Background: Proton-induced nucleon knockout $(p,pN)$ reactions have been successfully used to study the single-particle nature of stable nuclei in normal kinematics with the distorted-wave impulse approximation (DWIA) framework. Recently, these reactions have been applied to rare-isotope beams at intermediate energies in inverse kinematics to study the quenching of spectroscopic factors.
Purpose: Our goal is to investigate the effects of various corrections and uncertainties within the standard DWIA formalism on the $(p,pN)$ cross sections. The consistency of the extracted reduction factors between DWIA and other methods is also evaluated.
Method: We analyze the $(p,2p)$ and $(p,pn)$ reactions data measured at the R$^3$B/LAND setup at GSI for carbon, nitrogen, and oxygen isotopes in the incident energy range of 300--450 MeV/u. Cross sections and reduction factors are calculated by using the DWIA method. The transverse momentum distribution of the $^{12}$C($p$,$2p$)$^{11}$B reaction is also investigated.
Results: We have found that including the nonlocality corrections and the Møller factor affects the cross sections considerably. The proton-neutron asymmetry dependence of reduction factors extracted by the DWIA calculation is very weak and consistent with those given by other reaction methods and \textit{ab initio} structure calculations.
Conclusions: The results found in this work provide a detailed investigation of the DWIA method for $(p,pN)$ reactions at intermediate energies. They also suggest that some higher-order effects, which is essential for an accurate cross-section description at large recoil momentum, is missing in the current DWIA and other reaction models.
Both ($e$,$e'p$) and ($p$,$2p$) reactions have been performed to study the proton single-particle character of nuclear states with its related spectroscopic factor. Recently, the dispersive optical model (DOM) was applied to the ($e$,$e'p$) analysis revealing that the traditional treatment of the single-particle overlap function, distorted waves, and nonlocality must be further improved to achieve quantitative nuclear spectroscopy. We apply the DOM wave functions to the traditional ($p$,$2p$) analysis and investigate the consistency of the DOM spectroscopic factor that describes the ($e$,$e'p$…
The nonlocal implementation of the dispersive optical model (DOM) provides all the ingredients for distorted-wave impulse-approximation (DWIA) calculations of the $(e,e'p)$ reaction. It provides both the overlap function, including its normalization, and the outgoing proton distorted wave. This framework is applied to describe the knockout of a proton from the $0\textrm{d}\frac{3}{2}$ and $1\textrm{s}\frac{1}{2}$ orbitals in ${}^{40}$Ca with fixed normalizations of 0.71 and 0.60, respectively. Data were obtained in parallel kinematics for three outgoing proton energies: 70, 100, and 135 MeV. A…
Distorted wave impulse approximation analysis for spin observables in nucleon quasi-elastic scattering and enhancement of the spin-longitudinal response
Reaction cross sections of carbon isotopes for proton scattering are calculated in large energy region. Density distributions of carbon isotopes are obtained from relativistic mean field results. Calculations are based on two procedures: the Glauber theory and relativistic impulse approximation, and results are compared with each other as well as with experimental data. A strong relationship between reaction cross section and root-mean-square radius is clearly shown for 12C using a model distribution.
