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J. Phys. Chem. C 2010, 114, 8958–8964
Photodetachment of H- in a Metallic Microcavity Kai-Yun Huang† and De-Hua Wang* College of Physics, Ludong UniVersity, Yantai 264025, the People’s Republic of China ReceiVed: January 13, 2010; ReVised Manuscript ReceiVed: March 24, 2010
Using closed orbit theory, we study the photodetachment of H- in a metallic microcavity. An analytical formula of the photodetachment cross section is derived. It is found that the two-mirror metallic microcavity has a greater enhancement effect on the oscillations of the photodetachment cross section compared to the case of a single mirror configuration. The oscillations in the photodetachment cross section are caused by the superposition of the interference waves traveling along the closed orbits. To show the relation between the photodetachment cross section and the detached electron’s classical closed orbits clearly, we make a Fourier transformation for the scaled photodetachment cross section of this system. Each peak in the Fourier transformed cross section corresponds to the scaled action of a closed orbit. We hope that our results will be useful in understanding the photodetachment process of negative ions in the vicinity of interfaces, cavities, and ion traps. 1. Introduction Interests in the photodetachment of H- in various environments have grown rapidly over the past few years. Pioneering measurements of the photodetachment cross section of H- in the presence of a static electric field were performed by Bryant et al.1 Later, photodetachment of H- in other fields, such as in a gradient electric field,2 crossed electric and magnetic fields,3 and parallel electric and magnetic fields4,5 have also been investigated theoretically. On the other hand, since H- has been proposed to use to probe adsorbate state lifetime and charge transfer during backscattering,6 the photodetachment of H- near the surfaces has attracted much interest. In 2006, Yang et al. studied the photodetachment of H- near an elastic interface.7 Later, they discussed the photodetachment of H- in a quantum well.8 Besides, many authors have researched the photodetachment of H- near an elastic interface in different external fields.9-11 In these early studies, they all considered the interface as an elastic wall, the interaction potential between the electron and the surface is neglected. However, the elastic surface is only an ideal model and it is different from a practical surface.12 For a real metal surface, the detached electron at a distance z in front of the surface feels an attractive force which is identical to that produced by a positive charge arranged mirror-symmetrically at the distance -z from the plane. Hence, the electron is trapped in the potential well caused by the image charge. Recently, Rui, Yang, and Du et al. investigated the photodetachment of H- near a metal surface and found that when the photodetached electron is trapped in the image potential well, the photodetachment spectrum displays an oscillating structure.13,14 In their studies, they considered the case of the photodetachment of H- near a metal surface. Then what will happen if we locate the H- in a two-mirror metallic microcavity? Nobody has given this study. In this paper, using the closed orbit theory,15,16 we study the photodetachment of H- in a two-mirror metallic microcavity. Our results demonstrate that the two-mirror metallic microcavity has a greater enhancement effect on the oscillations of the * Corresponding author. E-mail:
[email protected]. † E-mail:
[email protected].
Figure 1. Schematic representation for the photodetachnent of H- in a metallic microcavity.
photodetachment cross section compared to the photodetachment of H- near a single metal surface. The paper is organized as follows: In section 2, we describe the dynamics of the photodetached electron in a two-mirror metallic microcavity. In section 3, we give a formula for calculating the photodetachment cross section. The scaled transformation of the cross section is also given in this section. Some numerical results and discussion are presented in section 4. Finally, section 5 gives some conclusions of this paper. Atomic units are used throughout this work unless indicated otherwise. 2. Dynamics of the Photodetached Electron in a Metallic Microcavity The schematic plot is shown in Figure 1. In this system, the microcavity is made up of two parallel metallic mirrors. Hsits at the origin and a z-polarized laser is applied for the photodetachment. The upper metallic mirror is at a distance d1
10.1021/jp100323a 2010 American Chemical Society Published on Web 04/28/2010
Photodetachment of H- in a Metallic Microcavity
J. Phys. Chem. C, Vol. 114, No. 19, 2010 8959 The Hamiltonian governing the motion of the detached electron can be described as
1 1 1 1 H ) (PF2 + Pz2) + + 2 4(d1 - z) 4(d2 + z) 4d1 1 (3) 4d2
Figure 2. Image potential between the detached electron and the metal surfaces for different imaging times n. The distances between the Hand the two metal surfaces are d1 ) 1000 au and d2 ) 100 au.
