For 52 target nuclei with deuteron as projectile, we calculate the reaction cross sections and elastic scattering angular distributions, as well as the $χ^2$ values for 11 kinds of deuteron optical model potentials: our global deuteron optical potentials and 10 folding optical potentials calculated with 2 phenomenological global nucleon optical potentials given by Koning \textit{et al}(KD) and by Varner\textit{et al}(CH89), and 8 microscopic nucleon optical potentials with the generalized Skyrme force parameters(GS1-6) and modified Skyrme force parameters(SKa, SKb). We find that for constructing the folding deuteron optical potential, both SKa and SKb are the best Skyrme force parameters of the microscopic nucleon optical potential proposed by Q. Shen \textit{et al}.
A simple single folding model for $Ω$-deuteron with maximal spin $\left(I\right)J^{P}=\left(0\right)5/2^{+}$ is investigated. $Ω$ is assumed to orbit an unperturbed deuteron in a $Ω$-deuteron potential based on a separable $Ω$-nucleon potential from lattice QCD. We show that the effective central folding potential of $Ωd$ in the $^{5}S_{2}$ channel has a simple Wood-Saxon form, and approximate the upper bound for the binding energy of $Ω$ particle on a deuteron. In order to investigate how changes in the wave functions affect the results, we consider four analytical forms for $S$-state deutero…
Improved potential solutions are presented for the inverse scattering problem for $d$+$^4$He data. The input for the inversions includes both the data of recent phase shift analyses and phase shifts from RGM coupled-channel calculations based on the NN Minnesota force. The combined calculations provide a more reliable estimate of the odd-even splitting of the potentials than previously found, suggesting a rather moderate role for this splitting in deuteron-nucleus scattering generally. The approximate parity-independence of the deuteron optical potentials is shown to arise from the nontrivial …
A general analytical expression for the double differential cross section of inclusive 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.
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 $(\vec{d},p)$ react…
We investigate the effect of the deuteron breakup on the optical potential for the elastic scattering of 56 MeV deuterons from $^{51}$V. The breakup probabilities calculated within the post-form distorted wave Born-approximation theory of breakup reactions are fitted to derive the contribution to the optical potential from the breakup channels. The breakup potentials are found to have large real as well as imaginary parts. Thus the dynamical polarization potential due to the breakup process is expected to modify strongly the real part of the optical potential calculated by the double folding m…
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 $A_{y}$…
The microscopic effective reaction theory is applied to deuteron-induced reactions. A reaction model-space characterized by a $p+n+{\rm A}$ three-body model is adopted, where A is the target nucleus, and the nucleon-target potential is described by a microscopic folding model based on an effective nucleon-nucleon interaction in nuclear medium and a one-body nuclear density of A. The three-body scattering wave function in the model space is obtained with the continuum-discretized coupled-channels method (CDCC), and the eikonal reaction theory (ERT), an extension of CDCC, is applied to the calcu…
The contribution of a three-nucleon (3N) force, acting between the neutron and proton in the incoming deuteron with a target nucleon, to the deuteron-target potential in the entrance channel of the $A(d,p)B$ reaction has been calculated within the adiabatic distorted wave approximation (ADWA). Four different 3N interaction sets from local chiral effective field theory ($χ$EFT) at next-to-next-to-leading order (N2LO) were used. Strong sensitivity of the adiabatic deuteron-target potential to the choice of the 3N force format has been found, which originates from the enhanced sensitivity to the …
From hyperon--nucleon interactions to deuteron--hyperon femtoscopy
Helmholtz Research Academy Hesse for FAIR (HFHF), GSI Helmholtz Center for Heavy Ion Physics（黑森亥姆霍兹FAIR研究学院（HFHF），GSI重离子物理中心）；Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität（约翰·沃尔夫冈·歌德大学理论物理研究所）
Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleon-nucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from `optimum factorized' approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good appr…
The contributions to the reaction cross section from the elastic and inelastic breakup processes, calculated within the post-form distorted wave Born-approximation theory, are used as constraints to determine the contributions to the imaginary part of the deuteron optical potentials (IPDOP) due to the breakup channels. The Coulomb part of this potential due to the elastic breakup process is seen to account for the long range absorption in the optical potential. The nuclear parts of the IPDOP due to the elastic and inelastic breakup modes peak in different regions of the nuclear surface, with t…
