Methods of analysis of nucleon-nucleus scattering data have progressed markedly over the past 50 years, yet many analyses of scattering data still use prescriptions specified at various stages of that progress. But the assumptions made or inherent in those analyses are poorly justified and most are no longer necessary to facilitate evaluations. We investigate some of those assumptions and highlight deficiencies and the uncertainties they may make in data analyses.
We use a Glauber-like approach to describe very energetic nucleus-nucleus collisions as a sequence of binary nucleon-nucleon collisions. No free parameters are needed: all the information comes from simple parametrizations of nucleon-nucleon collision data. Produced mesons are assumed not to interact with each other or with the original baryons. Comparisons are made to published experimental measurements of baryon rapidity and transverse momentum distributions, negative hadron rapidity and transverse momentum distributions, average multiplicities of pions, kaons, hyperons, and antihyperons, an…
The collision smearing of the nucleon momenta about their initial values during relativistic nucleus-nucleus collisions is investigated. To a certain degree, our model belongs to the transport type, and we investigate the evolution of the nucleon system created at a nucleus-nucleus collision. However, we parameterize this development by the number of collisions of every particle during evolution rather than by the time variable. It is assumed that the group of nucleons which leave the system after the same number of collisions can be joined in a particular statistical ensemble. The nucleon non…
We propose a mechanism of thermalization of nucleons in relativistic nucleus-nucleus collisions. Our model belongs, to a certain degree, to the transport ones; we consider the evolution of the system, but we parametrize this development by the number of collisions of every particle in the system rather than by the time variable. We based on the assumption that the nucleon momentum transfer after several nucleon-nucleon (-hadron) collisions becomes a random quantity driven by a proper distribution.
Charmonium productions in $p-p$ and $A-B$ collisions have been estimated within the ambit of colour evaporation model (CEM). The model parameters have been fixed by fitting the theoretical results with CDF data. The method is then applied to RHIC and LHC energies to obtain the transverse momentum distributions of $J/ψ$, $ψ^{\prime}$ and $χ_c$. Suppression due to Debye screening in a quark gluon plasma (QGP) is estimated at various centrality cuts. The final $p_T$ distributions of various resonances are then predicted convoluting with the survival probability.
The cross sections for producing K$^-$ mesons in nucleon-hyperon elementary processes are estimated assuming one-pion exchange and using the experimentally known pion-hyperon cross sections. The results are implemented in a transport model which is applied to calculation of proton-nucleus collisions. In significant difference to earlier estimates for heavy-ion collisions the inclusion of the nucleon-hyperon cross section roughly doubles the K$^-$ production in near-threshold proton-nucleus collisions.
Contains the conclusions and recommendations from this meeting regarding future experimental and theoretical work on the medium-energy nucleon-nucleus optical model.
Two causes of non-locality inherent in nucleon-nucleus scattering are considered. They are the results of two-nucleon antisymmetry of the projectile with each nucleon in the nucleus and the dynamic polarization potential representation of channel coupling. For energies $\sim 40 - 300$ MeV, a g-folding model of the optical potential is used to show the influence of the knock-out process that is a result of the two-nucleon antisymmetry. To explore the dynamic polarization potential caused by channel coupling, a multichannel algebraic scattering model has been used for low-energy scattering.
We investigate the effects of chiral NNLO three-nucleon force (3NF) on nucleus-nucleus elastic scattering, using a standard prescription based on the Brueckner-Hartree-Fock method and the g-matrix folding model. The g-matrix calculated in nuclear matter from the chiral N3LO two-nucleon forces (2NF) is close to that from the Bonn-B 2NF. Because the Melbourne group have already developed a practical g-matrix interaction by localizing the nonlocal g-matrix calculated from the Bonn-B 2NF, we consider the effects of chiral 3NF, in this first attempt to study the 3NF effects, by modifying the local …
The role played by nucleon-nucleon short-range correlations in photon- and electron-nucleus reactions is analyzed with a model which includes all the diagrams containing a single correlation function. The excitation of low-lying high-spin states, the reactions (e,e'), (e,e'N) and ($γ$,N) and the two-proton emission by both electrons and real photons are investigated. The results obtained for doubly-closed shell nuclei show that ($γ$,pp) appears to be the most adequate process to identify short-range correlations in the clearer way.
