Mechanisms of hydrogen atom negative ion formation in a low temperature plasma attract a great attention of researchers due to perspectives to use intense negative ion beams in both plasma technology and thermonuclear fusion research. In this connection considerable efforts performed in last years were addressed to understand the processes resulting in negative ion formation in low temperature hydrogen plasma (see e.g. [22–29]). The main mechanism for hydrogen negative ion formation is assigned to the dissociative attachment process the rate constant of which ka drastically increases with the increase of the vibrational excitation of hydrogen molecule. According to refs. [30, 31], the maximum value of ka occurs at n=8 reaching a value ka of the order of 10-8 cm3/s. Dissociative attachment cross sections for hydrogen molecule and its isotopes, calculated by Wadhera using the resonance model, have been extensively reported in a recent report [5].
Larger dissociative attachment rates of the order ka ~ 6¥10-5 cm3/s were estimated for the conditions of the experiment [6], where the negative hydrogen ions were produced irradiating the molecular hydrogen gas with high power ArF excimer laser (l=193 nm). This extraordinary high magnitude was assigned to high Rydberg (HR) states of hydrogen molecule as an effective source of negative ions via the dissociative attachment process [26–
27]
H2(n, v) + e ® H
+ H(n') (7)
(here n is the effective principal quantum number for HR molecular state, n is its vibrational quantum number and n' is the principal quantum number of one of the product atoms).
However until now the initial state of hydrogen molecule involved into the dissociative attachment process and the way for formation of this state via multi-quantum laser excitation have not been identified.
An attempt to explain the extraordinary high magnitude of the process (7) was performed in [27] through a classical description of polarization capture of incident electron by the HR molecule. However this mechanism does not explain the observed high sensitivity of the negative ion production rate constant to the initial electronic and vibrational state of the
hydrogen molecule. Thus the question about the specific state of HR hydrogen molecules as well as the origin of the extraordinary high magnitude of the observed dissociative attachment rate constant for these molecules is still open.
An alternative mechanism for dissociative attachment of an electron to a highly vibrationally excited hydrogen Rydberg molecule is analyzed. The comparison between the rate constant of this process measured in [26] and that estimated using the calculated data obtained recently [32,33] provides an indication to possible initial and final states involved into the high effective process of negative ion production. Moreover a possible way for formation of highly vibrationally excited hydrogen Rydberg molecule providing the negative ion formation through the high effective dissociative attachment mechanism in conditions of the experiment [26] is analyzed.
Our approach to estimate the cross section of the dissociative attachment of the electron to HR hydrogen molecule is based on the physical consideration that an HR hydrogen molecule can be considered as a small-size hydrogen molecular ion H+2 surrounded with a “cloud” of the weakly bound electron having the average radius of an orbit (in atomic units) as large as n2 (n is the effective principal quantum number of a Rydberg molecule). For this reason the interaction of an incident electron with H+2 and the weakly bound electron can be considered almost independently, so that one of possible channels of electron evolution should be ascribed to the dissociative recombination process
H+2(n) + e ® H + H(n'). (8)
According to the proposed mechanism one of products can be in an excited state with the principal quantum number n'. Therefore the ground state hydrogen atom formed as a result of process (8) is surrounded with the “cloud” of weakly bound electron belonging to the HR molecule. If the binding energy of the weakly bound electron in the HR molecule is close to the electron affinity of hydrogen atom (0.76 eV), one can suppose that the dissociative recombination (8) is followed by the negative ion formation. The small deficiency in energy of the weakly bound electron can be recovered due to interaction with the excited hydrogen atom:
e + H + H(n') ® H
+ H(n'). (9)
Therefore the cross section of the dissociative attachment (7) should be proportional (or equal) to that for dissociative recombination (8). As is known, the latter dramatically depends on the vibrational state of the molecular ion, in particular it increases with increasing the vibrational quantum number n [32,33]. According to quantum calculations of ref.[33], which has been performed on the basis of the super-dissociative recombination mechanism introduced by D.Bates [34], the maximum magnitude of cross section for process (8) is reached at n=16 for the electron energy near 0.01 eV and at n=15 for 0.07 – 0.1 eV. This maximum value in the indicated electron energy interval ranges between 8¥10-12 cm2 and 4¥10-13 cm2, decreasing smoothly with electron energy. The calculated cross section for neighbouring vibrational quantum numbers (e.g. n=17,18) decrease by factor 10 compared with the previous values. Thereby the dissociative recombination process results in the formation of Rydberg states of hydrogen atom with n' = 10–21, these levels being energetically allowed for initial vibrational state with n=16.