A calculation of vector and tensor polarization observables of a deuteron in an optical potential framework for elastic proton-deuteron scattering at the incident deuteron energy $E_d=880$ MeV is presented. The main aim is to point out the role of various effects in explaining the wide-range angle distribution of these observables. Under the investigation are a double-scattering mechanism in the optical potential, the influence of various $NN$-partial waves and as well a comparison of calculations with two different deuteron wave-functions derived from the Bonn-CD $NN$-potential model and dres…
Based on the extended optical model approach in which the polarization potential is decomposed into direct reaction (DR) and fusion parts, simultaneous $χ^{2}$ analyses are performed for elastic scattering and fusion cross section data for the $^{6}$Li+$^{208}$Pb system at near-Coulomb-barrier energies. A folding potential is used as the bare potential. It is found that the real part of the resultant DR part of the polarization potential is repulsive, which is consistent with the results from the Continuum Discretized Coupled Channel (CDCC) calculations and the normalization factors needed for…
We discuss optical potentials for the nuclear elastic scattering from a variational viewpoint. Density-dependence in the effective $N$-$N$ interaction leads to density rearrangement terms, in addition to the conventional folding term. Effects of the rearrangement on the $N$-$A$ optical potential are illustrated in the nuclear-matter limit. Closely relating to consistency with the saturation, the rearrangement appreciably improves the isoscalar optical potential depth over the previous folding model calculations. The rearrangement gives stronger effects as the density grows. We also present rea…
A set of global optical potential parameters, DA1p, for deuterons with the $1p$-shell nuclei is obtained by simultaneously fitting 67 sets of experimental data of deuteron elastic scattering from \nuc{6}{Li}, \nuc{9}{Be}, \nuc{10}{B}, \nuc{11}{B}, \nuc{12}{C}, \nuc{13}{C}, \nuc{14}{N}, \nuc{16}{O} and \nuc{18}{O} with incident energies between 5.25 and 170 MeV. DA1p improves the description of the deuteron elastic scattering from the $1p$-shell nuclei with respect to the existing systematic deuteron potentials and can give satisfactory reproduction to the experimental data with radiative nucle…
The real part of the optical potential for the nucleon-nucleus scattering at lower energies (E_i<100MeV) has been calculated including nucleonic and mesonic form factors by a double folding approach. Realistic density- and energy-dependent effective NN-interactions DDM3Y, BDM3Y and HLM3Y based on the Reid and Paris potentials are used in this respect. The effects of the nucleon density distribution and the average relative momentum on the folded potential have been analysed. A good agreement with the phenomenological potential of Lagrange-Lejeune, as well as with the parametrization of Jeukenn…
Realistic density dependent CDM3Yn versions of the M3Y interaction have been used in an extended Hartree-Fock (HF) calculation of nuclear matter (NM), with the nucleon single-particle potential determined from the total NM energy based on the Hugenholtz-van Hove theorem that gives rise naturally to a rearrangement term (RT). Using the RT of the single-nucleon potential obtained exactly at different NM densities, the density- and energy dependence of the CDM3Yn interactions was modified to account properly for both the RT and observed energy dependence of the nucleon optical potential. Based on…
A calculation of the deuteron polarization observables $A^d_y$, $A_{yy}$, $A_{xx}$, $A_{xz}$ and the differential cross-section for elastic nucleon-deuteron scattering at incident deuteron energies 270 and 880 MeV in lab is presented. A comparison of the calculations with two different deuteron wave-functions derived from the Bonn-CD $NN$-potential model and the dressed bag quark model is carried out. A model-independent approach, based on an optical potential framework, is used in which a nucleon-nucleon $T$-matrix is assumed to be local and taken on the energy shell, but still depends on the…
Based on the extended optical model with the double folding potential, in which the polarization potential is decomposed into direct reaction (DR) and fusion parts, simultaneous $χ^{2}$ analyses are performed of elastic scattering and fusion cross section data for the $^{9}$Be+$^{28}$Si, $^{144}$Sm, and $^{208}$Pb systems at near-Coulomb-barrier energies. We find that the real part of the resultant DR part of the polarization potential is systematically repulsive for all the targets considered, which is consistent with the results deduced from the Continuum Discretized Coupled Channel (CDCC) c…
Simultaneous $χ^{2}$ analyses are performed for elastic scattering and fusion cross section data for the $^{12}$C+$^{208}$Pb system at near-Coulomb-barrier energies by using the extended optical model approach in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and also that both DR and fusion parts of the polarization poten…
