨太空總署發射了費米伽瑪射線空間望遠鏡，該衛星搭載的伽瑪射線爆發監視系統（Gamma-ray Burst Monitor, GBM）可用來研究伽瑪射線爆發。
**質量 - 速度色散關係**
: 星系核球內的恆星的速度色散 $\sigma $ 與位於星系中心的超大質量黑洞的質量 $M$ 之間的經驗關係，稱為「質量 - 速度色散關係」：
: $M=\sigma ^{\alpha }$ ；
: 其中， $\alpha $ 是常數，大約為 $4.2-5.$ 。
: 質量 - 速度色散關係可以用來精確地計算超大質量黑洞的質量。但是，物理學者不清楚促成這關係的物理原因為何？
**觀測異常：**
: 飛掠異常: 為什麼衛星飛掠過地球後的能量會與理論預測不同？這異常最先發現於 1990 年伽利略號探測器的飛掠過地球。通過仔細檢查深空網路紀錄的都卜勒數據，天文學者意外地發現 66mHz 頻移，對應於速度在近地點增加了 3.92mm/s。天文學者尚未能夠給出滿意答案。
: 星系自轉問題
: 觀測到的星球繞著星系中心轉動的速度與應用牛頓力學預測的理論速度，兩者為何不一致？暗物質和暗物質暈是否是造成這問題的主要因素？
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未解決的physics問題 | : 地球附近根本沒有超高能量宇宙射線源，為何有一些宇宙射線會擁有不可能般高的能量？GZK 極限是源自遠處的宇宙射線所擁有能量的理論上限。超過 GZK 極限的宇宙射線會與宇宙微波背景輻射耦合，製造 π 介子。這程序會重覆發生，直到宇宙射線的能量低於 GZK 極限為止。所以，應該不可能觀測到任何源自遠處的超高能量宇宙射線。但是，這些似從遠處發射出的超高能量宇宙射線，並沒有遵守 GZK 極限的規則，與宇宙微波背景輻射發生反應，而奇蹟般地存活移動到地表附近，才被觀測到，請問原因為何？
**土星自轉週期**
: 航海家 1 號與航海家 2 號分別於 1981 年及 1982 年飛越土星時測量得到無線電訊號週期為 10 h 39 min。卡西尼太空飛行器在 2004 年接近土星時，發現無線電的週期增加至 10 h 45 m。造成變化的原因仍不清楚，但這種變化被認為是由於無線電的來源可能移動到土星內部不同的緯度位置，從而改變了自轉週期，而不是出自於土星本身自轉週期上的變化。目前還沒有方法可以直接測量土星核心的自轉速率。
**磁星**
: 到底是甚麼機制形成磁星的磁場？
### 凝聚態物理學
**非晶質物質**
: 液態或固態物質是怎樣玻璃化轉變至玻璃態物質？是甚麼物理過程給出了玻璃的一般物理性質？
**低溫電子發射**
: 在非常低溫、無光狀況，為什麼光電倍增管會自發性地發射電子，而且，隨著溫度降低，發射率會增加？
**高溫超導**
: 某些物質能夠在高於 50 K 以上的溫度仍舊具有超導電性。但是，物理學者不清楚促成這現象的機制為何。
**亂流**
: 能否設計出一個理論模型來解釋紊流的物理行為和內部結構？在甚麼條件下，納維 - 斯托克斯方程式有平滑解？這是克雷數學研究所於 2000 年設立的千禧年大獎難題中的一大難題。
## 近期已找到解答的問題
**希格斯玻色子（2013 年）**
: 希格斯玻色子是標準模型預言的一種自旋為零的玻色子，可以解釋宇宙萬物的質量。歐洲核子研究組織於 2013 年 3 月 14 日正式宣布發現此粒子。它是標準模型中最後一種被發現的粒子。
**先鋒號異常（2012 年）** | [
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] |
未解決的physics問題 | : 先鋒 10 號與先鋒 11 號是美國國家航空暨太空總署分別於 1972 年與 1973 年發射的兩艘太空飛行器，現在已逃離太陽系。在距離太陽大約 20 天文單位之後，觀測到的兩艘太空飛行器的加速度與預測發生差異，大約為 (8.74 ± 1.33)× 10−10 m/s2。物理學者現在認為這是因為先前未將熱反衝力（thermal recoil force）的效應納入計算
**長時間伽瑪射線爆發（2003 年）**
: 長時間伽瑪射線爆發分類為時間久過於 2 秒鐘的伽瑪射線爆發，這種爆發與大質量星體的死亡有關，此種星體的死亡過程類似於超新星事件，常稱為極超新星。
**太陽微中子問題（2002 年）**
: 這問題指的是測量到的太陽微中子通過地球的數量與理論計算有所差異。從對於微中子物理的研究結果，物理學者修改了粒子物理學的標準模型，提出微中子振盪的概念，要求微中子具有質量，可以在電微中子、緲微中子和濤微中子，這三種微中子之間相互變換。由於這些嶄新理論的提出，這問題已得解答。
**年齡危機（1990 年代）**
: 大約在 1990 年代中期，物理學者估計宇宙的年齡比銀河系最早的恆星還要年輕 30 至 80 億年。這意味著哈伯常數的估計不正確，或大霹靂理論不正確，或是需要宇宙學常數一類的暗能量。後來，對於恆星距離更精準的估計，將恆星年齡減少了好幾十億年，對於宇宙正在加速度擴張這論據也終於獲得天文實驗證實。由於這些進展，年齡危機不再成立。
**類星體（1980 年代）**
: 這是一種亮度特高、非常遙遠、紅移值特大的星體。最先發現於 1950 年代後期，多年以來，物理學者不清楚類星體的物理模型。後來，越來越多的證據顯示，類星體實際是一種活動星系核，其核心位置有一個超大質量黑洞，附近的物質不停地掉入黑洞裏，形成巨大的能量輻射與物質噴流向外噴出。現在，這理論已被學術界接受。
## 參考文獻
## 外部連結
* （英文）科學雜誌第 125 週年慶特別網頁：125 條問題，我們不知道甚麼 （頁面存檔備份，存於網際網路檔案館）？
* （英文）美國物理協會主持的每週物理新聞網頁：最新物理新聞。
* （英文）關於未解決問題的網頁：關於未解決的物理學問題、獎賞、研究的連結列表 （頁面存檔備份，存於網際網路檔案館）。
* （英文）美國國家航空暨太空總署網頁：根據我們想要達成的目標而想出的點子 （頁面存檔備份，存於網際網路檔案館）。 | [
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未解決的physics問題 | * （英文）2004 年史丹佛直線加速器中心夏季學院網頁：大自然最難的謎題 （頁面存檔備份，存於網際網路檔案館） | [
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胶子 | 在粒子物理學中，**膠子**（gluon）是負責在兩個夸克之間傳遞強作用力的基本粒子，類似光子負責在兩個帶電粒子之間傳遞電磁力一般。
用科學術語來說明，膠子是量子色動力學用來在兩個夸克之間傳遞強交互作用的矢量規範玻色子。膠子本身帶有強交互作用的色荷，這與光子不同，光子不帶有電荷。因此，膠子不但傳遞強交互作用，它還參與強交互作用，這使得量子色動力學的分析遠比量子電動力學困難。
## 性質
膠子是矢量規範玻色子，如同光子，它的自旋為 1。自旋為 1 的帶質量粒子可以擁有三種偏振態。在量子場論裏，為了滿足局域規範不變性，規範玻色子的質量必須為零，因此膠子不帶質量（實驗上限為 0.0002 eV），所以，只有兩種偏振態。
類似光子，膠子是個矢量粒子，所以膠子的內秉宇稱是負數 - 1。
## 膠子的工作機制
在量子色動力學裏，依照所帶有的色荷與反色荷來區分，一共存在有 8 種不同的膠子。每個夸克都帶有三個不同的色荷：紅色、藍色與綠色。每個反夸克都帶有三個不同的反色荷：反紅色、反藍色與反綠色。每個膠子帶有一個色荷與一個反色荷。要想正確了解它們怎樣組合在一起，就必需更仔細地思考色荷數學。
### 色荷與量子疊加
在量子力學裏，根據態疊加原理，假若粒子處於由幾種量子態組合而成的疊加態，則粒子處於其中任意量子態的機率為有限值；假若對於這系統測量某物理量，則可能得到幾種不同的數值。例如，設定膠子的色態為紅色 - 反藍色加上藍色 - 反紅色：
: $(r{\bar {b}}+b{\bar {r}})/{\sqrt {2}}$ ；
其中， $r$ 、 $b$ 、 ${\bar {r}}$ 、 ${\bar {b}}$ 分別為紅色、藍色、反紅色、反藍色。
假若測量此膠子的顏色，則它的色荷是紅色 - 反藍色的機會為 50%，是藍色 - 反紅色的機會為 50% 。
### 色單態
在科普界時常會提到，由幾個夸克或反夸克組成的穩定粒子，例如像質子與中子一類的強子，假若能夠在大自然被觀察得到，則總色荷必須是無色的（或白色的）：
更精準地說，所有自然發生的粒子都處於色單態，這是為了遵守夸克禁閉。例如，每一種重子的波函數在顏色部分必須是反對稱的色單態：
: $|\mathrm {baryon\ color} \rangle =(rgb-rbg+grb-gbr+brg-bgr)/{\sqrt {6}}$ ；
其中， $g$ 為綠色。
膠子的色單態為 | [
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胶子 | : $|\mathrm {gluon\ color} \rangle =(r{\bar {r}}+b{\bar {b}}+g{\bar {g}})/{\sqrt {3}}$ 。
由於色單態的膠子不違反夸克禁閉，它應該能夠以自由粒子的形式存在於大自然，並且在兩個強子之間傳遞強作用力，例如，在質子與中子之間傳遞強作用力，因此，強作用力也會變為遠距作用力，但是強作用力是一種短距作用力，因此色單態的膠子不存在。
### 八種膠子
每個膠子帶有一個單位色荷的顏色與一個單位色荷的反顏色。顏色可以是紅色 $r$ 、藍色 $b$ 或綠色 $g$ 。反顏色可以是反紅色 ${\bar {r}}$ 、反藍色 ${\bar {b}}$ 或反綠色 ${\bar {g}}$ 。所以，膠子可能處於九種不同的色態，分別為 $r{\bar {r}}$ 、 $r{\bar {b}}$ 、 $r{\bar {g}}$ 、 $b{\bar {r}}$ 、 $b{\bar {b}}$ 、 $b{\bar {g}}$ 、 $g{\bar {r}}$ 、 $g{\bar {b}}$ 、 $g{\bar {g}}$ 。實際而言，膠子是處於這九種色態的線性獨立組合，但是由於先前提到的色單態並不存在，所以只有八種色態，分別為
這些色態共同組成「八重態」，或「色八重態」。這些色態的色波函數等價於蓋爾曼矩陣，分別為：
:
在 $\lambda _{1}$ 蓋爾曼矩陣裏，第一橫排第二豎排的元素對應於紅色 - 反藍色，第二橫排第一豎排的元素對應於藍色 - 反紅色，整個矩陣對應於色態 $(r{\bar {b}}+b{\bar {r}})/{\sqrt {2}}$ 。
這八個色態彼此線性獨立，並且獨立於色單態；幾個色態的任何線性組合都無法複製其它色態；它也無法製成 $r{\bar {r}}$ 、 $b{\bar {b}}$ 、 $g{\bar {g}}$ ，否則，禁戒的色單態也可被製成。
上述八重態並不是唯一選擇，也可挑選其它種八重態，但它們都數學等價，會給出同樣的物理結果，並且運算過程不會更簡易。
### 群論
用群論來表述，色單態不存在這句話只是量子色動力學具有 SU (3) 對稱（八個線性獨立態），而不具有 U (3)（九個線性獨立態）對稱的體現。並沒有任何先天理由選擇這種群而不選擇那種群，但是實驗結果支持 SU (3) 對稱。
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胶子 | 由於膠子本身帶有色荷，膠子也參與強交互作用。膠子 - 膠子交互作用使得色場成為像絲弦一般的物體，稱為「通量管」（flux tube）。當通量管被拉長時，會出現張力，因此將夸克禁閉於強子內部，這機制有效地局限強作用力的範圍半徑至 10−15 m 以內，大約為原子核的尺寸。當超過某特定長度後，假若連結兩個夸克的通量管的長度越長，則能量越高，呈線性增長；當通量管被拉到足夠長之時，在能量方面，從真空製成一個夸克 - 反夸克對會比一味地增加通量管長度更為有利，這時，繼續拉長通量管還可能會導致通量管會斷裂，形成一個夸克 - 反夸克對。
雖然在量子色動力學的正常相，單獨膠子無法自由移動，物理學者猜測，可能存在純粹由膠子形成的強子，稱為膠球。其它種奇異強子也可能存在，這些奇異強子的重要成分將會是真實膠子，而不是虛膠子。當不處於正常相之時，即在極端高溫與極端高壓強狀況，會形成夸克 - 膠子漿，在這夸克 - 膠子漿裏，不會有機會形成強子，因為夸克與膠子都會變成自由粒子。
## 實驗觀察
夸克與膠子藉著分裂成更多夸克與膠子來顯現自己。這些分裂出的夸克與膠子又會強子化成為無色的正常粒子。1978 年夏季，在國際會議、座談會、專題研討會等等多個學術場合裏，德國電子加速器的正負電子對撞機與儲存環（DORIS）的 PLUTO 實驗團隊報告，發現非常狹窄共振 Y (9.46) 的強子型衰變可以詮釋為由三個膠子製成的 三重噴流事件的證據。同一團隊後來發表分析報告確定這詮釋正確無誤，並且展示出膠子的自旋為 1。
1979 年夏季，在德國電子加速器的正負電子對撞機 PETRA，TASSO 實驗團隊、MARK-J 實驗團隊、PLUTO 實驗團隊（後來，在 1980 年，JADE 粒子探測器)）又觀察到三重噴流事件，這被詮釋為 qq 膠子軔致輻射，現在更為明顯可見。
