Oscillatory Structure in Measured Total<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">Li</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>+ Li Charge Transfer and Comparison with Theory

Perel, Julius; Daley, Howard L.; Peek, James M.; Green, Thomas A.

doi:10.1103/physrevlett.23.677

Cited by 38 publications

(12 citation statements)

References 7 publications

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“…Smith 4 has shown that such oscillations result from a two-state theory for resonant chargetransfer collision in which the difference between gerade and ungerade potentials passes through an extremum. Peek et al 5 have used the known potential difference curve of the Li 2 + molecule to calculate the oscillatory cross section for Li + -Li charge transfer, which is in good agreement with the experimental results of Perel et al 6 The term XI(R) defined by Eq. (4) is equal to one half the difference between the gerade and ungerade potential states of the Na 2 + molecule.…”

supporting

confidence: 66%

Oscillations inNa+-Na Charge-Transfer Cross Sections

1972

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Total charge-transfer cross sections of fast sodium ions on sodium atoms are calculated by an impact-parameter method using an analytical Hartree-Fock wave function. The results show oscillations in the cross section as a function of the velocity of ions, and they are compared with the experimental result observed by Daley and Perel.Daley and Perel 1 measured the total chargetransfer cross section of sodium ions on sodium atoms as a function of ion energy ranging from 0.5 to 24 keV using a cross-beam technique and phase-sensitive lockin detection similar to that used to measure other alkali-metal cross sections. 1 * 2 The results of the Na + -Na cross-section measurement show oscillations in the cross section as a function of ion energy similar to those observed for different alkali-metal ionatom combinations. 1 ' 2 So far no theoretical results predicting such oscillations in the Na + -Na charge-transfer cross section have been reported. In the present work we have calculated the results of the Na + +Na-Na + Na + cross section by an impact-parameter method using dementi's analytical Hartree-Fock wave function. 3 All quantities are in atomic units. In this formulation, the cross section for charge transfer is given bywhere v is the velocity of the ion along the x axis and with H fi ' = {f\H f \i), H H ' = (i\w \i), and S = (i\f) = {f\i), i and/ denoting the initial and the final states, respectively. The interaction Hamilto-nian iswhere R is the distance between the two nuclei and y f the distance of the active electron from the ion. With the interaction Hamiltonian (3) and using dementi's eight-parameter analytical Hartree-Fock wave function 3 for sodium, the integrand of Eq. (2) is calculated numerically and is represented by XI(R) =e' aR [b + C R +dR 2 +eR? +/R 4 +gR 5 ]with an average error of 0.4% from R = 2.5 to R = 20. The values of the parameters are as follows: a = 0.724 994 88, b = 0.698 023 75, c = -1.239 414 2, d = 0.455 940 90, e =-0.052308 794, / = 0.003 847 385 8, #=-0.486 97075X10" 7 . Now we write Eq. (2) as £(fl 0 )=2X(# 0 ),where X(R 0 ) = 2f~QXI(R)RdR/(R 2 -tf, 2 ) 1 ' 2 .Integral (5) is evaluated in terms of modified Bessel functions of the third kind. The results 583

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confidence: 66%

Oscillations inNa+-Na Charge-Transfer Cross Sections

1972

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“…These values for the states (1) 2 and (1) 2 (as illustration) are given in Table 4. The comparison of these values with other results is not possible, since they are given here for the first time.…”

Section: The Resultsmentioning

confidence: 98%

“…Collisions between alkali-metal ions have been studied since the early work of Perel et al [1,2], Daley and Perel [3],Aquilanti et al [4][5][6][7][8][9][10], Brunetti et al [11], Talk et al [12], Anderson et al [13], and Olsen et al [14]. These collisions play an important role in the different areas of the physics and chemistry of lowdensity plasma and ionized gases and provide detailed information about long-range interatomic potentials, scattering length [15], and excited-state radioactive life times.…”

Section: Introductionmentioning

confidence: 99%

Theoretical study with spin-orbit effects and electronic transition moment calculation of the ion NaCs⁺

Korek¹,

Badreddine²,

Allouche³

2008

Can. J. Phys.

