Weak sensitivity of three-body ($d,p$) reactions to $np$ force models

Background: An adiabatic distorted-wave approximation (ADWA) study of three-body $(d,p)$ transfer reactions [G. W. Bailey, N. K. Timofeyuk, and J. A. Tostevin, Phys. Rev. Lett. 117, 162502 (2016)] reported strong sensitivity of cross sections to the neutron-proton $\left(np\right)$ interaction model when the nucleon-nucleus optical potential is nonlocal.

Purpose: The verification of this unusual finding using more reliable methods is aimed for in the present work.

Methods: A rigorous Faddeev-type three-body scattering theory is applied to the study of $(d,p)$ transfer reactions. The equations for transition operators are solved in the momentum-space partial-wave framework.

Results: Differential cross sections for ${}^{26}\mathrm{Al}(d,p){}^{27}\mathrm{Al}$ reactions are calculated using nonlocal nuclear optical potentials and a number of realistic $np$ potentials. Only a weak dependence on the $np$ force model is observed, typically one order of magnitude lower than in the previous ADWA study. The shape of the angular distribution of the experimental data is well reproduced.

Conclusions: Cross sections of $(d,p)$ transfer reactions calculated using a rigorous three-body method show little sensitivity to the $np$ interaction model. This indicates a failure of the ADWA in the context of nonlocal potentials. Some evident shortcomings of the ADWA are pointed out.

Figure 1

Differential cross sections for ${}^{26}\mathrm{Al}(d,p){}^{27}\mathrm{Al}$ reactions at $E_d=12$ MeV as functions of the c.m. scattering angle. The neutron separation energy $S_n$, spin and parity of the final nucleus $J^{\pi }$, and the orbital angular momentum transfer $L$ are indicated in each panel. Predictions obtained with different realistic $np$ potentials are compared.

Figure 2

Differential cross sections for ${}^{26}\mathrm{Al}(d,p){}^{27}\mathrm{Al}$ reactions at $E_d=12$ MeV as functions of the c.m. scattering angle. The excitation energy $E_x$, spin and parity of the final nucleus $J^{\pi }$, and the contributing orbital angular momentum transfer $L$ are indicated in each panel. CD Bonn predictions, rescaled by factors $X(E_x,L)$ given in the text, are compared with the experimental data from Ref. [14].