ENERGY SPECTRUM OF HYDROGEN ATOM IN AN CROSSED DC ...

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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)