1980 年，TASSO 實驗團隊與 PLUTO 實驗團隊確定膠子的自旋為 1。1991 年，在歐洲核子研究組織大型正負電子對撞機儲存環完成的一項後續實驗確定這結果正確無誤
在德國電子加速器的強子 - 電子環加速器，膠子的物理性質被特別地研究分析。H1 探測器實驗與 ZEUS 探測器實驗，這兩項實驗對於膠子在質子裏的數量分佈與動量分佈做出仔細測量。從 1996 年至 2007 年，HERMES 實驗研究膠子對於質子自旋的貢獻。從 H1 探測器實驗蒐集的光子製備數據，被用來計算光子內部的膠子密度，當光子呈現強子行為之時。 | [
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胶子 | 色禁閉可以用無法找到自由夸克來核對，也就是說無法找到非整數的電荷。通常，為了抵銷量子顏色與風味量子數，夸克會成對產生（夸克與反夸克）。可是，在費米實驗室的 CDF 實驗團隊與 D0 實驗團隊於 2009 年報告，探測到頂夸克單獨產生的證據（雖然這仍舊涉及到成對產生，但是夸克與反夸克的風味不同）。至今為止，尚未能找到任何膠球存在的證據。
2000 年，歐洲核子研究組織的超級質子同步加速器聲稱，在重離子對撞時觀察到退禁閉，這意味著觀察到一種新的物質態：夸克 - 膠子漿。2004 年至 2010 年，在布魯克黑文國家實驗室的 相對論性重離子對撞機（RHIC），四個不同實驗同時期找到夸克 - 膠子漿。2010 年，在歐洲核子研究組織的大型強子對撞機，三個實驗大型離子對撞機實驗、超環面儀器與緊湊緲子線圈確定探測到夸克 - 膠子漿。
## 參閱
* 夸克模型
## 註釋
## 參考文獻 | [
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W粒子 | 在物理學中，**W 及 Z 玻色子**（boson）是負責傳遞弱核力的基本粒子。它們是 1983 年在歐洲核子研究組織發現的，被認為是粒子物理標準模型的一大勝利。
**W 玻色子**是因弱核力的「弱」（**W**eak）字而命名的。而 **Z 玻色子**則因是「最後一個要發現的粒子」而名。另一個說法是因 Z 玻色子有零（**Z**ero）電荷而得名。
## 基本性質
W 玻色子有兩種，分別有 +1（W+）和−1（W−）單位電荷。W+ 是 W−的反粒子。而 Z 玻色子（Z0）則為電中性的，且為自身的反粒子。這三種粒子皆十分短命，其半衰期約為 $3\times 10^{-25}$ 秒。
這些玻色子在各種基本粒子之中屬重型的一類。W 的質量為 80.399 ± 0.023 GeV，而 Z 則為 91.1876 ± 0.0021 GeV。它們差不多是質子質量的一百倍 —— 比鐵原子還要重。玻色子的質量是十分重要的，因其限制了弱核力的作用範圍。相對地，因為光子無質量，故電磁力的作用範圍無限遠。
## 弱相互作用
W 和 Z 玻色子是傳遞弱相互作用的媒介粒子，就像光子是傳遞電磁相互作用的媒介粒子一樣。W 玻色子在核衰變過程中擔任一個重要的角色。以鈷 - 60 的 β 衰變為例，
: ${}_{27}^{60}{\hbox{Co}}\to {}_{28}^{60}{\hbox{Ni}}+{\hbox{e}}^{-}+{\overline {\nu }}_{e}$
此反應在超新星和中子彈爆炸時是非常重要的。可是它並不需牽涉到整個鈷核子，而只是它 33 個中子其中之一。此中子在衰變期間轉變成一個質子、電子（又叫 β 粒子）和反電微中子：
: ${\hbox{n}}\to {\hbox{p}}+{\hbox{e}}^{-}+{\overline {\nu }}_{e}$
但中子和質子都只是夸克的組合（中子是「上下下」(標準模型符號為:u,d,d)，質子是「上上下」(標準模型符號為:u,u,d)）。中子的一粒下夸克在 β 衰變中受弱相互作用的影響而變成上夸克：
: ${\hbox{d}}\to {\hbox{u}}+{\hbox{W}}^{-}$ ，
故弱相互作用可改變夸克的「味道」（參閱費米子）。而所發出的 W−粒子迅速衰變成電子和反電微中子： | [
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W粒子 | : ${\hbox{W}}^{-}\to {\hbox{e}}^{-}+{\overline {\nu }}_{e}$
因 Z 玻色子是自己的反粒子，故它的所有量子數皆為零。交換 Z 玻色子是一個中性流作用（Neutral current interaction），而接收和發出 Z 玻色子的粒子除動量外甚麼也沒變。要觀測中性流作用需要在粒子加速器和粒子偵察器上作很大的投資，故目前世界上只有幾所高能物理實驗室擁有這些儀器。關於這部分巨額經費的來源，可能有待未來尖端科技用以轉化一般金屬成金的技術的突破。
## W 和 Z 玻色子的預測
於 1950 年代量子電動力學的空前成功後，科學家希望為弱核力建立相似的理論。於 1968 年，這個論調在統一電磁力和弱核力後達到高潮。提出弱電統一的謝爾登・格拉肖、史蒂文・溫伯格和阿卜杜勒・薩拉姆因此得到 1979 年的諾貝爾物理學獎。他們的弱電理論不止假設了 W 玻色子的存在來解釋 β 衰變，還預測有一種未被發現的 Z 玻色子。
W 和 Z 玻色子有質量，而光子卻沒有 —— 這是弱電理論發展的一大障礙。這些粒子現時以一個 SU (2) 規範理論來精確描述，但理論中玻色子必定無質量。譬如，光子無質量是因為電磁力能以一個 U (1) 規範理論解釋。某些機制必須破壞 SU (2) 的對稱來給予 W 和 Z 玻色子的質量。其中一個解釋是由彼得・希格斯於 1960 年代晚期提出的希格斯機制。它預言了一種新粒子 —— 希格斯玻色子 (現今此粒子已被證實存在了)。
SU (2) 測量儀理論、電磁力和希格斯機制三者的組合稱為格拉肖 - 溫伯格 - 薩拉姆模型。它是目前廣泛接受為標準模型的一大支柱。
## W 和 Z 玻色子的發現
W 和 Z 粒子的發現是歐洲核子研究組織的主要成就之一。首先，於 1973 年，實驗觀察到了弱電理論預測的中性流作用；那時加爾加梅勒的氣泡室拍攝到有一些電子突然自行移動的軌跡。這些觀測結果被詮釋為中微子藉由交換沒有軌跡的 Z 玻色子與電子互相作用。由於中微子是偵測不到的，因此實驗中只能看到電子因著交互作用而造成的動量改變。 | [
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W粒子 | W 和 Z 粒子要到能量夠高的粒子加速器建立後才正式被發現。第一部這樣的加速器是超級質子同步加速器，其中卡洛・魯比亞和西蒙・范德梅爾在 1983 年一月進行的一連串實驗給出了明顯的 W 粒子證據。這些實驗稱作「UA1」（由魯比亞主導）和「UA2」，且為眾多人合作的努力成果。范德梅爾是加速器方面的驅策者（隨機冷卻）。UA1 和 UA2 在幾個月後（1983 年五月）找到 Z 粒子。很快地魯比亞和范德梅爾因而得到 1984 年的諾貝爾物理學獎，這可算是保守的諾貝爾獎基金會自成立以來相當不尋常迅速的一次。
## 參考資料
## 外部連結
* 粒子物理學回顧（The Review of Particle Physics） （頁面存檔備份，存於網際網路檔案館）：粒子性質資訊的首要來源。
* CERN 的 W 和 Z 粒子網頁 | [
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54037-57-9 | **𨭆**（拼音：hēi，注音：ㄏㄟ；英語：**Hassium**），是一種人工合成的化學元素，其化學符號為 **Hs**，原子序數為 108。𨭆是一種放射性極強的超重元素及錒系後元素，其所有同位素的半衰期都很短，非常不穩定，其中壽命最長的是 269Hs，半衰期僅約 16 秒。德國黑森邦達姆施塔特重離子研究所的研究團隊在 1984 年首次合成出𨭆元素，並以黑森邦命名此元素。到目前為止，多個研究通過不同的核反應，一共合成了超過 100 個𨭆原子，有的是母原子核，有的是更重元素的衰變產物。
𨭆是 8 族中最重的元素，實驗證明，𨭆是典型的 8 族過渡金屬，具穩定的 + 8 氧化態，類似於同族的鋨，是鋨的同系物。
## 概述
超重元素的原子核是在兩個不同大小的原子核的聚變中產生的。粗略地說，兩個原子核的質量之差越大，兩者發生反應的可能性就越大。由較重原子核組成的物質會作為靶子，被較輕原子核的粒子束轟擊。兩個原子核只能在距離足夠近的時候，才能聚變成一個原子核。原子核（全部都有正電荷）會因為靜電排斥而相互排斥，所以只有兩個原子核的距離足夠短時，強核力才能克服這個排斥力並發生聚變。粒子束因此被粒子加速器大大加速，以使這種排斥力與粒子束的速度相比變得微不足道。不過，只是靠得足夠近不足以使兩個原子核融合：當兩個原子核逼近彼此時，它們通常會融為一體約 10−20 秒，之後再分開（分開後的原子核不需要和先前相撞的原子核相同），而非形成單一的原子核。如果聚變發生了，兩個原子核產生的一個原子核會處於激發態，被稱為複合原子核，非常不穩定。為了達到更穩定的狀態，這個暫時存在的原子核可能會直接核分裂，或是放出一些帶走激發能量的中子。如果這些激發能量不足以使中子被放出，複合原子核就會放出 γ 射線。這個過程會在原子核碰撞後的 10−16 秒發生，並創造出更穩定的原子核。聯合工作團隊（JWP）定義，化學元素的原子核只有 10−14 秒內不進行放射性衰變，才能被識別出來，這個值大約是原子核得到它的外層電子，顯示其化學性質所需的時間。 | [
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54037-57-9 | 粒子束穿過目標後，會到達下一個腔室 —— 分離室。如果反應產生了新的原子核，它就會被這個粒子束攜帶。在分離室中，新產生的原子核會從其它核種（原本的粒子束和其它反應產物）中分離，並轉移到半導體探測器中，在這裡停住原子核。撞擊至探測器時的確切位置、能量和到達時間將會被記錄下來。這個轉移需要 10−6 秒的時間，意即這個原子核需要存活這麼長的時間才能被檢測到。若衰變發生，衰變的原子核被再次記錄，並測量位置、衰變能量和衰變時間。
原子核的穩定性源自於強核力，但強核力的作用距離很短，隨著原子核越來越大，強核力對最外層的核子（質子和中子）的影響減弱。同時，原子核會被質子之間，範圍不受限制的靜電排斥力撕裂。超重元素的主要衰變方式 ——α 衰變和自發裂變都是這種排斥引起的。α 衰變由發射出去的 α 粒子記錄，在實際衰變之前很容易確定衰變產物。如果這樣的衰變或一系列連續衰變產生了一個已知的原子核，則可以很容易地確定反應的原始產物。（衰變鏈中的所有衰變都必須在同一個地方發生。） 已知的原子核可以通過它經歷的衰變的特定特徵來識別，例如衰變能量（或更具體地說，發射粒子的動能）。然而，自發裂變會產生各種分裂產物，因此無法從其分裂產物確定原始核種。
嘗試合成超重元素的物理學家可以獲得的信息是探測器收集到的信息：粒子到達探測器的位置、能量和時間，以及粒子衰變的信息。物理學家分析這些數據並試圖得出結論，確認它確實是由新元素引起的，而非由不同的核種引起的。如果提供的數據不足以得出創造出來的核種確實是新元素的結論，並且對觀察到的效應沒有其他解釋，就可能在解釋數據時出現錯誤。
## 歷史
### 發現
1984 年，由彼得・安布魯斯特和哥特佛萊德・明岑貝格領導的研究隊於德國達姆施塔特重離子研究所首次進行了𨭆的合成反應。團隊以 58Fe 原子核撞擊鉛目標體，製造出 3 個 265Hs 原子，反應如下：
: $\,_{82}^{208}\mathrm {Pb} +\,_{26}^{58}\mathrm {Fe} \to \,_{108}^{265}\mathrm {Hs} +\,_{0}^{1}\mathrm {n} $
IUPAC/IUPAP 超鐨元素工作組在 1992 年的一份報告中承認，重離子研究所是𨭆的正式發現者。
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54037-57-9 | 𨭆曾經被稱為 eka 鋨。在命名爭議期間，IUPAC 使用的臨時系統名稱是 Unniloctium（符號為 Uno），來自數字 1、0、8 的拉丁語寫法。
德國發現者在 1992 年正式提出使用 Hassium 作為 108 號元素的名稱，取自研究所所在地德國黑森州的拉丁語名（Hassia）。
1994 年，IUPAC 的一個委員會建議把元素 108 命名為 Hahnium（Hn），雖然長期的慣例是把命名權留給發現者。在德國發現者抗議之後，1997 年 8 月 27 日 IUPAC 正式對國際上分歧較大的 101 至 109 號元素的重新英文定名中，國際承認了現用名稱 Hassium 作為 108 號元素的命名。
全國科學技術名詞化學名詞審定委員會據此於 1998 年 7 月 8 日重新審定、公佈 101 至 109 號元素的中文命名，其中首次給出 108 號元素中文名：「𨭆」（hēi，音同「黑」），名稱根據 IUPAC 決定的英文名 Hassium，源自發現該元素的德國重離子研究所所在的德國黑森州。
