Deuteron Stripping Research Articles

Detailed analysis of the 6Li breakup in the field of the 209Bi nucleus

Abstract At energies between 24 and 50 MeV, the angular distributions of 6Li + 209Bi elastic scattering are reanalyzed phenomenologically as well as microscopically. The performed analysis adds to previous studies and aims to further explore the cluster nature of the 6Li nucleus by examining the associated breakup effects on the elastic scattering channel, in addition to probing the consistency of the different implemented potentials in reproducing the considered data. The strong coupling to the breakup channel has a strong influence on elastic data and reproduces a repulsive dynamical polarization potential (DPP), which dramatically reduces the real potential strengths. Such an observed effect was simulated by introducing a semi-microscopic repulsive DPP as well as by applying the continuum discretized coupled channels (CDCC) method. The analysis was extended to check the effect of direct deuteron stripping 209Bi(6Li,d)211Po on the elastic 6Li + 209Bi channel.

Nonlocal optical potential with core excitation in [formula omitted] and [formula omitted] reactions

We propose a new nonlocal form of the nucleon-nucleus optical potential and demonstrate its reliability. We extend the nonlocal potential to include the excitation of the nuclear core and develop energy-independent proton-Be10 potential reasonably reproducing the experimental data at low energies. We apply the new potential to the study of deuteron stripping and pickup reactions Be10(d,p)11Be and Be11(p,d)10Be using rigorous three-body Faddeev-type equations for transition operators that are solved in the momentum-space partial-wave framework. The achieved description of the experimental data is considerably more successful as compared to previous studies with local potentials. The values of spectroscopic factors consistent with the data are determined, exhibiting only weak energy dependence. The results possibly indicate an increased predicting power of the proposed calculational scheme.

A Brief Review on the Development of Theories of Deuteron Stripping Reactions

As one type of single nucleon transfer reactions, deuteron stripping reaction has been playing an important role in the study of the single particle structure of atomic nuclei. Also, as a typical three-body nuclear reaction, deuteron stripping reaction is also an important subject in the development of direct nuclear reaction theories. We briefly review the history of the study of deuteron stripping reactions, focusing on the evolution of its theoretical descriptions, and the differences and the relations of the Plane Wave Born Approximation(PWBA), the distorted wave Born approximation(DWBA), the Continuum Discretized Coupled Channel method(CDCC), the Adiabatic Wave Approximation(ADWA), and the approach based on the Faddeev equations. Some important problems being currently addressed in deuteron stripping reaction theories and those should be addressed in near future are also discussed, including deuteron strippings at intermediate and high energies, theory for transfer to continuum states of the residue nuclei, applications of dispersive optical model potentials and non-local potentials, etc. Some preliminary results of our theoretical calculations for deuteron stripping at intermediate and high energies are presented.

Perturbative correction to the adiabatic approximation for (d, p) reactions

The adiabatic distorted wave approximation (ADWA) is widely used by the nuclear community to analyse deuteron stripping (d, p) experiments. It provides a quick way to take into account an important property of the reaction mechanism: deuteron breakup. In this work we provide a numerical quantification of a perturbative correction to this theory, recently proposed in Johnson (2014 J. Phys. G: Nucl. Part. Phys. 41 094005) for separable rank-one nucleon–proton potentials. The correction involves an additional, nonlocal, term in the effective deuteron–target ADWA potential in the entrance channel. We test the calculations with perturbative corrections against continuum-discretized coupled channel predictions which treat deuteron breakup exactly.

What kind of optical model potentials should be used for deuteron stripping reactions?

This paper presents the results of a study that compares CTOM, a microscopic optical model potential (OMP), which is an optical model co-created by the China Nuclear Data Center & Tuebingen University, to CH89, which is a typical phenomenological OMP. The respective OMPs were tested by applying them to the modelling of nucleon elastic scattering and (d, p) transfer reactions involving 14C, 36S, and 58Ni targets at both low and relatively high energies. The results demonstrated that although both potentials successfully accounted for the angular distributions of both the elastic scattering and transfer cross sections, the absolute values of the transfer cross sections calculated using CTOM were approximately 25% larger than those calculated using CH89. This increased transfer cross sections allowed CTOM to produce single particle strength reduction factors for the three reactions that were consistent with those extracted from (e, e′ p) reactions as well as with more recent (p, 2p) and (p, pn) reactions. Notch tests suggested that nucleon elastic scattering and transfer reactions are sensitive to different regions of the OMP; accordingly, phenomenological OMPs, which are constrained only by elastic scattering cross sections, may not be sufficient for nucleon transfer reactions. Therefore, we suggest that microscopic OMPs, which reflect more theoretical considerations, should be preferred over phenomenological ones in calculations of direct nuclear reactions.