away from the origin and the lower mirror is at a distance d2. As in the previous studies, we still consider the H- as a oneelectron system with the active electron loosely bound by a short-range spherically symmetric potential Vb(r).9 When the negative ion absorbs a photon, the active electron is detached and it moves away from the hydrogen atom. In the cylindrical coordinates (F, z, φ), the Hamiltonian of a detached electron is
H)
(
)
Lz2 1 2 1 PF + 2 + Pz2 + V(z) + Vb(r) 2 2 F
F(t) ) R sin θ + kt sin θ
1 1 1 1 + + 4(d1 - z) 4(d2 + z) 4d1 4d2
(4)
(1)
Due to the cylindrical symmetry of the system, the z component of the angular momentum is a constant of motion, which has been set to zero for the sake of convenient. V(z) is the electrostatic image potential between the detached electron and the metallic surfaces. Following the method of electrostatic image, we could obtain a series of image charges of the detached electron and the hydrogen atom.17 There are two classes of potentials acting on the detached electron. One kind of potential is caused by the hydrogen atom and its images, and the other kind is caused by the images of the detached electron. Since the potential between the detached electron and the hydrogen atom and its images are short-ranged, after photodetachment, this kind of potential can be neglected. Therefore, we only consider the interaction between the detached electron and its images. In Figure 2, we plot the electrostatic image potential V(z) for different imaging times. In this figure, the integral number n represents the imaging times, the distances between the H- and the two metal surfaces are d1 ) 1000 au, d2 ) 100 au. From this figure we can see that the difference between the image potentials for the first image and the second and third images is very little. Therefore, we ignore the multi-images and only consider the interaction potential between the detached electron and its first image. This potential can be described as follows:
V(z) ) -
We use semiclassical closed orbit theory to investigate the photodetachment of H- in a two-mirror metallic cavity. The physical picture of the photodetachment process can be described like this: when the H- is illuminated by a laser, the negative ion absorbs photon energy Eph and then the excited electron leaves the core region by way of an outgoing wave with an initial angle θ. Sufficiently far from the hydrogen atom, the waves propagate semiclassically, following classical trajectories. Due to the effect of the metallic microcavity, some of these waves cannot travel to infinity and eventually return to the vicinity of the core region. The returning waves interfere with the outgoing waves, and it is this interference that results in the oscillatory structure in the spectrum of the photodetachment cross section. The orbits that begin and finally end at the core are called closed orbits, which have significant contributions to the oscillations in the photodetachment cross section. Now we seek all the closed orbits for this system. By solving eq 3, we find that the motion in the F direction is free:
(2)
where 1/4d1 and 1/4d2 were added to shift the potential such that the value of the potential at z ) 0 is zero.
where k ) (2E)1/2 is the momentum of the detached electron. Because of the free motion in F direction, all of the closed orbits are along the z axis obviously. After making a derivation for the image potential, we have
(
)
dV(z) 1 1 d 1 1 + )0 ) + dz dz 4(d1 - z) 4(d2 + z) 4d1 4d2 (5) From the above formula, we get
z ) (d1 - d2)/2
(6)
Substituting eq 6 into V(z),we obtain
Vmax )
1 1 1 + 4d1 4d2 d1 + d2
(7)
This means that a potential barrier occurs at z ) (d1 - d2)/2, and the value of the barrier is Vmax ) 1/4d1 + 1/4d2 - 1/(d1 + d2). The motion of the photodetached electron varies with the distances d1 and d2, which can be described as follows: (1) For the case of d1 > d2, there are three different motions according to the energy of the photodetached electron. (i) The energy of photodetached electron is lower than the barrier: E < Vmax. If the electron goes up along the +z direction, it will always feel a downward force caused by the image charge, so its momentum decreases and reaches zero before hitting the upper surface. It then is pulled back to the hydrogen atom by the image potential. If the electron goes down along the -z direction, the
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Pz ) -
2E -
1 1 1 1 + + 2d1 2d2 2(d1 - z) 2(d2 + z) (11)
Since it is bounced back by the lower surface, the extreme point it can reach is zmax ) -d2, and its corresponding period and action can also be obtained by Figure 3. Four fundamental closed orbits of the detached electron for the case of d1 > d2.
