B样条基组方法在强外场中原子谱计算中的应用
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摘要
里德堡原子由于其长寿命和对外场的敏感等特性，是研究外场效应的理想体系。它们在外场中的行为涉及到原子物理和量子力学的许多基本概念和理论问题，如不可分离变量的量子力学体系的求解，连续态和束缚态的耦合及其对谱结构的影响，经典与量子的对应等。研究外场中的原子可以为天体物理、等离子体物理提供基本数据及其他应用。
本文发展了强外场下里德堡原子谱计算的有效方法，系统地应用于碱金属原子在电场、磁场、平行电磁场及交叉电磁场中的吸收谱、共振态的研究中。主要内容如下：
1．将B样条基与模型势相结合的方法用于锂原子和钠原子近离化阈的抗磁谱计算。波函数角向部分采用对称化的B样条基。对于处于磁场下的锂原子，在我们所讨论的能区内，该方法计算量小于R-矩阵与多通道量子亏损理论，但仍可给出与实验谱相符的结果。同样对钠原子离化阈附近的抗磁谱也做了计算，靠近电离阈时，发现体系连续态对谱线的影响变得很重要。
2．将B样条基与模型势相结合法推广到计算平行电磁场中碱金属里德堡原子的振子强度谱。对于锂原子，在B=0.594 T，F=5.33 V／cm的情况下，定量地分析了振子强度强弱的原因。在所讨论的能区内，我们比较了锂原子不同初态，例如2s和3s态的π光吸收谱，发现谱线结构非常相似，整体上相差一个常数因子。这表明，谱线结构主要由末态决定，几乎与初态无关。在平行电磁场下，对比锂原子与钠原子的吸收谱，发现原子实的作用对谱线的影响很大。
3．首次把B样条基展开方法推广到处理交叉电磁场中氢原子的Balmerα谱，计算结果与最近的理论结果非常吻合。进一步说明了B样条基矢展开法可有效处理原子在交叉电磁场中的问题。
4．首次采用B样条基与模型势和复坐标旋转相结合的方法，计算了低激发锂原子的Stark共振态。对最近文献中关于共振态能级位置和宽度的争论做了进一步的讨论和澄清，计算结果表明本文的方法是可行的、有效的，比较灵活且计算量小，便于推广到交叉电磁场下碱金属原子共振态的计算。
Rydberg atoms are ideal systems for studying the effect of external fields on atoms due to its long lifetime and sensitivity to external fields. Atoms in external fields relate to many basic theoretical problems in atomic physics, e.g. the solution for non-separable system, the coupling of discrete and continuum states and its influence on the structure of the spectrum, the quantum-classical correspondence and so on. The research on atoms in strong fields can provide essential data for astrophysics, plasma physics, and other applications.
In this paper, new effective methods dealing with the atoms in strong fields have been developed. These methods are applied to systematically investigate the spectra and resonances of alkali atoms in external electric and magnetic fields. The major contents of this paper are as follows:
1. We calculated near-threshold diamagnetic spectra of Li and Na atoms in strong fields by B-spline basis plus model potential (B-spline+MP) approach. The angular wave-functions are expanded in terms of the symmetry-adapted B-spline functions. For Li atom, in contrast with R-matrix+MQDT, the B-spline+MP method obtains a higher spectral accuracy with a smaller computational effort over the energy range of our study. For Na atom, the contribution of continuum states to the spectra becomes significant near threshold region.
2. We presented oscillator strength spectra of Li and Na in parallel electric and magnetic fields via the B-spline+MP method. In the case of Li atom, the oscillator strength is calculated and analysed in B = 0.594 T, F = 5.33 V/cm. We got the same form of spectrum byπphoto absorption from the Li (2s) initial state as that from the 3s state. The two spectra only differ by an overall constant. The structure of the spectrum, over the narrow energy ranges considered in this paper, can be independent of the initial state chosen for a given atom. The structure of the spectrum is determined by the final state only. Comparing the spectra of Li and Na, the marked effect of atomic core on the spectra can be found.
3. We presented oscillator strength spectra of the hydrogen Balmer α series in strong magnetic and electric fields with arbitrary mutual orientation via the B-spline basis method. The results are in good agreement with the ones in literatures. It shows that the B-spline basis method can effectively deal with the problem of atoms in crossed fields.