An exact determination of the size of the pseudospin symmetry violating part of the nucleon-nucleus scattering amplitude from scattering observables is presented. The approximation recently used by Ginocchio turns out to underestimate the violation of pseudospin symmetry. Nevertheless the conclusion of a modestly broken pseudospin symmetry in proton-208Pb scattering at EL=800MeV remains valid.
The nonlocality of the microscopic nucleon-nucleus optical potential is commonly localized by the Brieva-Rook approximation. The validity of the localization is tested for the proton+$^{90}$Zr scattering at the incident energies from 65 MeV to 800 MeV. The localization is valid in the wide incident-energy range.
A previous model on inclusive charged-current quasi-elastic nuclear reactions is extended to include neutral- and charged-current nucleon emission reactions. The problem of outgoing nucleon propagation is treated by means of a Monte Carlo simulation.
The sensitivity of nucleon-nucleus elastic scattering observables to the off-shell structure of nucleon-nucleon t-matrices, derived from realistic NN potentials, is investigated within the context of a full-folding model based on the impulse approximation. Our study uses recently developed NN potential models, which describe a subset of the NN data base with a $χ^2$ per datum $\sim$1, which means that the NN t-matrices are essentially on-shell equivalent. We calculate proton-nucleus elastic scattering observables for $^{16}$O, $^{40}$Ca, and $^{208}$Pb between 100 and 200 MeV laboratory energy…
Nucleon total reaction and neutron total cross sections to 300 MeV for 12C and 208Pb, and for 65 MeV spanning the mass range, are predicted using coordinate space optical potentials formed by full folding of effective nucleon-nucleon interactions with realistic nuclear ground state densities. Good to excellent agreement is found with existing data.
The intranuclear cascade model overestimates the multiplicity of produced mesons in nucleus-nucleus interactions without taking into account meson and baryon resonance production. Inclusion of the resonances leads to decreasing multiplicity of mesons, neutrons and protons. In order to overcome the problem, it is proposed to use the FRITIOF model adapted to low energies in a combination with the reggeon theory inspired model of nuclear destruction. It is shown that the combination allows one to reproduce satisfactory the meson and baryon yields in the nucleus-nucleus collisions at the energy of…
Within the key issues of hadronic physics one of the interesting issues in nuclear physics is whether there is a transition region between meson-nucleon and quark-gluon degrees of freedom in the NN interaction. This question is relevant for pairs of free nucleons as well as for nucleon pairs immersed in nuclear matter. From NN phase shifts we deduce a dibaryonic scale of 1 GeV for the soft core NN potential strengths at nucleon separation r equal 0.25 to 0.5 fm. A short range intermediate transition, with fusion and fission of the two scattered nucleons into a dibaryon with prevailing quark-gl…
In a recent paper [Phys.\ Rev.\ C{\bf 49}, 2142 (1994)], Haberzettl presented cluster N-body equations for arbitrarily large systems of nucleons and mesons. Application to the three-nucleon system is claimed to yield a new kind of three-nucleon force. We demonstrate that these three-nucleon equations contain double counting.