## 核合成
### 冷核融合
**136Xe(136Xe,xn)272−xHs**
未來重要的實驗將會包括通過該對稱反應利用裂變碎片合成𨭆同位素。這條反應曾於 2007 在杜布納進行，但未探測到任何原子，截面限制為 1 pb。一經證實，這種對稱聚變反應就應該算是熱核融合，而非一開始認為的冷核融合。這意味著，該反應用於合成超重元素的實際用途具有限制。
**198Pt(70Zn,xn)268−xHs**
該反應於 2002 年 5 月在重離子研究所進行。不過，由於鋅 - 70 粒子束的失敗，實驗被中斷了。
**208Pb(58Fe,xn)266−xHs (x=1,2)**
1978 年位於杜布納的團隊首次報告了該反應。在 1984 年的一次實驗中，他們利用滾筒技術探測到了來自 260Sg 的一次自發裂變行為，而 264Hs 是其母同位素。同年進行的重復實驗中，他們用化學辨識衰變產物，從而證明了元素 108 的成功合成。所探測到的有 253Es 和 253Fm 的 α 衰變，這些都是 265Hs 的衰變產物。 | [
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54037-57-9 | 在 1984 年正式發現𨭆元素的實驗中，重離子研究所的團隊使用了 α 衰變相關法，並辨認出 3 顆 265Hs 原子。在 1993 年改進設施之後，團隊在 1994 年重復進行了實驗，並在測量 1n 中子蒸發通道的部分激發函數時，探測到 75 個 265Hs 原子和 2 個 264Hs 原子。在 1997 年進行的另一次實驗中，測量到的 1n 通道的最大值為 69 pb，另探測到 20 個原子。
理化學研究所於 2002 年的重復實驗成功製造出 10 個原子，而國家大型重離子加速器於 2003 年製造出 7 個原子。
理化學院究所的團隊於 2008 年再次研究該反應，以對 264Hs 作出首次的光譜分析。他們另又發現 29 個 265Hs 原子。
**207Pb(58Fe,xn)265−xHs (x=1)**
1984 年在杜布納進行的實驗首次使用 Pb-207 目標。團隊探測到與使用 Pb-208 時的實驗相同的自發裂變，來自同位素 260Sg，264Hs 的子同位素。位於重離子研究所的團隊首次於 1986 年研究這條反應，並使用 α 衰變相關法發現了單個 264Hs 原子，截面為 3.2 pb。反應在 1994 年重復進行，同時探測到 α 衰變和自發裂變 264Hs。
理化學研究所在 2008 年研究了該反應，以進行首次對 264Hs 的光譜分析。該團隊探測到 11 個原子。
**208Pb(56Fe,xn)264−xHs (x=1)**
勞倫斯伯克利國家實驗室的團隊在 2008 年首次研究該反應，並製造及辨認出 6 個新發現的 263Hs 同位素原子。數月之後，理化學研究所的團隊也發佈了他們對同一條反應的研究結果。
**206Pb(58Fe,xn)264−xHs (x=1)**
理化學研究所的團隊在 2008 年首次研究了該反應，並識別出 8 個新發現的 263Hs 同位素原子。
**209Bi(55Mn,xn)264−xHs** | [
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54037-57-9 | 最初對𨭆原子核的合成實驗使用的就是這條反應，由杜布納的一支團隊在 1983 年進行。他們使用滾筒技術，探測到來自 255Rf 的自發裂變，而該同位素是 263Hs 的衰變產物。1984 年重復進行的實驗得到同樣的結果。1983 年的另一次實驗當中，他們通過化學辨識衰變產物，從而支持𨭆的合成結果。探測到的有鐨同位素的 α 衰變，該鐨同位素是 262Hs 的衰變產物。這條反應之後一直沒有進行嘗試，因此 262Hs 的存在至今仍未證實。
### 熱核融合
**226Ra(48Ca,xn)274−xHs (x=4)**
位於 Flerov 核反應實驗室由 Yuri Oganessian 領導的團隊聲稱在 1978 年曾研究過這條反應，但實驗結果沒有發佈在任何文獻當中。該反應於 2008 年 6 月在同一實驗室重復進行，結果探測到 4 個 270Hs 同位素原子，產量為 9 pb。該同位素的衰變數據得到証實後，發現 α 能量稍微更高。2009 年 1 月，團隊重復進行實驗，再探測到 2 個 270Hs 原子。
**232Th(40Ar,xn)272−xHs**
這條反應首次再 1987 年於杜布納進行。探測方式為自發裂變，但並未發現任何成功地反應，截面限制為 2 pb。
**238U(36S,xn)274−xHs (x=4)**
該反應使用罕見且昂貴的 36S 同位素，於 2008 年 4 月至 5 月在重離子研究所進行。初步結果顯示，實驗探測到 1 個 270Hs 原子，產量為 0.8 pb。數據証實了 270Hs 和 266Sg 的衰變特性。
**238U(34S,xn)272−xHs (x=4,5)**
1994 年 3 月，位於杜布納由 Yuri Lazerev 領導的團隊宣佈在 5n 中子蒸發通道探測到 3 個 267Hs 原子。在重離子研究所的團隊在同時研究鐽的時候証實了𨭆同位素的衰變特性。
這項實驗於 2009 年 1 月至 2 月在重離子研究所進行，用以發現新同位素 268Hs。由 Nishio 教授領導的團隊探測到 1 個 268Hs 和 1 個 267Hs 原子。新發現的同位素經過 α 衰變後形成已知的 264Sg 同位素。
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54037-57-9 | 重離子研究所與保羅謝爾研究所的合作團隊研究了鋦 - 248 和鎂 - 26 離子之間的反應。在 2001 年 5 月到 2005 年 8 月期間，團隊研究了產生 269Hs、270Hs 及 271Hs 的 3n、4n 及 5n 中子蒸發通道的激發函數。2006 年 12 月，慕尼黑工業大學的科學團隊發佈了合成 270Hs 同位素的重要結果。報告指出，該同位素經 α 衰變，能量為 8.83 MeV，預計半衰期約為 22 秒，形成 266Sg。
**248Cm(25Mg,xn)273−xHs**
這條新的反應在 2006 年 7 月至 8 月由重離子研究所用於合成新的同位素 268Hs。從中子蒸發通道未能探測到任何原子，計算的界面限制為 1 pb。
**249Cf(22Ne,xn)271−xHs**
杜布納的團隊在 1983 年研究了該反應，並用自發裂變作出探測。探測到的幾次短期自發裂變活動證明了𨭆原子核的生成。
## 同位素
目前已知的𨭆同位素有 12 個，全部都具有極高的放射性，半衰期極短，非常不穩定。其中壽命最長的是𨭆-269，半衰期約 16 秒。
### 待證實的同位素
**277bHs**
同位素 277Hs 曾在一次自發裂變事件中被觀察到，其半衰期為較長的 11 分鐘左右。在 281Ds 的大部分衰變過程中都未能探測到該同位素，其唯一一次被探測到是在同質異構核 281bDs 的未經証實的一次衰變當中。其半衰期對基態核來說很長，因此它有可能屬於 277Hs 的一個同質異構核。另外在 2009 年，重離子研究所的團隊觀察到 281aDs 的 α 衰變分鏈產生了 277Hs 同位素，其後該同位素進行自發裂變，半衰期較短。測量到的半衰期接近基態同質異構核 277aHs 的預期值。要證實該同質異構核的存在，需進行進一步的研究。
### 撤回的同位素
**273Hs**
勞倫斯伯克利國家實驗室於 1999 年聲稱合成元素 118，反應期間出現 273Hs 同位素核子。他們聲稱該同位素以能量 9.78 及 9.47 MeV 進行 α 衰變，半衰期為 1.2 秒。該發現在 2001 年被撤回。這一同位素最終在 2010 年被合成，而所記錄的數據證明先前的數據是虛假的。
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54037-57-9 | 根據宏觀微觀理論，Z=108 質子數是變形質子幻數，連同 N=162 的中子殼層。這代表這種原子核的基態是永遠變形的，但其裂變位壘高而窄，造成進一步變形，因此其自發裂變部分半衰期相對較長。此區域的自發裂變半衰期比接近球體雙重幻數的原子核 298114 小大約 109 倍。這是由於裂變位壘較窄，導致以量子隧穿效應穿越位壘的機率增加。另外，根據計算，N=162 中子數是變形中子幻數，因此 270Hs 原子核很有可能是變形雙重幻數核。Z=110 的同位素 271Ds 及 273Ds 的衰變數據，說明 N=162 支殼層有可能為幻數。對 269Hs、270Hs 和 271Hs 的合成實驗也指出 N=162 是幻數閉殼層。270Hs 的低衰變能量與計算的完全相符。
### Z=108 變形質子殼層的證據
證明 Z=108 質子殼層的幻數特性的證據有以下兩點：
1. 同中子異位素自發裂變的部分半衰期變化。
2. Z=108 和 Z=110 同中子異位素對 Qα 值間的大差距。
對於自發裂變，有必要測量同中子異位素核 268Sg、270Hs 和 272Ds 的半衰期。由於𨭎和鐽的這兩個同位素還是未知的，而 270Hs 的衰變還未經過測量，因此該方法目前能夠用來證實 Z=108 殼層的穩定性質。但 Z=108 的幻數特性可以從 270Hs、271Ds 及 273Ds 的 α 衰變能量間的大差距中推導出。測量 272Ds 的衰變能量能量後能夠得出更有力的證據。
### 同質異能核
**269Hs**
對 269Hs 的直接合成產生了三條 α 線，於 9.21、9.10 及 8.94 MeV。在 277112 的衰變當中，只觀察到能量為 9.21 MeV 的 269Hs 的 α 衰變，表示該衰變源自同質異能核。要證實這一點則需進一步研究。
**267Hs**
已知 267Hs 進行 α 衰變，α 線位於 9.88、9.83 和 9.75 MeV，半衰期為 52 ms。在合成 271m,gDs 的時候，觀察到額外的活動。包括一次 0.94 ms，能量為 9.83 MeV 的 α 衰變，其餘還有更長的約 0.8 s 和約 6.0 s 的活動。這些活動來源現時不清，需要更多的研究得到證實。
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] |
54037-57-9 | 對 265Hs 的合成也證明兩個能級的存在。基態進行能量為 10.30 MeV 的 α 衰變，半衰期為 2.0 ms。其同質異能態能量比基態高 300 keV，進行 10.57 MeV 的 α 衰變，半衰期為 0.75 ms。
## 化學特性
### 推算的化學特性
#### 氧化態
𨭆預計為過渡金屬中 6d 系的第 5 個元素及 8 族中最重的元素，在週期表中位於鐵、釕和鋨之下。該族中的後兩個元素表現出的氧化態為 + 8，而這種氧化態在族中越到下方越為穩定。因此𨭆的氧化態應為 + 8。鋨同時還有穩定的 + 5、+4 及 + 3 態，其中 + 4 態最為穩定。而釕則同時有 + 6、+5 及 + 3 態，當中 + 3 態最為穩定。𨭆也因此預計擁有穩定的低氧化態。
#### 化合物
第 8 族元素獨特的氧化物化學使對𨭆元素特性的推算更為容易。同族較輕的元素都已知擁有或預測擁有四氧化物，MO4。一直向下，該族的氧化力逐漸下降：FeO4 並不存在，因為極高的電子親合能使其形成常見的 FeO42−。釕 (VI) 在酸中經過氧化後形成四氧化釕，RuO4，而四氧化釕經過還原反應後形成 RuO42−。釕金屬在空氣中氧化後形成二氧化釕，RuO2。對比之下，鋨燃燒後產生穩定的四氧化鋨，OsO4，然後與氫氧根離子產生錯合物 [OsO4(OH)2]2−。因此，作為鋨對下的元素，𨭆應該會形成揮發性四氧化𨭆，HsO4，再與氫氧根離子配合形成 [HsO4(OH)2]2−。
#### 密度
𨭆預計體密度為 41 g/cm3，是所有 118 個已知元素中最高的，幾乎為鋨的兩倍，而鋨是目前已測量的元素中密度最高的，有 22.6 g/cm3。這是由於𨭆擁有高原子量，並加上鑭系與錒系收縮效應和相對論性效應，但是真正製造足夠𨭆元素以測量其密度是不可行的，因為樣本會即刻進行衰變。
### 實驗性化學
#### 氣態化學
𨭆的電子組態預計為 [Rn] 5f14 6d6 7s2，因此𨭆應會產生揮發性四氧化物 HsO4。其揮發性是由於該分子的四面體形。
對𨭆的首次化學實驗在 2001 年進行，運用了熱色譜分析法，以 172Os 作為參照物。利用反應 248Cm(26Mg,5n)269Hs，實驗探測到 5 個𨭆原子。產生的原子在 He/O2 混合物中經過熱能化及氧化後產生氧化物。
: 269
108Hs
+ 2 O
2 → 269
108Hs
O
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54037-57-9 | 所測量到的熱解離溫度表示四氧化𨭆的揮發性比四氧化鋨低，同時也肯定了𨭆的特性屬於 8 族。
為了進一步探測𨭆的化學屬性，科學家決定研究四氧化𨭆與氫氧化鈉間產生的𨭆酸鈉的反應。該反應是鋨的一條常見反應。在 2004 年，科學家公佈成功進行了第一次對𨭆化合物的酸鹼反應：
: HsO