A Benchmark Study of the Relativistic Plane Wave Impulse Approximation for Polarized ($\vec{p},2\vec{p}\,$) Reactions on the 3s$_{1/2}$ state in $^{208}$Pb at 392 MeV
Botswana International University of Science and Technology（博茨瓦纳国际科学与技术大学）
Impulse approximation in the n p --> d pi^0 reaction reexamined
本文重新考察了n p -> d π ^0反应中的冲量近似（单体算符），重点是约化和反冲修正问题。当一个π介子交换包含在产生算符中时，证明了一个不一致性，然后通过引入“波函数修正”来解决，该修正对于静态核子传播子几乎为零。包括反冲修正的核子传播子被发现改变的幅度和符号的脉冲产生振幅，恶化与实验截面约30%的协议。一个截止是用来占外部波函数的唯象性质，并发现有一个显着的影响高达约2.5 GeV。
Modeling direct and pre-equilibrium processes of neutron-induced reactions with noniterative finite amplitude method and distorted-wave Born approximation
We propose to extend the optimal Fermi averaging procedure theoretically in order to calculate an in-medium $K^-n\to π^- Λ$ amplitude for the exothermic ($K^-$, $π^-$) reaction on nuclei in the framework of a distorted-wave impulse approximation, taking into account the local momentum transfer generated by semiclassical distorted waves for $K^-$ and $π^-$ mesons. Angular distributions for the $^{12}$C($K^-$, $π^-$)$^{12}_Λ$C reaction in which a momentum transfer is $q \lesssim$ 80 MeV/$c$ at $p_K=$ 800 MeV/$c$ in the $π^-$ forward direction, are estimated by applying the extended procedure. Th…
Linear combinations $D_K$ of the complete polarization-transfer observables, Dij, in the (p,p') reaction at intermediate energies are demonstrated. A comparison between systematized measured and calculated values of the combinations $D_K$ for the $1^+$ (T = 0 and T = 1) levels in $^{12}$C, for the $4^-$ (T = 0 and T = 1) states in $^{16}$O, and for the $6^-$ (T = 0 and T = 1) levels in $^{28}$Si are reported. Particularities in angular distributions of transverse- and longitudinal-spin-transfer probabilities, $D_K$, for the T = 0 and T = 1 unnatural-parity states in the indicated nuclei are di…
Using adiabatic distorted-wave approximation (ADWA) with nonlocal optical potentials (NLOP) for $(d,p)$ transfer reactions [G.W. Bailey, N.K. Timofeyuk, and J.A. Tostevin, Phys. Rev. Lett. 117, 162502 (2016)] reported strong sensitivity to the $n$-$p$ force model. This sensitivity disappears in rigorous three-body Faddeev-type results. Some shortcomings of ADWA with NLOP are pointed out.
Semiclassical Distorted Wave Model Analysis of Backward Proton Emission from $(p,p^{\prime}x)$ Reactions at Intermediate Energies
本文提出了一个半经典扭曲波模型，该模型采用单体密度矩阵的Wigner变换，研究了多步直接$(p,p^{\prime}x)$反应到连续介质的过程。该模型使用的Wigner分布函数的方法，包括核子-核子的相关性在不同程度上，以及伍兹-撒克逊（WS）单粒子波函数。适当地考虑了在再现后向质子谱的高能部分中起关键作用的靶核子的高动量分量。用SCDW模型分析了入射能量为150- 392 MeV的$^{12}$ C $(p,p^{\prime}x)$、$^{40}$ Ca $(p,p^{\prime}x)$和$^{90}$ Zr $(p,p^{\prime}x)$的多步直接过程。双微分截面计算到三个步骤的过程。计算的角分布与实验数据吻合良好，特别是在向后的角度，以前的SCDW计算与WS单粒子波函数表现出很大的低估。结果表明，基于相干密度涨落模型的Wigner分布函数在整个发射能量范围内与实验数据吻合较好。
In this paper, I prove that the sub-Coulomb $A(d,p)B$ reaction amplitude, which is a solution of the three-body Faddeev equations in the Alt-Grassberger-Sandhas (AGS) form, is peripheral if a peripheral is the corresponding DWBA amplitude. Hence the Faddeev's reaction amplitude for the sub-Coulomb $A(d,p)B$ reactions can also be parametrized in terms of the ANC of the $(n\,A)$ bound state. First, I consider the original AGS equations with separable potentials and prove that such equations are peripheral at sub-Coulomb energies. After that, the two-particle AGS equations are derived for the gen…
The $p p \to p pπ^0$ Reaction near Threshold: A Chiral Power Counting Approach
我们使用功率计数参数作为组织原则，适用手征微扰理论，包括一个明确的$Δ$，$p p \rightarrow p p π^0$反应阈值附近。有两个最低阶的主导机制，预计有助于幅度相似的幅度：脉冲项，和$Δ$ -激发机制。我们研究正式次领导，但潜在的大机制，包括π介子再散射和短期的贡献。我们发现，π介子的再散射贡献增强的离壳效应，并有一个相反的符号，最近的估计的基础上PCAC π介子插值字段。我们的结果是，脉冲项破坏性地干扰π介子再散射和$Δ$ -激发项。此外，我们还利用$σ$和$ω$交换机制模拟了短程相互作用。对冲量近似的反冲修正很小。包括所有这些过程得到的总振幅被发现产生的截面大大小于测量的。
