Description of nucleon transfer reactions at intermediate energies within the impulse picture

TL;DR

This work directly compares two theoretical frameworks for intermediate-energy transfer reactions by applying $DWBA$ and $DWIA$ to $^{16}$O$(p,d)^{15}$O at 200 MeV. It finds that $DWBA$ reproduces both the angular distribution shape and the absolute cross section without scaling, whereas $DWIA$ underestimates the cross section by about two orders of magnitude despite capturing the trend, prompting questions about $DWIA$’s transfer-reaction applicability. A momentum-sharing analysis suggests that momentum transfer can be accommodated by distributing it between the deuteron and proton, challenging naive requirements for high internal nucleon momentum. The results underscore the need for systematic studies to delineate the conditions under which each mechanism is valid and to refine the $p$–$d$ transition treatment and possible $0d$-state contributions. This has implications for extracting neutron single-particle information and for modeling intermediate-energy nuclear reactions more reliably.

Abstract

Background: At intermediate energies, transfer reactions are suppressed because the momentum-matching condition is difficult to satisfy. In the standard distorted wave Born approximation (DWBA), a high momentum component of the transferred particle is required to match the large momentum transfer. Purpose: We investigate the applicability of the distorted wave impulse approximation (DWIA) for describing ($p,d$) transfer reactions at intermediate energies by performing a comparative study with the standard DWBA. DWIA, which has been successful for knockout reactions, is expected to provide an alternative reaction mechanism at this energy region. Methods: Both DWBA and DWIA formalisms are applied to the $^{16}$O($p,d$){}$^{15}$O reaction at 200~MeV. In DWBA, the reaction is described as a neutron pickup, while in DWIA, it is treated as a quasi-elastic scattering from a preformed deuteron cluster in the target. Results: The DWBA calculation is in good agreement with the experimental data, reproducing both the angular distribution and the absolute magnitude of the cross section with a reasonable spectroscopic factor. In contrast, the DWIA calculation, while qualitatively reproducing the trend of the angular distribution, severely underestimates the cross section by about two orders of magnitude. Conclusions: Our findings suggest that conventional DWBA provides a more suitable description for the $^{16}$O($p,d$){}$^{15}$O reaction at 200~MeV. The failure of DWIA in this case, unlike its success in knockout reactions, raises open questions about its applicability to transfer reactions. This motivates the need for systematic investigations to delineate the applicability of both reaction mechanisms under various conditions.

Figures (6)

• Figure 1: Coordinates of the A($p$, $d$)B reaction system.
• Figure 2: The momentum distributions of the deuteron (red solid line) and proton (blue dashed line).
• Figure 3: The transfer cross section of $^{16}$O$(p,d)^{15}$O at 200 MeV as a function of the scattering angle $\theta$. (a) Comparison between the results with DWIA (red solid line) and PWIA (blue dashed line). (b) The PWIA result (red solid) is decomposed into the $m=0$ (orange dash-dotted line) component and the sum of the $m=\pm 1$ (green dotted line) components. (c) Same as (b) but for the DWIA result.
• Figure 4: (a) $\left|\mathcal{T}_{01,1/2,0}^{\rm PW}\right|$ at $\theta=0^{\circ}$ as a function of $k_d$ and $\theta_d$. (b) The deuteron (red solid line) and proton (blue dashed line) momentum distributions along $\theta_d=0^{\circ}$.
• Figure 5: Same as Fig.\ref{['fig:4']} but for $\theta=40^{\circ}$. See the text for details.