發(fā)布時(shí)間：2018-01-05 13:08

  本文關(guān)鍵詞：B樣條基組在原子物理及人工受限結(jié)構(gòu)中的若干應(yīng)用　出處：《中國科學(xué)院研究生院(武漢物理與數(shù)學(xué)研究所)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： B樣條基組 氫原子 堿土離子 超極化率 量子環(huán)

【摘要】：B樣條函數(shù)基組是定義在有限空間的由分段多項(xiàng)式構(gòu)成的基組,具有高局域性、近似完備性、和高可塑性等特點(diǎn)。這些獨(dú)有的特征使得其能夠很好地描述原子、分子的束縛態(tài)和連續(xù)態(tài),因而在原子結(jié)構(gòu)計(jì)算、碰撞動(dòng)力學(xué)以及原子與分子外場效應(yīng)研究中得到廣泛的應(yīng)用。本文把B-樣條基組方法應(yīng)用到簡單原子體系的精密能譜計(jì)算與外場效應(yīng)的研究中；同時(shí)構(gòu)建了滿足周期性邊界條件的新的基組,并應(yīng)用于量子環(huán)體系的能譜、磁場和雜質(zhì)效應(yīng)的研究中。論文主要內(nèi)容包括：(1)采用B樣條基組方法得到了氫原子精確的非相對(duì)論和相對(duì)論能級(jí)、波函數(shù)以及電偶極極化率和超極化率,精確確定了氫原子1s→2s和1s→3s躍遷的系列幻波長；針對(duì)1s→3s躍遷光譜測量,提出利用1371nm幻波長適用于氫原子的光囚禁方案以提高該躍遷光譜測量的精度。(2)發(fā)展了基于B樣條基組的有限場方法,利用模型勢計(jì)算得到了堿土離子Be+、Mg+、Ca+和Sr+離子低能態(tài)的極化率和超極化率理論值,為躍遷頻移的高階極化效應(yīng)的理論評(píng)估提供了參考數(shù)值；利用準(zhǔn)靜態(tài)近似給出了超極化效應(yīng)對(duì)光阱囚禁Ca+離子鐘躍遷頻移的影響。(3)氫原子QED修正領(lǐng)頭項(xiàng)涉及貝特對(duì)數(shù)項(xiàng)計(jì)算,本文采用B樣條基組在三種不同的規(guī)范下計(jì)算了氫原子的貝特對(duì)數(shù)項(xiàng),給出了不依賴前人結(jié)果的自洽驗(yàn)證；發(fā)展了有外電場存在時(shí)的貝特對(duì)數(shù)項(xiàng)的高效計(jì)算方法,為極化率的QED修正計(jì)算打下了基礎(chǔ)。(4)設(shè)計(jì)構(gòu)造了一種環(huán)形B樣條基組用于計(jì)算量子環(huán)中的電子波函數(shù),這種構(gòu)造的B樣條基組避免了傳統(tǒng)B樣條基組在定義區(qū)間兩端處存在導(dǎo)數(shù)不連續(xù)問題,滿足周期性邊界條件,并成功應(yīng)用于等人工受限結(jié)構(gòu)(量子環(huán))的能譜、磁場和雜質(zhì)效應(yīng)的研究中。
[Abstract]:The basis set of B-spline function is defined in finite space, which is composed of piecewise polynomials. It has the characteristics of high locality, approximate completeness, and high plasticity. These unique characteristics enable it to describe atoms well. The bound state and continuous state of the molecule are thus calculated in atomic structure. The collision dynamics and the field effect of atoms and molecules have been widely used. In this paper, the B-Spline basis set method has been applied to the precise energy spectrum calculation of simple atomic systems and to the study of external field effects. At the same time, a new basis group satisfying periodic boundary condition is constructed and applied to the energy spectrum of quantum ring system. In the study of magnetic field and impurity effect, the main contents of this paper include: 1) the exact nonrelativistic and relativistic energy levels, wave functions, electric dipole polarizabilities and hyperpolarizabilities of hydrogen atoms are obtained by using B-spline basis set method. The hydrogen atom was accurately determined by 1s. 鈫，

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