We solved the nonlocal scattering and bound state equations using the Perey-Buck type interaction, and compared to local equivalent calculations. Using the distorted wave Born approximation we construct the T-matrix for (p,d) transfer on 17O, 41Ca, 49Ca, 127Sn, 133Sn, and 209Pb at 20 and 50 MeV. Additionally we studied (p,d) reactions on 40Ca using the the nonlocal dispersive optical model. We have also included nonlocality consistently into the adiabatic distorted wave approximation and have investigated the effects of nonlocality on on (d,p) transfer reactions for deuterons impinged on 16O, …
We investigate the impact of ambiguities coming from the choice of optical potentials and nucleon-nucleon scattering cross sections on the spectroscopic factors extracted from the $^{12}$C($p,2p$)$^{11}$B reaction. These ambiguities are evaluated by analyzing the cross sections of the $^{12}$C($p,2p$)$^{11}$B reaction at 100 and 200 MeV within the framework of the distorted-wave impulse approximation with realistic choices of nuclear inputs. The results show that the studied ambiguities are considerably large in this energy region and careful choices of nuclear inputs used in the reaction calc…
We present a suite of codes (NLAT for nonlocal adiabatic transfer) to calculate the transfer cross section for single-nucleon transfer reactions, $(d,N)$ or $(N,d)$, including nonlocal nucleon-target interactions, within the adiabatic distorted wave approximation. For this purpose, we implement an iterative method for solving the second order nonlocal differential equation, for both scattering and bound states. The final observables that can be obtained with NLAT are differential angular distributions for the cross sections of $A(d,N)B$ or $B(N,d)A$. Details on the implementation of the T-matr…
An important ingredient for applications of nuclear physics to e.g. astrophysics or nuclear energy are the cross sections for reactions of neutrons with rare isotopes. Since direct measurements are often not possible, indirect methods like (d,p) reactions must be used instead. Those (d,p) reactions may be viewed as effective three-body reactions and described with Faddeev techniques. An additional challenge posed by (d,p) reactions involving heavier nuclei is the treatment of the Coulomb force. To avoid numerical complications in dealing with the screening of the Coulomb force, recently a new …
Nucleon-knockout reactions on proton targets (p, pN ) have experienced a renewed interest due to the availability of inverse-kinematics experiment with exotic nuclei. Various theoretical descriptions have been used to describe these reactions, such as the Distorted-Wave Impulse Approximation (DWIA), the Faddeev-type formalism and the Transfer to the Continuum method. Our goal is to benchmark the observables computed with the Faddeev and Transfer to the Continuum formalisms in the intermediate energy regime relevant for the experimental (p, pn) and (p, 2p) studies. In this paper, we analyze the…
We investigate theoretically production cross sections of the $J^π=$ 0$^+$ ground state of a $^4_Λ$He hypernucleus in the $^4$He($π$,~$K$) reaction with a distorted-wave impulse approximation using the optimal Fermi-averaged $πN\to KΛ$ $t$ matrix. We demonstrate the sensitivity of the production cross sections to the $Λ$ wavefunctions obtained from $3N$-$Λ$ potentials and to meson distorted waves in eikonal distortions. It is shown that the calculated laboratory cross sections of the 0$^+$ ground state in $^4_Λ$He amount to $dσ/dΩ_{\rm lab} \simeq$ 11 $μ$b/sr at $p_π=$ 1.05 GeV/$c$ in the $K$ …
We investigate theoretically $Λ$ production spectra of $^3$He($π$, $K$) reactions at $p_π=$ 1.05--1.20 GeV/$c$ in the distorted-wave impulse approximation, using the continuum-discretized coupled-channel method. The production cross section of a $^3_Λ$H(1/2$^+$) ground state is also discussed.
