We present a theoretical treatment of four two-dimensional electrons in a harmonic confinement potential in the presence of an external magnetic field using the exact diagonalization approach. The ground state properties and the spin and angular momentum transitions for different electron interaction strengths and magnetic fields are obtained. A magnetic field-confinement strength phase diagram is presented indicating a rich variety of ground states. An interesting feature of this system is the depolarization of spins by application of a magnetic field. The results are compared to several approximate theories.

Exact many-body wave functions for quantum dots containing up to four interacting electrons are computed and we investigated the distribution of the wave function nodes, also called vortices. For this purpose, we evaluate the reduced wave function by fixing the positions of all but one electron and determine the locations of its zeros. We find that the zeros are strongly correlated with respect to each other and with respect to the position of the electrons and formulate rules describing their distribution. No multiple zeros are found, i.e. vortices with vorticity larger than one. Our exact calculations are compared to results extracted from the recently proposed rotating electron molecule (REM) wave functions

The K x-ray spectrum arising from doubly JC-ionized gallium atoms has been studied by means of a coincidence experiment with two solid-state detectors. A new energy range in K x-ray spectra (hyper satellite range) is observed. Hyper satellite lines are shifted about 15 times more than the usual satellite lines. The if-satellite spectrum following KL -ionized states has also been studied.

Eu x-ray spectra of heliumlike titanium, Tixxr, from Tokamak Fusion Test Reactor (TFTR) plasmas have been observed with a high-resolution crystal spectrometer and have been used as a diagnostic of central plasma parameters. The data allow detailed comparison with recent theoretical predictions for the Tixxr heliumlike lines and the associated satellite spectrum in the wavelength 0 range from 2.6000 to 2.6400 A. Improved values for the excitation rate coefficients of the Tixxl resonance linc, the intercombination lines, and the forbidden line, and new theoretical results on the wavelengths and transition probabilities for berylliumlike satellites due to transitions of the type 1s 2lnl'-1s2p2l"nl"' with n =2 -4 have been calculated. These data complement the theory given in an earlier paper [F. Bely-Dubau et al. , Phys. Rev. A 26, 3459 (1982)]. The experimental data are in excellent agreement with the theoretical predictions for the entire satellite spectrum. For plasmas with electron temperatures, T" in the range from 1.2 to 1.8 keV, there is also good general agreement between theory and experiment for the heliumlike lines of TixxI. The observed intensity ratios of the intercombination and forbidden lines to the resonance line are, however, larger than the predicted values by as much as an order of magnitude for electron temperatures T, & 1.2 keV. The enhancement of these lines is correlated with the abundance of lithiumlike titanium. The experimental data indicate that still other atomic processes, in addition to those considered by the theory, are important for the excitation of these lines. The experimental results are documented to stimu-0 late further analysis. The observed wavelengths agree to within an uncertainty of 0.5 mA with predictions from calculations which include relativistic and radiative corrections up to the third order in a. The central ion temperature and the central toroidal rotation velocity of TFTR plasmas with ohmic and neutral beam heating were obtained from Doppler measurements of the Ti xxr resonance line. %wavelength shifts of the apparent resonance line profile due to unresolved dielectronic satellites, which can be important corrections to Doppler-shift measurements of plasma rotation velocities, have been determined as a function of the ion and electron temperatures and the fitting limits. Results on the electron temperature and the relative charge-state density of lithiumlike and heliumlike titanium were derived from the satellite spectrum and have been interpreted with plasma modeling. These results are of interest for the determination of the ionization equilibrium and the impurity transport.