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INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 1885–1898 PII: S0953-4075(03)54875-1 Disalignment rate coefficient of neon excited atoms due to helium atom collisions at low temperatures M Seo1 , T Shimamura1 , T Furutani1 , M Hasuo1,3 , C Bahrim2 and T Fujimoto1 1 Department of Engineering Physics and Mechanics, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan 2 Department of Chemistry and Physics, Lamar University, Beaumont, TX 77710–10046, USA E-mail: [email protected] Received 24 September 2002 Published 24 April 2003 Online at stacks.iop.org/JPhysB/36/1885 Abstract Disalignment of neon excited atoms in the fine-structure 2pi levels (in Paschen notation) of the 2p5 3p configuration is investigated in a helium–neon glow discharge at temperatures between 15 and 77 K. At several temperatures, we plot the disalignment rate as a function of the helium atom density for Ne∗ (2p2 or 2p7 ) + He(1s2 ) collisions. The slope of this dependence gives the disalignment rate coefficient. For both collisions, the experimental data for the disalignment rate coefficient show a more rapid decrease with the decrease in temperature below 40 K than our quantum close-coupling calculations based on the model potential of Hennecart and Masnou-Seeuws (1985 J. Phys. B: At. Mol. Phys. 18 657). This finding suggests that the disalignment cross section rapidly decreases below a few millielectronvolts, in disagreement with our theoretical quantum calculations which predict a strong increase below 1 meV. The disagreement suggests that the long-range electrostatic potentials are significantly more repulsive than in the aforementioned model. 1. Introduction The analysis of inter- and intra-multiplet transitions induced in atom–atom collisions within the framework of a molecular theory has been discussed in many papers (e.g. [1]) and textbooks (e.g. [2]). In order to test the accuracy of the molecular potentials between colliding atoms proposed in theoretical models, a few elementary processes have been investigated experimentally. In particular, the disalignment, which represents the angular momentum relaxation of uniaxially polarized (aligned) atoms, due to atom–atom collisions gives a good indication of the accuracy of anisotropic molecular potentials. More exactly, the disalignment is 3 Author to whom any correspondence should be addressed. 0953-4075/03/091885+14$30.00 © 2003 IOP Publishing Ltd Printed in the UK 1885 1886 M Seo et al 60meV 3 -1 Potential ( x10 cm ) 151.5 5meV 151.0 2p2 2p4 2p5 150.5 60meV 5meV 150.0 2p6 2p7 2p8 4 6 8 10 R (a0) 12 14 Figure 1. Some adiabatic potentials for the Ne∗ (2pi )–He system with = 1. is the quantum number for the projection of the total electronic angular momentum on the internuclear axis. A typical collision energy (60 meV) for our previous experiment [4] and another one, representative of the present experiment (5 meV), are indicated by broken horizontal lines. The origin for the adiabatic energies is the ground state of the neon atom, while the collision energy is given with respect to the asymptotic limit 2pi of the molecular channel with i = 2 and 7. defined as the relaxation of the alignment ρ02 /ρ00 of atoms, where ρ02 and ρ00 are the irreducible tensor components of the atomic density matrix (for more details see [3]). Recently, both experimentalists [4] and theorists [5] have analysed the disalignment of Ne∗ (2pi ) atoms (in Paschen notation) due to thermal collisions with He atoms. Wakabayashi et al [4] have measured the disalignment rate coefficient of excited neon atoms in the 2p2 and the 2p7 states of the 2p5 3p configuration due to neon or helium atom collisions in a discharge cell for temperatures between 42 and 650 K. Bahrim et al [5] have performed full quantum calculations of the disalignment cross sections based on the model potential of Hennecart and Masnou-Seeuws [6], which describes the electrostatic interaction between Ne∗ (2p5 3p) and He ground-state atoms, for the same range of temperatures. Figure 1 in [5] shows good agreement between the theoretical disalignment rate coefficients and the experimental data from [4]. However, at lower temperatures, the disalignment rate coefficient has neither been calculated nor measured, until now. The investigation of the disalignment process at very low collision energies is important because it provides a sensitive test for the long-range electrostatic potentials between the colliding atoms. In this paper, we report new experimental results in the low temperature range between 15 and 77 K, and compare them with full quantum calculations. In section 2, we briefly review our quantum mechanical model for computation of the disalignment cross section and rate coefficient, and we report new theoretical results. In section 3, we present our experimental set-up, while our procedure to find the disalignment rate coefficient is described in section 4. In section 5, we compare our theoretical results with our experimental data. Our conclusion follows in section 6. 