Simultaneous $χ^{2}$ analyses previously made for elastic scattering and fusion cross section data for the $^{6}$Li+$^{208}$Pb system is extended to the $^{7}$Li+$^{208}$Pb system at near-Coulomb-barrier energies based on the extended optical model approach, in which the polarization potential is decomposed into direct reaction (DR) and fusion parts. Use is made of the double folding potential as a bare potential. It is found that the experimental elastic scattering and fusion data are well reproduced without introducing any normalization factor for the double folding potential and that both t…
In the framework of the double folding model, we used the α+2n and di-triton configurations for the nuclear matter density of the 6He nucleus to generate the real part of the optical potential for the system 6He+12C. As an alternative, we also use the high energy approximation to generate the optical potential for the same system. The derived potentials are employed to analyze the elastic scattering differential cross section at energies of 38.3, 41.6 and 82.3 MeV/nucleon. For the imaginary part of the potential we adopt the squared Woods-Saxon form. The obtained results are compared with the …
The nonrelativistic full-folding optical model approach for nucleon-nucleus scattering is extended into the relativistic regime. In doing so, kinematical issues involving the off-shell Lorentz boost of the colliding particles between the two nucleons and the projectile-nucleus center-of-mass reference frames have been taken into account. The two-body effective interaction is obtained in the framework of the nuclear matter g-matrix using nucleon-nucleon optical model potentials that fully account for the inelasticities and isobar resonances in the continuum at nucleon energies up to 3 GeV. Dive…
By solving the Faddeev equations for the ppn system, we compute the antiproton-deuteron level shifts and widths for the lowest hydrogenic states as well as the corresponding pd scattering lengths and volumes. The pd annihilation densities are obtained and compared to the nuclear density of deuterium. The validity of the Trueman relation for composite particles is studied. The strong part of NN interaction is described by two different optical models, including the pp-nn coupling and n-p mass difference, while for NN several realistic interactions are used.
Calculations of microscopic optical potentials (OP's) (their real and imaginary parts) are performed to analyze the $^6$He+p elastic scattering data at a few tens of MeV/nucleon (MeV/N). The OP's and the cross sections are calculated using three model densities of $^6$He. Effects of the regularization of the NN forces and their dependence on nuclear density are investigated. Also, the role of the spin-orbit terms and of the non-linearity in the calculations of the OP's, as well as effects of their renormalization are studied. The sensitivity of the cross sections to the nuclear densities was t…
It has recently been reported [Phys. Rev. Lett. 117, 162502 (2016)] that (d, p) cross sections can be very sensitive to the n-p interactions used in the adiabatic treatment of deuteron breakup with nonlocal nucleon-target optical potentials. To understand to what extent this sensitivity could originate in the inaccuracy of the adiabatic approximation we have developed a leading-order local- equivalent continuum-discretized coupled-channel model that accounts for non-adiabatic effects in the presence of nonlocality of nucleon optical potentials. We have applied our model to the astro- physicall…
We review a concept of the Moscow potential (MP) of the $NN$ interaction. On the basis of this concept we derive by quantum inversion optical partial potentials from the modern partial-wave analysis (PWA) data and deuteron properties. Point-form (PF) relativistic quantum mechanics (RQM) is applied to the two-body deuteron photodisintegration. Calculations of the cross-section angular distributions cover photon energies between 1.1 and 2.5 GeV. Good agreement between our theory and recent experimental data confirms the concept of deep attractive Moscow potential with forbidden $S$- and $P$-stat…
Based on the spectator expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calculations of the effective (optical) potential for nucleon-nucleus scattering for light nuclei.
Total reaction cross sections of deuteron, $σ_d^{\rm R}$, are calculated by a microscopic three-body reaction model. The reaction model has no free adjustable parameter and applicable to reactions at various deuteron incident energies $E_d$ and with both stable and unstable nuclei. The predicted $σ_d^{\rm R}$ are consistent with those evaluated by a phenomenological optical potential for $E_d\leq 200$ MeV in which the potential has been parametrized. A simple formula of $σ_d^{\rm R}$ up to $E_d=1$ GeV, as a function of $E_d$, the target mass number $A$ and its atomic number $Z$, is given.
