The N = 2 and N = 3 series of the 1 P c doubly excited helium states are investigated by a partial-wave analysis, and by inspecting the one-body densities and the shape-densities. Many features in the anisotxopism of the electronic cloud, in the geometric configuration, and in the details of radial-radial correlation are found. A comparison between the x P e and 3 P S states is made.
I. IntroductionThe investigation of electron-electron (e-e) correlation is a basic task of atomic physics. Since helium is the simplest atom with e-e correlation, it deserves to be investigated in detail. In our recent papers^1-4 !, the 1 S", 3 S e 1 P°, 3 P° and 3 P e doubly excited helium states have been explored in detail. The present one is a continuation of previous paper dedicated to the 1 P e states. The interest, just as before, is not in the quantitative aspect, but in the qualitative features of the structures. The same procedure as in Ref.[1] is used to diagonalize the Hamiltonian in a model space to obtain the eigenenergies E{ and the eigenwavefunctions $,-. Only the results of N = 2 and N = 3 series (N labels the shell of the inner electron) are reported in the following.Let us first list some features arising from the symmetry inherent in the 1 P e states: i) Let /,-be the orbital angular momentum of the i-th electron (e,), then we have ^ = / 2 ^ 0. ii) In the (K,T) A classification scheme' 5 ' 6 !, T is now an exact quantum number (in general it is mostly not exact) and T = 1. iii) Let L be the total orbital angular momentum, and M its Z-component. In the following discussions, we fix M = \L\; it implies that we have L essentially lying along the Z-axis. Under this prescription, the probability of both electrons staying in the XY plane is zero. The above three points are common in both the 1 P e and 3 P" states, but different from the odd parity i '+ 1 p° states. In the later, the electrons prefer lying in the XY plane, iv) In the (K, T) A scheme, A is now an exact quantum number (in general it is mostly not exact) and A = "-". v) The probability of both electrons having the same distance apart from the nucleus (i.e., r*i = r 2 ) is zero. The above points iv) and v) are in contrary to the 3 P e states. The later has A -"+", and r\ = r 2 is available. The proof of the above features is referred to Ref. [8], these features are helpful in understanding the following results.
II. Energy Spectrum and the Weights of Partial Wave ChannelThe first column of Table 1 gives the n (/-ir,T)jv notation to specify the states, N (n) is the shell where the inner (outer) electron stays. It is evident that K = 0 is in the N = 2 series, and K = ±1 in the N = 3 series. The second column gives the energies calculated in this work to be compared with those in the fourth column by Lipsky^, two sets of energies are in general one-to-one close to each other. The third column gives e,-defined in Ref.[2] to roughly 'The project supported by National Natural Science Foundation of China.