2. Quantum calculation of disalignment cross section and rate coefficient In the present quantum mechanical calculations of disalignment cross sections, we use the same model potential of Hennecart and Masnou-Seeuws [6] as in [5]. In the framework of this model potential, the interaction between an excited neon atom and the ground-state helium perturber Disalignment rate coefficient of neon excited atoms due to helium atom collisions 1887 is treated as a perturbation. Also, the complex multibody interaction between the two rare gas atoms is simplified in three two-body problems: the interactions between the active electron (3p) and each of the two cores, Ne+ (2p5 ) and He(1s2 ), at which the core–core interaction is added. For slow collisions, such as those investigated here, the inner electrons of the Ne+ core and the He atom are not perturbed. The electron-core electrostatic potentials are given in [6]. The core–core interaction is represented at long range by a polarization term, and at short range by an empirical term fitted to reproduce the spectroscopic data for potential curves of the HeNe+ molecular ion [7]. In figure 1, we present some molecular potentials of the Ne∗ (2pi )– He system with = 1 (where is the quantum number of the projection of the total electronic angular momentum on the internuclear axis). A complete picture of the molecular potentials with = 1 includes the 2p9 and 2p10 states, too. But because they are much less relevant for our discussion in section 5, we exclude them in figure 1. Of course, all the molecular states of the Ne∗ (2p5 3p)–He system are included in our present calculations. The accuracy of the model potential proposed by Hennecart and Masnou-Seeuws was tested in a wide range of collision energies (between 10 and 1250 meV) by comparison with measurements of absolute cross sections to describe polarization effects in Ne∗ atoms due to collisions with He ground state atoms in experiments with crossed atomic beams [7], and disalignment effects due to atomic collisions in gas cells [5, 8]. Excellent agreement between theory and experiment was found in all cases. In order to describe the Ne∗ (2pi ) + He collision, we choose a convenient diabatic representation using as a basis set the unperturbed atomic wavefunctions. All 2p1 –2p10 fine-structure levels of the 2p5 3p configuration of neon are included, which generates 36 molecular channels for the Ne∗ (2p5 3p)–He system. Therefore for each collision energy the total wavefunction of the system is expanded as a linear combination of all 36 diabatic electronic states. The expansion coefficients correspond to the radial functions for the nuclear motion. These radial functions are computed by numerical integration of the time-independent Schrödinger equation using an improved version of the log-derivative method [7]. Both open and closed molecular channels are included in our full quantum calculations. From the asymptotic solutions of the coupled equations we calculate the collision S-matrix. In order to guarantee the convergence of the S-matrix elements for very low collision energies, we integrate the coupled equations up to an internuclear distance Rmax of 40 a0 , which is twice as large as in our previous calculations [5, 7, 8]. In order to test our theoretical cross sections, we have performed separate calculations in two reference systems: (a) the space-fixed frame, where the quantization axis is chosen along the relative incident velocity of the colliding atoms, and (b) the body-fixed frame, where the quantization axis is chosen along the internuclear axis. Details about the calculations in these two reference frames are given in section 3 of [7]. From the S-matrix elements computed at various collision energies E, we calculate the isotropic intra-multiplet cross sections σm J ,m J (E) between the magnetic sublevels m J and m J of the same fine-structure 2pi (J ) level of a neon atom by using equation (3) in [5], for the 2p2 (J = 1) and 2p7 (J = 1) levels. In figure 2, we show the energy dependence of our theoretical cross sections σm J =1,m J =0 (thick full curves) for (a) the 2p2 and (b) the 2p7 levels of neon. Finally, the disalignment cross section σ (E) is calculated as σ (E) = 3σm J ,m J (E) (1) where the quantum numbers (m J , m J ) can be either (0, ±1) or (±1, 0). Because of the symmetry relationships between the isotropic intra-multiplet cross sections σm J ,m J (which means that σ1,0 = σ−1,0 = σ0,1 = σ0,−1 ) we can derive σ (E) by using in equation (1) the cross section σ10 from figure 2. 