Classical S‐matrix calculation for vibrationally inelastic transitions in three dimensional collisions of Li+ with H2
The ``partially averaged'' version of classical S‐matrix theory is applied to three dimensional collisions of Li+ with H2. For an initial collision energy of 0.684 eV cross sections for the vibrational deactivation of H2 from the initial state (n1,j1) = (1, 0) to final states (n2,j2), n2 = 0, j2 = 0, 2, 4,... are computed and compared with the recent quantum mechanical coupled channel calculations of Schaefer and Lester. The agreement is quite good, indicating that this approach is an accurate and practical way of describing these weak, ``classically forbidden'' processes which cannot be treated by ordinary classical trajectory methods.
Abstract The torsional impact response of a penny-shaped crack lying on a bimaterial interface is considered in this study. Laplace and Hankel transforms are used to reduce the problem to the solution of a pair of dual integral equations. The solution to the dual integral equations is expressed in terms of a Fredholm integral equation of the second kind with a finite integral kernel. A numerical Laplace inversion routine is used to recover the time dependence of the solution. The dynamic stress intensity factor is determined and its dependence on time and material constants is discussed.