The method of complex-coordinate rotation is used to investigate electric-field effects on the doublyexcited 2s2p P, 2p DC, 2p PC and 2s2p P states of He. Strong electric-field strengths up to F"0.02 Ry are used in our present study. Products of Slater orbitals are used to represent the two-electron wave functions, with l "8 being employed for the individual electron. Block matrices with up to¸ "5 (H-states) are used to investigate the convergence behavior for the resonance parameters (resonance energy and width). When the external electric field is turned on, ''classic'' Stark effect is observed for the M"0 and M"$1 components of the two singlet-spin states and for the M"$1 components of the triplet-spin states. Comparisons are made with other calculations when available.PACS: 31.15.Ar; 32.80.Dz; 32.60. #i
I IntroductionThis work presents a theoretical investigation of electricfield effects on the doubly-excited states of He below the He>(N"2) threshold. The states under the present study are the 2p DC, 2s2p P, 2p PC and 2s2p P states. From the experimental side, the P states have been observed in laboratories using synchrotron radiation light sources [1,2]. Electric-field effects on such P-wave states in He have not been investigated, even though the experimental study of the field effects on their counterparts in H\ has a long history [3][4][5][6][7]. On the theoretical side, Nicolaides and Themelis [8] have recently carried out a calculation of DC field effects on the He 2s SC and 2s2p P states. In light of the theoretical and possible experimental interest, we now present a theoretical investigation of DC field effect on the doubly-excited 2p DC, 2s2p P, 2p PC and 2s2p P states of He. The method of complex-coordinate rotation [9!11] is used in the present study. This method was used to examine the Stark effect of hydrogen [12,13], and on the N"2 P shape resonance in H\ [14]. Recently, we have carried out investigations of the electric-field effects on the doubly-excited states of H\ by using the method of complex-coordinate rotation [15][16][17][18][19]. Electric-field effects on the M"0 of the 2s SC states were also investigated [20]. A comparison was made between our results for the 2s SC state with those in [8]. In the present work we extend the investigations to study the electric-field effects on the M"$1 components of the P and DC states, and the M"$2 components of the latter state. Furthermore, the present work also reports the electric-field effects on the M"0 and M"$1 components of the 2s2pP and 2p PC states.
II Theory and wave functionsThe Hamiltonian of an atom in an external field iswhere F is the external field, and ¹ and » are the usual kinetic and potential operators, respectively. For the He system, ¹ and » are given byandwhere r and r are the coordinates of the electrons with respect to the nucleus and r ""rN !rN ". Z is the charge of the helium nucleus and Z"2. Atomic units are used in our work with energy in Rydberg units. The field strength is in Rydberg units, and 1 Ry"2.57;10 V/cm.In th...