4 + 2 NaOH → Na
2[HsO
4(OH)
2]
#### 化合物與錯離子
## 注釋
## 參考資料
## 外部連結
* 元素𨭆在洛斯阿拉莫斯國家實驗室的介紹（英文）
* EnvironmentalChemistry.com —— 𨭆（英文）
* 元素𨭆在 _The Periodic Table of Videos_（諾丁漢大學）的介紹（英文）
* 元素𨭆在 Peter van der Krogt elements site 的介紹（英文）
* WebElements.com – 𨭆（英文） | [
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随机数 | **隨機數**這一概念在不同領域有著不同的含義。
## 密碼學範疇的隨機數
根據密碼學原理，隨機數的隨機性檢驗可以分爲三個標準：
1. 統計學偽隨機性。統計學偽隨機性指的是在給定的隨機位元流樣本中，1 的數量大致等於 0 的數量，同理，「10」「01」「00」「11」四者數量大致相等。類似的標準被稱為統計學隨機性。滿足這類要求的數字在人類「一眼看上去」是隨機的。
2. 密碼學安全偽隨機性。其定義為，給定隨機樣本的一部分和隨機演算法，不能有效的演算出隨機樣本的剩餘部分。
3. 真隨機性。其定義為隨機樣本不可重現。實際上只要給定邊界條件，真隨機數並不存在，可是如果產生一個真隨機數樣本的邊界條件十分複雜且難以捕捉（比如當地的背景輻射波動值），可以認為用這個方法演算出來了真隨機數。但實際上，這也只是非常接近真隨機數的偽隨機數，一般認為，無論是背景輻射、物理噪音、拋硬幣等等都是可被觀察了解的，任何基於經典力學產生的隨機數，都只是偽隨機數。
相應的，隨機數也分爲三類：
1. **偽隨機數**：滿足第一個條件的隨機數。
2. **密碼學安全的偽隨機數**：同時滿足前兩個條件的隨機數。可以透過密碼學安全偽亂數生成器計算得出。
3. **真隨機數**：同時滿足三個條件的隨機數。
隨機數在密碼學中非常重要，保密通信中大量運用的會話密鑰的生成即需要真隨機數的參與。如果一個隨機數生成演算法是有缺陷的，那麽會話密鑰可以直接被推算出來。若果真發生這種事故，那麽任何加密演算法都失去了意義。
密碼學中大量利用偽隨機數生成器的應用還有流密碼。流密碼的著名例子是 RC4 和 ChaCha20。流密碼的原理是利用一個密碼學安全的偽隨機數生成器根據密鑰產生一串密碼學安全的偽隨機位元列，再將訊息與上述隨機位元列按位元互斥或運算。
目前沒有數學證明表示密碼學安全的僞隨機數生成器是確實存在的。其存在性證明涉及到 P 和 NP 的數學難題。
## 密碼學以外的隨機數
亂數是專門的隨機試驗的結果。
在統計學的不同技術中需要使用亂數，比如在從統計總體中抽取有代表性的樣本的時候，或者在將實驗動物分配到不同的試驗組的過程中，或者在進行蒙特卡羅類比法計算的時候等等。
產生亂數有多種不同的方法。這些方法被稱為亂數生成器。亂數最重要的特性是它在產生時後面的那個數與前面的那個數毫無關係。 | [
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] |
随机数 | 真正的亂數是使用物理現象產生的：比如擲錢幣、骰子、轉輪、使用電子元件的噪音、核分裂等等。這樣的亂數生成器叫做物理性亂數生成器，它們的缺點是技術要求比較高。
在實際應用中往往使用偽亂數就足夠了。這些數列是「似乎」隨機的數，實際上它們是透過一個固定的、可以重複的計算方法產生的。它們不真正地隨機，因為它們實際上是可以計算出來的，但是它們具有類似於亂數的統計特徵。這樣的生成器叫做偽亂數生成器。
在真正關鍵性的應用中，比如在密碼學中，人們一般使用真正的亂數。
## 參考文獻
## 外部連結
* 量子真亂數 - 國家密碼管理局 （頁面存檔備份，存於網際網路檔案館） | [
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轻子 | **輕子**（Lepton）是一種不參與強交互作用、自旋為 1/2 的基本粒子。電子是最為人知的一種輕子；大部分化學領域都會涉及到與電子的交互作用，原子不能沒有它，所有化學性質都直接與它有關。輕子又分為兩類：「帶電輕子」與「中性輕子」。帶電輕子包括電子、緲子、陶子，可以與其它粒子組合成複合粒子，例如原子、電子偶素等等。 在所有帶電輕子中，電子的質量最輕，也是宇宙中最穩定、最常見的輕子；質量較重的緲子與陶子會很快地衰變成電子，緲子與陶子必須經過高能量碰撞製成，例如使用粒子加速器或在宇宙線探測實驗。中性輕子包括電中微子、緲中微子、陶中微子；它們很少與任何粒子交互作用，很難被觀測到。
輕子一共有六種風味，形成三個世代。第一代是電輕子，包括電子（
e−
）與電中微子 （
ν
e）。第二代是緲輕子，包括緲子（
μ−
）與緲中微子 （
ν
μ）。第三代是陶輕子，包括陶子（
τ−
）與陶中微子（
ν
τ）。
輕子擁有很多內秉性質，包括電荷、自旋、質量等等。輕子與夸克有一點很不相同：輕子不會感受到強作用力。輕子會感受到其它三種基礎力：引力、弱作用力、電磁力。但是，由於中微子的電性是中性，中微子不會感受到電磁力。每一種輕子風味都有其對應的反粒子，稱為「反輕子」。帶電輕子與對應的反輕子唯一不同之處是帶有電荷的正負號相反。根據某些理論，中微子是自己的反粒子，但這論點尚未被證實。
在標準模型裏，輕子扮演重要角色，電子是原子的成分之一，與質子、中子共同組成原子。在某些被合成的奇異原子裏，電子被更換為緲子或陶子。像電子偶素一類的輕子 - 反輕子粒子也可以被合成。
## 詞源學
英文術語「lepton」源自希臘語「λεπτόν」（_leptón_），是「λεπτός」（_leptós_）的中性，含意為 "小、薄"。萊昂・羅森菲爾德於 1948 年最先為英文術語「lepton」命名。
> 在克理斯蒂安・莫勒教授的建議之後，決定用「lepton」（從「λεπτός」，小、薄）這字來稱呼一種小質量的粒子。
>
>
這命名不正確地假定所有輕子的質量都很小。在洛森斐命名那時，學術界只知道有電子與緲子兩種輕子。它們的質量的確很小，電子的質量為 0.511 MeV，緲子的質量為 105.7 MeV，比質子的質量 938.3 MeV 輕很多。可是，在 1970 年代中期發現的陶子，它的質量是 1777 MeV，幾乎是質子的兩倍。
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轻子 | 最先被辨識的輕子是電子，英國物理學者約瑟夫・湯姆森與實驗團隊於 1897 年發現電子。1930 年，沃爾夫岡・包立大膽假設電中微子存在，這是為了解釋 β 衰變的能量缺失問題，挽救能量守恆定律；包立認為，所有最初與最終觀察到的粒子的能量差，都被一種尚未探測到的粒子帶走了，這粒子具有電中性，不會留下軌跡，所以很難探測到。三年後，恩里科・費米給出理論，成功描述 β 衰變，強力支持包立的假設。費米將這粒子命名為「中微子」，意思為「微小的中子」。在那時期，電中微子被稱為中微子，因為尚未發現其它世代的中微子。1956 年，克萊德・科溫與弗雷德里克・萊因斯共同完成科溫 - 萊因斯中微子實驗首先直接觀察到中微子的存在。
在電子被發現大約 40 年之後，卡爾・安德森於 1936 年發現了緲子。由於它的質量，緲子最初被歸類為介子，而不是輕子。漸漸地，學者發覺緲子的性質更接近電子，只是質量比較大，而且緲子不會感受到強相對作用，不具有介子的性質。1947 年，才有學者開始提議一群粒子被歸類為輕子的概念。 後來，緲子被重新歸類，緲子、電子與電中微子一起被歸類為輕子。1962 年 利昂・萊德曼、梅爾文・施瓦茨與傑克・施泰因貝格爾做實驗直接探測到緲中微子，證實不只一種中微子存在。
馬丁・佩爾與他的實驗團隊於 1975 年完成實驗首先探測到陶子。如同電子與緲子，物理學者認為它應該也有伴隨的中微子，這是因為他們觀察到類似 β 衰變的缺失能量問題。費米實驗室的直接觀察陶中微子實驗（Direct Observation of the NU Tau，DONUT ）團隊於 2000 年探測到陶中微子參與作用的證據。
雖然現有數據符合三個世代的輕子，有些粒子物理學者仍在尋找第四代帶電輕子。這種帶電輕子的質量下限為 100.8 GeV，伴隨它的中微子最少應該帶有質量 45.0 GeV。
## 性質
### 自旋與手徵性
輕子是自旋 1⁄2 粒子，只能處於兩種自旋態：上旋或下旋。自旋統計定理將它們按照自旋歸類為費米子，遵守包立不相容原理，因此任何兩個全同的輕子不能同時佔有相同的量子態。 | [
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轻子 | 手徵性與螺旋性（helicity）是與自旋緊密相關的兩種性質，螺旋性跟粒子的自旋與動量之間的相對方向有關；假若是同向，則粒子具有右手螺旋性，否則粒子具有左手螺旋性。對於不帶質量粒子，這相對方向與參考系無關，可是，對於帶質量粒子，由於可以藉著洛倫茲變換來改換參考系，從不同的參考系觀察，粒子動量不同，因此翻改螺旋性，可以從右手螺旋性翻改為左手螺旋性，或從左手螺旋性翻改為右手螺旋性。手徵性是通過龐加萊群（Poincaré group）的變換來定義的性質。對於不帶質量粒子，手徵性與螺旋性一致；對於帶質量粒子，手徵性與螺旋性有別。
在很多量子場論裏，例如量子電動力學與量子色動力學，並沒有對左手與右手費米子作任何區分，可是，在標準模型的弱交互作用理論裏，按照手徵性區分的左手與右手費米子被非對稱地處理，只有左手費米子參與弱交互作用，右手中微子不存在。這是宇稱違反的典型例子。
### 電磁交互作用
輕子的電荷 $Q$ 決定了它所產生的電磁場，也決定了它怎樣響應外電磁場。輕子的每個世代的組員都有一個帶電輕子 $Q=-1$ 與一個中性輕子 $Q=0$ ，例如，第一代輕子為電子
e−
與電中微子
ν
e。
使用量子場論的語言，帶電輕子所涉及的電磁交互作用表達為這輕子與電磁場的量子（光子）彼此之間的交互作用。右圖是電子 - 光子交互作用的費曼圖。
由於輕子具有自旋，帶電輕子會產生磁場，磁偶極矩 $\mu $ 為
: $\mu =g{\frac {Qe\hbar }{4m}}$ ；
其中， $m$ 是輕子的質量， $g$ 是輕子的 g - 因數（g-factor）。
一階近似量子力學預測，對於所有輕子，g - 因數為 2；可是高階量子效應，因為費曼圖裏的虛粒子圈對於這數字給出修正。這些修正，稱為反常磁偶極矩（anomalous magnetic dipole moment），對於量子場論模型的細節非常敏感，因此是準確檢驗標準模型的好機會。對於電子測量其反常磁偶極矩所得到的實驗數值符合理論結果至 8 個有效數字。
### 弱交互作用
在標準模型裏，輕子可以按照手徵性分為左手輕子與右手輕子；左手輕子的弱同位旋 T 為 1⁄2，左手帶電輕子與左手中微子的弱同位旋投影（弱同位旋的第三分量）T3 分別為 -1⁄2、+1⁄2，弱交互作用是由它們組成二重態（doublet state）(
ν
eL,
e− | [
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轻子 | L) 共同實現；右手帶電輕子的弱同位旋 T 為 0，形成單態，不參與弱交互作用；右手中微子並不存在。
希格斯機制將弱同位旋 SU (2) 與弱超荷 U (1) 對稱的四個規範場，重新組合成傳遞弱相對作用的三個帶質量玻色子 （
W+
、
W−
、
Z0
）與傳遞電磁相對作用的不帶質量玻色子（光子）。通過蓋爾曼 - 西島方程式，可以從弱同位旋投影 _T_3 與弱超荷 _Y_W 計算出電荷 _Q_：
: $Q=T_{3}+Y_{W}/2$ 。
為了符合觀察到的任何粒子所帶有的電荷，所有左手弱同位旋二重態 (
ν
eL,
e−
L) 的弱超荷 _Y_W 必須為 - 1，而右手弱同位旋單態 (
e−
R) 的弱超荷 _Y_W 必須為 - 2。
### 質量
在標準模型裏，每一個輕子原本不具有內秉質量；通過與希格斯場耦合，帶電輕子獲得有效質量，但中微子仍舊不帶質量，這意味著不同世代的帶電輕子不會相互混合，與夸克的物理行為大不相同。這結果符合當今實驗數據。
但是，從實驗中得知（最顯著的是中微子振盪實驗），中微子實際帶有微小質量，大約小於 2 eV。這意味著後標準模型 （beyond the Standard Model）的物理現象。當今最被物理學者青睞的理論延伸是翹翹板機制，它可以解釋為甚麼左手中微子的質量遠輕於對應的帶電輕子，為甚麼做實驗尚未能觀察到任何右手中微子。
### 輕子數
每一代輕子的成員組成一個弱同位旋二重態：
: ${\binom {\nu _{e}}{e^{-}}}$ 、 ${\binom {\nu _{\mu }}{\mu ^{-}}}$ 、 ${\binom {\nu _{\tau }}{\tau ^{-}}}$ 。
每一代弱同位旋二重態的成員都被分派一個輕子數。在標準模型裏，輕子數守恆。電子與電中微子的電子數 Le 為 1。緲子與緲中微子的緲子數 Lμ 為 1。陶子與陶中微子的陶子數 Lτ 為 1。 反輕子的輕子數為對應輕子的輕子數乘以−1。
輕子數守恆的意思就是同類氫子數的代數和保持不變，當粒子耦合時；這意味著只有同一代的輕子與反輕子才能成對產生。例如，以下過程是被允許的：