1888 M Seo et al 30 σ10 vf14(E) vf23(E) vf32(E) vf77(E) vf300(E) (a) 20 σ10 ( x 10 -20 2 m ) 25 15 10 5 0 0 10 20 30 E (meV) 40 50 30 σ10 vf14(E) vf23(E) vf32(E) vf77(E) vf300(E) (b) 20 σ10 ( x 10 -20 2 m ) 25 15 10 5 0 0 10 20 30 E (meV) 40 50 Figure 2. The isotropic intra-multiplet cross section σ10 (thick full curve) of the Ne∗ atom on the (a) 2p2 and (b) 2p7 states induced by collisions with the He ground-state atom as a function of collision energy. The multiplicative factor v f T (E) in equation (2) is indicated for several temperatures by thin curves. For the purpose of a direct comparison between theory and experiment, the disalignment rate coefficient, K , is needed. Assuming that the energy distribution of atoms in a cell is well described by a Maxwell function, f T (E), we find K (T ) as ∞ σ (E)v f T (E) d E, (2) K (T ) = 0 where E = mv 2 /2 (with v the relative asymptotic velocity and m the reduced mass of the colliding atoms) and T is the temperature of atoms in the cell. Several examples of v f T (E) are shown in figure 2. In order to obtain convergent results of K (T ) for T between 15 and 77 K, the integration in equation (2) is done over an energy interval from 0.1 up to 200 meV. Our theoretical results for the disalignment rate coefficient are shown in figure 3 (by full curves). 3. Experimental set-up The experimental set-up and procedure are basically the same as described in [4], and therefore in this section we will only briefly review them and emphasize the changes made to perform the Disalignment rate coefficient of neon excited atoms due to helium atom collisions 6 4 1889 (a) 2 10 -16 3 -1 K (m s ) 6 4 2 10 -17 6 4 Theory Experiment [4] Experiment (This work) 2 10 -18 2 3 10 10 4 5 6 7 2 3 4 5 6 7 100 T (K) -15 8 6 (b) 3 -1 K (m s ) 4 2 10 -16 8 6 Theory Experiment [4] Experiment (This work) 4 2 10 -17 2 10 3 4 5 6 7 2 3 4 5 6 7 100 T (K) Figure 3. The disalignment rate coefficients K for (a) Ne∗ (2p2 ) + He and (b) Ne∗ (2p7 ) + He collisions as a function of temperature from our quantum calculations (full curve), experimental data from [4] (open circles) and the present experiments (full circles). The experimental error bars are within twice the size of the symbols in (a) and within the size of the symbols in (b). present measurements. A schematic diagram of the experimental set-up is shown in figure 4. A tube made of fused quartz was filled with a mixture of neon and helium gases. A glow discharge was produced with a DC of 0.1–0.4 mA. The structure of the discharge channel was similar to that shown in figure 1 of [4] except for another slit and the viewing window as shown in figure 2 of our preceding paper [9]. The two slits and windows were used for the self reabsorption measurements as explained in [9]. The temperature of the discharge channel below 77 K was produced by a continuous flow of evaporated helium gas from a liquid helium Dewar through the temperature control layer surrounding the channel. This layer was surrounded by a vacuum. By adjusting the current through a heater immersed in liquid helium, we stabilized the flow of the cold helium gas from the Dewar. The temperature of the channel was measured by a thermocouple attached to the outside wall of the channel. Fluctuations of the temperature were less than 0.5 K during a series of measurements over 3 min. For the temperature of 77 K, the temperature control layer was filled with liquid nitrogen. We measured the gas pressure by a ceramic capacitance manometer (ULVAC CCMT100) at room temperature, which was calibrated against an oil manometer, assuming the same 1890 M Seo et al Dichroic Mirror 1064nm YAG Laser 1064nm SHG 532nm ND Filter Dye Laser Aperture (d=1mm) Photo Diode GTP Polarizer Digitizing Signal Analyser (DSA) PM Liquid N2 (77K) or He gas (17K~55K) Monochromator Fluorescence Discharge Cell PC x z y Figure 4. A schematic diagram of the experimental set-up. SHG: second harmonic generator, GTP: Glan–Thompson prism, ND filter: neutral density filter, PM: photomultiplier, PC: personal computer. pressure for the gas in the discharge channel at a low temperature. In situations where the temperatures of parts of a system are different, the above assumption may not be justified due to the thermal transpiration effect [10]. This effect is due to insufficient collisions between the gas particles, and is pronounced at low densities. In our case, the inner diameter of the discharge tube was 5 mm, which is several hundred times larger than the mean free path length of the helium and neon atoms. Therefore this effect was considered insignificant and was neglected. The excitation light source was a dye laser (DCM in ethanol) pumped by a frequencydoubled YAG laser (Spectra Physics GCR-100). The laser pulse duration (measured as the full width at half maximum and shown in figure 5(a)) was 6 ns, while the repetition rate was 50 Hz. The spectral bandwidth was typically 0.01 nm. The laser light was linearly polarized by a Glan–Thompson prism in the z direction shown in figure 4. A