Elastic cross sections are calculated and compared with the data on $π^{\pm}$ scattering on $^{28}$Si, $^{40}$Ca, $^{58}$Ni, $^{208}$Pb nuclei in the energy range from 130 to 290 MeV. To this end, both the folding optical potential (OP) and the local modified Kisslinger-type OP were calculated, and then the $πA$ cross sections were obtained by solving the Klein-Gordon equation to account for the relativization and distortion wave effects. In the folding OPs, the parameters of the elementary $πN$ amplitude were fitted when describing the $πA$ scattering data, and thus the essential in-medium ef…
Microscopic optical potentials have been successful in describing nucleon-nucleus and nucleus-nucleus scattering. Some essential ingredients of the framework, however, have not been examined in detail. Applicability of the microscopic folding model is systematically investigated. Effect of an antisymmetrization factor (ASF) appearing in multiple scattering theory, theoretical uncertainty regarding the local density approximation (LDA), and the validity of a prescription for nonlocality, the Brieva-Rook (BR) localization, of the microscopic potential, are quantitatively estimated for nucleon-nu…
A microscopic description of the quasielastic (p,n) charge-exchange reaction (here, charge-exchange scattering between analogue states) is presented and discussed. Emphasis is focused on the spin-isospin structure of the projectile-target coupling. The model is a coupled-channel extension of the full-folding optical model approach (OMP) developed for nucleon elastic scattering, where emphasis is placed on retaining the genuine off-shell behavior of realistic effective interactions in the nuclear medium. The resulting non-local optical potentials are applied to the calculation of (p,n) differen…
Elastic scattering observables (differential cross section and analyzing power) are calculated for the reaction $^6$He(p,p)$^6$He at projectile energies starting at 71 MeV/nucleon. The optical potential needed to describe the reaction is based on a microscopic Watson first-order folding potential, which explicitly takes into account that the two neutrons outside the $^4$He-core occupy an open p-shell. The folding of the single-particle harmonic oscillator density matrix with the nucleon-nucleon t-matrix leads for this case to new terms not present in traditional folding optical potentials for …
Based on the mean-field determination of the single-particle energy in nuclear matter that contains naturally a rearrangement term (RT) implied by the Hugenholtz-van Hove theorem, the folding model of the nucleon optical potential (OP) is extended to take into account the RT using the effective, density dependent CDM3Yn interaction. With the exchange part of the nucleon folded OP treated exactly in the Hartree-Fock manner, a compact nonlocal version of the folding model is suggested in the present work to determine explicitly the isospin-dependent, nonlocal central term of the nucleon OP. To s…
Model uncertainties, arising due to suppression of target excitations in the description of deuteron scattering and resulting in a modification of the two-body interactions in a three-body system, are investigated for several $(d,p)$ reactions serving as indirect tools for studying the astrophysical $(p,γ)$ reactions relevant to $rp$-process. The three-body nature of deuteron-target potential is treated within adiabatic distorted wave approximation (ADWA) which relies on dominant contribution from the components of the three-body deuteron-target wave function with small $n$-$p$ separations. Th…
We present a determination of optical potentials using the double-folding method based on chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with dispersion relations to constrain the imaginary part. This approach is benchmarked on $^{16}$O--$^{16}$O collisions, and extended to the $^{12}$C--$^{12}$C and $^{12}$C--$^{16}$O cases. Predictions derived from these potentials are compared to data for elastic scattering at energies up to 1000 MeV, as well as for fusion at low energy. Without adjusting parameters, excellent agreement with experiment i…
Theoretical models of the (d,p) reaction are exploited for both nuclear astrophysics and spectroscopic studies in nuclear physics. Usually, these reaction models use local optical model potentials to describe the nucleon- and deuteron-target interactions. Within such a framework the importance of the deuteron D-state in low-energy reactions is normally associated with spin observables and tensor polarization effects - with very minimal influence on differential cross sections. In contrast, recent work that includes the inherent nonlocality of the nucleon optical model potentials in the Johnson…
We present a determination of optical potentials for $^4$He-target collisions using the double-folding method. We use chiral effective field theory nucleon-nucleon interactions at next-to-next-to-leading order combined with state-of-the-art nucleonic densities. The imaginary part of the optical potential is obtained from the real double-folding interaction either through a proportionality constant or applying Kramers-Kronig dispersion relations. With these potentials, we compute the elastic scattering of $^4$He off various targets, from $^4$He to $^{120}$Sn. We study the sensitivity of our pre…
