ENERGY SPECTRUM OF HYDROGEN ATOM IN AN CROSSED DC

ELECTRIC AND MAGNETIC FIELDS: NEW APPROACH

S.V.Ambrosov

, A.V.Glushkov, D.A.Korchevsky

Atomic Atomic-Nuclear-Laser Spectroscopy Centre and Inst. Applied Mathematics,

P.O. Box 116, Odessa-9, 65009, Ukraine

A creation of the powerful sources of optical

radiation has stimulated experimental and theo-

retical studies of atomic, molecular systems in

strong external fields (c.f.{1-5}). In our paper we

present a new method for exact calculation of the

structure of quantum states and energy spectra

for hydrogen atom in a crossed DC electric and

magnetic field. The Schrödinger equation for

atomic system in a DC magnetic field is solved

by the finite-differences method. Further for ac-

count of an electric field (it is supposed that the

electric field is quite weak) it is possible to use

the perturbation theory. We constructed the finite

differences scheme, which is in key aspects simi-

lar to method {2}. The three-point symmetric

differences scheme is used for second derivative

on z. The derivatives on r are approximated by

(2m+1)-point symmetric differences scheme with

the use of the Lagrange interpolation formula

differentiation. The eigen-values of hamiltonian

are calculated by means of the inverse iterations

method. The corresponding system of inhomoge-

neous equations is solved by the Thomas method.

To calculate the values of the width G for reso-

nances in spectra of hydrogen atom in crossed

electric and magnetic field we use the modified

operator perturbation theory method (see details

in ref.{3}. We have used our approach to calcula-

tion of the energies for hydrogen atom in a

crossed electric and magnetic fields. Let us pre-

sent some numerical results for the ground state

of hydrogen atom (the following notations are

used below: E1= E+E

||

is energy (in Ry) of sys-

tem when vectors of electric and magnetic fields

F (a.u.) and B (a.u.) are parallel; correspondingly,

E2= E+E

⊥

is energy of system, when vectors of

electric and magnetic fields F and B are perpen-

dicular):

Table. Energy (Ry) of hydrogen in electric F

(a.u=5,14⋅10

11

V/m) and magnetic B

(a.u=2,35⋅10

5

Tl) fields

F B E+E

||

E+E

⊥

0,000

0,010

0,020

0,030

0,040

0,050

0,000

0,010

0,020

0,030

0,040

0,050

-1,000000

-1,000402

-1,001617

-1,003685

-1,006659

-1,010642

-1,000000

-1,000401

-1,001615

-1,003674

-1,006628

-1,010558

We have carried out a comparison of our data

with analytical data, obtained within an analyti-

cal perturbation theory approach of Turbiner (c.f.

{4}) and results of calculations by numerical

methods (c.f. refs. {5}). Comparison has shown a

full agreement (note a weakness of the field

strengths). It would be noted that the analytical

perturbation theory approach is not acceptable

for large values of the field strengths. At the

same time, our approach can be used in a case of

the strong electric (an electric field is directly

introduced into the Schrödinger equation) and

magnetic fields.

{1} Photonic, Electronic and Atomic Collisions,

Ed. By F.Aumayr, H. Winter., (Singapore, 1993)

{2} M.V.Ivanov, P.Schnelcher, Phys.Rev.A. 61,

022505-1 (2000)

{3} A.V.Glushkov, L.N.Ivanov, Phys. Lett. A

170, 36 (1992); J.Phys.B:At.Mol.Opt.Phys. 26,

L379 (1993); Journ. Techn. Phys. 37 (2), 215

(1997)

{4} V.S.Lisitsa, Usp.Phys.Nauk, 153, 379 (1987)

{5} B.R.Johnson, K.F.Schreibner D.Farrely, Phys.

Rev.Lett. 51, 2280 (1983);J.H.Wang, C.S.Hsue,

Phys.Rev.A A52, 4508 (1995); I.Seipp,

W.Shweizer, Astr.Astrophys. 318, 990 (1997)

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