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Figure 11 (a) Dissociative recombination cross sections, for different vibrational levels, from ref. [33]; (b) corresponding dissociative recombination rates.
The extraordinary high magnitude of the rate constant of negative ion production observed in [26] can be explained supposing that the Rydberg molecules in the experiment [26] are formed presumably in the vibrationally excited state n=16. The presence of the weakly bound electron does not affect practically the potential energy curve for the hydrogen molecular ion H+2 , so that one can believe that the processes (8), (9) involving the HR state molecule occur independently from each other. We can therefore suppose that the maximum probability for the negative ion formation via processes (8), (9) is realized when the binding energy of a weakly bound electron in the hydrogen Rydberg molecule is close to that of the negative hydrogen ion (0.76 eV). This provides therefore the estimated effective principal quantum number of the Rydberg hydrogen molecule n=4.
Apparently the process of negative ion formation (7) involves the vibrationally excited Rydberg hydrogen molecule with n@16 and n@4. In accordance with calculation results of [33] the final states of Rydberg atom formed in result of this process range between n'@10 and n'@21.
We have calculated the electron temperature dependence of the rate constant of the dissociative recombination process (8) for different vibrational quantum numbers of the hydrogen molecular ion v using the cross sections of the process evaluated in [33] and Maxwell electron energy distribution function. This calculation gives a maximum magnitude of the rate constant for n=16 exceeding 10-5 cm3/s, i.e. the same order of magnitude as the dissociative attachment coefficient reported in [26].
Special attention should be devoted to the origin of the highly vibrationally excited Rydberg hydrogen molecules in an ArF laser-irradiated hydrogen gas. The hydrogen molecule potential curves involved into the considered mechanism of population of the set of levels are shown on figure 12.
Internuclear distance (a0)
X1g+
Figure 12 Pictorial view of the proposed mechanism for negative ion formation in H2 system irradiated by ArF excimer laser.
The energy of three-quantum populated super-excited states proposed in the work [26] as a source of such molecules exceeds considerably the dissociation limit of the molecular ion H+2 , so that rather high energy release at the collisionless transition can result in destroying Rydberg molecule. As an alternative way one can suppose a sequence of radiation and collision processes the first of which is two-photon absorption of laser radiation by the ground state hydrogen molecule [6]
H2(X 1S+g, n=0) + 2Dw(l=193 nm) ® H2(E,F 1S+g, n=6). (10) The double well state H2(E,F 1S+g) is not subjected to the inverted spontaneous radiation
decay, because single quantum transition (10) is forbidden. However it is possible the collision-driven transition
H2(E,F 1S+g, n=6) + H2 ® H2(B 1S+u, n=12) + H2 - 0.01 eV, (11)
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which does not require almost for a small additional energy supply and therefore should be characterized by a large cross section. This transition is followed by the fast spontaneous radiation decay of B state characterized by the time constant of about 2 ns which results in formation of vibrationally excited molecules:
H2(B 1S+u, n=12) ® H2(X 1S+g , n') + Dw, (12)
the vibrational quantum number of which n’ is distributed within a rather wide range of values 0<n’<14 [35]. Lifetime of these vibrationally excited molecules in relation to the collisional quenching in the conditions of the experiments [26,27] (H2 pressure ranges in 5-50 Torr) is much longer than the laser pulse duration. So it is possible the two-quantum excitation of these molecules under the action of the high intense laser irradiation, for example
H2(X 1S+g, n'=12) + 2Dw(l=193 nm) ® H2(n,n) (13) resulting in the formation of a state with the energy 17.38 eV, as accounted from the bottom of the ground state term. This state lies about 0.97 eV below the dissociation limit of the molecular ion H+2, which is close to the vibrationally excited Rydberg molecules H2(n=4,n=15). The energy of this state accounted from the dissociation limit of the molecular ion H+2 , is amounted as 0.955 eV, supposing the similarity between the potential curves of the molecular ion H+2 and Rydberg molecule H2(n>>1) established in the work [36].
It should be noted that the exact coincidence in the energy of two laser quanta and relevant energy difference in accord to (13) is hardly attainable. It is caused by the number of molecular terms related to the asymptotic atomic states H(1s)+H(n=4), differed in the electronic moment and its projection (see for example ref. [37] for the case H(1s)+H(n=3)).
The difference in energy of these terms is in the range of accuracy of existing calculations, so that the specific term involved into the process (13) can not be surely shown in the frame of the used approach.
Therefore the dissociative attachment of these molecules can have very high values of rate constant comparable to that experimentally estimated in ref.[26].