: e−
+
e+
→
γ
+
γ
、
: τ−
+
τ+
→
Z0
+
Z0
。
以下過程是不被允許的：
: γ
→
e−
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] |
轻子 | μ+
、
: W−
→
e−
+
ν
τ
、
: Z0
→
μ−
+
τ+
。
但是，中微子振盪違反單獨輕子數守恆，這是後標準模型物理的確鑿證據。更強的守恆定律是總輕子數守恆。中微子振盪遵守總輕子數守恆。但是，手徵反常稍微違反了這守恆定律。
## 普適性
輕子與對應的中微子之間的交互作用與風味無關，換句話說，對於電子與電中微子之間的交互作用、緲子與緲中微子之間的交互作用、陶子與陶中微子之間的交互作用，假若將質量差別納入考量，則這三種交互作用的效應相等。這性質稱為輕子交互作用的「普適性」。所有已知實驗數據與這種普適性一致做實驗測量陶子與緲子的平均壽命，或 Z 玻色子衰變為輕子的部分衰變寬度，可以檢驗這性質。在大型正負電子對撞機與史丹佛直線加速器裏，完成了很多這類檢驗普適性的實驗。
對於過程
μ−
→
e−
+
ν
e
+
ν
μ，緲子的衰變率 $\Gamma $ 以方程式表示為（更詳盡內容，請參閱緲子衰變）
: $\Gamma \left(\mu ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)=K_{1}G_{F}^{2}m_{\mu }^{5}$ ；
其中， $K_{1}$ 是常數， $G_{F}$ 是費米耦合常數， $m_{\mu }$ 是緲子的質量。
對於過程
τ−
→
e−
+
ν
e
+
ν
τ，陶子的衰變率 $\Gamma $ 以同樣形式的方程式表示為
: $\Gamma \left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)=K_{2}G_{F}^{2}m_{\tau }^{5}$ ；
其中， $K_{2}$ 是常數， $m_{\tau }$ 是陶子的質量。
緲子 - 陶子普適性意味著 $K_{1}=K_{2}$ 。普適性也能夠解釋緲子壽命與陶子壽命之間的關係。輕子的壽命 $L_{l}$ 與衰變率 $\Gamma $ 之間的關係為 | [
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] |
轻子 | : $L_{l}={\frac {1}{\Gamma _{total}}}={\frac {B\left(l^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{l}\right)}{\Gamma \left(l^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{l}\right)}}$ ；
其中， $B(x\rightarrow y)$ 與 $\Gamma (x\rightarrow y)$ 分別標記過程 $x\rightarrow y$ 的分支比與共振寬度。
陶子與緲子的壽命比因此為
: ${\frac {L_{\tau }}{L_{\mu }}}={\frac {B\left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)}{B\left(\mu ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\mu }\right)}}\left({\frac {m_{\mu }}{m_{\tau }}}\right)^{5}$ 。
從實驗獲得的緲子分支比與陶子分支比，可以計算出壽命比為大約 1.328×10−7，實驗測量得到的壽命比為～1.323×10−7。兩者之差異是因為 $K_{1}$ 、 $K_{2}$ 實際並不是常數，它們與輕子的質量有關。
另外，由於電子 - 緲子普適性，陶子衰變為電子的分支比 (17.85%) 與衰變為緲子的分支比 (17.36%) 相同（在誤差範圍內）：
: $\Gamma \left(\tau ^{-}\rightarrow e^{-}+{\bar {\nu _{e}}}+\nu _{\tau }\right)=\Gamma \left(\tau ^{-}\rightarrow \mu ^{-}+{\bar {\nu _{\mu }}}+\nu _{\tau }\right)$ 。
## 輕子列表
## 參閱
* 粒子列表
* 夸克
## 參考文獻 | [
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氧氣 | **氧氣**（英語：**Oxygen, Dioxygen**，分子式：O2）是氧元素最常見的單質形態，在空氣中按體積分數算大約占 21%，在標準狀況下是氣體，不易溶於水，密度比空氣略大，氧氣的密度是 1.429g/L 。不可燃，可助燃。
## 科學史
氧氣最先是由卡爾・威廉・舍勒發現的，約瑟夫・普利斯特里也於之後成功發現，但由於約瑟夫首先發表論文，所以很多人仍然認為氧氣是約瑟夫首先發現的。氧氣的英文名是「Dioxygen」，由拉瓦錫定名於 1777 年，他利用氧氣所進行的試驗在燃燒和腐蝕的方面打敗了當時流行的燃素說。
### 普利斯特里的實驗
約瑟夫・普利斯特里將一隻燃燒的蠟燭放入密閉的玻璃罩中，蠟燭燃燒一段時間即熄滅；如果將一隻老鼠與燃燒的蠟燭一同放在密閉的玻璃罩中，老鼠在蠟燭燃盡後不久即死亡；如果以植物取代老鼠並以陽光照射，植物不僅不會在蠟燭燃盡後死亡，在蠟燭燃盡一段時間後再放入另一支點燃的蠟燭，該蠟燭甚至可以燃燒的更劇烈。
由於普利斯特里為燃素說的支持者，他推論植物可產生能助燃、維持生物生存的氣體，即氧氣，而燃燒則會使氧氣與燃素結合而被「污染」，因此在著作中將氧氣稱為「脫去燃素的氣體」，氧氣燃燒後產生的二氧化碳則被稱為「固定氣體」。
### 拉瓦節的研究
### 中文命名
「氧氣」這一中文名稱是十九世紀清朝科學家徐壽命名的。他認為人的生存離不開氧氣，所以就命名為「養氣」即「養氣之質」，後來就用「氧」代替了「養」字，便叫「氧氣」。
氧氣舊稱「酸素」，來自日語，英語「oxygen」（希臘語：Οξυγόνο）也是來自希臘詞根「Οξυ」（oxy），表示「酸」，因為曾認為所有的酸都含有這種氣體。現在日文裡氧氣的名稱仍然是「酸素／さんそ _Sanso_」。而台語受到台灣日治時期的影響，也以「酸素」之日語發音稱呼氧氣。
## 分布
地球空氣中大約含有體積為 20.947% 的以單質形式存在的氧氣。拉瓦錫曾利用汞與曲頸甑測出空氣中氧氣的含量。實驗室里也可以通過紅磷或白磷大致測出空氣中的氧氣含量。
在八大行星中，地球是含氧氣最多的，其他的星體（例如金星、火星）幾乎沒有氧氣。而很久以前地球上的原始大氣也沒有氧氣。
在森林等植被豐富的地區，氧氣含量相對更加豐富。一般，在一天之內，早晨是含氧氣中最少的時候。
### 大氣層氧氣的歷史
大氣層氧氣的出現源於兩種作用，一個是非生物參與的水的光解，一個是例如藍綠菌等生物參與的光合作用。 | [
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氧氣 | 生物的光合作用對大氣層的影響巨大。它造成了大氣層由還原氛圍向氧化氛圍的轉變。使得水光解產生的氫氣能重新被氧化為水回到地球而不至於擴散到外太空去，從而防止了地球上的水的流失。同時光合作用也加速了大氣層氧氣的積累，深刻地改變了地球上物種的代謝方式和形態。大氣層含氧量在石炭紀的時候一度上升到了 35%。 氧氣含量的增加造成了依賴於滲透方式輸氧的昆蟲在形態上的巨型化，在石炭紀曾出現過翼展達一米的巨脈蜻蜓。
## 結構
氧氣由氧分子（O2）構成。每一個氧氣分子由 2 個氧原子構成。
氧氣是雙原子分子，兩個氧原子形成共價鍵，一個 2p 軌道形成 σ 鍵，另兩個 2p 軌道形成 π 鍵。其分子軌域式為 (σ1s)2(σ1s\*)2(σ2s)2(σ2s\*)2(σ2p)2(π2p)4(π2p\*)2，因此氧氣是奇電子分子，具有順磁性。
### 分子結構
氧氣分子 ${\ce {O2}}$ 由兩個氧原子鍵合組成，又稱雙原子氧。分子軌域理論能夠很好地解釋氧氣分子的鍵合和性質（見圖）。兩個氧原子各自的 s 軌域和 p 軌域結合後，形成一系列成鍵與反鍵分子軌域。 $1s$ 和 $2s$ 原子軌域分別結合，形成 $\sigma _{s}$ 成鍵分子軌域和 ${\sigma _{s}}^{*}$ 反鍵分子軌域。 $2p$ 原子軌域結合後，成為 6 個能級不同的分子軌域── $\sigma _{p}$ 、 $\pi _{x}$ 和 $\pi _{y}$ 成鍵軌域，以及對應的 ${\sigma _{p}}^{*}$ 、 ${\pi _{x}}^{*}$ 和 ${\pi _{y}}^{*}$ 反鍵軌域，其中兩個 $\pi $ 軌域及兩個 π\* 的能量分別相同。
電子按照構造原理，從低能量至高能量順序填入分子軌域。 $2p$ 電子共有 8 個，其中兩個填入 $\sigma _{p}$ ，四個分別成對填入兩個 π 軌域，餘下兩個不成對地分別填入兩個 $\pi ^{*}$ 軌域。從成鍵軌域電子數和反鍵軌域電子數可得出，氧氣分子的鍵級為 ${\frac {6-2}{2}}=2$ 。這兩個不成對電子是氧氣分子的價電子，它們決定了氧氣的性質。 | [
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氧氣 | 根據洪德規則，在基態下兩個價電子的自旋互相平行，因此氧氣分子的最低能態為三重態，即有三個能量相同而自旋不同的量子態。由於兩個價電子不成對，所以兩個 $\pi ^{*}$ 軌域均處於半滿的狀態。這使得氧氣有雙自由基的性質，還可以解釋氧氣的順磁性。（氧氣分子之間的負交換能也導致一部分的順磁性。）由於含不成對電子，所以氧氣與多數有機分子的反應較慢，有機物因而不會自發燃燒。
氧氣分子除了有能量最低的三重態（ $^{3}\textstyle \sum _{g}$ ）以外，還有兩種能量高得多的單態。在這兩個激發態下，兩個價電子的自旋互相反平行，違反洪德規則。這兩種單態的差別在於，兩個價電子是位於同一個 $\pi ^{*}$ 軌域中（ $^{1}\Delta _{g}$ ），還是分開佔據兩個 $\pi ^{*}$ 軌域（ $^{1}\textstyle \sum _{g}$ ）。 $^{1}\textstyle \sum _{g}$ 在能量上不穩定，會迅速變為更穩定的 $^{1}\Delta _{g}$ 。 $^{1}\textstyle \sum _{g}$ 狀態下的氧氣有抗磁性，而 $^{1}\Delta _{g}$ 狀態下的氧氣則因為既有的軌道磁矩而具有順磁性，其磁強度與三重態氧相約。
單態氧對於有機物的反應性比普通氧氣分子強得多。短波長光在分解對流層中的臭氧時會產生單態氧。在免疫系統中，單態氧是活性氧的來源之一。光合作用會利用陽光的能量，從水產生出單態氧。在進行光合作用的生物中，類胡蘿蔔素有助吸收單態氧的能量，並將它轉換成基態氧，從而避免單態氧對組織造成損壞。
## 製取
### 發生
#### 化學方法
**加熱氯酸鉀**
: 實驗室小規模製氧一般會加熱氯酸鉀和催化劑二氧化錳的混合物，生成氧氣和氯化鉀。其中，二氧化錳是催化劑。其發生裝置是固固加熱型，需要使用試管。
: ${\ce {2KClO3{\overset {MnO2}{\underset {\vartriangle }{=\!=\!=\!=}}}{2KCl}+3O2\uparrow }}$
: 用此方法製得的氧氣通常混有少量刺激性氣味的氣體氯氣。
**加熱高錳酸鉀**
: 加熱高錳酸鉀生成錳酸鉀、二氧化錳和氧氣。發生裝置與加熱氯酸鉀制氧氣的裝置相同，但試管口需要塞棉花，避免加熱時高錳酸鉀粉末進入導管而堵塞導管。導管被堵塞時，試管內壓強增大，有可能導致試管炸裂。 | [
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氧氣 | : ${\ce {2KMnO_{4}{\overset {\vartriangle }{=\!=}}{K2MnO4}+{MnO2}+O2\uparrow }}$
**分解過氧化氫**
: 用過氧化氫溶液（雙氧水）和催化劑二氧化錳反應的方法也可以製得氧氣，同時產生水。發生裝置為固液不加熱型裝置，通常使用錐形瓶，有時需要分液漏斗。
: ${\ce {2H2O2{\overset {MnO2}{=\!=\!=\!=}}{2H2O}+O2\uparrow }}$
: 這種方法簡單易操作，節約能源，且生成物沒有污染，是實驗室製取氧氣的常用方法之一。
**電解水**
: 電解水也能製得氧氣。電解水時，正極產生氧氣，負極產生氫氣。氫氣的體積比氧氣體積的 2 倍多一點點（氧氣不易溶於水，氫氣難溶於水）。
: ${\ce {2H2O{\overset {\text{通 电}}{=\!=\!=\!=}}{2H2\uparrow }+O2\uparrow }}$
: 需要注意的是，化學方程式中的「通電」不能寫成「電解」。
#### 物理方法
物理製取氧氣的方法通常用於工業上。使用分離液態空氣法（利用空氣中各氣體的沸點不同來分離出氧氣）。
