AbstncLThe J = 0 and J = 2 men parity spectra of calcium are studied through a combination of the eigcnchannel R-matrix and mullichannel quantum defecl (MQm) methods. The bound and autoionizing spectra below the 3d3,* threshold are invesligated. The calculation reproduces well the perturbations of the 4y1s 'So, 4sid 1,3D2 series by low-lying doubiy excited states observed experimentaly and provides new insight on the identification of the perturkrs. Theoretical predictions of lhc positions of the 3dnI and low-wing 4pnp I = 0' and I = Ze resonances are given. Several photoionization spectra from low-lying stales are presented. ParIicular attention is paid to analysc the effects of the slrong interadon klween the 3dnd and 4pnp single1 channels which dominates the bound and autoionizing spectra above the lint limit. Comparisons are made with lhe results of previous experimental and theoretical studies. "r;, a,," J",,c.J 1 7 1 I , "autla rr U, L 7 7 Y ) 1 I"C3* I ' Y C I I b I all" 11a115w.1 I7"I, 170+ {,*GJVaeck el a1 1991) or configuration interaction approaches (Friedrich and 'Refftz 1%9, Nomura and 'htewaki 1982). Disagreements exist between the various authors for the assignments of several perturbers. The main question is which of the two configurations 4p* or 3d2 represents the lowest IS, and ID, perturbers better. For both ; ; 3 , 2 limit .w.hcreas pietious eApeiir,en-a;

Bose-Einstein condensation (BEC) of an ideal gas is investigated, beyond the thermodynamic limit, for a finite number N of particles trapped in a generic three-dimensional power-law potential. We derive an analytical expression for the condensation temperature Tc in terms of a power series in x0 = ε0/kBTc, where ε0 denotes the zero-point energy of the trapping potential. This expression, which applies in cartesian, cylindrical and spherical power-law traps, is given analytically at infinite order. It is also given numerically for specific potential shapes as an expansion in powers of x0 up to the second order. We show that, for a harmonic trap, the well known first order shift of the critical temperature ∆Tc/Tc ∝ N −1/3 is inaccurate when N 10 5 , the next order (proportional to N −1/2 ) being significant. We also show that finite size effects on the condensation temperature cancel out in a cubic trapping potential, e.g. V (r) ∝ r 3 . Finally, we show that in a generic power-law potential of higher order, e.g. V (r) ∝ r α with α > 3, the shift of the critical temperature becomes positive. This effect provides a large increase of Tc for relatively small atom numbers. For instance, an increase of about +40% is expected with 10 4 atoms in a V (r) ∝ r 12 trapping potential.