The modelling of various media of fundamental or technological interest [1-7]: interstellar molecular clouds, supernovae, planetary atmospheres, plasma-assisted combustion and depolluation, atmospheric re-entry of hypersonic spacecrafts, edge fusion plasma is strongly based on the knowledge of cross sections and rate coefficients of the elementary radiative and collisional processes.
In the reactive collisions between slow electrons and diatomic molecular ions AB
+
the dissociative recombination (DR) plays a decisive role
AB
+
(N i
+
,v i
+
)+e
-
(

)

AB
**
,AB
* 
A+B where ** stands for a dissociative electronic state, i.e. a state whose separated-atom limit is situated below the initial ro-vibrational level of the target ion, and * for a bound
Rydberg state. The diatomic molecular ions AB
+ is considered in its electronic ground state. The two type of states (AB
**
and AB
*
) of the neutral system are related to two mechanisms: i) the capture into an AB
**
states, so-called the direct process, and ii) the temporary capture into an AB
*
state followed by quick predissociation by AB
**
, so-called the indirect process.
These two mechanisms quantically interfere within the so-called total process. N i
+
and v i
+
, are the initial rotational and vibrational quantum numbers of the target molecular ion,

is the energy of the incident electron.
With the increasing of the energy of the incident electron, when the collision energy is above the dissociation threshold of the cation, the dissociative excitation holds on:
AB
+
(N i
+
,v i
+
)+e
-
(

)

AB
**
,AB
* 
A+B
+
+ e
-
(
 ’)
Obviously, autoionization to bound ion level is always a competitive process with respect to the electronic capture, resulting in elastic (EC,

=
 ’), inelastic (IC, or vibrational excitation,

>
 ’) or superelastic (SEC, or vibrational deexcitation, 
<
 ’) collisions:
AB
+
(N i
+
,v i
+
)+e
-
(

)

AB
**
,AB
* 
AB
+
(N f
+
,v f
+
)+ e
-
(
 ’) where N f
+
and v f
+
are the final rotational and vibrational quantum numbers of the molecular ion,
 ’ is the energy of the scattered electron.
The most usual theoretical methods are Multi-Channel Quantum Defect Theory (MQDT)
[8-14] and time-dependent wave-packet method (TDWP) [15-20]. These 2 approaches have different areas of application that allow a broad range of problems to be studied.
MQDT is extremely effective at low energy where standard TDWP breaks down. It includes both the direct process (electron capture into a dissociative state) through the resonance and the indirect process where the electron first is captured into a vibrationally excited Rydberg state and then neutral system dissociates. TDWP proceeds by direct integration of the time-dependent Schrodinger equation, propagating a wave packet on a

complex potential energy surface. TDWP can handle molecular systems with many atoms, and is effective in determining the time evolution of the vibrational populations.
Among theoretical methods, only MQDT gives an unitary treatment of the reactive collisions between electrons and molecular ions, giving the cross sections for all above mentioned competing processes (dissociative recombination, elastic collision, vibrational excitation, vibrational deexcitation or dissociative excitation).
Although reactive collision between electrons and diatomic molecular ions has been studied in the past 20 years, both experimentally [21-34] and theoretically [35-47] (a topical review [48]), there has not yet been a definitive comparison of theory and experiment. This fact is due to the complexity of the process. A very important aspect is the high sensitivity of the magnitude of the cross section to the initial state of the molecular ion. Regarding numerical calculation, we mention the sensitivity of the magnitude of the cross section to the input molecular data, quantum defect and electronic coupling, respectively. The improvement of the molecular data still remains an important task for theoretical calculations.
The most complete experiments on these ions in the last decade have been performed in ion storage rings [23-34] where fully vibrationally relaxed molecular ions can be stored for several seconds and cooled by electronic collisions, thus allowing high resolution measurements of cross sections. The rotational distribution is still a more complex subject and in most cases, Boltzmann distribution is assumed, corresponding to some hundreds of Kelvin.
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Dissociative recombination and excitation are the most important destruction mechanisms of molecular ions in the cold plasmas. So, the industrial applications assisted by low temperature plasmas are based on the knowledge of the cross sections and rate coefficients of dissociative recombination and excitation. Obviously, the great number of polyatomic molecular systems explains the importance of the TDWP

approach. The constant interest in the study of the reactive molecular ion-electron collisions is determined by the great number of the industrial and technological applications.
In this project we shall study the dissociative excitation of H
2
+ and its isotopomers, and the dissociative recombination of CH
2
+
, CH
3
+
and CHO
+
. In literature there are few numerical results regarding the dissociative excitation of H
2
+
and its isotopomers (H
Takagi, Phys. Scripta, T96 , 52, 2002). Experimental results based on ion storage rings are reported (D Zajfman and Z Amitay, Dissociative Recombination: Theory,
Experiments and Applications IV, (World Scientific 1996), p 114; T Tanabe et al,
Dissociative Recombination: Theory, Experiments and Applications IV, (World
Scientific 2000), p 170, and M O Abdellahi El Ghazaly et al, J Phys B, 37 , 2467, 2004).
Refering to the dissociative recombination of CH
2
+
, CH
3
+
and CHO
+
we mentioned that there are no numerical results reported.
1.
Research objectives
Our research is focused on 3 main objectives: i) Elaboration of the theoretical models
- Elaboration of a theoretical model for dissociative excitation in the non-rotational case
- Elaboration of a theoretical model for dissociative excitation in the rotational case
- Elaboration of a theoretical model for the study of polyatomic systems using
TDWP ii) Elaboration of the computer programs coded in Fortran 77 for the evaluation of cross sections and rate coefficients of
- dissociative excitation in the non-rotational case
- dissociative excitation in the rotational case
- dissociative recombination of polyatomic systems iii) Systematic calculations on
- dissociative excitation of H
2
+ , D
2
- dissociative excitation of H
2
+
, D
2
+ , HD + and DT + (non-rotational case)
+
, HD
+
and DT
+
(rotational case)
- dissociative recombination of CH
2
+
, CH
3
+
, and CHO
+
2.
Training
The training program, entirely consistent with the research program of the project, is focused in the following modules: i) theoretical study on electron-molecular ion collision, using MQDT and
TDWP ii) systematic calculations on different molecular systems

iii) complementary training: communication, ethics, report writing iv) personalized research projects
Our theoretical method used in the study of DE is a development of the present method based on Multi-Channel Quantum Defect Theory. It consists in the accounting of the ionization channels associated to the continuous parts of the vibrational spectra of the molecular ion. On the theoretical side, our method relies on the discretization of these continua, and numerically, on the optimal management of a huge number of channels and, consequently, of high rank interaction matrices.
In the study of molecular systems using TDWP, our contribution consists in the improvement of the present numerical codes in order to investigate polyatomic systems proposed in this project.