反質子原子生成反應的反應截面積之理論模型

Abstract

反質子是質子的反粒子。在真空中，反質子的平均壽命幾乎是無限久；但在物質中，反質子的壽命非常短，因為反質子與質子碰撞會造成兩個粒子湮滅變成能量。在實驗上已經有很多關於反質子在液體或氣體的阻攔、捕獲和湮滅的研究，結果發現在反質子入射液態或氣態氦的實驗中，大多數被阻攔的反質子在〖10〗^(-11) 秒內湮滅，大約3％的反質子在湮滅前有平均3微秒的壽命。這極長的壽命由反質子被捕抓形成一個反質子氦原子(P ̅He^+)的推論解釋。然而，不論在實驗或理論上都很難求得捕抓的反應截面積(capture cross section)。從理論的角度來看，用完全量子的理論或非微擾的方法解這個問題的計算量仍超出現今超級電腦的運算能力；而可靠的近似計算只能適用在反質子碰撞較輕原子的情況，如氫、氦以及鋰。 在這篇論文中，我們提出了一個簡單的模型來計算原子捕抓反質子的反應截面積。根據Fermi和Teller的理論，捕抓過程可以用絕熱電離(adiabatic ionization) 的機制解釋，但他們模型的推論結果與可靠的計算結果不一致。我們研究他們模型中可能出現的錯誤，像是在非絕熱效應(nonadiabatic effects)和古典直線軌跡的假設。我們研究這兩個效應，提出了一種新的模型。在較低能量（約低於0.1 a.u.），反應截面積跟1/√E成正比的；在較高的能量（約高於0.1 a.u.），反應截面積是1/E.的線性函數。我們理論求得的反應截面積與可靠的理論結果相符。

Antiproton is the antiparticle of the proton. The lifetime of antiproton is almost infinite in the vacuum, but it is typically short in media since any collision with a proton will cause both particles to be annihilated in a burst of energy. The stopping, capture and annihilation of antiprotons in liquids and gases has been much studied experimentally, and found that, although most stopped antiprotons annihilate promptly (〖10〗^(-11) s), about 3% of all antiprotons (P ̅) annihilated with a 3 μs overall lifetime after being brought to rest in helium, if the stopping medium is solid, liquid or gaseous helium. This extremely long lifetime is explained by the idea of the capture of antiproton to form an antiprotonic helium atom (P ̅He^+). It is difficult, however, to obtain the capture cross section both theoretically and experimentally. From the theoretical point of view, the full quantal and nonperturbative solution of this problem is still out of the reach of the current high-power supercomputers, and reliable calculation has been achieved only in the cases of the collision of antiproton with the simple atoms, H, He, and Li. In this thesis, we propose a simple model to calculate the capture cross section of antiproton by atoms. According to Fermi and Teller, capture process can be explained by so called the adiabatic ionization mechanism, but the results of their model do not agree with the reliable results. We examine the possible faults in the model, that are the nonadiabatic effects and the assumption of classical straight line trajectory. We examined those two effects to propose a new model. In low energy (about lower than 0.1 a.u.), the formation cross section is proportional to 1/√E. In higher energy (about higher than 0.1 a.u.), the formation cross section is a linear function of 1/E. We found that our cross section agrees well with that obtained by reliable theories.