4 Discussion

In the circumstellar envelope of IRC +10216 a number of molecules in the vibrationally excited state have been observed. Since the scientists are optimistic to detect SiC₂ in the vibrationally excited state at 177 cm^-1 above the ground state, therefore Chandra & Sahu (1993) calculated Einstein A-coefficients for rotational transitions in the $\nu_3$ vibrationally excited state of SiC₂. Their belief has a strong support since a number of molecules observed in the vibrationally excited state(s) in the envelope of IRC +10216 have the excited state(s) at quite high energies above the ground state. However, for the detailed study one has to account for both the ground and vibrationally excited states for the same physical conditions in the atmosphere. Therefore, Einstein A-coefficients for the rotational transitions in the ground vibrational state are also needed. Besides ²⁸SiC₂, Einstein A-coefficients for rotational transitions in the ground vibrational state of ²⁹SiC₂ and ³⁰SiC₂ are also calculated.

  

Figure 2: Energy level diagram if rotationl levels in the ground vibrational state of 28SiC2

After the careful survey of the energy level diagram in the ground vibrational state of ²⁸SiC₂ (Silicon Dicarbide) (Fig. 2), we predict that the transition between the backbone levels 2₀₂, 3₀₃, 4₀₄, 5₀₅ $\ldots$ are of specific interest. Furthermore the ratios of the radiative lifetime of upper level to that of the lower level for the transitions 3$_{03} \rightarrow$ 2₀₂, 4₀₄ $\rightarrow$ 3₀₃, 5$_{05} \rightarrow$ 4₀₄, 6$_{06} \rightarrow$ 5₀₅, 7₀₇ $\rightarrow$ 6₀₆, 8₀₈ $\rightarrow$ 7₀₇, 9₀₉ $\rightarrow$ 8₀₈ are 0.281, 0.415, 0.514, 0.586, 0.642, 0.683, 0.716, respecively. This trend of increasing the value of the ratio of radiative lifetimes with the quantum number J reflects the probability for the detection of transition between the levels with higher values of J. However, the population of the levels decreases with the increase of J. Thus, in the ground vibrational state a compromising state may come around the transition 6₀₆ $\rightarrow$ 5₀₅. Hence, in the ground vibrational state, the rotational transition 6₀₆ $\rightarrow$ 5₀₅ may play an important role regarding the conclusions to be drawn about the excitation mechanism in the envelope of IRC +10216. However, a detailed analysis of radiative transfer for the three cases

(i) For rotational transitions in the ground vibrational state.

(ii) For rotational transitions in the vibrationally excited $\nu_3$ state.

(iii) For the rotational and vib-rotational transitions in the ground and vibrationally excited state

are to be carried out. In the further work, we intend to investigate the radiative transfer calculations.

Acknowledgements

The work is financially supported by the Department of Science and Technology, New Delhi through the project No. SP/S2/004/94 in which Ms. Rashmi has joined as a Junior Research Fellow. Thanks are due to Indira Gandhi National Open University, New Delhi for providing necessary facilities. We are grateful to the learned referee for making fruitful suggestions.