electron will move toward the lower surface acceleratedly. After hitting the lower surface, it will be bounced back to the origin. So there are four fundamental closed orbits under this condition. (a) The electron goes up along the +z direction, reaches its maximum before hitting the upper surface and then bounces back by the potential and returns to the origin. We call this orbit the up orbit. (b) The electron goes down in the -z direction and hits the lower surface and bounces back and finally returns to the origin. We call this orbit the down orbit. (c) The electron completes the up orbit first and then passes through the origin and continues to complete the down orbit. (d) This orbit is similar to the one of (c) but in reverse order: the electron completes the down orbit first and then the up orbit. The four fundamental orbits are shown in Figure 3. For the up orbit, the peak position where the detached electron would reach can be calculated as follow. Assuming the electron’s initial kinetic energy is E, we have
T2 ) 2
∫0-d
2
1 dz Pz
S2 ) 2
∫0-d Pz dz 2
(12)
Because there is a π phase loss13 when the electron collides with the lower surface, the value of the Maslov index for the down closed orbit is µ2 ) 2. As for the other two fundamental closed orbits, their periods, actions, and Maslov index are as follows:
T3 ) T4 ) T1 + T2 S3 ) S4 ) S1 + S2 µ3 ) µ4 ) µ1 + µ2
(13)
(10)
Besides these four fundamental closed orbits, there are some other closed orbits, which are just the simple combination and repetition of the four closed orbits. Since their influence on the photodetachment cross section is quite smaller than the four fundamental closed orbits, we did not consider their contributions in the following calculation. (ii) The energy of photodetached electron is equal to the barrier: E ) Vmax. If the electron goes up along the +z direction, it would reach the potential peak at which its speed is zero and would stop keeping an unstable balance. The motion of the electron along the -z direction will still return to the origin after hitting the lower surface. So only the down orbit exists in this case. (iii) The energy of photodetached electron is higher than the barrier: E > Vmax. In this case, the fundamental closed orbits are similar to the case described in (i). The only difference is that the motion of the electron along the +z direction will return after hitting the upper surface; i.e., the turning point of the up closed orbit is zmax ) d1. And its Maslov index becomes µ1 ) 2. (2) For the case of d1 ) d2, the potential barrier Vmax ) 0, which is absolutely less than the energy of photodetached electron. So the upward and downward electrons will both return after hitting the upper and lower surfaces, respectively. The closed orbits are similar to case (iii) of the first kind d1 > d2. (3) For the case of d1 < d2, whatever the energy of detached electron is, the electron moving along the +z direction will return after hitting the upper surface. But for the electron moving along the -z direction, there are also three different motions according to the energy of the photodetached electron. In fact, this is quite similar to the case of d1 > d2 but place the metallic microcavity in a reverse direction.
The Maslov index is related to the topological structure of the trajectory manifold and can be obtained simply by counting the singular points such as caustics and foci along the trajectory.18 For the current case, the Maslov index can be easily found by counting the returning points; so for the up closed orbit µ1 ) 1. For the down closed orbit,
3. Photodetachment Cross Section and Scaled Transformation 3.1. Photodetachment Cross Section. According to the closed orbit theory,15,16 we split the whole space into two spatial regions: (1) The core region inside a small sphere with the radius R ≈ 5 au, where the laser field and the core field influences exist, while the attractive interaction by the metallic microcavity can be neglected. (2) The outer region, where the influence of
1 1 E ) (PF2 + Pz2) 2 4(d1 - z) 1 1 1 + + 4(d2 + z) 4d1 4d2
(8)
For the up orbit, PF can be set as zero. Inserting it to eq 8, we get
Pz )
1 1 1 1 + + 2d1 2d2 2(d1 - z) 2(d2 + z)
2E -
(9)
When the detached electron arrives at the top (z ) zmax) of the closed orbit, its momentum along the z-direction is zero. By setting Pz ) 0, we obtain the turning point of the closed orbit zmax. Using it, we could get the period and action of the up closed orbit:
T1 ) 2
∫0z
max
1 dz Pz
S1 ) 2
∫0z
max
Pz dz
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the metallic microcavity is so dominant that the interaction between the active electron and the residue of the ion can be neglected. In other words, the electron only feels the interaction caused by the metallic microcavity. So we can use classical closed orbit theory to describe the electron motion. Correspondingly, the photodetachment cross section of H- lies in a twomirror microcavity that can be divided into two parts:
σ(Eph,d1,d2) ) σ0(Eph) + σosc(Eph,d1,d2)
16√2B2π2(Eph - Eb)3/2 3cEph3
σosc(Eph,d1,d2) ) -
4π E Im〈Dψini |ψret〉 c ph
Aj )
(16)
R R + kTj
j ψret (r≈0) ) Nje(ikz
ψ0(R,θ,φ) ) -i
4Bk2 ei(kR-π) cos(θ) kR (kb2 + k2)2
(17)
On the basis of closed orbit theory, the returning wave ψret is related to the initial outgoing detached electron as
ψret(r) )
∑ ψ0(R,θ,φ)Ajei(S -µ π/2) j
i
Nj ) Aj(Rf0)ei(Sj-ujπ/2)ψ0(R,θ ) 0, π)
j
Aj ) where
|
Jj(F,z,0) Jj(F,z,Tj)
|
1/2
(19)
∑
ψret )
4
j ψret (r≈0) )
j)1
∑ Nje(ikz
(24)
j)1
Substituting eq 24 into eq 16 and carrying out the overlap integral, we obtain the oscillatory part of the cross section: 4
σosc(Eph,d1,d2) )
∑
h(j)
8π2B2√2(Eph - Eb) cEph3Tj
j)1
π sin(Sj - µj ) 2 (25)
where h(j) is a sign factor. For the up and down closed orbits h ) -1, while for the other two fundamental closed orbits h ) 1. Therefore, the total photodetachment cross section is
σ(Eph,d1,d2) )
16√2B2π2(Eph - Eb)3/2
∑ h(j) j)1
where the sum runs over all the electron closed orbits going out from and returning to the hydrogen atom, Sj, Aj, and µj are respectively the action, amplitude, and Maslov index of the closed orbit j. And the amplitude Aj is given by10
(23)
In the present system, there are four fundamental closed orbits. So the total returning waves are the sum of each returning wave:
4
(18)
(22)
in which “+” corresponds to the waves propagating in the negative z-direction and “-” corresponds to the waves traveling in the positive z-direction. Nj is a constant and given by
4
in which ψini is the initial bound state wave function of H- and is given by ψini ) B(e-kbr/r). In the present one active electron approximation for photodetachment kb ) (2Eb)1/2. D is the dipole operator. For the z-polarized light, D ) z. ψret is the returning wave, which overlaps with the outgoing source wave to give the interference pattern in the photodetachement cross section. For the purpose of getting the returning wave function associated with each closed orbit, we need to study the propagation of the outgoing wave. The outgoing wave on the surface of the sphere with radius R ≈ 5 au is20
(21)
Tj is the period of the jth closed orbit. Inside the sphere, the wave function can be approximated by an incoming plane wave traveling along the z axis:
(15)
Here B ) 0.31522 is a normalization constant, c is the speed of light and its value is approximately 137 au. Eph is the photon energy, Eb is the binding energy and it is approximately 0.754 eV. σosc(Eph,d1,d2) is the oscillating term corresponding to the oscillatory structure in the photodetachment cross section:
(20)
Outside the sphere, due to the classical free motion of the detached electron, we obtain
(14)
where σ0(Eph) is the smooth background term of the photodetachment cross section of H in free space:19
σ0(Eph) )
| |
∂z ∂z ∂t ∂θ J(F,z,t) ) F(t) ∂F ∂F ∂t ∂θ
3cEph3 8π2B2√2(Eph - Eb) cEph3Tj
+ π sin(Sj - µj ) (26) 2
3.2. Scaling Transformation. Scaling relations are important in the analysis of photodetachment cross section. For the present system,21 scaling relations also exist and can be explored. Assuming d1 ) Rd, d2 ) (1 - R)d and transforming variables according to r ) dr˜, p ) d-1/2p˜, we get the scaled Hamiltonian:
˜ ) 1 (P˜F2 + P˜z2) H 2 1 1 1 1 + + 4(R - z˜) 4(1 - R + z˜) 4R 4(1 - R)
(27)
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Figure 4. Photodetachment cross section of H- in a metallic microcavity. The lower metallic mirror is placed at z2 ) -100 au. The distance between the upper metal mirror and the H- is (a) d1 ) 1000 au, (b) d1 ) 400 au, (c) d1 ) 100 au, and (d) d1 ) 50 au. The solid lines represent the cross section of H- in the two-mirror metallic microcavity, and the dashed line refers to the case of the cross section of H- in the absence of the upper metallic mirror, which amounts to d1 f ∞.
˜ as the scaled energy ε, we find If we define the value of H that the scaled Hamiltonian does not depend on the energy E and on the ion-surface distances, but only on the scaled energy ε and R, and then the scaled period T˜j and action S˜j can be derived. Keeping ε constant and simultaneously changing E and d such that ε ) Ed results in the oscillatory term in eq 26 being 4
σ˜ osc )
√
2 2
∑ h(j) c(E 8π+ Bε/ς22ε)3ς4T˜ j)1
b
j
π sin(S˜j - µj ) 2
(28)
in which ς ) (ε/E)1/2. Using this equation, we can make a Fourier transform for the scaled cross section and further study the relations between the oscillations in the cross section and the closed orbits. The Fourier transformed cross section is defined as
σ˜ (S˜) )
∫ςς σ˜ osce-iSς dς 2
1
˜
(29)
4. Results and Discussion By using eq 26, we calculate the photodetachment cross section of H- in a metallic microcavity for different values of
the distances between the ion and the two mirrors. In all of our calculations, we keep the lower metal mirror at distance at d2 ) 100 au; then we change the distance between the ion and the upper mirror. The results are given in Figure 4. For comparison, we also calculate the photodetachment cross section of H- near a single metallic surface using the method given by Yang et al.13 In this situation, the distance between the H and the metallic surface is maintained at 100 au, and the result is represented by the dashed line. In Figure 4a, the upper metal surface is placed at d1 ) 1000 au. From this graph we can see that as the photon energy is less than 0.804 eV, the solid line and the dashed line are similar. However, as the energy is larger than 0.804 eV, although the general trends of the two curves are about the same, a dramatic difference appears: there are still many small oscillations in the solid line while the dashed line becomes much smoother. Besides, with the increasing photon energy, the oscillating amplitude of the solid line increases and the oscillating frequency decreases. These phenomena can be explained as follows: as d1 ) 1000 au, d2 ) 100 au, which belongs to the case of d1 > d2 and the potential barrier is just Vmax ) 0.804 eV. So if the photon energy is less than the potential barrier, the motion of the detached electron traveling along the +z direction will return before hitting the upper metallic mirror, which is like the situation of only the lower
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J. Phys. Chem. C, Vol. 114, No. 19, 2010 8963
Figure 5. Fourier transformed scaled photodetachment cross section of H- in a two-mirror metallic microcavity. The lower metallic mirror is kept at d2 ) 100 au. The upper metallic mirror is placed at (a) d1 ) 1000 au, (b) d1 ) 400 au, (c) d1 ) 100 au, and (d) d1 ) 50 au. Each peak corresponds to the action of a fundamental closed orbit, which is denoted in the plots. And the corresponding closed orbits are also plotted near the peaks.
metallic mirror existing. When the photon energy is higher than the potential barrier, the motion of the electron traveling along the +z direction will come back after colliding with the upper metallic mirror. The period of the closed orbit gets longer, so the oscillating frequency decreases. However, in the case of only a single metal surface existing, due to the absence of the upper mirror, the electron moving along the +z direction will escape the potential barrier and travel to infinity. Only the down closed orbit exists here. As a result, the number of the closed orbit is decreased and the photodetachment cross section becomes much smoother, as we can see from the dashed line. In Figure 4b, the upper mirror moves closer to the negative ion, d1 ) 400 au, and the potential barrier becomes 0.785 eV, which is quite small. Then there will be more closed orbits bounced back by the upper mirror and their contribution to the cross section becomes greater. Therefore, except in the small region of photon energy less than 0.785 eV, the difference between the two lines is becoming more obvious. In Figure 4c, d1 ) d2 ) 100 au and the potential barrier is zero. Under this condition, all of the closed orbits are formed after hitting the upper and lower mirrors. Hence, the two lines are becoming completely different even in the threshold region. Figure 4d is the case with d1 ) 50 au (d1 < d2) and the potential barrier becomes Vmax ) 0.777 eV, which is still very small, so the closed orbits are also generated after hitting the two metallic mirrors. As the two