We analyze $^{16}$O-$^{16}$O and $^{12}$C-$^{12}$C scattering with the microscopic coupled-channels method and investigate the coupled-channels and three-nucleon-force (3NF) effects on elastic and inelastic cross sections. In the microscopic coupled-channels calculation, the Melbourne g-matrix interaction modified according to the chiral 3NF effects is used. It is found that the coupled-channels and 3NF effects additively change both the elastic and inelastic cross sections. As a result, the coupled-channels calculation including the 3NF effects significantly improves the agreement between the…
The sensitivity of nucleon-nucleus elastic scattering to the off-shell behavior of realistic nucleon-nucleon interactions is investigated when on-shell equivalent nucleon-nucleon potentials are used. The study is based on applications of the full-folding optical model potential for an explicit treatment of the off-shell behavior of the nucleon-nucleon effective interaction. Applications were made at beam energies between 40 and 500 MeV for proton scattering from 40Ca and 208Pb. We use the momentum-dependent Paris potential and its local on-shell equivalent as obtained with the Gelfand-Levitan …
We investigate the roles of chiral three-nucleon force (3NF) in nucleon-nucleus elastic scattering, using the standard framework based on the Brueckner-Hartree-Fock method for nuclear matter and the $g$-matrix folding model for the nucleon-nucleus scattering. In nuclear matter, chiral 3NF at NNLO level (mainly the 2$π$-exchange diagram) makes the single particle potential less attractive for the singlet-even channel and more absorptive for the triplet channels. The single-particle potential calculated from chiral two-nucleon force (2NF) at N$^{3}$LO level is found to be close to that from Bonn…
The theory of the elastic scattering of a nucleon from a nucleus is presented in the form of a Spectator Expansion of the optical potential. Particular attention is paid to the treatment of the free projectile$\,-\,$nucleus propagator when the coupling of the struck target nucleon to the residual target must be taken into consideration. First order calculations within this framework are shown for neutron total cross-sections and for proton scattering for a number of target nuclides at a variety of energies. The calculated values of these observables are in very good agreement with measurement.
Experimental values of Coulomb sums for q > 2 fm^(-1) are considered. Assuming that a part of nucleons is modified in the nucleus, an approach is offered, in the framework of which the calculation is in agreement with the experimental data. It gives the nuclear matter density value, above which the nucleon changes its properties. The radius of a modified proton is estimated, the possibilities for a further investigation into its properties are discussed.
The role of the nucleon recoil corrections in low--energy meson--nucleus interactions is examined. We demonstrate explicitly when calculations within the static approximation are justified and when the recoil terms need to be kept explictly in the propagators, depending on whether the S-wave two--nucleon intermediate state is Pauli blocked or not, while the meson is in flight. While the effect is studied in detail for $πd$ scattering only, a large class of other reactions is discussed for which the findings are relevant as well.
By introducing a mass asymmetry in a non-Borromean three-body system, without changing the energy relations, the virtual state pole cannot move from the negative real axis of the complex energy plane (with nonzero width) and become a resonance, because the analytical structure of the unitarity cuts remains the same.
A new development in the antisymmetrization of the first-order nucleon-nucleus elastic microscopic optical potential is presented which systematically includes the many-body character of the nucleus within the two-body scattering operators. The results reduce the overall strength of the nucleon-nucleus potential and require the inclusion of historically excluded channels from the nucleon-nucleon potential input. Calculations produced improve the match with neutron-nucleus total cross section, elastic proton-nucleus differential cross section, and spin observable data. A comparison is also done…
We have analyzed the consequences of introducing the local density approximation combined with an effective nuclear momentum-dependent potential into the CC quasi-elastic neutrino-nucleus scattering. We note that the distribution of the recoil nucleons momenta becomes smooth for low momentum values and the sharp threshold is removed. Our results may be relevant for Sci-Fi detector analysis of K2K experiments. The total amount of observed recoil protons is reduced because some of them remain bound inside the nucleus. We compare theoretical predictions for a probability of such events with the r…
Authors of Phys. Rev. C 60, 062201 (1999) presented a calculation of the electromagnetic form factors of the nucleon using a diquark ansatz in the relativistic three-quark Faddeev equations. In this Comment it is pointed out that the calculations of these form factors stem from a three-quark bound state current that contains overcounted contributions. The corrected expression for the three-quark bound state current is derived.
Detailed comparisons are made between results of calculations for intermediate energy nucleon--208Pb scattering using optical potentials obtained from Dirac phenomenology and a microscopic Schrodinger model. The two approaches yield quite similar results for all of the observables with each projectile, including spin observables, suggesting the two models are physically equivalent. A new phenomenon in the analyzing power is confirmed in the results for 100 MeV scattering.