**低溫製取**
: 氧氣的熔點、沸點與其他氣體不同，所以可以利用這一特性將空氣冷卻至 - 200℃以下，然後濾出氧氣。
**分子篩**
: 高分子透氧膜可以快速將氧氣過濾出來。
### 收集
氧氣不易溶於水，密度比空氣大，所以可以用排水集氣法收集比較純的氧氣，或者使用向上排空氣法收集較乾燥的氧氣。
### 裝瓶
中國國家標準規定，氧氣氣瓶為淡藍色，而美國則用綠色。
## 單重態氧和三重態氧
普通氧氣含有兩個未配對的電子，等同於一個雙游離基。兩個未配對電子的自旋狀態相同，自旋量子數之和 S = 1，2S + 1 = 3，因而基態的氧分子自旋多重性為 3，稱為三重態氧。
在受激發下，氧氣分子的兩個未配對電子發生配對，自旋量子數的代數和 S = 0，2S + 1 = 1，稱為單重態氧。
空氣中的氧氣絕大多數為三重態氧。紫外線的照射及一些有機分子對氧氣的能量傳遞是形成單重態氧的主要原因。單重態氧的氧化能力高於三重態氧。
單重態氧的分子類似烯烴分子，因而可以和雙烯發生狄爾斯 - 阿爾德反應。
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氧氣 | 雖然呼吸需要氧氣，但是人和動物長期待在高壓氧艙中，或者呼吸純氧會發生氧氣中毒，造成神經中毒的現象。其毒理過程為肺部毛細管屏障被破壞，導致肺水腫、肺淤血和出血，嚴重影響呼吸功能，進而使各臟器缺氧而發生損害。
## 用途
氧氣的運用包括鋼鐵的冶煉、塑料和紡織品的製造以及作為火箭推進劑與進行氧氣療法，也用來在飛機、潛艇、太空船、潛水及火災中維持生命。
### 供給呼吸
除厭氧菌外，幾乎所有的生物都需要氧氣來呼吸。生物細胞內的粒線體會將氧氣轉化為二氧化碳，同時釋放能量。同時，綠色植物葉綠體光合作用迅速產生氧氣。當生物圈內消費者（或二氧化碳排放）過多而綠色植物（生產者）過少，氧氣就會減少，即破壞碳 — 氧平衡、溫室效應。
在太空船等封閉空間，人呼吸會消耗氧氣，此時可以通過催化劑使二氧化碳轉化為氧氣。在室內等封閉空間擺放綠色植物也可以增加氧氣，但是綠色植物在晚上或者陰雨天不適宜擺在室內。
### 助燃
幾乎所有的可燃物燃燒都需要氧氣。能夠支持聚合物燃燒的氧氣的最小濃度叫作極限氧指數。
可燃物燃燒是劇烈氧化反應，常見的燃燒有：
* 硫： ${\ce {S{}+O2{\overset {\text{点 燃}}{=\!=\!=\!=}}SO2}}$
* 碳：
* 氧氣充足時： ${\ce {C{}+O2{\overset {\text{点 燃}}{=\!=\!=\!=}}CO2}}$
* 氧氣不充足時： ${\ce {2C{}+O2{\overset {\text{点 燃}}{=\!=\!=\!=}}2CO}}$
* 鎂： ${\ce {2Mg{}+O2{\overset {\text{点 燃}}{=\!=\!=\!=}}2MgO}}$
* 鐵：只能在純氧中燃燒： ${\ce {3Fe{}+2O2{\overset {\text{点 燃}}{=\!=\!=\!=}}Fe3O4}}$
* 一氧化碳： ${\ce {2CO{}+O2{\overset {\text{点 燃}}{=\!=\!=\!=}}2CO2}}$
* 磷： ${\ce {4P{}+5O2{\overset {\text{点 燃}}{=\!=\!=\!=}}2P2O5}}$
* ……
鎂是一個例外。鎂在氧氣、二氧化碳、氮氣中都能夠燃燒。
## 參考來源
## 參見
* 氧
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渺子 | **緲子**（**渺子**，**muon**）是一種帶有一個單位負電荷、自旋為 1/2 的基本粒子。緲子與同屬於輕子的電子和陶子具有相似的性質，人們至今未發現輕子具有任何內部結構（理論上，這是因為重夸克組經過弱作用力衰變時，同時，重夸克組內部結構的強子共振生命期結束 -- 注意到這過程需遵守狹義相對論規範的因果律，蛻變成較輕的輕子如電子，並因質能虧損放出能量由做週期味變換的基本粒子如微中子家族帶走）。歷史上，人們曾經將緲子稱為 **μ 介子**，但現代粒子物理學認為緲子並不屬於介子（參見歷史）。
每一種基本粒子都有與之對應的反粒子，緲子的反粒子是**反緲子**(**反渺子**,**antimuon**)。反緲子（μ+）與緲子（μ-）相比只是帶一個單位的正電荷，質量、自旋等性質完全相同，因此又叫做正緲子。
與其他帶電的輕子一樣，緲子有一個與之伴隨的微中子 —— **緲微中子**（νμ）。緲微中子與電微中子 νe 參與的反應不同，是兩種不同的粒子。
## 性質
緲子的質量為 105.7MeV/c2，大約是電子質量的 206~207 倍。由於緲子的性質與電子相似，因而可以把緲子想像成一個靜止質量「加重版」的電子。由於質量較電子為大，緲子在電磁場中的加速和偏轉比電子要慢，發出的軔致輻射也較電子少，這使得緲子比相同能量的電子能夠穿透更厚的物質。例如，宇宙射線中的緲子能夠穿透厚達數十萬米的大氣層到達地表，甚至能到達數百米深的礦井之中。
緲子的質量和能量遠大於常見放射性衰變的衰變能，因此緲子不能通過放射性衰變產生。緲子可以在加速器上進行的高能物理實驗中通過強子參與的核反應產生，此外，宇宙射線與地球大氣作用也會產生大量緲子，這也是已知唯一的天然的緲子來源（見來源）。
緲子是一種不穩定的次原子粒子，平均壽命為 2.2 微秒。與其他不穩定的次原子粒子相比，緲子的壽命相對較長（僅短於中子的 881.5 秒）。
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渺子 | 緲子最早由卡爾・安德森和賽斯・內德梅耶於 1936 年發現。他們在研究宇宙射線在電磁場中的運動時，發現了一種彎曲程度不同於電子和其他已知粒子的徑跡。根據在磁場中的偏轉方向能夠判斷這種粒子帶有帶負電，對於同樣的速度，這種粒子的偏轉半徑比電子的大得多，同時又比質子的小的多。他們假定這種粒子帶有與電子相同的電荷量，由此他們計算出這種粒子的質量介於電子和質子之間，大約是電子的 200 倍，據此他們將這種粒子命名為「**mesotron**」，意為「中間的粒子」。1937 年，J. C. Street 和 E. C. Stevenson 在雲室實驗中再次確認了緲子的存在。
在此之前，日本理論物理學家湯川秀樹已經預言過介子的存在
>
> 「對海森堡和費米的理論作如下改進是很自然的，重粒子從中子態到質子態的躍遷不總是伴隨著輕粒子的發射，有時也會發射另一個重粒子。」
>
>
由於質量與預言的範圍相符，人們認為緲子就是湯川秀樹理論中的介子，因此將它稱為 μ 介子（mu meson）。但是後來發現緲子並不參與強交互作用，從而與理論不符。湯川預言的粒子直到 1947 年才（同樣是從宇宙射線中）被發現。在此之前，介子指的是質量介於電子和質子之間的（那種）粒子，為了區別這兩種「介子」，將之前安德森發現的並被稱為「μ 介子」（希臘字母小寫 μ），而這種新的介子則被稱為 π 介子。
後來，更多的介子在加速器實驗上被人們發現，最終人們發現最早發現的 μ 介子不僅與 π 介子性質差異很大，而且與其他介子的性質差異也很大。這種差異主要有以下幾點：
1. π 介子和其他新發現的介子能夠參與強交互作用，而 μ 介子不能；
2. 新發現的介子在核反應中的行為與 π 介子相似，而與 μ 介子不同；
3. μ 介子衰變後產生一個微中子和一個反微中子，而 π 介子和其他介子則產生一個微中子或一個反微中子。
直到 1970 年代，粒子物理的標準模型建立以後，人們才最終明白，除 μ 介子以外的其他所有介子都是強子，即由夸克組成的粒子，因而可以參與強交互作用。在夸克理論中，介子不再根據粒子的質量來定義，而是重新定義為「由兩個夸克（一個正夸克和一個反夸克）構成的粒子」（由三個夸克構成的粒子叫做重子）。此時人們發現，μ 介子並不存在夸克結構，是一種類似於電子的基本粒子。從此人們不再稱其為「μ 介子」，而是簡單地稱為緲子（muon）。 | [
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渺子 | 理論計算可知若想產生緲子，粒子的質心系能量要大於 105.7MeV，在核反應中這個能量是相當大的，因而通常的放射性衰變、核分裂甚至是核融合都無法產生緲子。只有裂變中產生的單核子事件有可能超過此能量，但是這樣產生單個的緲子的反應中的量子數不守恆，從而不會發生（見衰變）。
在地球上，大部分天然產生的緲子來源於宇宙射線。在初級宇宙射線（最初照射到地球上的宇宙射線）中，有大約 89% 是質子，這些質子來自宇宙深處，具有非常高的能量。這些質子與地球外圍大氣中的分子發生碰撞，產生 π 介子。π 介子在經過一段相對較短（米量級）的距離後就衰變為緲子和微中子。高空觀測表明大多數的緲子是在海平面 15 公里左右產生的，產生的緲子能量很高，它們幾乎保持著原來質子的方向以接近光速的速度沖向地面。
### 與狹義相對論的關係
若根據古典力學的速度公式，以 2.2 微秒的平均壽命計算，產生的緲子運動的平均距離只有約 660 米，這樣一來似乎只有極少數的緲子能夠穿過 15 千米的大氣到達地面。但是事實上在海平面能夠觀測到的緲子事例（大約 1000 個 /(平方米・分鐘)）數量遠高於這一預計，這需要用狹義相對論來解釋。2.2 微秒是緲子靜止時的平均壽命，根據狹義相對論的鍾慢效應，若以地面作為參照系，緲子是在高速運動著的，因此它的時間會變慢。緲子的速度越是接近光速，時間變慢越明顯，因此在地球上的觀察者看來，緲子的壽命比 2.2 微秒長得多，所以大部分緲子能夠在衰變前到達地面。若以緲子作為參照系，它的壽命仍是 2.2 微秒，但地面卻是相對於自身以接近光速的速度「迎面撲來」，根據狹義相對論的尺縮效應，原本厚達 15 千米的大氣層變得很薄，大部分的緲子能夠在衰變前穿過這一厚度。需要注意的是以上兩種分析是完全等價的，這一實驗也被認為是證明相對論效應存在的古典證據。
在到達海平面的宇宙射線（次級宇宙射線）中，緲子占了超過一半的比例，剩餘主要是中子、正負電子和 π 介子。由於具有很強的穿透力，在幾百米深的地下或山體中進行的科學實驗（如微中子探測實驗）中也需要認真考慮緲子的影響。
上面描述的初級宇宙射線中質子打出 π 介子，進而衰變成緲子的反應，也可以通過高能加速器來產生。加速器能夠產生通量很高的緲子束流，用於多種科學實驗。
## 衰變
緲子是一種不穩定的基本粒子，通過弱交互作用發生衰變，最常見的衰變路線為一個電子、一個反電微中子和一個緲微中子： | [
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渺子 | : $\mu ^{-}\to e^{-}+{\bar {\nu }}_{e}+\nu _{\mu },$
反緲子對應的衰變方式是它的鏡像：
: $\mu ^{+}\to e^{+}+\nu _{e}+{\bar {\nu }}_{\mu }$ .
由費米黃金定則得到的緲子衰變寬度為
: $\Gamma ={\frac {G_{F}^{2}m_{\mu }^{5}}{192\pi ^{3}}}I\left({\frac {m_{e}^{2}}{m_{\mu }^{2}}}\right),$
其中 $I(x)=1-8x-12x^{2}\ln x+8x^{3}-x^{4}$ ，而 $G_{F}^{2}$ 是費米耦合常數。
緲子衰變中電子的衰變分布由四個米歇爾參量 $\rho ,\eta ,\xi $ 和 $\delta $ 來描述，這些參數的值能夠由標準模型準確得到。將標準模型預測的參數代入後得到的衰變寬度的表達式為：
: ${\frac {d^{2}\Gamma }{dx\,d\cos \theta }}\sim x^{2}[(3-2x)+P_{\mu }\cos \theta (1-2x)].$
將此式對電子能量積分即得生成電子的角分布：
: ${\frac {d\Gamma }{d\cos \theta }}\sim 1-{\frac {1}{3}}P_{\mu }\cos \theta .$
所有方向上電子的能量分布為：
: ${\frac {d\Gamma }{dx}}\sim (3x^{2}+2x^{3}).$
通過實驗測量到的結果與標準模型的預言符合得很好，這是對弱交互作用時空結構很好的一個檢驗。
由於緲子通過弱交互作用進行衰變，因此不滿足宇稱守恆。用 $\cos \omega t$ 代替米歇爾參量中的 $\cos \theta $ ，其中 $\omega $ 是緲子在勻強磁場中做拉莫爾進動的頻率，即拉莫爾頻率：
: $\omega ={\frac {egB}{2m}}$
其中 m 是緲子的質量，e 是電子電量，g 是緲子的 g - 因數（g-factor），B 是磁場的磁感應強度。
不通過發射微中子發生的緲子衰變雖然在能量上看是允許的，但是被標準模型禁止。如以下兩種衰變因不滿足味量子數守恆而禁戒：
: $\mu ^{-}\to e^{-}+\gamma $ | [
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渺子 | : $\mu ^{-}\to e^{-}+e^{+}+e^{-}$ .
