Abstract

Deuteron stripping and pick-up experiments - (d,p) and (p,d) - have been used for a long time to study the structure of nuclei. Today these experiments are often carried out in inverse kinematics in state-of-the-art radioactive beams facilities around the world, extending the boundaries of our knowledge of the nuclear chart. The nuclear structure information obtained from these experiments relies entirely on transfer reaction theory. We review the theory of (d,p) and (p,d) reactions starting from early formulations and ending with the most recent developments. In particular, we describe the recent progress made in the understanding of the three-body dynamics associated with the deuteron breakup degrees of freedom, including effects of nonlocality, and discuss the role of many-body degrees of freedom within the three-body context. We also review advances in structure model calculations of one-nucleon overlap functions — an important structure input to (d,p) and (p,d) reaction calculations. We emphasize the physics missing in widely-used standard approaches available to experimentalists and review ideas and efforts aimed at including this physics, formulating the crucial tasks for further development of deuteron stripping and pick-up reaction theory.

Highlights

  • Removing or adding one neutron from a nucleus using a (d, p) or (p, d) transfer reaction has been a popular choice over a half-century of nuclear structure studies

  • In both the post- and prior formulations the amplitude T contains a contribution from an auxiliary matrix element, which determines the contribution from the nuclear interior and has its origin in the inconsistent treatment of VnA in the entrance and exit channels

  • We have presented a comprehensive review of modern developments in the theory of deuteron stripping and pickup reactions as used in the analysis of experimental data

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Summary

Introduction

The deuteron is an n-p system bound by only 2.22 MeV. There is a large probability of finding the neutron and proton in the classically-forbidden region with n-p separations outside the range of Vnp. Where Up and Un are nucleon-A complex optical potentials and T3 is the three-body kinetic energy operator in the overall centre-of-mass system This Hamiltonian can only describe a process in which the target state is unchanged, but it does couple bound and different continuum states of the n − p system because of tidal forces associated with Up + Un. As applied to elastic deuteron scattering the additional assumption made in [98] was that the deuteron itself was not excited (broken-up) in the reaction. Effects in final nucleus B since Ψk(−p,)B(p, B) contains components in which the relative motion of A and n in the nucleus B is in its ground state or excited to one of its bound or continuum breakup states The latter components are mixed in by the p − A interaction, i.e., by the recoil of A being transmitted to n through VnA. Note that the amplitude (48) includes multistep population of B via exciting states (bound or unbound) because Ψk(+d )(n, p) has non-zero projections to these states

Main features of the distorted-wave theory
Exact formulation and antisymmetrization
Separating out the DWBA term
The DWBA transition operator
Optical potential uncertainty in the DWBA
The effective three-body Hamiltonian
Formulation of the ADWA
Continuum-discretized coupled channel approach
Connection between the CDCC and Weinberg basis wave functions
Perturbative corrections to the ADWA distorting potential
A localized version of the nonlocal two-body problem and the DWBA
Nonlocal potentials in the ADWA
Velocity-dependent potentials
Nonlocality in the CDCC approach
Faddeev calculations with nonlocal nucleon optical potentials
Faddeev–Alt–Grassberger–Sandhas approach
Energy-dependent interactions in the ADWA
Model calculations of overlap integrals
Potential model with excited core
Ab-initio calculations of overlap integrals
Pre-asymptotic abnormalities in overlap functions near drip-lines
10. Transfer to the continuum
10.1. Vincent–Fortune contour integration
10.2. Continuum bins
10.3. Surface formulations of the transfer amplitude
Findings
11. Conclusions and outlook
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