laser light pulse of λ = 616.4 nm excited the neon atoms from the 1s3 (J = 0) level of the 2p5 3s configuration to the 2p2 ( J = 1) state, while a λ = 653.3 nm pulse produced the 2p7 ( J = 1) atoms from the same lower level. The energy of the laser light pulse was about 0.05 mJ. The diameter of the light beam was 2 mm at the location of the observation. The direct fluorescence of 1s2 (J = 1) ← 2p2 (J = 1)(λ = 659.9 nm) and 1s4 (J = 1) ← 2p7 (J = 1) (λ = 638.3 nm) transitions were observed for the 2p2 and 2p7 states, respectively. The fluorescence was observed through the slit on the side wall of the discharge channel and the viewing window along the x direction in figure 4. The x axis is perpendicular to the discharge channel axis. We define the quantization axis along the polarization vector of the laser light (the z direction in figure 4). We observed the fluorescence with the analysing polarizer located in front of the monochromator (Nikon G-250). Thus we could measure separately the intensities of the π and σ components. The entrance slit was parallel to the discharge channel axis. The width and height of the entrance slit were 0.5 and 5 mm, respectively, and those of the exit slit were Disalignment rate coefficient of neon excited atoms due to helium atom collisions Intensity (arb.units) 1.0 1891 (a) 0.8 Iσ 77 K Ne:He=1:100 Helium atom density 23 -3 = 4.81 x 10 m 0.6 laser 0.4 Iπ 0.2 0.0 0 20 40 60 Time (ns) -0.6 (b) -0.8 log( - A L ) -1.0 -1.2 -1.4 -1.6 -1.8 -2.0 0 20 40 60 Time (ns) Figure 5. An example of the observed temporal developments for (a) the fluorescence 1s4 (J = 1) ← 2p7 (J = 1) (λ = 638.3 nm) intensities of the π and σ components (dots) and the temporal development of the laser pulse (dotted curve) and (b) the longitudinal alignment. 0.5 and 10 mm. The temporal change of the output signal of the photomultiplier was recorded by a transient digitizing signal analyser (Tektronix DSA601). In order to determine the relative sensitivity of the π to the σ polarization component in our detection system, we polarized the excitation light to the x direction. In this case, the fluorescence intensity is independent of its polarization direction around the x axis. From measurements of the fluorescence intensities for the π and σ polarization components, the relative sensitivities were determined to be 0.670 and 0.698 for the wavelengths 659.9 and 638.3 nm, respectively. In [4] the temperature of the metastable atoms was confirmed to be virtually equal with the wall temperature of the discharge channel. At a low temperature of 20 K, we measured the profile of the absorption line for the neon 1s3 (J = 0) → 2p7 (J = 1) transition (of 1892 M Seo et al λ = 653.3 nm) using a single-mode CW diode laser. The line profile was found to be well reproduced by a Voigt profile with a Lorentzian width of 12 MHz and a Gaussian width of 334 MHz. The Lorentzian width corresponds to the natural lifetime of the upper level. From the Gaussian width the apparent temperature of the metastable neon atoms was found to be 22.4 K. We attribute the slight difference from the discharge tube temperature to the broadening of the spectrum by the pump-over saturation effects discussed in [4]. We thus conclude that the actual atom temperature is 20 K in this example. 4. Experimental results Figure 5(a) shows an example of the temporal developments of the fluorescence intensities with the π and σ components resolved. The intensities Iσ (t) and Iπ (t) were calibrated with the relative sensitivity of the π to the σ polarization component in our detection system. Since the excitation is done with π polarized light in the J = 0 → 1 transition, the initial population of the upper level is produced only in the m J = 0 magnetic sublevel. In this case, the fluorescence of the J = 1 ← 1 transition has only the σ component due to the selection rules. During the lifetime of the upper level, excitation transfer from the m J = 0 magnetic sublevel to m J = ±1 magnetic sublevels, or disalignment, may take place due to atom collisions or trapped radiation. As a consequence the π component appears in the fluorescence. The atomic processes involved are: the laser light excitation, the excitation transfer, the radiative decay and the collisional depopulation. The coupled rate equations are dn 0 (t) = −(2k + r )n 0 (t) + 2kn 1 (t) + l(t) dt (3) dn 1 (t) = kn 0 (t) − (k + r )n 1 (t), dt where n 0 and n 1 are the ‘populations’ of the m J = 0 and +1 (or m J = −1) magnetic sublevels of the upper 2pi level, respectively. Because the magnetic sublevels m J = +1 and −1 are equally populated (the disalignment process investigated here being isotropic), in equations (3) we need to include the ‘population’ for the m J = +1 magnetic sublevel only. The rates k and r correspond to the excitation transfer between the magnetic sublevels, m J = 0 and ±1, of the same 2pi level and