Numerical assessment of post-prior equivalence for inclusive breakup reactions

We address the problem of the post-prior equivalence in inclusive breakup reactions induced by weakly bound nuclei. The problem is studied within the distorted-wave Born approximation (DWBA) model of Ichimura, Austern, and Vincent [Phys. Rev. C 32, 431 (1985)]. The post and prior formulas obtained in this model are briefly recalled and applied to several breakup reactions induced by deuterons and ${}^6\mathrm{Li}$ projectiles, to test their actual numerical equivalence. The different contributions of the prior-form formula are also discussed. A critical comparison with the prior-form DWBA model of Udagawa and Tamura [Phys. Rev. C 24, 1348 (1981)] is also provided.

Figure 1

Proton energy spectra for ${}^{62}\mathrm{Ni}(d,pX)$ at $E_d=25.5$ MeV. (a) Convergence of the angle-integrated energy distribution (in c.m.) of the NEB cross sections with respect to the bin width (in ${\mathrm{fm}}^{-1}$) used for the $b$ distorted waves. (b) Comparison of the post and prior results. (c) Comparison of IAV and UT models with the data from Refs. [17, 30], corresponding to the double differential cross section as a function of the proton energy in the laboratory frame, for ${\theta }_p={20}^{\circ }$.

Figure 2

(a) Angle-integrated energy differential cross section, as a function of the $\alpha$ c.m. energy, for the ${}^{209}\mathrm{Bi}({}^6\mathrm{Li},\alpha X)$ reaction at 36 MeV. (b) Experimental and calculated angular distribution of $\alpha$ particles, in the laboratory frame, for the same reaction. The data are from Ref. [32].