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The near-threshold associative ionization N(2D)+O(3P) → NO+(X1Σ+)+e− reaction
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ISSN 10283358, Doklady Physics, 2014, Vol. 59, No. 3, pp. 122–125. © Pleiades Publishing, Ltd., 2014. Original Russian Text © G.V. Golubkov, G.K. Ozerov, 2014, published in Doklady Akademii Nauk, 2014, Vol. 455, No. 3, pp. 275–278. 122 The reaction of associative ionization (AI) of nitro gen and oxygen atoms , (1) proceeding through the stage of the intermediate Ryd berg complex NO**, is one of the most important pro cesses responsible for the formation of a charge in the lowtemperature plasma of the E and D layers in the Earth’s ionosphere during increased solar activity [1]. This study is devoted to investigation of the resonance structure of the differential and total cross sections for endothermic reaction (1) and to the determination of temperature dependences of the corresponding rate constants. This structure was obtained for the first time and previously was not considered in publications [2]. The necessity of its study is directly related to the problem of correct reconstruction of the parameters of the theory of multichannel quantum defects (MQDs) from highresolution optical spectra because for the Rydberg states of molecules, this problem cannot be solved by methods of quantum chemistry [3]. Reaction (1) proceeds with the participation of three interacting electron configurations: the dissocia tive states, the Rydberg states (including the autoion ization resonance states), and the intermediate valence states (with the quasifinite motion of the nuclear subsystem). The theory that is most conve nient for investigating the AIreaction dynamics is the theory based on using the renormalized Lippman– Schwinger equations for the operator of inelastic col lisions T [4]: , (2) , (3) where t is the matrix of the system reaction e – + NO + , G is Green’s operator describing the electron motion 2 3 N( D) O( P) NO** NO X e 1 ( ) + + - + → → Σ + ( ) 0 = + - T t G G T 0 = + t V VG t in the Coulomb center field and an ionic core nonin teracting with the center, G 0 is the part of the opera tor G that is smooth in energy. The operator V includes nonCoulomb interaction V nc of an electron with an ionic core and the operator V CI responsible for nona diabatic coupling with dissociative and valence config urations; i.e., V = V nc + V CI . The analytical properties of the operator are wellknown and make it possible to reduce integral Eq. (2) to the set of algebraic equations writing them in the form [4] (4) Here, E is the total energy of the system counted from the ion ground state, E q is the energy of vibrational and rotational excitation of the ionic core, is the basis wave function of the Rydberg configuration in the laboratory system of coordinates corresponding to the total momentum J and its projections M to the set direction, ρ is the effective electron angular momentum [5], N is the rotation momentum of nuclei, and ν is the vibrational quantum number. The vector corresponds to the wave functions of disso ciative channels. The valence configurations in formu lation (3) are included in the definition of matrix ele ments of the operator t constructed, as is known, on standing waves. In this case, the functions and are normalized as [4]. The operator t is related to the quantumdefect matrix by the formula , (5) which enables us to express its elements through the adiabatic quantum defects observed in the highreso lution spectra [5]. ( ) 0 - G G ( ) cot , 2 , . q q q q q q q q i E E β ⎧ ⎫ ⎪ ⎪ = + πν − ββ ⎨ ⎬ ⎪ ⎪ ⎩ ⎭ ν = −ε ε = − ∑ ∑ T t t T q JMlN = ν β q β ( ) ' ' ' qq E E =ββ = πδ − tan( ) =− πμ t The NearThreshold Associative Ionization Reaction G. V. Golubkov and G. K. Ozerov Presented by Academician A.A. Berlin October 7, 2013 Received July 18, 2013 DOI: 10.1134/S1028335814030094 + + + → + − Σ 2 3 1 ( ) ( ) ( ) D P X N O NO e Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 117977 Russia email: [email protected] PHYSICS
Transcript of The near-threshold associative ionization N(2D)+O(3P) → NO+(X1Σ+)+e− reaction
ISSN 1028�3358, Doklady Physics, 2014, Vol. 59, No. 3, pp. 122–125. © Pleiades Publishing, Ltd., 2014.Original Russian Text © G.V. Golubkov, G.K. Ozerov, 2014, published in Doklady Akademii Nauk, 2014, Vol. 455, No. 3, pp. 275–278.
