Quasiadiabatic three-body dynamics of deuteron stripping and breakup reactions

A convenient new method, the quasiadiabatic approximation, is developed for the standard three-body model of deuteron-induced stripping and breakup. The approximation gives the breakup wave function at "coincidence" (${\overrightarrow{\mathrm{r}}}_{\mathrm{n}}={\overrightarrow{\mathrm{r}}}_{\mathrm{p}}$) directly as the solution of a simple differential equation with a source term that depends on the elastic channel wave function. The derivation assumes only that the internal Hamiltonian of the broken up deuteron can be replaced by a constant, ${\overline{\epsilon }}_L$, whose value depends on the c.m. angular momentum $L$. No approximation restricting the relative n-p angular momentum is needed. The quasiadiabatic approximation reduces to the Johnson-Soper adiabatic approximation if ${\overline{\epsilon }}_L$ is replaced by $-{\epsilon }_{\mathrm{d}}$, the internal energy of the bound deuteron. The adiabatic approximation for the elastic channel wave function gives an estimate of the quasiadiabatic approximation source term. The behavior of the coincidence breakup wave function in the nuclear interior (previously calculated using a coupled channels method) is well explained by the quasiadiabatic approximation with the use of a simple prescription for ${\overline{\epsilon }}_L$. The separation of internal and external breakup, and the "$L=9\mathrm{}$" effect are easily explained by the use of the quasiadiabatic approximation. The decrease of the coincidence breakup wave function at large distances is not reproduced by this approximation. In applications to stripping calculations the quasiadiabatic approximation coincidence wave function gives a marked improvement over the Johnson-Soper adiabatic wave function, and it seems promising for practical calculations. This is tested by means of a previously described distorted-wave Born iteration applied to the adiabatic wave function. The rather lengthy distorted-wave Born iteration adiabatic calculations agree with the stripping derived by coupled channel calculations and give a good description of the long-range features of the coincidence breakup wave function. The stripping comparisons are complicated by the necessity of allowing for "closed" breakup channels, which are absent from the coupled-channel comparison, optional in the distorted-wave Born iteration adiabatic approximation, and fully included in the quasiadiabatic approximation. The empirical use of phenomenological local deuteron optical potentials is discussed.