Chirality in $(\vec{p},2p)$ reactions induced by proton helicity
Research Center for Nuclear Physics, Osaka University（大阪大学核物理研究中心）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN（理化学研究所交叉理论与数学科学项目(iTHEMS)）；Department of Advanced Energy Science and Engineering, Kyushu University（九州大学先进能源科学与工程系）；Department of Physics, Kyushu University（九州大学物理学系）；RIKEN Nishina Center（理化学研究所西村中心）
The cross-sections of proton-induced reactions on 184W at incident proton energy below 200MeV are calculated and analyzed including reaction cross-sections, elastic scattering angular distributions, energy spectra and double differential cross section. Nuclear theoretical models which integrate the optical model, distorted born wave approximation theory, the intra-nuclear cascade model, the exciton model, the Hauser-Feshbach theory and the evaporation model are used in the reactions. Theoretical results are compared with the existent experimental data.
We study parity violation in quasielastic (QE) electron-nucleus scattering using the relativistic impulse approximation. Different fully relativistic approaches have been considered to estimate the effects associated with the final-state interactions. We have computed the parity-violating quasielastic (PVQE) asymmetry and have analyzed its sensitivity to the different ingredients that enter in the description of the reaction mechanism: final-state interactions, nucleon off-shellness effects, current gauge ambiguities. Particular attention has been paid to the description of the weak neutral cu…
The theoretical approach to a sequential heavy ion double charge exchange reaction is presented. A brief introduction into the formal theory of second-order nuclear reactions and their application to Double Single Charge Exchange (DSCE) reactions by distorted wave theory is given, thereby completing the theoretical background to our recent work [1]. Formally, the DSCE reaction amplitudes are shown to be separable into superpositions of distortion factors, accounting for initial and final state ion--ion interactions, and nuclear matrix elements. A broad space is given to the construction of nuc…
Background: Traditionally, nucleon-nucleus optical potentials are made local for convenience. In recent work we studied the effects of including nonlocal interactions explicitly in the final state for (d,p) reactions, within the distorted wave Born approximation. Purpose: Our goal in this work is to develop an improved formalism for nonlocal interactions that includes deuteron breakup and to use it to study the effects of including nonlocal interactions in transfer (d,p) reactions, in both the deuteron and the proton channel. Method: We extend the finite-range adiabatic distorted wave approxim…
We consider exclusive two-pion production in antiproton-deuteron interactions at the beam momenta around 10 GeV/c in the kinematics with large momentum transfer in the underlying hard process $\bar p n \to π^- π^0$. The calculations are performed taking into account the antiproton and pion soft rescattering on the spectator proton in the framework of the generalized eikonal approximation. We focus on the color transparency effect that is modeled by introducing the dependence of rescattering amplitudes on the relative position of the struck and spectator nucleons along the momentum of a fast pa…
We propose to use proton knockout reactions (p,2p) from a deeply bound orbit as a new probe into three-nucleon-force (3NF) effects. The remarkable advantage of using (p,2p) reaction is that we can choose an appropriate kinematical condition to probe the 3NF effects. We analyze (p,2p) reactions on a 40Ca target within the framework of distorted-wave impulse approximation with a g-matrix interaction based on chiral two- and three-nucleon forces. The chiral 3NF effects significantly change the peak height of the triple differential cross section of (p,2p) reaction. We also clarify the corresponde…
The $^{120}$Sn($p$,$pα$)$^{116}$Cd reaction at 392 MeV is investigated with the distorted wave impulse approximation (DWIA) framework. We show that this reaction is very peripheral mainly because of the strong absorption of $α$ by the reaction residue $^{116}$Cd, and the $α$-clustering on the nuclear surface can be probed clearly. We investigate also the validity of the so-called factorization approximation that has frequently been used so far. It is shown that the kinematics of $α$ in the nuclear interior region is significantly affected by the distortion of $^{116}$Cd, but it has no effect o…