122
The reaction of associative ionization (AI) of nitro�gen and oxygen atoms
, (1)proceeding through the stage of the intermediate Ryd�berg complex NO**, is one of the most important pro�cesses responsible for the formation of a charge in thelow�temperature plasma of the E and D layers in theEarth’s ionosphere during increased solar activity [1].This study is devoted to investigation of the resonancestructure of the differential and total cross sections forendothermic reaction (1) and to the determination oftemperature dependences of the corresponding rateconstants. This structure was obtained for the first timeand previously was not considered in publications [2].The necessity of its study is directly related to theproblem of correct reconstruction of the parameters ofthe theory of multichannel quantum defects (MQDs)from high�resolution optical spectra because for theRydberg states of molecules, this problem cannot besolved by methods of quantum chemistry [3].
Reaction (1) proceeds with the participation ofthree interacting electron configurations: the dissocia�tive states, the Rydberg states (including the autoion�ization resonance states), and the intermediatevalence states (with the quasi�finite motion of thenuclear subsystem). The theory that is most conve�nient for investigating the AI�reaction dynamics is thetheory based on using the renormalized Lippman–Schwinger equations for the operator of inelastic col�lisions T [4]:
, (2)
, (3)
where t is the matrix of the system reaction e– + NO+,G is Green’s operator describing the electron motion
2 3N( D) O( P) NO** NO X e1( )+ + −
+ → → Σ +
( )0= + −T t G G T
0= +t V VG t
in the Coulomb center field and an ionic core nonin�teracting with the center, G0 is the part of the opera�tor G that is smooth in energy. The operator V includesnon�Coulomb interaction Vnc of an electron with anionic core and the operator VCI responsible for nona�diabatic coupling with dissociative and valence config�urations; i.e., V = Vnc + VCI.
The analytical properties of the operator are well�known and make it possible to reduce integralEq. (2) to the set of algebraic equations writing themin the form [4]
(4)
Here, E is the total energy of the system counted fromthe ion ground state, Eq is the energy of vibrational and
rotational excitation of the ionic core, is the basis wave function of the Rydberg configurationin the laboratory system of coordinates correspondingto the total momentum J and its projections M to theset direction, ρ is the effective electron angularmomentum [5], N is the rotation momentum ofnuclei, and ν is the vibrational quantum number. Thevector corresponds to the wave functions of disso�ciative channels. The valence configurations in formu�lation (3) are included in the definition of matrix ele�ments of the operator t constructed, as is known, onstanding waves. In this case, the functions and
are normalized as [4].
The operator t is related to the quantum�defectmatrix by the formula
, (5)
which enables us to express its elements through theadiabatic quantum defects observed in the high�reso�lution spectra [5].
( )0−G G
( )cot ,
2 , .
q
q
q q q q
q q i
E E
β
⎧ ⎫⎪ ⎪= + πν − β β⎨ ⎬
⎪ ⎪⎩ ⎭ν = − ε ε = −
∑ ∑T t t T
q JMlN= ν
β
q β
( )' ' 'q q E E= β β = πδ −
tan( )= − πμt
The Near�Threshold Associative Ionization Reaction
G. V. Golubkov and G. K. OzerovPresented by Academician A.A. Berlin October 7, 2013
Received July 18, 2013
DOI: 10.1134/S1028335814030094
+ ++ → +
−Σ2 3 1( ) ( ) ( )D P XN O NO e
Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, 117977 Russiae�mail: [email protected]
PHYSICS
DOKLADY PHYSICS Vol. 59 No. 3 2014
THE NEAR�THRESHOLD ASSOCIATIVE IONIZATION 123
In the case under consideration, the nonadiabaticcoupling with the rotational motion in the intermedi�ate Rydberg complex NO** can be disregarded, andthe molecule�axis direction is fixed when determiningthe elements of the T operator by averaging over theorientations at the end stage of calculation. As a result,the total cross section for the reaction is written as [6]
, (6)
where Mc is the reduced mass of colliding atoms, E isthe energy of the system counted from the reactionthreshold , j is the angular momentum, and isthe statistical weight of the dissociative β channel.Because near the ionization threshold the matrix ele�
ments are practically independent of j, they can betaken out of the summation sign, and the cross sectionfor the reaction can be presented in final form as
, (7)
where Rβ is the point of intersection of ionic and dis�sociative β terms.
