Sequential amplitudes in heavy-ion induced two-proton transfer reactions

Abstract

Angular distributions have be'en measured for the reactions Sr(' 0, ' C) Zr and Zr(' 0, ' C) Mo at 80 MeU, and 'Sr('~C, ' Be) Zr and Zr("C, ' Be) Mo at 60 MeV. The data were analyzed with full recoil, coupled-channel Born approximation calculations, in which both direct (one-step) and sequential (two-step) reaction routes were considered. Detailed shell model wave functions were used to corstruct all form. factors. The calculated sequential contributions to the cross sections were found to be significantly larger than those associated with direct transfer, and inclusion of the two-step routes substantially improved agreement with experiment. The calculated angular distribution shapes were found to depend on both the intermediate Q value of the sequential process, and also on the microscopic configurations involved in the transfer. In addition, a previously unreported configuration dependence of the recoil corrections was noted in the calculations.NUCLEAR REACTIONS 88Sr(160 160) 88Sr(16 0 14C) 90Z r(160, 16 0), OZr (16 p 14C), 0 MeV. 88Sr (12C 12C 12C) 88Sr (12C 10ge) 9 OZ r (12C 12C) 904 r(12C 10ge) @ 6P MeV; enriched targets, measured 0'(&). Finite range DWBA and CCBA analyses of direct and sequential transfer, compared with data. .

Energy dependence of one- and two-particle transfer reactions in the system16O+90Zr

“…While at 80 MeV the ratio R between experimental and theoretical cross sections is about 690 the value decreases to 194 and 54 at 138.2 MeV and 194.4 MeV, respectively. Figure 6 shows these values plotted as function of E/~ together with data obtained for other systems [6,7,24].…”

“…Angular distributions were measured for 160+ 9~ in the angular range 0=5.5~ ~ (194.4MeV) and 0=6o-35 ~ (138.2). Some data were also taken at Elab = 80 MeV for comparison with the earlier results of [7]. A monitor detector located at 8 ~ was used for relative normalization.…”

“…Previous experiments at energies in the vicinity of the barrier revealed that the agreement between experiment and one-step DWBA calculations was extremely poor [6,7]. If the 9~ 14C)92M0(0 + gs) reaction is treated as transfer of a spin-0 cluster the cross section can be written as [23] d a -~ 'e 'r ( d~-o) The spectroscopic factors S for two protons bound in 160 and 92Mo are the same as the ones used in E7] and are summarized in Table 3.…”

“…Also included (Fig. 3 b) are some results from earlier measurements at 80 MeV [7] and 50 MeV [13]. An optical model fit has been performed to the new high energy data with the program PTOLEMY El2] using an energy independent potential.…”

“…Normalization factors up to 1000 have to be invoked to obtain agreement between experiment and theoretical calculations [6,7]. The reason for this discrepancy is the increasing importance of contributions from successive two-step transfer reactions [4], such as (160, lSN)(lSN, 14C), which are the dominant reaction modes at low bombarding energies.…”