Inclusive Breakup Reactions Research Articles

Equivalence of post and prior sum rules for inclusive breakup reactions.

A critical examination of sum rules derived previously by Austern and Vincent (post form) and by Udagawa and Tamura (prior form) demonstrates that agreement between the two approaches is obtained if certain approximations implicit in the Udagawa-Tamura prior-form derivation are avoided. We examine the relation of the two approaches to singularities of the post-form distorted wave Born approximation matrix element and to the procedures for reduction of a many-body theory by use of effective operators in a model space. The two-step heuristic model is seen to be invalid for prior-form inelastic breakup; it is necessary to take account of nuclear excitations during projectile breakup. Careful treatment of the non-Hermiticity of kinetic energy operators with respect to continuum wave functions is required.

Explanation ofHe3and triton rates in the alpha breakup inclusive cross sections

($\ensuremath{\alpha}$, $^{3}\mathrm{He}$) and ($\ensuremath{\alpha}, t$) continuum inclusive spectra are measured on target nuclei ranging from $^{58}\mathrm{Ni}$ to $^{209}\mathrm{Bi}$. Systematic differences in the absolute magnitudes of the $^{3}\mathrm{He}$ and triton spectra are found. To explain these differences the distorted-wave Born approximation calculations in the post form for inclusive breakup reactions are performed. It is shown that Coulomb effects are responsible for these differences.NUCLEAR REACTIONS ($\ensuremath{\alpha}, t$), ($\ensuremath{\alpha}$, $^{3}\mathrm{He}$) breakup reactions: measured $\frac{{d}^{2}\ensuremath{\sigma}}{d\ensuremath{\Omega}\mathrm{dE}}$; targets: $^{58}\mathrm{Ni}$, $^{90}\mathrm{Zr}$, $^{120}\mathrm{Sn}$, $^{209}\mathrm{Bi}$; post form DWBA breakup theory.

A new formalism of inclusive breakup reactions and validity of the surface approximation

Austern and Vincent's formalism for the inclusive breakup reactions in DWBA is rewritten in a form in which the elastic and inelastic breakup processes are well discernible. This form is calculable exactly and hence we test the validity of the surface approximation used by Baur et al.

Inclusive break-up reactions of 6Li at an incident energy of 26 MeV/nucleon

Inclusive charged particle spectra were measured from nuclear reactions induced by 156 MeV 6Li on 40Ca. At forward angles the spectra exhibit broad break-up distributions centered around the energy corresponding to the beam velocity. The double differential cross sections together with previous results for a 208Pb target were analyzed in the framework of the DWBA approach to projectile break-up taking into account elastic and inelastic reactions of the break-up fragments. The high energy tails of the background due to preequilibrium emission of complex charged particles were estimated on the basis of the coalescence model.

Inclusive breakup reactions

Inclusive breakup reactions of the type $d+A\ensuremath{\rightarrow}p+\mathrm{anything}$ require sums over excited states of the unobserved $n+A$ system. We show that the summed distorted-wave Born approximation cross section can be expressed in closed form as an elastic distorted-waves expectation of an optical model propagator for the unobserved system. The contribution of fluctuations to the energy-averaged cross section is automatically contained in the derived identity. Previous results can be recovered from this identity if corresponding surface approximations are introduced. A new approximation simplifies the identity by omitting the imaginary part of the optical potential. This approximation selects the energy-shell part of the propagator and reduces the inclusive cross section to the same form obtained for the ground state reaction $A(d,pn)A$, with a modified (real) optical potential for the unobserved neutron.NUCLEAR REACTIONS Scattering theory, closed form sum rule for inclusive breakup, DWBA, approximations extracted.