For describing reaction (1), it suffices to restrictourselves to consideration of the five dissociative
states: B2Π, L2Π, , , and [7, 8]. Thestates B2Π and L2Π interact with the Rydberg pπ
series, the state correlates with dδ series, the state
correlates with sσ and dδ series, and cor�relates with , respectively. The states L2Π and I2Σ+,introduce no substantial contribution to the depen�dence of the total cross section on energy and, conse�quently, are not included in the general scheme of cal�culation.
The configuration correlating with the
ground states of the atoms and is popu�lated due to the nonadiabatic transition from thestate I2Σ+ at the point [6]. The dependencesof the adiabatic quantum defect on the interatomicdistance R and the electron matrix elements of theconfiguration interaction between the Rydberg anddissociative states are taken from [6–8]. Because in theenergy range under consideration the Rydberg serieswith vibrational quantum numbers introduces anegligibly small contribution to the total cross section(7), it suffices to restrict ourselves to the Morse poten�tial when describing the NO+ ion. For the potentialcurves of dissociative states, which (except for I2Σ+)intersect the ion term, we used the results of [7, 8]. Thedependences of the potential curves on the inter�
( ) ( )AI | |( ) 2
0, 0
2 2 1 j
c j
gE j T
M E Eβ
β
ββ = =
⎡ ⎤πσ = + ⟨ ⟩⎢ ⎥+ ⎢ ⎥⎣ ⎦
∑ ∑ v
v
E β g β
( )jTβv
AI | |2
( ) 2
, 0
( ) 4 jg RE E T
E Eβ β
β
ββ =
σ = π ⟨ ⟩
+∑ v
v
B 2' Δ A 2' +Σ I2 +
Σ
B 2' Δ
I2 +Σ A 2' +
Σ
pσ
A 2' +Σ
N S)4( O P)3(
03cR a≈
9ν >
atomic distance for the terms B2Π, L2Π, , ,
I2Σ+, and are shown in Fig. 1.
The dependences of the cross sections for reaction (1)on the threshold energy E calculated from Eq. (7) withthe data [6–8] for vibrational states ν = 0–8 and theavailable experimental results [9] are shown in Figs. 2and 3. These cross sections have a strongly pro�nounced resonance structure, which is formed as aresult of multichannel interaction of autoionization
states of the Rydberg series , , and
of the intermediate complex NO** with thedissociative β continua. It is easy to understand that
B 2' Δ A 2' +Σ
1X +Σ
2( )np +σ Σ
2( )npπ Π
2( )ndσ Δ
2
5.0R, a0
E, eV
2.0 4.54.03.53.02.5
4
5
3
2
N(4S) + O(3P)
1
0
−1
1
−2
−3
−4
N(2D) + O(3P)
NO+(X1Σ
+)
Fig. 1. Diabatic potential curves of the molecule NO, theenergies of which are counted from the ground state of the
ion . The terms (1) L2Π, (2) I2
Σ+, (3) B'2Δ,
(4) , and (5) B2Π except for the term (cor�
responding to the ground state of the atoms with the energy E = –2.16 eV at infinity) converge to the
limit of separated atoms with the energyE = –0.38 eV.
NO X1( )+ +
Σ
A 2' Σ+ A 2' Σ
+
N S O P4 3( ) ( )+
N D O P2 3( ) ( )+
124
DOKLADY PHYSICS Vol. 59 No. 3 2014
GOLUBKOV, OZEROV
this structure contains the principal features of theenergy spectrum of the autodecaying states, which aredescribed in detail in [10].