the total depopulation of the 2pi level, respectively. The latter process consists of radiative decay and collisional depopulation. l(t) is the temporal development of laser light excitation to the 2pi level. The intensity of the polarized components of the fluorescence is given by Iσ (t) = C 12 [n 0 (t) + n 1 (t)] (4) Iπ (t) = Cn 1 (t), where C is a constant that depends on Einstein’s A coefficient of the observed transition, which is the same for all the magnetic sublevels of the same 2pi level, and the detection efficiency of the fluorescence. We define the longitudinal alignment for the emitted radiation, which is proportional to the longitudinal alignment parameter of the 2pi level [3], as 1 n 1 (t) − n 0 (t) Iπ (t) − Iσ (t) A L (t) ≡ = . (5) Iπ (t) + 2Iσ (t) 2 n 0 (t) + 2n 1 (t) The second equality was found by introducing the intensities Iσ and Iπ from equation (4) in the definition of A L (t). Figure 5(b) shows the temporal development of the longitudinal alignment obtained from the fluorescence intensities presented in figure 5(a). After the cessation of the laser pulse (for t > 20 ns in figure 5), the term l(t) in equation (3) vanishes and the longitudinal alignment derived from the system of differential equations (3) becomes (6) A L (t) = − 21 e−3kt . 40 17K 35K 77K 30 10 40 0.5 1.0 1.5 2.0 2.5 24 -3 He atom density ( x10 m ) (b) 6 -1 20K 55K 300K 20 0 0.0 Disalignment rate ( x10 s ) 1893 (a) 6 -1 Disalignment rate ( x10 s ) Disalignment rate coefficient of neon excited atoms due to helium atom collisions 30 17K 35K 77K 20K 55K 300K 20 10 0 0.0 0.5 1.0 1.5 2.0 2.5 24 -3 He atom density ( x10 m ) Figure 6. Experimental values for the disalignment rate of the 2p2 state of neon as a function of the helium atom density. In (a) we present our direct measurements of disalignment rate, while in (b) the effect of the radiation re-absorption (included in (a)) is separated [9]. The full lines in (b) show the results of the linear fit within the least-squares method with the null intercept for each temperature. The experimental error bars are within the size of the symbols. From the slope of log[−A L (t)], we get the relaxation time, (3k)−1 , which is due to intramultiplet transitions within the same 2pi (J = 1) level. The term 3k due to He atom collisions in equation (6) is related to the disalignment rate coefficient K defined in equation (2), 3k = n He K , where n He is the He atom density. By varying the He atom density in the discharged cell we determine the disalignment rate coefficient K (T ). The longitudinal alignment in figure 5(b) for t > 20 ns shows a single exponential decay with time. The disalignment rate coefficient is determined by fitting the experimental data points with equation (6). The result of this least squares fitting is indicated by the full line in figure 5(b). 4.1. Disalignment of the 2 p2 state neon Figure 6(a) shows the disalignment rate of the 2p2 state of neon as a function of the helium atom density for several temperatures. The uncertainty of each data point is within the size of M Seo et al 80 6 -1 Disalignment rate ( x10 s ) 1894 60 40 15K 20K 32K 300K 20 0 0.0 0.2 0.4 0.6 0.8 He atom density ( x10 24 17K 26K 77K 1.0 1.2 -3 m ) Figure 7. Disalignment rate of the 2p7 state of neon as a function of the helium atom density. The full lines are the results of a linear fit within the least-squares method. The experimental error bars are within the size of the symbols. the symbols in the figure. In our experiment we prepared the mixture of neon gas at 0.05 Torr with helium gas of variable pressures at room temperature. The ratio of their partial pressures was varied from 1:15 to 1:150. In our cell experiment, disalignment due to electron collisions, neon atom collisions and radiation trapping are always present together with helium atom collisions. Because the electron density is of the order of 1016 m−3 in our experimental conditions [11], the disalignment rate due to electron collisions is of the order of 104 s−1 [12] and therefore can be neglected. Since we kept the neon density constant for all the helium densities at each T , the disalignment rate due to neon atom collisions is constant for all the helium densities at each T . For the 2p2 state, the disalignment rate coefficient for Ne∗ + Ne collisions is almost the same as that for Ne∗ + He collisions [4]. The disalignment rate due to Ne∗ + Ne collisions is estimated to be about 2.5 × 105 s−1 for the 2p2 state at 77 K and therefore it can be also neglected. Disalignment due to radiation re-absorption depends on the 1si (i = 2–5) populations in the discharge channel, and therefore on the discharge conditions. Since at low temperatures the increase in the disalignment rate with the increase in helium atom density is relatively small, the determination of the disalignment rate coefficient due to helium atom collisions is sensitive