-
metallic surfaces are located so close to the H , the period of the closed orbits becomes much shorter. This leads to the stronger oscillations of the cross section in Figure 4d. From the above analysis, we find that the two-mirror metallic microcavity has a greater enhancement effect on the oscillations of the photodetachment cross section compared to the case of a single-mirror configuration. To show the relation between the oscillations and closed orbits clearly, we calculate the Fourier transformed photodetachment cross section of H- in a two-mirror metallic microcavity by using eq 29. The calculations are carried out using ς1 ) 1, ς2 ) 60. The results are given in Figure 5. Each peak in Figure 5 corresponds to the contribution of one fundamental closed orbit. For example, in Figure 5a, the first peak appears at 1.35 and corresponds to the scaled action of the down closed orbit. The second peak occurs at 10.73 and corresponds to the scaled action of the up closed orbit. As the third and fourth closed orbits are of the same value, they share the same peak of scaled action, equal to 12.08. To be clearer, we plot the corresponding closed orbits beside each peak. 5. Conclusion In summary, we have studied the photodetachment of H- in a two-mirror metallic microcavity using closed orbit theory. It
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is found that the photodetachment cross section of H is not only related to the photon energy but also related to the distance between the ion and the two metallic mirrors. Due to the existence of the upper metallic mirror, the photodetachment cross section of H- for the present system oscillates much stronger than when only a lower metallic mirror is present. And the closer the upper metallic surface moves toward the H , the greater the oscillations become. In addition, each peak in the Fourier transformed cross section corresponds to the scaled action of one fundamental closed orbit, which suggests that the oscillations in the photodetachment cross section are caused by the superposition of the interference waves traveling along the closed orbits. We hope that our results will be useful for directing the future experimental study of the photodetachment of negative ions in the vicinity of interfaces, cavities, and ion traps.22-24 Acknowledgment. This work is supported by the National Natural Science Foundation of China (Grant No. 10604045), the University Science & Technology Planning Program of Shandong Province (Grant No. J09LA02), and the Discipline Construction Fund of Ludong University. We also thank the referee’s good suggestions. References and Notes (1) Bryant, H. C. Phys. ReV. Lett. 1987, 58, 2412. (2) Yang, G.; Mao, J. M.; Du, M. L. Phys. ReV. A 1999, 59, 2053.
(3) Peters, A. D.; Delos, J. B. Phys. ReV. A 1993, 4, 3020. (4) Peters, A. D.; Jaffe, C.; Delos, J. B. Phys. ReV. A 1997, 56, 331. (5) Peters, A. D.; Jaffe, C.; Delos, J. B. Phys. ReV. Lett. 1994, 73, 2825. (6) Sjakste, J.; Borisov, A. G.; Gauyacq, J. P. Phys. ReV. Lett. 2004, 92, 156101. (7) Yang, G. C.; Zheng, Y. Z.; Chi, X. X. J. Phys. B 2006, 473, 311. (8) Yang, G. C.; Rui, K. K.; Zheng, Y. Z. Physica B 2009, 404, 1576. (9) Wang, D. H. Eur. Phys. J. D 2007, 45, 179. (10) Yang, G. C.; Zheng, Y. Z.; Chi, X. X. Phys. ReV. A 2006, 73, 04313. (11) Afaq, A.; Du, M. L. J. Phys. B 2007, 40, 1309. (12) Wang, D. H.; Du, M. L.; Lin, S. L. J. Phys. B 2006, 39, 3529. (13) Rui, K. K.; Yang, G. C. Surf. Sci. 2009, 603, 632. (14) Zhao, H. J.; Du, M. L. Phy. ReV. A 2009, 79, 023408. (15) Du, M. L.; Delos, J. B. Phy. ReV. A 1988, 38, 1896. 38 1913. (16) Du, M. L.; Delos, J. B. Phys. ReV. Lett. 1987, 58, 1731. (17) Ganesan, K.; Taylor, K. T. J. Phys. B 1996, 29, 1293. (18) Knudson, S. K.; Delos, J. B.; Bloom, B. J. Chem. Phys. 1985, 83, 5703. (19) Ohmrua, T.; Ohmrua, H. Phys. ReV. 1960, 118, 154. (20) Du, M. L. Phys. ReV. A 1989, 40, 4983. (21) Keeler, M. L.; Flores-Rueda, H.; Wright, J. D.; Morgan, T. J. J. Phys. B 2004, 37, 809. (22) Wethek, S.; Mertens, A.; Winter, H. Phys. ReV. Lett. 2003, 90, 037602. (23) Lloyd, G. R.; Procter, S. R.; Slftley, T. Phy. ReV. Lett. 2005, 95, 133202. (24) Busani, R.; Cheshnovsky, O. J. Phys. Chem. C 2007, 111, 17725.
JP100323A
