ULTRASIMPLE CALCULATION OF VERY-LOW-ENERGY MOMENTUM-TRANSFER AND ROTATIONAL-EXCITATION CROSS-SECTIONS - E-N-2 SCATTERING

The calculation of electron-molecule cross sections at scattering ener gies well below 0.1 eV using conventional algorithms for solving the S chrodinger equation is often rendered problematic by severe numerical problems. Here we describe and implement an alternative procedure that combines known analytic properties of the body-frame electron-molecul e scattering matrix, as codified in the modified effective range theor y, with an analytic correction that imposes physically correct thresho ld laws. This approach eliminates completely the need for numerically solving the Schrodinger equation at energies below about 0.1 eV. Inste ad, one uses scattering matrices above this energy to determine parame ters for an extrapolation to subthermal energies. We apply this method to the calculation of e-N-2 momentum-transfer and rotational excitati on cross sections from threshold to 1.25 eV. The results resolve a lon g-standing apparent anomaly in the analysis of experimental data for v ery low-energy electron scattering from N-2. Finally, we use linear re gression to present our theoretical results in a user-friendly form.