to the correction for the disalignment rate due to radiation re-absorption. In order to separate the effect of radiation re-absorption, we measured the self re-absorption of relevant emission lines by our discharge channel under the same conditions of the disalignment measurement. We have evaluated the disalignment rate due to radiation re-absorption with a Monte Carlo simulation program using the measured values of the self re-absorption. The method is explained in detail in the preceding paper [9]. The disalignment rate due to radiation re-absorption is found to be between 1 × 105 and 5 × 106 s−1 . Figure 6(b) shows the disalignment rate against the helium atom density after this correction has been made. The full lines are the results of the linear fit within the least-squares method with a null intercept. Finally we determine the disalignment rate coefficient, K (T ), of the 2p2 state of neon for the collisions with the ground-state helium atoms as the slope of each fitted line. The results for K (T ) are shown in figure 3(a). The uncertainty of each data point is within twice the size of the symbols. Disalignment rate coefficient of neon excited atoms due to helium atom collisions 1895 4.2. Disalignment of the 2 p7 state of neon Figure 7 shows the disalignment rate of the 2p7 state of neon as a function of the helium atom density for several temperatures. The uncertainty of each data point is within the size of the symbols. In the experiment we prepared the mixture of neon gas of 0.1 Torr with helium gas of variable pressure at room temperature. The ratio of their partial pressures was varied from 1:10 to 1:25. As was the case for the 2p2 state, the disalignment rate due to electron collisions is negligible for the 2p7 state, too. The disalignment rate due to Ne∗ + Ne collisions is estimated to be about 3 × 106 s−1 for the 2p7 states at 77 K. Since we keep the neon density constant for all helium densities for each T , the disalignment rate due to neon atom collisions is constant and contributes to the intercept. We note that the disalignment rate coefficient for the 2p7 state at low temperatures is about one order of magnitude larger than that for the 2p2 state. In this case we expect the correction of the disalignment rate due to radiation re-absorption to have a similar magnitude as for the 2p2 state, which is rather small. In fact, by adjusting the discharge current we tried to make the disalignment effects approximately constant for each temperature. We assume that the correction due to the radiation re-absorption is constant and contributes to the intercept. Therefore we determined the disalignment rate coefficient of the 2p7 state of neon due to the ground-state helium atoms as the slope of each linear fit (figure 7). The results are shown in figure 3(b). The uncertainty of each data point is within the size of the symbols. 5. Comparison between theory and experiment Figure 3 shows the disalignment rate coefficient for (a) Ne∗ (2p2 ) + He and (b) Ne∗ (2p7 ) + He collisions as a function of temperature. The present results are consistent with our previous measurements at higher temperatures [4]. However, in contrast to the excellent agreement between theory and experiment above 77 K [5], the experimental disalignment rate coefficient shows a more rapid decrease with the decrease in temperature below 40 K than is predicted by our quantum calculations. This is more salient in the 2p2 case. The analysis of the experimental data for the disalignment rate coefficient as a function of temperature indicates that K (T ) varies as T 1.6 for the Ne∗ (2p2 ) + He collision and as T 0.9 for the Ne∗ (2p7 ) + He collision below 40 K. Because the temperature dependence of the multiplicative factor v f T (E) in equation (2) is T 0.5 , the collision energy dependence of σ (E) may be E 1.1 for the 2p2 state and E 0.4 for the 2p7 state. This dependence suggests that the strong increase in the theoretical cross section below a few millielectronvolts shown in figure 2 is absent, and that σ (E) converges to zero for E → 0. At the present stage, the origin of the discrepancy between the quantum calculations and experiment is not fully clear. Here we discuss possible sources of error. For quantum calculations, the close-coupling method has a well-established conceptual basis in the framework of atom–atom collision theory (for details see [7] and the references therein). In particular, for the Ne∗ (2pi ) + He collisions, this method has been tested successfully in order to explain various experiments [5, 7, 8]. However, such quantum calculations depend on the accuracy of the molecular potentials which describe the atom–atom interaction. The analysis of the adiabatic potentials presented in figure 1 indicates that, for collision energies of about 60 meV, which are relevant for the domain of temperatures investigated by Wakabayashi