Influence of target deformation and deuteron breakup in $(d,p)$ transfer reactions

Background: The effect of core excitations in transfer reactions of the form $A(d,p)B$ has been reexamined by some recent works by using the Faddeev–Alt–Grassberger–Sandhas reaction formalism. The effect was found to affect significantly the calculated cross sections and to depend strongly and nonlinearly on the incident deuteron energy.

Purpose: Our goal is to investigate these effects within a coupled-channel formulation of the scattering problem which, in addition to being computationally less demanding than the Faddeev counterpart, may help shed some light onto the physical interpretation of the cited effects.

Method: We use an extended version of the continuum-discretized coupled-channel (CDCC) method with explicit inclusion of target excitations within a coupled-channel Born approximation (CDCC-BA) formulation of the transfer transition amplitude. We compare the calculated transfer cross sections with those obtained with an analogous calculation omitting the effect of target excitation. We consider also an adiabatic coupled-channel (ACC) method. Our working example is the ${}^{10}\mathrm{Be}(d,p){}^{11}\mathrm{Be}$ reaction.

Results: We find that the two considered methods (CDCC-BA and ACC) reproduce fairly well the reported energy dependence of the core excitation effect. The main deviation from the pure three-body model calculation (i.e., omitting core excitations) is found to mostly originate from the destructive interference of the direct one-step transfer and the two-step transfer following target excitation.

Conclusions: The proposed method; namely, the combination of the CDCC method and the CCBA formalism, provides a useful and accurate tool to analyze transfer reactions including explicitly, when needed, the effect of target excitations and projectile breakup. The method could be useful for other transfer reactions induced by weakly bound projectiles, including halo nuclei.

Figure 1

Pictorial representation of the ${}^{10}\mathrm{Be}(d,\mathrm{p}){}^{11}\mathrm{Be}$ reaction, highlighting the different paths considered in this work. The initial $d+{}^{10}\mathrm{Be}$ system includes breakup of the deuteron and excitation of ${}^{10}\mathrm{Be}$ coupled to all orders. The transfer channel is then coupled in first order to these channels, and four paths are distinguished: I (elastic transfer), II (inelastic transfer), III (breakup transfer), and IV (inelastic breakup transfer). See text for details.

Figure 2

$R_x$ factors (see text) for different deuteron energies. The green circles correspond to the results from Faddeev-AGS calculations [14]. In black circles the factors for the full CDCC-BA calculations are presented, while the red diamonds correspond to calculations where ${\mathcal{T}}_{dp}^{\text{inbu}}$ (path IV from Fig. 1) is blocked and the blue squares correspond to calculations where ${\mathcal{T}}_{dp}^{\text{inel}}$ and ${\mathcal{T}}_{dp}^{\text{inbu}}$ are blocked (II and IV from Fig. 1). See text for details.

Figure 3

Differential transfer cross section for $E_d=20$ MeV (top) and 60 MeV (bottom). All results correspond to full CDCC calculations for the elastic channel, while the transfer channel has been calculated through the Born approximation from all paths, and paths I, II, III, and IV (see Fig. 1) for the black solid, red solid, blue solid, red dashed, and blue dashed lines, respectively (see text).

Figure 4

Ratio between cross sections at the peak as a function of the deuteron incident energy. For each energy the ratio is between the calculation where one of the transfer paths is selected (as in Fig. 3) and the full calculation. As can be seen, path II, corresponding to the inelastic excitation of ${}^{10}\mathrm{Be}$, gains importance with increasing energy so that at the higher energies, where the $R_x$ factors are smaller, it is of the same magnitude as path III, corresponding to deuteron breakup.

Figure 5

$R_x$ ratio, as defined in Eq. (9). The black solid symbols correspond to calculations using a CDCC-BA formalism while the red empty symbols are obtained from a coupled-channel adiabatic calculation (ACC). The circles, squares, and triangles refer to the full calculations, the calculations where the transfer from ${}^{10}\mathrm{Be}\left(2^{+}\right)$ has been blocked, and the calculations where the sign of the overlaps involving ${}^{10}\mathrm{Be}\left(2^{+}\right)$ has been reversed, respectively (see text).

Figure 6

Differential cross-section angular distributions at $E_d=20$ MeV (top) and $E_d=80$ MeV (bottom) for the ${}^{10}\mathrm{Be}(d,p){}^{11}\mathrm{Be}$ reaction calculated with the Faddeev-AGS [14], CDCC-BA and ADWA formalisms.