Polarization of Nucleons in the Deuteron Stripping Reaction on Nuclei

A general analytical expression has been obtained in the diffraction approximation for the polarization of nucleons arising in the deuteron stripping reaction on nuclei at intermediate energies of the incident particles. A tabulated density distribution of the target nucleus and a realistic wave function of the deuteron with correct asymptotic limits at large internucleon distances were used in the calculations. The nucleon-nucleus phase shifts were calculated in the Glauber formalism using the double folding potential. The calculated angular dependencies for the vector analyzing power $A_{y}$ of the reaction $^{3}\text{He}(\vec{d},p)^{4}\text{He}$ are found to be in satisfactory agreement with the corresponding experimental data.

Polarized-deuteron stripping reaction at intermediate energies

A general analytical expressions for the cross-section and the polarization of nucleons arising in the inclusive deuteron stripping reaction have been derived in the diffraction approximation. The nucleon–nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The tabulated distributions of the target nucleus density and the realistic deuteron wave function with correct asymptotic at large nucleon–nucleon distances were used. The calculated angular dependences for the cross-sections and the analyzing powers of the [Formula: see text] reaction are compared with corresponding experimental data.

Deuteron-induced nucleon transfer reactions within anab initioframework: First application top-shell nuclei

Background: Low-energy transfer reactions in which a proton is stripped from a deuteron projectile and dropped into a target play a crucial role in the formation of nuclei in both primordial and stellar nucleosynthesis, as well as in the study of exotic nuclei using radioactive beam facilities and inverse kinematics. Ab initio approaches have been successfully applied to describe the $^3$H$(d,n)^4$He and $^3$He$(d,p)^4$He fusion processes. Purpose: An ab initio treatment of transfer reactions would also be desirable for heavier targets. In this work, we extend the ab initio description of $(d,p)$ reactions to processes with light $p$-shell nuclei. As a first application, we study the elastic scattering of deuterium on $^7$Li and the ${}^{7}$Li($d$,$p$)${}^{8}$Li transfer reaction based on a two-body Hamiltonian. Methods: We use the no-core shell model to compute the wave functions of the nuclei involved in the reaction, and describe the dynamics between targets and projectiles with the help of microscopic-cluster states in the spirit of the resonating group method. Results: The shape of the excitation functions for deuteron impinging on ${}^{7}$Li are qualitatively reproduced up to the deuteron breakup energy. The interplay between $d$-$^7$Li and $p$-$^8$Li particle-decay channels determines some features of the ${}^{9}$Be spectrum above the $d$+${}^{7}$Li threshold. Our prediction for the parity of the 17.298 MeV resonance is at odds with the experimental assignment Conclusions: Deuteron stripping reactions with $p$-shell targets can now be computed ab initio, but calculations are very demanding. A quantitative description of the ${}^{7}$Li($d$,$p$)${}^{8}$Li reaction will require further work to include the effect of three-nucleon forces and additional decay channels, and improve the convergence rate of our calculations.

Deuteron stripping on nuclei at intermediate energies

A general analytical expression for the double differential cross section of deuteron stripping reaction on nuclei at intermediate energies of incident particles was obtained in the diffraction approximation. Nucleon–nucleus phases were calculated in the framework of Glauber formalism and making use of the double-folding potential. The exact wave function of deuteron with correct asymptotics at short and long distances between nucleons was used. The calculated angular dependencies of cross sections are in good agreement with corresponding experimental data.

Asymptotic normalization coefficients and spectroscopic factors from deuteron stripping reactions

We present the analysis of three deuteron stripping reactions, $^{14}\mathrm{C}(d,p)^{15}\mathrm{C},^{58}\mathrm{Ni}(d,p)^{59}\mathrm{Ni}$, and $^{116}\mathrm{Sn}(d,p)^{117}\mathrm{Sn}$ using the combined method [A. M. Mukhamedzhanov and F. M. Nunes, Phys. Rev. C 72, 017602 (2005)], in which each reaction is analyzed at low and significantly higher energies. At low energies all these reactions are peripheral and the experimental asymptotic normalization coefficients (ANCs) are determined with accuracy about $10%$. At higher energies we determine the spectroscopic factors (SFs) by fixing the normalization of the peripheral parts of the reaction amplitudes governed by the ANCs found from the low-energy data. The combined method imposes a strict limitation on the variation of the geometrical parameters of the single-particle potential, which can be arbitrarily taken in the standard approach. By checking the compatibility of the ANCs and SFs using the combined method we reveal the flaw in the contemporary nuclear reaction theory in treating the nuclear interior, which is the most crucial part in the determination of the SFs.

