1 Introduction

Spectral lines from astronomical objects at 95.579 GHz, 115.383 GHz and 140.918 GHz could not be assigned to any of the known molecular species for several years. Besides these lines some more spectral lines at 93.065 GHz, 94.245 GHz, 137.180 GHz, 141.751 GHz, 141.755 GHz and 170.742 GHz from cosmic objects, were identified as generated due to the transitions between the rotational levels in the cyclic molecule SiC₂ (²⁸SiC₂) by Thaddeus et al. (1984). Thaddeus et al. (1984) assigned 9 lines in the molecular envelope of the evolved carbon star IRC +10216 to SiC₂ and determined its rotational and lower order centrifugal distortion constants with sufficient accuracy to enable Snyder et al. (1985) to detect lowest lying 1_0,1 $\rightarrow$ 0_0,0 transition. Till now over 30 transitions of SiC₂ are known in IRC +10216. In order to provide accurate frequencies, Bogey et al. (1991) recorded the rotational spectrum of SiC₂ in the ground and vibrationally excited $\nu_3$ states.

The IRC +10216 (=CW Leo) is a cool carbon star with a rich molecular chemistry. A number of molecules are detected in the envelope of the star. Some of these molecules have been detected even in vibrationally excited states. In some cases scientists were not successful detecting molecules in vibrationally excited states. On the basis of these negative results it has been concluded that the excitation mechanisms in the envelope of IRC +10216 are rather complex. In order to learn more about these excitation mechanisms, one should search for the vibrationally excited states of other abundant molecules, already detected in IRC +10216 in the ground vibrational state. Among these molecules, SiC₂ is of special interest as it has already been detected in the ground vibrational state in IRC +10216 (Thaddeus et al. 1984; Gensheimer et al. 1992).

For analysing a spectrum, Einstein A-values for the transitions are one of the required data. Therefore, Einstein A-coefficients for rotational transitions in the vibrationally excited $\nu$₃ state have been reported by Chandra & Sahu (1993). (In the paper of Chandra & Sahu (1993), ortho and para states may please be read with interchange. Further, the results for the para states (earlier reported ortho states) may please be treated as cancelled because the para states in the molecules are missing as the carbon nuclei do not posses any nuclear spin). Since one would like to study SiC₂ in the ground and vibrationally excited $\nu_3$ states for the same physical conditions in the atmosphere of an astronomical object. Thus, in the present investigation, we have calculated the Einstein A-values for the rotational transitions between the levels up to 51 cm^-1 in the ground vibrational state of SiC₂. Since ²⁹SiC₂ and ³⁰SiC₂ isotopomers of Silicon Dicarbide have been observed (Cernicharo et al. 1986), therefore, Einstein A-coefficients for rotational transitions in the ground vibrational state of these isotopomers are also calculated. Einstein A-values are used for calculating the radiative life times of the levels.