176 CHINESE OPTICS LETTERS / Vol. 7, No. 3 / March 10, 2009
Photodetachment of H
−
near a metal surface
Dehua Wang (
uuu
)
∗
, Yongjiang Yu (
uuu[[[
), and Hongrun Wang (
ööö
ddd
)
School of Physics and Electronic Engineering, Ludong University, Yantai 264025
∗
E-mail: jnwdh@sohu.com
Received March 31, 2008
By using the closed orbit theory, the photodetachment cross section of H
−
near a metal surface is derived
and calculated. The results show that the metal surface has great influence on the photodetachment
process. As the ion-surface distance is very large, the influence of the electrostatic image potential caused
by the metal surface becomes small and can be neglected. The period, action, and length of the detached
electron’s closed orbit are nearly the same as the case of the photodetachment of H
−
near an elastic
interface. However, with the decrease of the ion-surface distance, the influence of the metal surface becomes
significant. The amplitude of the oscillation in the photod etachment cross section becomes complicated.
Each resonance peak in the Fourier transformed cross section is associated with one electron’s closed
orbit. Unlike the case of the photodetachment of H
−
near an elastic interface, the length of the closed
orbit does not equ al the twice distance between the ion and the surface. But with the increase of the
ion-surface distance, the length of the closed orbit approaches the case of the closed orbit near an elastic
interface, which suggests the correctness of our method. This study provides a new understanding on the
photodetachment process of H
−
in the presence of a metal surface.
OCIS codes: 020.0020, 020.4900, 300.6300, 300.6350.
doi: 10.3788/COL20090703.0176.
Interactions of Rydberg atoms, ions, and molecules with
metallic surfaces have attracted much attention in re-
cent years
[1−3]
. It is found that as the atoms, ions, and
molecules approach the surface, the Rydberg electron
is subjected to fields caused by the presence of image
charges in the metal, therefore this physical phenomenon
is closely related to the external field behavior of atoms,
ions, and molecules. In these systems, the metal surface
appears as an external per tur ber of the electronic mo-
tion, with the atom-surface distance d as the parameter.
Over the last decade, many researchers have studied the
problem of Rydberg atom near a metal surfa c e . Among
them, the closed orbit theory has been provided to be
a clear framework to understand the oscillation in the
complicated spe c tra for atoms near a metal surface
[4]
.
Contrary to many studies of the Rydbe rg atom near a
metal surface, the photodetachment of negative ion near
a metal surface has attracted little attention. Early ex-
periment and theory showed that the photodetachment
cross s e c tion of H
−
in the presence of external field dis-
plays oscillatory structures a nd a number of authors have
analyzed this phenomenon theoretically at the quantum
and the semiclassic al levels
[5−9]
. Very recently, Yang et
al. applied closed orbit theory to study the photodetach-
ment of negative ion near an elastic interface
[10]
. Later,
many authors have studied the photodetachment of H
−
near an elastic interface in different external fields
[11−13]
.
In these early studies, the interface is always considered
as a n elastic wall, the interaction potential between the
electron and the surface is neglected and the co llis ion of
the electron with the surface is elastic. Therefore, this
system is a real integrable one and the classical motion of
the detached ele c tron is analytically, its theoretical treat-
ment is relatively ea sy. In fact, the e lastic wall is only a
simple model, which is different from a metal surface
[4]
.
For the pho todetachment of negative ion near a metal in-
terface, the method used in these early studies does not
suit. Since the electron is subjected to the fields caused
by the pr e sence of image charges in the metal after be-
ing detached, this system becomes a nonintegrable one.
Its theoretical analysis is complicated. In this letter, by
using the closed orbit theory, we study the photodetach-
ment of H
−
near a metal surface. We obtain an analy tical
expression for the cross section, which is a smooth back-
ground term plus a cosine oscillating term. Formally,
this formula is like the one given by Yang et al.
[10]
, but
the parameters in the formulas are different. In o rder
to show the relation between the photodetachment cro ss
section and the detached e le c tron’s class ical closed orbit,
we make a Fourie r transfo rmation of the cross section for
this system. Each peak in the Fourier transformed cross
section co rresponds to the leng th of one detached elec-
tron’s closed orbit going out from and returning to the
nucleus.
The schematic plot of the system can be described as
follows. The H
−
ion sits at the origin with the active
electron loo sely bound by a short-range, spherically sym-
metric potential V
b
(r), where r is the distance between
the active electron and the nucleus. A z-polarized laser
is used for the photodetachment. A metal surface per-
pendicular to the z axis is placed at z = d. So the photo -
detached electr on can be reflected by the metal surface.
According to the electrostatic image method
[14]
, the po-
tential acting on the detached electron in the ion-metal
system can be described as V = V
c
+ V
i
, in which V
c
is
the interaction potential o f the electron with the image
nucleus, which is also a short-range potential, V
i
is the
interaction potential between the detached elec tron and
the image electron, V
i
= −
1
4(d−z)
. Ther efore, the Hamil-
tonian of H
−
ion near a metal sur face has the following
form (in cylindr ic al coordinates and a tomic units):
H =
1
2
(P
2
ρ
+
l
2
z
ρ
2
) +
1
2
P
2
z
+ V
b
(r) + V
c
−
1
4(d − z)
, (1)
where P
ρ
and P
z
are the components of the electron’s
1671-7694/2009/030176-04
c
2009 Chinese Optics Letters