Surface-integral formalism of deuteron stripping

The purpose of this paper is to develop an alternative theory of deuteron stripping to resonance states based on the surface integral formalism of Kadyrov et al. [Ann. Phys. 324, 1516 (2009)] and continuum-discretized coupled channels (CDCC). First we demonstrate how the surface integral formalism works in the three-body model and then we consider a more realistic problem in which a composite structure of target nuclei is taken via optical potentials. We explore different choices of channel wave functions and transition operators and show that a conventional CDCC volume matrix element can be written in terms of a surface-integral matrix element, which is peripheral, and an auxiliary matrix element, which determines the contribution of the nuclear interior over the variable $r_{nA}$. This auxiliary matrix element appears due to the inconsistency in treating of the $n-A$ potential: this potential should be real in the final state to support bound states or resonance scattering and complex in the initial state to describe $n-A$ scattering. Our main result is formulation of the theory of the stripping to resonance states using the prior form of the surface integral formalism and CDCC method. It is demonstrated that the conventional CDCC volume matrix element coincides with the surface matrix element, which converges for the stripping to the resonance state. Also the surface representation (over the variable $r_{nA}$ of the stripping matrix element enhances the peripheral part of the amplitude although the internal contribution doesn't disappear and increases with increase of the deuteron energy. We present calculations corroborating our findings for both stripping to the bound state and the resonance.

Determination of the asymptotic normalization coefficients forC14+n↔C15, theC14(n,γ)C15reaction rate, and evaluation of a new method to determine spectroscopic factors

The $^{14}\mathrm{C}$ + $n\ensuremath{\leftrightarrow}^{15}\mathrm{C}$ system has been used as a test case in the evaluation of a new method to determine spectroscopic factors that uses the asymptotic normalization coefficient (ANC). The method proved to be unsuccessful for this case. As part of this experimental program, the ANCs for the ${}^{15}$C ground state and first excited state were determined using a heavy-ion neutron transfer reaction as well as the inverse kinematics ($d$,$p$) reaction, measured at the Texas A Cyclotron Institute. The values ${C}_{2s1/2}^{2}=1.88\ifmmode\pm\else\textpm\fi{}0.18$ fm${}^{\ensuremath{-}1}$ for the ground state and ${C}_{1d5/2}^{2}=4.25\ifmmode\pm\else\textpm\fi{}0.38\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ fm${}^{\ensuremath{-}1}$ for the first excited state (${E}_{\text{exc}}=740$ keV) were obtained. The ANCs were used to evaluate the astrophysical direct neutron capture rate on $^{14}\mathrm{C}$, which was then compared with the most recent direct measurement and found to be in good agreement. A study of the $^{15}\mathrm{C}$ SF via its mirror nucleus $^{15}\mathrm{F}$ and a new insight into deuteron stripping theory are also presented.

Publisher’s Note: Nonlocality in Deuteron Stripping Reactions [Phys. Rev. Lett.110, 112501 (2013)

Publisher’s Note: Nonlocality in Deuteron Stripping Reactions [Phys. Rev. Lett.<b>110</b>, 112501 (2013)

Nonlocality in deuteron stripping reactions.

We propose a new method for the analysis of deuteron stripping reactions, A(d,p)B, in which the nonlocality of nucleon-nucleus interactions and three-body degrees of freedom are accounted for in a consistent way. The model deals with equivalent local nucleon potentials taken at an energy shifted by ∼40 MeV from the "E(d)/2" value frequently used in the analysis of experimental data, where E(d) is the incident deuteron energy. The "E(d)/2" rule lies at the heart of all three-body analyses of (d, p) reactions performed so far with the aim of obtaining nuclear structure properties such as spectroscopic factors and asymptotic normalization coefficients that are crucial for our understanding of nuclear shell evolution in neutron- and proton-rich regions of the nuclear periodic table and for predicting the cross sections of stellar reactions. The large predicted shift arises from the large relative kinetic energy of the neutron and proton in the incident deuteron in those components of the n+p+A wave function that dominate the (d, p) reaction amplitude. The large shift reduces the effective d-A potentials and leads to a change in predicted (d, p) cross sections, thus affecting the interpretation of these reactions in terms of nuclear structure.

Generalized Faddeev equations in the Alt-Grassberger-Sandhas form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction

Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the future. Here deuteron-stripping processes off a target nucleus consisting of $A$ nucleons are treated within the framework of the few-body integral equations theory. The generalized Faddeev equations in the Alt-Grassberger-Sandhas (AGS) form, which take into account the target excitations, with realistic optical potentials provide the most advanced and complete description of the deuteron stripping. The main problem in practical application of such equations is the screening of the Coulomb potential, which works only for light nuclei. In this paper we present a formulation of the Faddeev equations in the AGS form taking into account the target excitations with explicit inclusion of the Coulomb interaction. By projecting the $(A+2)$-body operators onto target states, matrix three-body integral equations are derived, which allow for the incorporation of the excited states of the target nucleons. Using the explicit equations for the partial Coulomb scattering wave functions in the momentum space we present the AGS equations in the Coulomb distorted wave representation without screening procedure. We also use the explicit expression for the off-shell two-body Coulomb scattering $T$ matrix, which is needed to calculate the effective potentials in the AGS equations. The integrals containing the off-shell Coulomb $T$ matrix are regularized to make the obtained equations suitable for calculations. For $NN$ and nucleon-target nuclear interactions we assume the separable potentials what significantly simplifies solution of the AGS equations.