The total cross section for reaction (1) increaseswith the energy up to eV and is characterizedby the presence of step jumps during the transitionthrough the threshold of each open channel [9].According to [6], such behavior is reproduced whenaveraging Eq. (7) over the Rydberg resonances andagrees well with the experimental data. The calcula�tions showed that the partial cross sections decreaseapproximately by an order of magnitude with increas�ing the vibrational quantum number of the formed ion
by unity.
In the energy range from zero to eV, thecross section for reaction (1) can be approximated bythe linear dependence , which is shown in Fig. 3.
11E ≈
NO X1( )+ +
Σ
1.18E ≈
~ Eσ
It results in the following form of the rate constant in awide range of variation of the temperature T:
, 10–12 cm3/s,(8)
where the value of T is set in eV. It should be noted thatobtained dependence (8) can be used with good accu�racy in particular applications.
In summary, we discuss the possibilities of theMQD theory for determining the partial cross sectionsfor AI exothermic reactions upon slow collision of theRydberg atom A** with the neutral atom B (for the
principal quantum number , where Di is the
energy of molecular�ion dissociation). They are nec�essary for the quantum calculation of the level�by�level kinetics of population of highly excited Rydbergstates in the photoionization plasma formed in theupper atmosphere of the Earth under the action of
( )AI exp1/2 0.381.58 (2 0.38)k T TT
≅ + −
12 i
nD
>
2.0
0.7E, eV
σ, 10−18 cm2
0.60.50.40.30.1 0.20
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
8pπ, v = 1
9pπ, v = 0
7pπ, v = 1
10pπ, v = 2
10pπ, v = 1
Fig. 2. Dependence of the cross section for reaction (1) onthe energy E counted from the ground state of the ion
. Points are the experimental data [9]. Arrowsmark the positions of peaks for the Fano–Feshbach reso�nances corresponding to the positions of levels of the Ryd�berg series of the intermediate complex NO**.
NO X1( )+ +
Σ
1.4E, eV
σ, 10−18 cm2
1.21.00.80.60.2 0.40
3.5
3.0
2.5
2.0
1.5
1.0
0.5
Fig. 3. Resonance structure of the dependence of the crosssection for reaction (1) on the energy E. The solid blackline is the approximation . Resonance�structure crowdings correspond to the thresholds of open�ing of each new vibronic channel.
const( )E Eσ =
DOKLADY PHYSICS Vol. 59 No. 3 2014
THE NEAR�THRESHOLD ASSOCIATIVE IONIZATION 125
a luminous flux coming from the solar flare [1]. Forthis purpose, it is convenient to consider the reverseprocess of dissociative recombination e– + AB+ and touse the principle of detailed equilibrium for the partialprobabilities of collisional transitions.
REFERENCES
1. G. V. Golubkov, M. G. Golubkov, and M. I. Manzhelii,Dokl. Phys. 57 (12), 461 (2012).
2. G. V. Golubkov and A. Z. Devdariani, Rus. J. Phys.Chem. 5 (6), 892 (2011).
3. G. V. Golubkov, G. K. Ivanov, and M. G. Golubkov,Chem. Phys. Repts. 18 (7), 1305 (2000).
4. G. V. Golubkov and G. K. Ivanov, Rydberg States ofAtoms and Molecules and Elementary Processes withtheir Participation (URSS, Moscow, 2001) [in Russian].
5. M. G. Golubkov, G. V. Golubkov, and G. K. Ivanov,J. Phys. B. 30 (23), 5511 (1997).
6. G. V. Golubkov and G. K. Ivanov, J. Phys. B. 21 (11),2049 (1988).
7. H. Sun and H. Nakamura, J. Chem. Phys. 93 (9), 6491(1990).
8. I. F. Schneider, I. Rabadan, L. Carata, et al., J. Phys. B33 (21), 4849 (2000).
9. G. Ringer and W. R. Gentry, J. Chem. Phys. 71 (4),1902 (1979).
10. G. V. Golubkov and G. K. Ivanov, Nuovo Cimento12D, 1 (1990).
Translated by V. Bukhanov
