Ming-Keh Chen

Accurate oscillator strengths for S-P transitions in the He atom

The authors obtain the accurate wavefunctions and energies for n1,3S and n1,3P states of He for n<or=5 by variational configuration calculation with B-spline basis functions. The accurate wavefunctions have been used to calculate oscillator strengths for the transitions mS-nP, m, n<or=5 in He. The results of f values are accurate to within 0.01 per cent or better. The error estimate is based on the numerical convergence as the number of the angular partial waves of the employed wavefunctions is increased, and on the agreement between the results obtained using the dipole length and velocity formula. The accuracy of the results does not deteriorate with increasing principal quantum number and results is better than the previous highly accurate calculated results of Schiff et al. (1971) and Kono and Hattori (1984-6). The results also agree with some recent accurate experimental results. Therefore, the results can be regarded as being as reliable as those of Kono and Hattori at least, which are likely to be the most accurate theoretical results. Some radial expectation values are also calculated to give some indication of the accuracy of the wavefunctions.

Dipole polarizabilities of the 1, 21S and 23S states of the helium sequence

The dipole polarizabilities of the 1, 21S and 23S states of helium-like ions (2<or=Z<or=10) are calculated through a variation-perturbation approach. The polarized wavefunctions are constructed by using selecting B-spline basis functions in a CI scheme. The values of alpha d are converged to an accuracy of at least 0.01% and are in excellent agreement with those obtained from explicitly correlated wavefunctions and with experiment (Leonard and Barker, 1975).

The energies and oscillator strengths of bound states of Be

The energies and wavefunctions of the , and states of beryllium are calculated with a model-potential method by using selected B-spline basis functions in a configuration-interaction (CI) scheme. Our length results of the oscillator strengths for electric dipole transitions and the energies, which are set to be zero at the ground state of Be III, are compared with the experimental and other theoretical results. The agreement showed that our method is capable of giving accurate results for various states of beryllium efficiently.

F values for high-lying s-p and p-d transitions in the He atom by selected B-spline basis functions

By selecting B-spline basis functions systematically in variational calculations, we obtain the accurate wavefunctions and energies for n1,3 P and n1,3D states of He for n<or=9. In comparing with our previous results e.g. 2-51,3P, it is indistinguishable between our present and previous results. The present results were obtained with smaller number of basis functions. We can therefore use the accurate wavefunctions to calculate oscillator strengths for the transitions mS-nP, mP-nD, m, n<or=9, in He. The results of f values are accurate to within 0.01% at least. The error estimate is based on the uncertainty of the difference of the corresponding energy levels as in our previous work. Our results agree with the previous highly accurate calculated results of Kono and Hattori (1986) impressively, which are likely the most accurate theoretical results. We also give hybrid f values of transitions between m1P and m1D (or between 11S and m1P) for m<or=9. Our results also agree with some recent accurate experimental results as good as those of Kono and Hattori.

Doubly excited resonant states in below the hydrogen threshold

We calculated the (n=2,3,4), (n=3,4,5), (n=3,4), (n=2,3,4) and autoionizing states in below the n = 2 hydrogen threshold by the saddle-point complex-rotation method. The close-channel part of wavefunctions are constructed by B-spline basis functions. The resonance energies and autoionization widths are determined. They are compared with other theoretical and experimental results to examine the feasibility of applying B-spline basis functions through the saddle-point complex-rotation method in resonance states.

1sns Rydberg states of the He atom

The authors carried out the variational configuration interaction calculation to obtain the energies for n1S series in He for n=7-16, and for n3S series in He for n=14-18 with B-spline basis functions. As found in their previous report, the accuracy of the results does not deteriorate with increasing principal quantum number. The accuracy of their results is better than the previous best results calculated by Accad et al. (1971). The authors give lower variational energies than Accad et al. for n1S states (n>or=10) and n3S states (n>or=15). They also calculated the radial expectation values, the mass-polarization effect, and the expectation values of delta (r1) and delta (r12), which have not been calculated before. They can give some indication of the accuracy of the high-lying Rydberg-state wavefunctions.

Hyperfine splitting for the ground-state muonic 3He atom-corrections up to alpha 2

The author examines the relativistic, QED and nuclear finite-size corrections of the hyperfine splitting for ground-state muonic 3He up to alpha 2. The author finds that the nuclear finite-size correction and the magnetic correction to the electron wavefunction of the hyperfine splitting, Delta ve, which accounts for the magnetic interaction between the electron and the 3He nucleus, are quite different from the previous results of Huang and Hughes (1979,1980,1982). The author obtains the total hyperfine splitting, Delta v=4166.540 MHz, with the uncertainty, +or-0.001 MHz, which only originates from the calculation of the Schrodinger wavefunction, and the uncertainty, +or-0.004 MHz, which originates from the neglect of order alpha 3 and above in calculating the relativistic, QED and nuclear finite-size correction, and the uncertainties of the parameters of the electric and magnetic form factors of the 3He nucleus. This result is more consistent with the experimental result, 4166.3+or-0.2 MHz, than the previous theoretical results.

Hyperfine structure in the muonic 3He atom

In order to examine the recoil effect, the authors calculate the ground-state hyperfine structure of the muonic 3He by the variational approach, employing an improved set of Hylleraas-type basis functions to deal with the non-relativistic three-body wavefunctions of the muon, electron and 3He nucleus. The convergence of the series is very fast, thus eliminating the problem with the propagation of the truncation errors of the computer machine. Using the recoil correction, delta rec= Delta nu F(3 alpha / pi )(me/mmu ) ln(mmu /m

Hyperfine splitting in muonic 4He and 3He atoms : a global-operator approach

0 they arrive at the value Delta nu =4166.56+or-0.05 MHz for the total hyperfine-structure splitting of the ground state of the muonic 3He atom. But if they follow the treatment of Borie (1979) for the recoil corrections by treating the ( mu -3He)+ system as a pseudonucleus, they will arrive instead at the value Delta nu =4165.91+or-0.05 MHz. The former seems to be in slightly better agreement with the only experimental result, 4166.3+or-0.2 MHz.

RETARDATION LONG-RANGE POTENTIALS BETWEEN TWO HELIUM ATOMS

The author uses a global operator to examine the wavefunctions which he employed in calculating the ground-state hyperfine structure of the muonic 4He and 3He atoms. Using the recoil correction, delta rec=( Delta nu )F(3 alpha / pi )(me/mmu ) ln(mmu /me), he arrived at the values of Delta nu =4464.907+or-0.001 and 4166.620+or-0.001 MHz respectively for the total hyperfine structure of the muonic 4He and 3He atoms including relativistic and radiative corrections up to alpha 2. Comparing with his previous works, Delta nu =4464.87+or-0.05 MHz and 4166.56+or-+or-0.05 MHz, this supports his choice of the wavefunctions and indicates that it is reasonable to find the second-order corrections. The small uncertainties, which originate from the calculation of the three-body Schrodinger wavefunctions, make it meaningful to find the second-order corrections, and provide the possibility of testing the relativistic and QED effects.