et al [4], the distance of closest approach is about 3.5 a0 for the Ne∗ (2p7 ) + He collision and 8 a0 for the Ne∗ (2p2 ) + He collision [5]. Therefore at higher temperatures the disalignment rate coefficient is very sensitive to the influence of the short-range electrostatic potentials, especially for Ne∗ (2p7 ) + He collisions. At temperatures below 40 K, the most significant 1896 M Seo et al -1 Potential (cm ) 400 Vσ Vπ Wcc V 'σ 300 200 100 0 6 8 10 12 14 R (a0) 16 18 20 Figure 8. The electrostatic potentials for the Ne∗ (2p5 3p)–He system in the framework of the model potential of Hennecart and Masnou-Seeuws [6]: Vσ and Vπ describe the e(3p)–He system according to [13], Wcc is the polarization dipole term in the long-range core–core potential and Vσ is a modified Vσ potential. contribution to the rate coefficients K (T ) is given by collision energies below 10 meV. This can be observed from figure 2, where the multiplicative factor v f T (E) in equation (2) is indicated for several temperatures by thin curves. For E < 5 meV, the classical turning point is located at internuclear distances, R, larger than 10 a0 for both systems. For R between 11 and 13 a0 , the molecular potentials for the 2p2 and 2p7 states are repulsive, with energies decreasing from about 40 to 10 cm −1 (these values are given with respect to the asymptotic 2p2 and 2p7 atomic levels). At low collision energies, the long range interactions dominate the collision, and very accurate long range electrostatic potentials (for R > 10 a0 ) are needed. In figure 8, we show the long-range electrostatic potentials for the Ne∗ (2p5 3p)–He(1s2 ) system in the framework of the model potential of Hennecart and Masnou-Seeuws [6] for internuclear distances between 6 and 20 a0 . In the present quantum calculations, we used electrostatic potentials in a larger range of internuclear distances, between 2 and 40 a0 . The core–core potentials, Wcc , were computed in [7] using accurate spectroscopic data for the HeNe+ molecular ion. In our previous studies [7], we found that, for internuclear distances larger than 6 a0 , the exchange interaction between the electronic wavefunction of the Ne+ (2p5 ) ion and the ground-state He atom is negligible. Therefore, for such distances we characterize the core–core interaction by an electric dipole potential, αd /(2R 4 ) (where αd is 1.384 au and represents the dipole polarizability of the helium atom). The e(3p)–He(1s2 ) system is described by a model potential fitted to the low energy electron–helium scattering data by Valiron et al [13]. The Vσ and Vπ potentials of the e(3p)–He system were included by Hennecart and Masnou-Seeuws in their model potential [6] for internuclear distances up to 15 a0 . In our present quantum calculations, we adopt the same Vσ and Vπ potentials and show them in figure 8 for internuclear distances between 6 and 20 a0 . According to [6], Vπ vanishes for R > 8.5 a0 . The Vσ potential is strongly repulsive, and for R > 9 a0 it can be fitted with a simple exponential decay function: Vσ (R) = 171 687.78 exp(−R/1.493 92) (in cm−1), within a maximum deviation of 25%. The experimental results for K (T ) suggest that the long-range electrostatic potentials are significantly more repulsive than in the model potential of Hennecart and Masnou-Seeuws [6]. Disalignment rate coefficient of neon excited atoms due to helium atom collisions 1897 This assumption would explain the rapid decrease of the experimental results for K (T ) with the decrease in T , as shown in figure 3. Also, it suggests that σ (E) decreases rapidly with the decrease in E below 1 meV, contrary to our quantum calculations. The strong increase of the theoretical disalignment cross section at energies below 1 meV (about 8 cm−1 ) can be explained by the overlap between the attractive asymptotic electrostatic potentials and the repulsive centrifugal barrier. At energies below 1 meV, only the asymptotic part of the Wcc potentials contributes to collisions. The overlap between the attractive dipole potential, Wcc , and the repulsive centrifugal barrier (which is due to the rotation of the internuclear axis) produces a potential well which is favourable to the formation of a resonance in the scattering cross section. We tested this assumption by using various empirically modified core–core potentials. However, calculations with modified Wcc do not solve the disagreement between theory and experiment. Our studies indicate that the disalignment cross sections for low collision energies is sensitive to the repulsive Vσ potential for R > 10 a0 . We have done some test calculations with modified Vσ potentials. In figure 8 we show an example of such a modified potential, labelled by Vσ . Quantum calculations below 10 meV performed with Vσ change σ (E) by only 10%, and do not solve the disagreement between theory and experiment. Tests with a Vσ potential more repulsive than Vσ from figure 8 change σ (E) significantly for E > 10 meV, and modify the agreement between theory and experiment for higher temperatures [5]. Such a problem exists because, in our quantum calculations, the collision S-matrix depends on nonlocal electrostatic interactions (over a large domain of internuclear distances). The problem becomes even more complex if we consider the influence of the rotational coupling. In our quantum calculations, the rotational coupling between molecular channels was explicitly included. The strong influence of the rotational coupling on the disalignment cross section for higher temperatures was presented in figure 3 of [5]. At lower temperatures, the rotational coupling has a similar contribution to σ (E). In conclusion, our quantum calculations based on the model potential of Hennecart and Masnou-Seeuws [6] fails to reproduce the present experimental data for collision energies below a few millielectronvolts. New quantum calculations for very slow Ne∗(2p5 3p) + He(1s2 ) collisions require a new model for the description of the long-range atom–atom interaction, with the inclusion of the asymptotic multipole interactions between the two colliding atoms. Such models were recently proposed by Doery et al [14] for homonuclear diatomic systems of heavy rare gas atoms. For the Ne∗ + He system, a similar model is somehow more difficult to find because, in this case, different angular coupling schemes should be used for each colliding atom. Indeed, the helium atom is described within the standard Russell–Saunders coupling scheme, while the description of the Ne atom requires the non-standard coupling scheme which corresponds to the Paschen notation. Finally, we note that the effect of the short lifetime of the 2p2 and 2p7 states (of about 20 ns) was not included in the theoretical model which leads to equation (1). However, a helium atom having a speed of 70 m s−1 , which corresponds to a kinetic energy of about 1 meV, travels about 1400 nm during its lifetime. This value is three orders of magnitude larger than the internuclear distance considered here (40 a0 ) and therefore the effect of the short lifetime may indeed be neglected. 6. Conclusion Experimental results for the disalignment rate coefficients in Ne∗ (2p2 or 2p7 ) + He groundstate collisions at temperatures between 15 and 77 K are presented and compared with quantum close-coupling calculations based on the model potential of Hennecart and Masnou- 1898 M Seo et al Seeuws [6]. Contrary to the excellent agreement between theory and experiment above 77 K, the experimental values for the disalignment rate coefficient show a more rapid decrease with the decrease in temperature from 40 to 15 K than the theoretical results. Our experimental data indicate that the disalignment cross sections vary as E 1.1 for Ne∗ (2p2 ) + He collisions and E 0.4 for Ne∗ (2p7 ) + He collisions at energies below a few millielectronvolts, while our quantum calculations predict a strong increase of the disalignment cross section below 1 meV. Further investigations are necessary in order to clarify the origins of the discrepancy between theory and experiment. Acknowledgments We would like to thank Professor F Masnou-Seeuws for her useful comments. This work was partially supported by the Grant-in-Aid for Scientific Research (A) and Grant-in-Aid for Exploratory Research of the Ministry of Education, Culture, Sports, Science and Technology in Japan. References [1] Mies F H 1973 Phys. Rev. A 7 942 Manders M P I, Driessen J P J, Beijerinck H C W and Verhaar B J 1988 Phys. Rev. A 37 3237 Hickman A P 1997 Int. Rev. Phys. Chem. 16 177 [2] Nikitin E E and Umanskii S Ya 1984 Theory of Slow Atomic Collisions (Berlin: Springer) [3] Fujimoto T and Kazantsev S A 1997 Plasma Phys. Control. Fusion 39 1267 Omont A 1977 Prog. Quantum Electron. 5 69 [4] Wakabayashi T, Yamamoto A, Yaneda T, Furutani T, Hishikawa A and Fujimoto T 1998 J. Phys. B: At. Mol. Opt. Phys. 31 341 [5] Bahrim C, Kucal H, Dulieu O and Masnou-Seeuws F 1997 J. Phys. B: At. Mol. Opt. Phys. 30 L797 [6] Hennecart D and Masnou-Seeuws F 1985 J. Phys. B: At. Mol. Phys. 18 657 [7] Bahrim C, Kucal H and Masnou-Seeuws F 1997 Phys. Rev. A 56 1305 [8] Bahrim C, Hennecart D, Kucal H and Masnou-Seeuws F 1999 J. Phys. B: At. Mol. Opt. Phys. 32 3091 [9] Seo M, Nimura M, Hasuo M and Fujimoto T 2003 J. Phys. B: At. Mol. Opt. Phys. 36 1869 [10] Takaishi T and Sensui Y 1963 Trans. Faraday Soc. 59 2953 [11] Uetani Y and Fujimoto T 1984 Opt. Commun. 49 258 Uetani Y and Fujimoto T 1984 Opt. Commun. 55 457 (erratum) [12] Hirabayashi A, Nambu Y, Hasuo M and Fujimoto T 1988 Phys. Rev. A 37 83 [13] Valiron P, Gayet R, McCarroll R, Masnou-Seeuws F and Philippe M 1979 J. Phys. B: At. Mol. Phys. 12 53 [14] Doery M R, Vredenbregt E J D, Tempelaars J G C, Beijerinck H C W and Verhaar B J 1998 Phys. Rev. A 57 3603