We present a simultaneous analysis of the elastic scattering and fusion cross-section data of the $^{12}$C+$^{24}$Mg system around the Coulomb barrier and over energies by using the microscopic $α$-$α$ double folding cluster potential within the framework of the optical model and the coupled-channels formalism. The $α$-$α$ double folding cluster potential is obtained by using the $α$-cluster distribution densities of the nuclei in the usual double folding procedure. The microscopic potential results are compared with the findings of the phenomenological deep and shallow potentials. It is subse…
The radiative thermal neutron capture cross sections over the range of thermal energies from 1 keV to 1 MeV are studied in statistical Hauser-Feshbach formalism. The optical model potential is constructed by folding the density dependent M3Y nucleon-nucleon interaction with radial matter densities of target nuclei obtained from relativistic-mean-field (RMF) theory. The standard nuclear reaction code TALYS1.8 is used for calculation of cross sections. The nuclei studied in the present work reside near the $Z=28$ proton shell closure and are of astrophysical interests taking part in p-, s-, and …
Calculating microscopic optical potentials for elastic nucleon-nucleus scattering has already led to large body of work in the past. For folding first-order calculations the nucleon-nucleon (NN) interaction and the one-body density of the nucleus were taken as input to rigorous calculations in a spectator expansion of the multiple scattering series. Based on the Watson expansion of the multiple scattering series we employ a nonlocal translationally invariant nuclear density derived from a chiral next-to-next-to-leading order (NNLO) and the very same interaction for consistent full-folding calc…
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…
A generalized optical potential for elastic scattering induced by light nuclei is calculated within the Feshbach projection operator method. The model explicitly takes into account the contribution of the projectile break-up continuum treated within a microscopic few-cluster model. In this work we formulate the model, deriving an explicit expression for the optical potential, and show ability of the model applying it to deuteron elastic scattering.
Cross sections for $^{40}$Ca + $α$ at low energies have been calculated from two different models and three different $α$-nucleus potentials. The first model determines the cross sections from the barrier transmission in a real nuclear potential. Second, cross sections are derived within the optical model using a complex nuclear potential. The excitation functions from barrier transmission are smooth whereas the excitation functions from the optical model show a significant sensitivity to the chosen imaginary potential. Cross sections far below the Coulomb barrier are lower from barrier transm…
We present a reliable double-folding (DF) model for $^{4}$He-nucleus scattering, using the Melbourne $g$-matrix nucleon-nucleon interaction that explains nucleon-nucleus scattering with no adjustable parameter. In the DF model, only the target density is taken as the local density in the Melbourne $g$-matrix. For $^{4}$He elastic scattering from $^{58}$Ni and $^{208}$Pb targets in a wide range of incident energies from 20~MeV/nucleon to 200~MeV/nucleon, the DF model with the target-density approximation (TDA) yields much better agreement with the experimental data than the usual DF model with …
Differential cross sections of ($p,n$) and ($^3$He,$t$) charge-exchange reactions leading to the excitation of the isobaric analog state (IAS) of the target nucleus are calculated with the distorted wave Born approximation. The $G$-matrix double-folding method is employed to determine the nucleus-nucleus optical potential within the framework of the Lane model. $G$-matrices are obtained from a Brueckner-Hartree-Fock calculation using the Argonne Av18 nucleon-nucleon potential. Target densities have been taken from Skyrme-Hartree-Fock calculations which predict values for the neutron skin thick…
We propose a practical folding model to describe $^{3}$He elastic scattering. In the model, $^{3}$He optical potentials are constructed by making the folding procedure twice. First the nucleon-target potential is evaluated by folding the Melbourne $g$-matrix with the target density and localizing the nonlocal folding potential with the Brieva--Rook method, and second the resulting local nucleon-target potential is folded with the $^{3}$He density. This double single-folding model well describes $^{3}$He elastic scattering from $^{58}$Ni and $^{208}$Pb targets in a wide incident-energy range fr…
Theoretical description of reactions in general, and the theory for $(d,p)$ reactions, in particular, needs to advance into the new century. 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 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 Coul…
An approach is outline to constructing an optical potential that includes the effects of antisymmetry and target recoil. it is based on the retarded Green's function, which could make it a better starting point for applications to direct nuclear reactions, particularly when extended to coupled channels. Its form retains a simple connection to folding potentials, even in the presence of three-body forces.
