Theoretical Studies On The Spectral Structures Of Few-Electron Atomic And Molecular Systems In Strong Magnetic Fields

The properties of atoms and molecules under strong magnetic fields have always been a research focus in physics. In this thesis, we study the spectral structures of two-electron atomic and molecular systems under uniform strong magnetic fields using a configuration-interaction (CI) method. The main achievements are as follows:The total energies, derivatives of the total energy with respect to the magnetic field and ionization energies involving the 110+, 11(-1)+ and 11(-2)+ states of helium atoms in the magnetic field regime between 0 and 100 a.u. are calculated with the help of Hylleraas basis functions and Hylleraas-Gaussian basis functions. The results obtained by this method are more accurate than those obtained by other methods, due to the two kinds of basis functions containing the electron-electron distance explicitly employed for the expansion of the wave functions near the cusp. In the intermediate field regime, the lower total energies and higher ionization energies are achieved, and the two ionization energy curves join smoothly by means of the total energies and derivatives of the total energy with respect to the magnetic field obtained with the two above-mentioned basis functions at the two ends of this field regime. And, the transition wavelengths and oscillator strengths of the 110+→11(-1)+ and 11(-1)+→11(-2)+ transitions are calculated for helium atoms with Hylleraas-Gaussian basis functions. Besides that, we find that the complicated interplay of the different interactions makes the total energies of the 110+ state in the field regimeγ=0-100 a.u., and those of the 11(1)+ and 11(-2)+ states in the field regimeγ=0.1-100 a.u. increase monotonically with increasing magnetic field.The total energies, derivatives of the total energy with respect to the field strength and electron detachment energies involving the 110+,11(-1)+ and 11(-2)+ states of hydrogen negative ions are calculated with Hylleraas-Gaussian basis functions in a magnetic field between 0 and 100 a.u.. The numerical results obtained with Hylleraas-Gaussian basis functions are more accurate than those obtained with Gaussian basis functions. The field regimes 3<γ< 4 a.u. and 0.02<γ< 0.05 a.u., in which the 11(-1)+ and 11(-2)+ states start to become bound, respectively, are determined based on the calculated electron detachment energies. The calculations show that the 11(-2)+ state are stronger bound than the 11(-1)+ state. Also, the transition wavelengths and the corresponding oscillator strengths of the 110+→11(-1)+ and 11(-2)+→11(-1)+ transitions are presented for hydrogen negative ions at selected magnetic field strengths.In addition, the use of Hylleraas-Gaussian basis functions is extended to the calculation of hydrogen molecules in strong magnetic fields. The presentations of the matrix elements of the overlap matrix and Hamiltonian matrix are also given.