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A theoretical study was done of the electronic structure of the molecular ion NaCs + . The calculation is based on nonempirical pseudopotentials and parameterized -dependent polarization potential. Gaussian basis sets were used for both atoms and spin-orbit effects were taken into account. Potential energy curves were obtained for 56 lowest electronic states for the symmetries 2 + , 2 , 2 , and of the molecular ion NaCs + . The spectroscopic constants were calculated for 19 electronic states by fitting the calculated energy values to polynomials in terms of the internuclear distance r. Through the canonical functions approach the eigenvalue E v , the rotational constant B v and the abscissas of the turning points were calculated up to 52 vibrational levels for 6 bound states. The dipole moment were calculated in the considered range of the internuclear distance r. The comparison of the calculated values to those available in the literature shows a good agreement.Résumé : Nous avons complété une étude théorique de la structure électronique de l'ion moléculaire NaCs + . Le calcul est basé sur des pseudopotentiels non empiriques et sur un potentiel de polarisation dépendant de . Nous avons utilisé une base gaussienne pour les deux atomes et nous avons tenu compte des effets de spin-orbite. Nous obtenons les courbes équipotentielles pour les 56 états de plus basse énergie dans les symétries 2 + , 2 , 2 et de l'ion moléculaire NaCs + . Nous avons calculé les constantes spectroscopiques pour 19 états électroniques par ajustement polynomial des énergies calculées en fonction de la séparation internucléaire r. Via une approche en fonctions canoniques, nous avons évalué la valeur propre E v , la constante rotationnelle B v et l'abcisse du point tournant jusqu'à 52 états vibrationnels pour 6 états liés. Nous avons calculé le moment dipolaire dans le domaine considéré de la distance internucléaire r. La comparaison des valeurs calculées avec les valeurs expérimentales publiées montre un bon accord.[Traduit par la Rédaction]

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“…Alkali ion interactions with neutral atoms or molecules play an important role in different areas of physical and chemical systems in both gas and condensed matter, their behaviour being closely related with the ion kinetic energy. In the range of a few keV, the pioneering studies by Perel et al 1 and Aquilanti and Casavecchia 2 among others 3,4 showed that electron transfer leading to electronically excited states and neutral target excitation was the main non-adiabatic excitation process. More recently, and in the same energy range, systems involving heavier alkali ions and atoms have been studied by some of us 5 using also Mg atoms as targets, 6,7 complemented for (Rb-Mg) + with a multisurface dynamical study.…”

Section: Introductionmentioning

confidence: 99%

Cross-section energy dependence of the [C6H6–M]+ adduct formation between benzene molecules and alkali ions (M = Li, Na, K)

Lopez

Lucas

Andrés

et al. 2011

Phys. Chem. Chem. Phys.

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The association reactions of benzene molecules with alkali ions M(+) (Li(+), Na(+) and K(+)) under single collision conditions have been studied using a radiofrequency-guided-ion-beam apparatus and mass spectrometry characterization of the different adducts. Cross-section energy dependences for [M-C(6)H(6)](+) adduct formation have been measured at collision energies up to 1.20 eV in the center of mass frame. All excitation functions decrease when collision energy increases, showing the expected behaviour for barrierless reactions. From ab initio chemical structure calculations at the MP2(full) level, the formation of the adducts makes evident the alkali ion-benzene non-covalent chemical bond. The cross-section energy dependence and the role of radiative cooling rates and unimolecular decomposition on the stabilization of the energized collision complex are also discussed.

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Oscillatory Structure in Measured TotalLi++ Li Charge Transfer and Comparison with Theory

Cited by 38 publications

References 7 publications

Oscillations inNa+-Na Charge-Transfer Cross Sections

Oscillations inNa+-Na Charge-Transfer Cross Sections

Theoretical study with spin-orbit effects and electronic transition moment calculation of the ion NaCs⁺

Cross-section energy dependence of the [C6H6–M]+ adduct formation between benzene molecules and alkali ions (M = Li, Na, K)

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Oscillatory Structure in Measured TotalLi++ Li Charge Transfer and Comparison with Theory

Cited by 38 publications

References 7 publications

Oscillations inNa+-Na Charge-Transfer Cross Sections

Oscillations inNa+-Na Charge-Transfer Cross Sections

Theoretical study with spin-orbit effects and electronic transition moment calculation of the ion NaCs+

Cross-section energy dependence of the [C6H6–M]+ adduct formation between benzene molecules and alkali ions (M = Li, Na, K)

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Theoretical study with spin-orbit effects and electronic transition moment calculation of the ion NaCs⁺