John Riley Holt. 15 February 1918 — 6 January 2009

John Riley Holt was an experimental physicist who dedicated his working life to research in nuclear and particle physics at the University of Liverpool. He was born in 1918 in Runcorn, Cheshire, and in 1938 was awarded a first-class honours degree in physics at Liverpool University. He obtained his PhD in 1941 and became a member of Sir James Chadwick’s team working on the UK atomic weapon project. After the war he developed several new experimental techniques, which he used to make a systematic study of the deuteron stripping process with the use of the Liverpool cyclotron. After the Liverpool synchro-cyclotron became operational in 1954 he initiated a programme of precision measurements of cross-sections for proton–proton and pion–proton scattering. After the first observation of parity violation in 1957, his group completed an important experiment that observed parity violation in muon decay. When the construction of an electron synchrotron (NIN A, at the Daresbury Laboratory) was proposed, he became leader of the magnet design team. As NIN A became operational in 1966, John established a group to measure the cross-sections for the photoproduction of neutral and charged pions. The group then developed a collaboration with colleagues in other universities to measure the spin dependence of cross-sections for meson photoproduction by using a polarized photon beam and a polarized proton target. Before his retirement he contributed to the design of the experiment to determine the spin structure of the proton, performed by the European Muon Collaboration.

Theory of deuteron stripping: From surface integrals to a generalizedR-matrix approach

There are two main reasons for the absence of a practical theory of stripping to resonance states that could be used by experimental groups: The numerical problem of the convergence of the distorted-wave Born approximation (DWBA) matrix element when the full transition operator is included and the ambiguity over what spectroscopic information can be extracted from the analysis of transfer reactions populating the resonance states. The purpose of this paper is to address both questions. The theory of the deuteron stripping is developed, which is based on the post continuum discretized coupled channels (CDCCs) formalism going beyond of the DWBA and surface integral formulation of the reaction theory [A. S. Kadyrov et al., Ann. Phys. 324, 1516 (2009)]. First, the formalism is developed for the DWBA and then it is extended to the CDCC formalism, which is the ultimate goal of this work. The CDCC wave function takes into account not only the initial elastic $d+A$ channel but also its coupling to the deuteron breakup channel $p+n+A$ missing in the DWBA. Stripping to both bound states and resonances is included. The convergence problem for stripping to resonance states is solved in the post CDCC formalism. The reaction amplitude is parametrized in terms of the reduced width amplitudes (asymptotic normalization coefficients), inverse level matrix, boundary condition, and channel radius, which are the same parameters used in the conventional $R$-matrix method. For stripping to resonance states, many-level and one- and two-channel cases are considered. The theory provides a consistent tool to analyze both binary resonant reactions and deuteron stripping in terms of the same parameters.

Nuclear threshold effects and neutron strength functions

The present work is devoted to study of spectroscopic aspects, in terms of neutron strength function, for the threshold effects with non-light nuclei. Relations to the neutron strength functions of the anomal effects observed at threshold of neutron analogue channel, in deuteron stripping reactions on A ≈ 90 mass target nuclei and in nucleon mirror reactions with A ≈ 30 nuclei, are established. It is proved that these threshold effects follow the mass dependance of the neutron strength functions.

Deuteron stripping and pickup involving the halo nucleiBe11andC15

Three-body calculations of (d,p) and (p,d) reactions involving one-neutron halo nuclei 11Be and 15C are performed using the framework of Faddeev-type scattering equations. Important effects of the optical potential nonlocality are found improving the description of the experimental data. The obtained values for the neutron spectroscopic factor are consistent with estimations from other approaches.

THE DEUTERON STRIPPING ANOMALY AT THRESHOLD OF ANALOGUE CHANNEL AND THE 3 - p WAVE NEUTRON STRENGTH FUNCTION

We prove in this paper that the magnitude of anomaly in deuteron stripping reactions on A ≈ 80–110 mass target nuclei, at threshold of analogue channel, is proportional to the 3 - p wave neutron strength function. The result is obtained from analysis, within an empirical approach and computational frameworks, of the cross-section and analyzing power experimental data related to this (d,p) anomaly.