如果在實驗中發現以上衰變道，將成為支持標準模型以外理論的證據。對上述衰變道的實驗測量已經持續了幾十多年，MEG 給出的最新實驗結果顯示： $\mu ^{-}\to e^{-}+\gamma $ 反應分支比的上限為 2.4×10−12。
## μ 原子
緲子是人類發現的第一種在不存在於原子內部的基本粒子，但是由於緲子可以被看做是一個加重了的電子，它有時可以取代原子中的一個電子而形成類原子結構，這種結構被稱為 **μ 原子**，如一個緲子能夠取代氫原子中唯一的電子而形成「μ- 氫原子」。μ- 氫原子的半徑比氫原子小得多，因為緲子的質量比電子大，形成原子的基態波函數更向原子核集中。在有多個電子的原子中，當只有一個電子被緲子取代的情況下，測量到的原子的半徑主要由其他的電子決定，因而基本上保持不變。但是在這種原子中緲子的軌道半徑仍然要比其他電子的小很多。由原子核和緲子組成的原子核具有更小的庫侖障壁，因而有可能在室溫下發生冷融合。
μ- 氦原子是一個緲子取代了氦 4 原子中的一個電子後形成的。μ- 氦原子中緲子距離氦核很近，中和掉了一個質子的電量，因而可以近似被當成是氫的一種同位素。在這種「同位素」中，核內含有兩個質子、兩個中子和一個緲子，只有一個核外電子。由於緲子的質量近似是 0.1 原子質量，因而稱這種同位素為「氫 4.1」。μ- 氦原子可以跟其他原子結合形成分子，在化學反應上的行為更像是一個氫原子而非氦原子。
一個正緲子也可以與一個電子結合，形成一個以正緲子為「原子核」的奇異原子，稱為緲子素，這時的正緲子可以當成一個的氫的一種假同位素。由於質量只有質子的 1/9，緲子素的波耳半徑與氫原子的很接近。這種短壽命的「原子」的化學性質類似於氕、氘和氚。
## 應用
宇宙射線中的緲子可以被看作是「免費」的粒子源，緲子的強穿透能力使它可以穿透很厚的屏蔽層從而用於對重元素材料的檢測。1955 年，George E P 利用緲子注量在地下的衰減測量了岩層的厚度。後來 Alcarez L 等人將該方法應用於大的建築物考古成像及地質結構的測量。近年來緲子成像技術得到了關注和研究，即利用緲子穿過原子質量不同的物質時具有不同的散射角原理，對大型物質進行輻射成像。這種新型的檢測方法應用於核安全領域，能夠有效探測到封裝良好的核材料，如鈾 - 235、鈽 - 239 等。
* 標準模型
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] |
渺子 | * 粒子列表
## 資料來源
## 外部連結
* http://arxiv.org/ftp/physics/papers/0003/0003023.pdf （頁面存檔備份，存於網際網路檔案館）
* https://web.archive.org/web/20041213184419/http://www.bartleby.com/65/el/elemparTABLE.html
* http://www.pbs.org/wgbh/nova/elegant/part-flash.html （頁面存檔備份，存於網際網路檔案館） | [
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凡得瓦力 | **凡得瓦力**（英語：van der Waals force）又名**范德華力**、**范德瓦耳斯力**，在化學中指分子或原子之間非定向的、無飽和性的、較弱的交互作用力，根據荷蘭物理學家約翰內斯・范德瓦耳斯命名。凡得瓦力是一種電性重力，但它比化學鍵或共價鍵弱得多，通常其能量小於 5kJ/mol。凡得瓦力的大小和分子的大小成正比。
凡得瓦力的主要來源有三種機制：
1. 取向力（偶極－偶極力）：極性分子之間的交互作用力
2. 誘導力（偶極－誘導偶極力）：極性分子極化非極性分子，產生誘導偶極矩，並交互作用
3. 分散力：一對非極性分子由於本身電子的機率運動，可以相互配合產生一對方向相反的瞬時偶極矩，這一對瞬時偶極矩交互作用。這種機制是非極性分子中凡得瓦力的主要來源，1930 年由 F.W. 倫敦首先根據量子力學原理給出解釋
凡得瓦力的大小會影響物質尤其是分子晶體的熔點和沸點，通常分子的分子量越大，凡得瓦力越大。**水**（氧化氫）比硫化氫的相對分子質量小，因此凡得瓦力比後者弱，但由於水分子間存在更強的氫鍵，熔沸點反而更高。壁虎能夠在牆及各種表面上行走，便是因為腳上極細緻的匙突（spatulae）和接觸面產生的凡得瓦力所致。
## 方程式
對於無極性分子，兩分子間作用力可近似用以下半經驗公式表示：
: $F(r)={\frac {\lambda }{r^{s}}}-{\frac {\mu }{r^{t}}}$
## 參見
* 范德華方程式
* 蘭納 - 瓊斯勢
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电容 | 在電路學裡，給定電壓，電容器儲存電荷的能力，稱為**電容**（capacitance），標記為 **C**。採用國際單位制，電容的單位是法拉（farad），標記為 **F**。
平行板電容器是一種簡單的電容器，是由互相平行、以空間或介電質隔離的兩片薄板導體構成。假設這兩片導板分別載有負電荷與正電荷，所載有的電荷量分別為 $-Q\,\!$ 、 $+Q\,\!$ ，兩片導板之間的電位差為 $V$ ，則這電容器的電容 $C$ 為
: $C={\frac {Q}{V}}$ 。
由上式知 1 法拉 (Farad) 等於 1 庫侖 (Coulomb) 每伏特 (Voltage)。在正常狀況下 1 法拉的電容多加 1 伏特的電位差可以多儲存 1 庫侖的電荷。
電容器所儲存的能量等於充電所做的功。思考前述平行板電容器，搬移微小電荷元素 $\mathrm {d} q$ 從帶負電薄板到帶正電薄板，每對抗 1 伏特的電位差，需要作功 $\mathrm {d} W$ ：
: $\mathrm {d} W={\frac {q}{C}}\,\mathrm {d} q$ 。
將這方程式積分，可以得到儲存於電容器的能量。從尚未充電的電容器（ $q=0$ ）開始，搬移電荷從帶負電薄板到帶正電薄板，直到這兩片薄板分別擁有電荷量 $-Q$ 、 $+Q$ ，所需要作的功 $W$ 為
: $W_{\text{charging}}=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {Q^{2}}{2C}}={\frac {1}{2}}CV^{2}=U_{\text{stored}}$ ；
其中， $U_{\text{stored}}$ 是儲存的能量。
## 單位
電容的單位是法拉，簡稱「法」，單位符號為「F」，是國際單位制導出單位。與其他物理量的關係：一法拉等於一庫侖除以一伏特。一般來說，1 法拉算是很大的電容，大多數用於電子電路的電容器，其電容會小於法拉幾個數量級，常用的單位有「微法拉」（microfarad，μF），等於 $10^{-6}$ 法拉；以及「奈法拉」（nanofarad，nF），等於 $10^{-9}$ 法拉。在微波工程領域中，有時會使用到較小的「皮法拉」（picofarad，pF），等於 $10^{-12}$ 法拉；甚至更小的「飛法拉」（femtofarad，fF），等於 $10^{-15}$ 法拉。
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] |
电容 | 1F=10^{6}\mu F=10^{9}nF=10^{12}pF=10^{15}fF.
$$
## 電容器
假設，給定電容器的幾何形狀和電容器內部的介質性質，則可以計算出電容。如前圖所示，假設平行板電容器的兩片導板的面積都是 $A$ ，間隔距離為 $d$ ，則兩片導板的面電荷密度分別為 $-\sigma $ 、 $+\sigma $ ：
: $\sigma =Q/A$ 。
應用高斯定律（詳盡細節，請參閱條目電位移），在兩片導板之間的電場 $E$ 為
: $E=\sigma /\varepsilon =Q/\varepsilon A$ ；
其中， $\varepsilon $ 是介質的電容率。
兩片導板的電位差為
: $V=Ed=\sigma d/\varepsilon =Qd/\varepsilon A$ 。
所以，電容為
: $C=Q/V=\varepsilon A/d$ 。
電容與導板面積 A 成正比，與導板間隔距離 d 呈反比，這是在假設平板電容器的面積 A 相當大的情況下，可以忽略電容器邊緣的效應。假設間隔距離 $d$ 遠小於導板的長度與寬度，則上述方程式乃優良近似；在電容器內大部分區域的電場是均勻的；在電容器周圍的邊緣電場只給出很小貢獻，可以被忽略。
### 電壓依賴性電容器
許多常用的電介質，其電容率會隨著外電場的變化而改變，是外電場的函數。鐵電性物質就是這種電介質。使用這種電介質的電容器，其電容會比較複雜。例如，當這種電容器在充電時，電荷與電壓（電位差）的關係為
: $\mathrm {d} Q=C(V)\ \mathrm {d} V$ 。
在上述方程式裏，電容對於電壓的依賴性 $C(V)$ ，是因為電場產生的。一個平行板電容器的電場為
: $E=V/d$ 。
這電場將電介質電極化，從而增加導板儲存電荷的能力。如右圖所示，對於鐵電性物質，電極化強度對電場曲線顯示出遲滯現象。這是一個非線性關係。
假設電極化強度 $P$ 與電場、電壓的關係為
: $P=f(E)=f(V/d)=g(V)$ ；
其中， $f(E)$ 、 $g(V)$ 分別為良態函數（well-behaved function）。
根據電位移 $D$ 的定義，
: $D=P+\epsilon _{0}E=g(V)+\epsilon _{0}V/d$ 。
應用自由電荷高斯定律，導板載有的電荷量為 | [
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电容 | : $Q=DA=(g(V)+\epsilon _{0}V/d)A$ 。
所以，電容為
: $C(V)={\frac {Q}{V}}={\frac {g(V)A}{V}}+{\frac {\epsilon _{0}A}{d}}$ 。
假設 $g(V)$ 是線性函數， $g(V)=kV$ ， $k$ 是常數，則電容與電壓無關：
: $C={\frac {Q}{V}}=kA+{\frac {\epsilon _{0}A}{d}}$ 。
否則，假設 $g(V)$ 是非線性函數，則電容與電壓成非線性關係。
繼續思考這跟電壓有關的電容，假若將電容器充電至電壓 $V$ ，則電容器的兩片導板會分別帶有電量 $+Q$ 、 $-Q$ ：
: $Q=\int _{0}^{V}C(V')\ \mathrm {d} V'$ 。
當電容與電壓無關時，這方程式變為 $Q=CV$ 。
儲存於電容器的微分能量為
: $\mathrm {d} U_{\text{stored}}=Q\mathrm {d} V''=\left[\int _{0}^{V''}\ C(V')\ \mathrm {d} V'\right]\mathrm {d} V''$ 。
應用分部積分法：
: $\int _{a}^{z}f(x)g'(x)\ \mathrm {d} x=\left[f(x)g(x)\right]_{a}^{z}-\int _{a}^{z}f'(x)g(x)\ \mathrm {d} x$ ，
分別設定 $f(x)=\int _{a}^{x}\ h(y)\ \mathrm {d} y$ 、 $g(x)=x$ ，帶入上述方程式，則可得到
: $\int _{a}^{z}\int _{a}^{x}\ h(y)\ \mathrm {d} y\ \mathrm {d} x=\left[\int _{a}^{x}\ xh(y)\ \mathrm {d} y\right]_{a}^{z}-\int _{a}^{z}xh(x)\ \mathrm {d} x=\int _{a}^{z}zh(y)\ \mathrm {d} y-\int _{a}^{z}yh(y)\ \mathrm {d} y=\int _{a}^{z}\ \left(z-y\right)h(y)\ \mathrm {d} y$ 。 | [
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电容 | 設定 $x=V''$ 、 $y=V'$ 、 $h(y)=C(V')$ 、 $a=0$ 、 $z=V$ ，則可計算出儲存於電容器的能量：
: $U_{\text{stored}}=\int _{0}^{V}\ \left[\int _{0}^{V''}\ C(V')\ \mathrm {d} V'\right]\mathrm {d} V''=\int _{0}^{V}\ \left(V-V'\right)C(V')\ \mathrm {d} V'$ 。
掃描非線性介質顯微鏡（scanning nonlinear dielectric microscope）的探針掃描於鐵電性物質表面所測量到的非線性電容，可以用來研究鐵電性物質的鐵電疇（ferroelectric domain）結構。
有些半導體元件的電容可以用電壓控制。例如，當變容二極體的逆向偏壓增加時，空乏層厚度也會增加，因而使得電容降低。
### 頻率依賴性電容器
假若電容器兩端驅動的含時電壓變化太快，則電介質的電極化強度可能會無法跟上訊號。從微觀層次解釋這機制，在電介質內部，決定電容率的微小電偶極子無法瞬時地移動，因此，當施加的交流電壓的頻率增加時，電偶極子只能給出有限的響應，從而造成電容率降低。電容率與頻率的關係稱為介電色散（dielectric dispersion），是由介電弛豫（dielectric relaxation）過程所主控，像德拜弛豫（Debye relaxation）。從更基本的微觀分析來計算，例如對於介質內的電偶極子行為的微觀分析，處於暫態狀況，電位移場可以表達為（更詳盡細節，請參閱電極化率）
: ${\boldsymbol {D}}(t)={\frac {\varepsilon _{0}}{\sqrt {2\pi }}}\int _{-\infty }^{t}\mathrm {d} t'\ \varepsilon _{r}(t-t'){\boldsymbol {E}}(t')$ ；
其中， $\varepsilon _{0}$ 是電常數， $\varepsilon _{r}\ {\stackrel {def}{=}}\ \varepsilon /\varepsilon _{0}$ 是相對電容率。 | [
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电容 | 相對電容率的時間依賴可以用線性響應函數（linear response function）來描述。上述方程式顯示出相對電容率的時間依賴所產生的滯後響應。這積分式的積分域從整個過去歷史一直延伸至現時。假設每當 $\Delta t<0\,\!$ 時， $\varepsilon _{r}(\Delta t)=0\,\!$ ，則這積分的上限可以延伸至無窮大：
: ${\boldsymbol {D}}(t)={\frac {\varepsilon _{0}}{\sqrt {2\pi }}}\int _{-\infty }^{\infty }\mathrm {d} t'\ \varepsilon _{r}(t-t'){\boldsymbol {E}}(t')$ 。
對於時間做傅立葉變換，根據摺積定理，可以得到
