Importance of deuteron breakup in the deuteron knockout reaction

Background: An isoscalar $pn$ pair is expected to emerge in nuclei that have similar proton and neutron numbers and it may be a candidate for a deuteron “cluster.” There is, however, no experimental evidence for it.

Purpose: The purpose of this paper is to construct a new reaction model for the $(p,pd)$ reaction including the deuteron breakup in the elementary process and the deuteron reformation by the final-state interactions. How these processes contribute to the observables of the reaction is investigated.

Methods: The distorted wave impulse approximation is extended twofold. The elementary processes of the $(p,pd)$, i.e., the $p\text{−}d$ elastic scattering and the $d(p,p)pn$ reaction, are described with an impulse picture employing a nucleon-nucleon effective interaction. The three-body scattering waves in the final state of the $(p,pd)$ reaction are calculated with the continuum-discretized coupled-channels method. The triple-differential cross section (TDX) of the $(p,pd)$ reaction is calculated with the new model.

Results: The elementary processes are described reasonably well with the present model. As for the $(p,pd)$ reaction, the deuteron reformation can either increase or decrease the TDX height depending on the interference between the elastic and breakup channels of deuteron, while the back-coupling effect always decreases it.

Conclusions: It is shown that the deuteron reformation significantly changes the TDX of the $(p,pd)$ reaction through the interference. It is important to include this process to quantitatively discuss the $(p,pd)$ cross sections in view of the deuteron formation in nuclei. For more quantitative discussion regarding the experimental data, further improvement will be necessary.

Figure 1

Spatial coordinates of the $\mathrm{A}(p,pd$)B reaction system.

Figure 2

Differential cross sections of the $p\text{−}d$ elastic scattering and the $d(p,p)pn$ reaction at $T_p^{\text{L}}=$ (a) 120, (b) 135, (c) 155, (d) 170, (e) 190, and (f) 250 MeV. The horizontal axis is the scattering angle in the c.m. frame of the $p\text{−}d$ system. The solid (dashed) line shows the numerical result of elastic scattering (breakup reaction) in each panel. The dots are the experimental data of the $p\text{−}d$ elastic scattering taken from Ref. [37] (120, 135, 170, and 190 MeV), Ref. [38] (155 MeV), and Ref. [39] (250 MeV).

Figure 3

Schematic illustration of the reaction processes included in the present CDCCIA calculation. EL- and RF-CDCCIA are CDCCIA considering the elastic and breakup channels of the wave function (7), respectively.

Figure 4

Triple-differential cross sections (TDXs) of the ($p,pd$) reactions at 250 MeV. The target nuclei are (a) ${}^{16}\mathrm{O}$, (b) ${}^{40}\mathrm{Ca}$, and (c) ${}^{56}\mathrm{Ni}$. The solid lines show the CDCCIA results of Eq. (23). The dashed (dotted) lines show the TDXs obtained by taking the $c=0$ ($c\ne 0$) component(s) in Eq. (23), referred to as EL-CDCCIA (RF-CDCCIA). The dot-dashed lines are the results without any deuteron breakup, i.e., NB-CDCCIA of Eq. (27).

Figure 5

Norm of $f\left(\mathit{R}\right)$ defined by Eq. (30) at the recoilless condition, $T_1^{\text{L}}=150$ MeV, for ${}^{16}\mathrm{O}(p,pd){}^{14}\mathrm{N}$ along the direction of the outgoing deuteron; the direction of the deuteron is taken to be parallel to the $z$ axis in this plot. The meanings of the line types are the same as in Fig. 4.