Knowledge Bank

Usually, the well-known RKR method is applied in order to determine the interatomic potential from experimental energy values. Difficulties with the RKR method arise if only a small number of rovibrational levels has experimentally been observed. In addition, the correct long-range behaviour of the interaction potential is not included. A quantum-mechanical recalculation of the molecular energy values from the RKR potential leads to deviations between the input and output values in the order of $0.1cm-1$ which is frequently much larger than the experimental error. For the case of Na-Kr in the $X\Sigma$ and in the $A\Pi$ state we have developed a computer routine which avoids some of the imperfections mentioned above. The program calculates the molecular energy levels by solving the Schr""{o}dinger equation for the nuclear motion using an analytical expression for the interatomic potential. By means of a standard least-squares fit procedure the parameters of the analytical expression are varied until the deviation between experimental and calculated energy values is minimal. Several analytical expressions with suitable long-range behaviour have been tried, for example the Thakkar-potential, the Tang-Toennies potential and the HFD potential. For the case of the $A\Pi$-state our laserspectroscopic data /1/ consist of energy values of rovibrational levels with $v\prime =7\dots 14$. In order to save computing time only 5 rotational levels with total angular momentum up to 20.5 have been included in our analysis for each vibrational state. In order to give an example, 30 experimental energy values of rovibrational levels of the $A3/2$ state are reproduced by a 5-parameter Thakkar potential with an accuracy of less than $0.002cm-1(p=4.60,Re=3.059(2)\backslash AA,De2=774(10)cm-1)$. For the $X\Sigma$ state 76 rovibrational levels with $v\prime \prime =0,1$ and 2 and $N\prime \prime$ ranging up to about 30 have been measured /1/. The corresponding energies are all reproduced by a 5-parameter HFD potential to within $0.001cm-1$ accuracy yielding $Re=4.197(1)\backslash AA,De=68.4(1.5)cm-1$ and $C6=8.65\cdot 106cm-1\backslash AA6$. In addition, the repulsive part of the $X\Sigma$ potential has been determined from our experimental spectral distribution of the fluorescence light by means of a comparison with calculated spectra.