: ${\boldsymbol {D}}(\omega )=\varepsilon _{0}\varepsilon _{r}(\omega ){\boldsymbol {E}}(\omega )$ ；
其中， $\omega $ 是角頻率。
$\varepsilon _{r}(\omega )$ 是複函數，其虛值部分與介質的電場能量吸收有關。更詳盡細節，請參閱條目電容率。由於電容與電容率成正比，電容也具有這頻率行為。對於時間做傅立葉變換於高斯定律：
: $Q(\omega )=\oint _{\mathbb {S} }\mathbf {D} (\mathbf {r} ,\omega )\cdot \mathrm {d} \mathbf {a} $ ；
其中， $\mathbb {S} $ 是閉曲面， $Q$ 是在 $\mathbb {S} $ 內的自由電荷量， $\mathbf {r} $ 是場位置， $\mathrm {d} \mathbf {a} $ 是微小面元素。
流入閉曲面 $\mathbb {S} $ 的電流 $I(t)={\frac {dQ}{dt}}$ ，變換至角頻率空間為 | [
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电容 | : ${\begin{aligned}I(\omega )&=j\omega Q(\omega )=j\omega \oint _{\mathbb {S} }\mathbf {D} (\mathbf {r} ,\omega )\cdot \mathrm {d} \mathbf {a} \\&=\left[G(\omega )+j\omega C(\omega )\right]V(\omega )={\frac {V(\omega )}{Z(\omega )}}\\\end{aligned}}$ ；
其中， $j$ 是虛數單位， $G(\omega )$ 、 $C(\omega )$ 、 $V(\omega )$ 、 $Z(\omega )$ 、分別是角頻率空間的電導、電容、電壓、複值阻抗。
假設平行板電容器的兩片導板之間填滿了電介質，按照下述關係式，電介質的性質可以測量出來：
: $\varepsilon _{r}(\omega )=\varepsilon _{r}'(\omega )-j\varepsilon _{r}''(\omega )={\frac {1}{j\omega Z(\omega )C_{0}}}={\frac {C(\omega )}{C_{0}}}$ ；
其中， $\varepsilon _{r}'(\omega )$ 是實值部分， $\varepsilon _{r}''(\omega )$ 是虛值部分， $C(\omega )$ 是填滿電介質時的複值電容， $C_{0}$ 是沒有電介質時的電容（即平行板電容器的兩片導板之間是自由空間時的電容）。
深能級暫態譜學（deep-level transient spectroscopy）利用電容的時間響應來研究半導體的深能級缺陷。按照能級在半導體能隙的位置，缺陷分類為淺能級缺陷和深能級缺陷。淺能級缺陷的能級離導帶或價帶的能帶邊緣比較近，在 0.1eV 以內，處於這能級的電子或電洞很容易因熱運動而變成自由電子或自由電洞；一般而言，深能級缺陷離能帶邊緣比較遠，超過 0.1eV。但也有些物質的深能級缺陷離能帶邊緣雖然只有 0.001eV，仍舊能夠顯示出深能級缺陷的通常性質。 | [
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电容 | 金屬氧化物半導體電容器（MOS capacitor）是另一個電容與頻率有關的例子。對於這案例，少數載流子的緩慢生成意味著在高頻率狀況，只有多數載流子的響應能夠貢獻出電容，而在低頻率狀況，兩種載流子的響應都能夠貢獻出電容。
當頻率為光學頻率時，半導體的電容會展示出類似固體的能帶結構。精密的調制光譜學（modulation spectroscopy）測量方法，使用壓力或其它種應力來調制晶體結構，然後觀測光波的吸收或反射的相關變化。這方法貢獻出很多關於這些物質的性質的結果。
## 電容矩陣
前面論述的範圍局限於兩片任意尺寸、形狀的平行導板的案例。對於單獨的帶電導板，電容的定義方程式 $C\ {\stackrel {def}{=}}\ Q/V$ 仍舊成立；這單獨的帶電導板案例，可以視為這帶電導板處於帶有異性同量電荷圓球的中心，而這圓球的半徑趨向無窮大的案例。
對於多個導體的案例，或當兩個導體所帶淨電荷量不等於零的案例，方程式 $C=Q/V$ 不成立。為了處理這案例，詹姆斯・馬克士威提出了「電位係數」和「感應係數」（coefficients of induction）的概念。假設三個導體分別帶有電荷量 $Q_{1}$ 、 $Q_{2}$ 、 $Q_{3}$ ，則這三個導體的電位 $V_{1}$ 、 $V_{2}$ 、 $V_{3}$ 分別為
: $V_{1}=P_{11}Q_{1}+P_{12}Q_{2}+P_{13}Q_{3}$ 、
: $V_{2}=P_{21}Q_{1}+P_{22}Q_{2}+P_{23}Q_{3}$ 、
: $V_{3}=P_{31}Q_{1}+P_{32}Q_{2}+P_{33}Q_{3}$ ；
其中， $P_{ij}$ 是電位係數， $i,j=1,2,3$ 。
解析這線性方程組，可以得到電荷量分別為
: $Q_{1}=C_{11}V_{1}+C_{12}V_{2}+C_{13}V_{3}$ 、
: $Q_{2}=C_{21}V_{1}+C_{22}V_{2}+C_{23}V_{3}$ 、
: $Q_{3}=C_{31}V_{1}+C_{32}V_{2}+C_{33}V_{3}$ ；
其中， $C_{ii}$ 是第 $i$ 個導體的電容， $C_{ij}$ 是感應係數， $i\neq j$ 。
延伸至 $n$ 個導體， | [
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电容 | : $V_{i}=\sum _{j=1}^{n}P_{ij}Q_{j},\qquad \qquad i=1,2,\dots ,n$ 、
: $Q_{i}=\sum _{j=1}^{n}C_{ij}V_{j},\qquad \qquad i=1,2,\dots ,n$ 。
設定第 $i$ 個導體的電位為 1Volt，其它導體的電位為 0Volt，則對於這系統，第 $i$ 個導體的載電量等於其電容。
這樣，整個系統可以用一組係數來描述，稱為「倒電容矩陣」，以方程式定義為
: $P_{ij}\ {\stackrel {def}{=}}\ {\frac {\partial V_{i}}{\partial Q_{j}}}$ 。
整個系統又可以用另一組係數來描述，稱為「電容矩陣」，以方程式定義為
: $C_{ij}\ {\stackrel {def}{=}}\ {\frac {\partial Q_{i}}{\partial V_{j}}}$ 。
赫爾曼・馮・亥姆霍茲和威廉・湯姆森證明這些電位係數與感應係數都具有對稱性：
: $P_{ij}=P_{ji}$ 、
: $C_{ij}=C_{ji}$ 。
對於這 $n$ 導體系統，假設任意兩個導體分別載有負電荷 $-Q\,\!$ 與正電荷 $+Q\,\!$ ，其它導體皆與接地連結，則這兩個導體的電容定義為 $Q\,\!$ 除以其電位差：
: $C\ {\stackrel {def}{=}}\ Q/\Delta V$ 。
假設第 $i$ 與第 $j$ 個導體分別載有負電荷 $-Q\,\!$ 與正電荷 $+Q\,\!$ ，則第 $i$ 與第 $j$ 個導體的電位與電荷的關係式分別為
: $V_{i}=-P_{ii}Q+P_{ij}Q$ 、
: $V_{j}=-P_{ji}Q+P_{jj}Q$ 。
這兩個導體的電容為
: $C=Q/(V_{j}-V_{i})=1/(P_{ii}+P_{jj}-2P_{ij})$ 。
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电容 | 在電路學裏，電容通常是術語「互電容」（mutual capacitance）的簡稱，即兩個鄰近導體（像平行板電容器的兩片薄板）之間的電容。另外還有一種電路學性質術語「自電容」（self-capacitance），即單獨導體的電位每增加 1V 所需的電荷量。設定這電位等於零的參考點為一個理論球殼導體，其半徑為無窮遠，其球心與單獨導體同位置。假設這單獨導體是半徑為 $R$ 的球形導體，則其球表面電位為
: $V=Q/4\pi \varepsilon _{0}R$ ，
其自電容是
: $C=Q/V=4\pi \varepsilon _{0}R$ 。
### 範例
范德格拉夫起電機頂端的圓球形金屬導體，其半徑通常為 20 cm，這金屬導體的自電容為
: $C=4\pi \varepsilon _{0}R=4\pi \times 8.85\times 10^{-12}\times 0.2\approx 22[pF]$ 。
地球的半徑約為 6.378×106m，其自電容為
: $C=4\pi \times 8.85\times 10^{-12}\times 6.378\times 10^{6}\approx 700[\mu F]$ 。
## 雜散電容
任意兩個相鄰導體，除非長久保持很近的距離，其電容通常很微小，但仍舊可以被視為電容器。這不受歡迎的效應稱為「雜散電容」。原本各自孤立的電路，由於雜散電容的作用，可能會讓兩個電路互相干擾對方的信號，這效應稱為串擾。雜散電容是電路在短波波段正常操作的限制因子。
為了消除跟遠方形成的雜散電容，可以將電路裝置於金屬機殼內，再將金屬機殼跟地線連結。
## 簡單系統的電容
欲求得一個系統的電容，必須先解析拉普拉斯方程式 $\nabla ^{2}\phi =0$ ，並且滿足其邊界條件，即在每一個導體表面的電位 $\phi $ 為某不同的已設定常數。對於具有高對稱性的案例，這方法很簡單。但是，對於較複雜案例，可能不存在以基本函數表示的解答。
對於準二維問題，不同的幾何構形之間可以用解析函數互相映射。詳盡細節，請參閱條目施瓦茨 - 克里斯托費爾映射
## 英文名稱
電容的英文也稱為 Capacity。但現在 Capacity 又另有電量的意思。
## 參閱
* 電容位移傳感器
* 水力學類比
* 量子電容
* 國際單位制導出單位
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时间复杂性 | 在電腦科學中，演算法的**時間複雜度**（time complexity）是一個函式，它定性描述該演算法的執行時間。這是一個代表演算法輸入值的字串的長度的函式。時間複雜度常用大 O 符號表述，不包括這個函式的低階項和首項係數。使用這種方式時，時間複雜度可被稱為是漸近的，亦即考察輸入值大小趨近無窮時的情況。例如，如果一個演算法對於任何大小為 _n_ （必須比 _n0_ 大）的輸入，它至多需要 5_n_3 + 3_n_ 的時間執行完畢，那麼它的漸近時間複雜度是 O (_n_3)。
為了計算時間複雜度，我們通常會估計演算法的操作單元數量，每個單元執行的時間都是相同的。因此，總運行時間和演算法的操作單元數量最多相差一個常數係數。
相同大小的不同輸入值仍可能造成演算法的執行時間不同，因此我們通常使用演算法的最壞情況複雜度，記為 **_T_(_n_)** ，定義為任何大小的輸入 _n_ 所需的最大執行時間。另一種較少使用的方法是平均情況複雜度，通常有特別指定才會使用。時間複雜度可以用函式 _T_(_n_) 的自然特性加以分類，舉例來說，有著 _T_(_n_) = _O_(_n_) 的演算法被稱作「線性時間演算法」；而 _T_(_n_) = _O_(_M_n) 和 _M_n= O(_T_(_n_)) ，其中 _M_ ≥ _n_ > 1 的演算法被稱作「指數時間演算法」。
## 常見時間複雜度列表
以下表格統整了一些常用的時間複雜度類別。表中，poly (_x_) = _x_O(1)，也就是 _x_ 的多項式。
## 常數時間
若對於一個演算法， $T(n)$ 的上界與輸入大小無關，則稱其具有**常數時間**，記作 $O(1)$ 時間。一個例子是存取陣列中的單個元素，因為存取它只需要一條指令。但是，找到無序陣列中的最小元素則不是，因為這需要遍歷所有元素來找出最小值。這是一項線性時間的操作，或稱 $O(n)$ 時間。但如果預先知道元素的數量並假設數量保持不變，則該操作也可被稱為具有常數時間。
雖然被稱為「常數時間」，執行時間本身不須與問題規模無關，但它的**上界**必須是與問題規模無關的確定值。舉例，「如果 a > b 則交換 a、b 的值」這項操作，儘管具體時間會取決於條件「a > b」是否滿足，但它依然是常數時間，因為存在一個常數 t 使得所需時間總**不超過** t。
以下是一個常數時間的代碼片段：
```
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时间复杂性 | int item = list[index];
**if** (condition true) **then**
perform some operation that runs in constant time
**else**
perform some other operation that runs in constant time
**for** i = 1 **to** 100
**for** j = 1 **to** 200
perform some operation that runs in constant time
```
如果 $T(n)=O(c)$ ，其中 $c$ 是一個常數，這記法等價於標準記法 $T(n)=O(1)$ 。
## 對數時間
若演算法的 _T_(_n_) = **O(log _n_)**，則稱其具有**對數時間**。電腦使用二進位的記數系統，對數常常以 2 為底（即 log2 _n_，有時寫作 lg _n_）。然而，由對數的換底公式，loga _n_ 和 logb _n_ 只有一個常數因子不同，這個因子在大 O 記法中被丟棄。因此記作 O（log _n_），而不論對數的底是多少，是對數時間演算法的標準記法。
常見的具有對數時間的演算法有二元樹的相關操作和二分搜尋。
對數時間的演算法是非常有效的，因為每增加一個輸入，其所需要的額外計算時間會變小。
遞迴地將字串砍半並且輸出是這個類別函式的一個簡單例子。它需要 O（log n）的時間因為每次輸出之前我們都將字串砍半。
這意味著，如果我們想增加輸出的次數，我們需要將字串長度加倍。
## 冪對數時間
對於某個常數 _k_，若演算法的 _T_(_n_) = O((log _n_)k)，則稱其具有**冪對數時間**。例如，矩陣鏈排序可以通過一個 PRAM 模型。被在冪對數時間內解決。
## 次線性時間
對於一個演算法，若其符合 _T_(_n_) = o(_n_)，則其時間複雜度為**次線性時間**（**sub-linear time** 或 **sublinear time**）。實際上除了符合以上定義的演算法，其他一些演算法也擁有次線性時間的時間複雜度。例如有 O (_n_½) 葛羅佛搜尋演算法。 | [
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