4. The B-spline-based coordinate rotation method plus model potential approach is applied for the first time to investigate the complex energies of low-lying Stark resonances of the lithium atoms. We further discuss and clarify the argument on energy positions and widths of resonance states in recent literatures. The calculated results show that this method has the advantages of simplicity, flexibility and small computational effort. The method can be extended easily to deal with the problem of alkali atoms in crossed fields.
本文发展了强外场下里德堡原子谱计算的有效方法，系统地应用于碱金属原子在电场、磁场、平行电磁场及交叉电磁场中的吸收谱、共振态的研究中。主要内容如下：
1．将B样条基与模型势相结合的方法用于锂原子和钠原子近离化阈的抗磁谱计算。波函数角向部分采用对称化的B样条基。对于处于磁场下的锂原子，在我们所讨论的能区内，该方法计算量小于R-矩阵与多通道量子亏损理论，但仍可给出与实验谱相符的结果。同样对钠原子离化阈附近的抗磁谱也做了计算，靠近电离阈时，发现体系连续态对谱线的影响变得很重要。
2．将B样条基与模型势相结合法推广到计算平行电磁场中碱金属里德堡原子的振子强度谱。对于锂原子，在B=0.594 T，F=5.33 V／cm的情况下，定量地分析了振子强度强弱的原因。在所讨论的能区内，我们比较了锂原子不同初态，例如2s和3s态的π光吸收谱，发现谱线结构非常相似，整体上相差一个常数因子。这表明，谱线结构主要由末态决定，几乎与初态无关。在平行电磁场下，对比锂原子与钠原子的吸收谱，发现原子实的作用对谱线的影响很大。
3．首次把B样条基展开方法推广到处理交叉电磁场中氢原子的Balmerα谱，计算结果与最近的理论结果非常吻合。进一步说明了B样条基矢展开法可有效处理原子在交叉电磁场中的问题。
4．首次采用B样条基与模型势和复坐标旋转相结合的方法，计算了低激发锂原子的Stark共振态。对最近文献中关于共振态能级位置和宽度的争论做了进一步的讨论和澄清，计算结果表明本文的方法是可行的、有效的，比较灵活且计算量小，便于推广到交叉电磁场下碱金属原子共振态的计算。
Rydberg atoms are ideal systems for studying the effect of external fields on atoms due to its long lifetime and sensitivity to external fields. Atoms in external fields relate to many basic theoretical problems in atomic physics, e.g. the solution for non-separable system, the coupling of discrete and continuum states and its influence on the structure of the spectrum, the quantum-classical correspondence and so on. The research on atoms in strong fields can provide essential data for astrophysics, plasma physics, and other applications.
In this paper, new effective methods dealing with the atoms in strong fields have been developed. These methods are applied to systematically investigate the spectra and resonances of alkali atoms in external electric and magnetic fields. The major contents of this paper are as follows:
1. We calculated near-threshold diamagnetic spectra of Li and Na atoms in strong fields by B-spline basis plus model potential (B-spline+MP) approach. The angular wave-functions are expanded in terms of the symmetry-adapted B-spline functions. For Li atom, in contrast with R-matrix+MQDT, the B-spline+MP method obtains a higher spectral accuracy with a smaller computational effort over the energy range of our study. For Na atom, the contribution of continuum states to the spectra becomes significant near threshold region.
2. We presented oscillator strength spectra of Li and Na in parallel electric and magnetic fields via the B-spline+MP method. In the case of Li atom, the oscillator strength is calculated and analysed in B = 0.594 T, F = 5.33 V/cm. We got the same form of spectrum byπphoto absorption from the Li (2s) initial state as that from the 3s state. The two spectra only differ by an overall constant. The structure of the spectrum, over the narrow energy ranges considered in this paper, can be independent of the initial state chosen for a given atom. The structure of the spectrum is determined by the final state only. Comparing the spectra of Li and Na, the marked effect of atomic core on the spectra can be found.
3. We presented oscillator strength spectra of the hydrogen Balmer α series in strong magnetic and electric fields with arbitrary mutual orientation via the B-spline basis method. The results are in good agreement with the ones in literatures. It shows that the B-spline basis method can effectively deal with the problem of atoms in crossed fields.
4. The B-spline-based coordinate rotation method plus model potential approach is applied for the first time to investigate the complex energies of low-lying Stark resonances of the lithium atoms. We further discuss and clarify the argument on energy positions and widths of resonance states in recent literatures. The calculated results show that this method has the advantages of simplicity, flexibility and small computational effort. The method can be extended easily to deal with the problem of alkali atoms in crossed fields.
引文
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