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…
Self-consistent single-nucleon potential at positive energy produced by semi-realistic interaction and its examination via nucleon-nucleus elastic scattering
The structure function of the nucleus in the cumulative region $x>1$ is studied in terms of nucleon degrees of freedom. At high $Q^2$ the resulting expressions are presented as a sum of contributions from few-nucleon correlations. Two-nucleon correlations are studied in some detail. Spin variables are averaged out. In the region $1<x<2$ the structure functions are calculated for the relativistic interaction proposed by F.Gross {\it et al}. They are found to fall with $x$ faster than the exponential. For Carbon at $x=1.05$, where the method is not rigorously applicable, they turn out to be roug…
The partition function of nonequilibrium distribution which we recently obtained [arXiv:0802.0259] in the framework of the maximum isotropization model (MIM) is exploited to extract physical information from experimental data on the proton rapidity and transverse mass distributions. We propose to partition all interacting nucleons into ensembles in accordance with the number of collisions. We analyze experimental rapidity distribution and get the number of particles in every collision ensemble. We argue that even a large number of effective nucleon collisions cannot lead to thermalization of n…
The criticisms in manuscript arXiv:0803.4371 do not change the renormalization group equation for the "$\vlowk$" interaction nor do they affect any results in the literature. Several other potentially misleading statements about low-momentum interactions are also addressed.
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…
We develop for the first time a microscopic global nucleon-nucleus optical potential with quantified uncertainties suitable for analyzing nuclear reaction experiments at next-generation rare-isotope beam facilities. Within the improved local density approximation and without any adjustable parameters, we begin by computing proton-nucleus and neutron-nucleus optical potentials from a set of five nuclear forces from chiral effective field theory for 1800 target nuclei in the mass range 12 $\leq$ A $\leq$ 242 for energies between 0 MeV $<$ E $\lesssim$ 150 MeV. We then parameterize a global optic…
We study elastic proton-nucleus scattering at intermediate energies. The nucleon-nucleus optical potential is derived from the Bonn nucleon-nucleon potential and the Dirac-Brueckner approach for nuclear matter. Our calculations, which do not contain any adjustable parameters, yield good agreement with experiment.
This paper presents reaction cross section predictions. These predictions are the result of a continuous pipeline which originates from a microscopic nuclear interaction. Density parameters and effective nucleon-nucleon cross sections (both involved in the reaction calculations) are by-products of the same equation of state. First, we perform tests of sensitivity to medium effects using reactions involving 208-Pb, a stable but weakly isospin-asymmetric nucleus. We also show predictions for collisions of some neutron-rich isotopes of Calcium and Argon. We observe significant sensitivity of the …
Background: Effective interactions for elastic nucleon-nucleus scattering from first principles require the use of the same nucleon-nucleon interaction in the structure and reaction calculations, as well as a consistent treatment of the relevant operators at each order. Purpose: Previous work using these interactions has shown good agreement with available data. Here, we study the physical relevance of one of these operators, which involves the spin of the struck nucleon, and examine the interpretation of this quantity in a nuclear structure context. Methods: Using the framework of the spectat…
The extent to which information about fluctuations in hadron-nucleon total cross sections in the frozen approximation can be extracted from very high energy hadron-nucleus total cross section measurements for a range of heavy nuclei is discussed. The corrections to the predictions of Glauber theory due to these fluctuations are calculated for several models for the distribution functions, and differences of the order of 50 mb are found for heavy nuclei. The generating function for the moments of the hadron-nucleon cross section distributions can be approximately determined from the derivatives…
Shell model wave functions have been used to form microscopic g-folding optical potentials with which elastic scattering data from 8He, 10,11C, and 18,20,22O scattering on hydrogen has been analyzed. Those potentials, the effective two-nucleon interaction used in their formation, and the shell model details, then have been used in distorted wave approximation calculations of differential cross sections from inelastic scattering to the first excited states of five of those radioactive ions.
This paper deals with the possible motion of nucleons in the nucleus, which is due to realistic inter-nucleonic forces. This approach provides new or more substantiated conclusions about the nuclear structure than those based on the effective interaction of nucleons, while the shell model of the nucleus may lead to questionable conclusions regarding the nuclear structure and nuclear reaction mechanisms.
The total neutron-Nucleus cross section has been calculated within an approach which takes into account nucleon-nucleon correlations, Glauber multiple scattering and inelastic shadowing corrections. Nuclear targets ranging from 4He to 208Pb and neutron incident momentum ranging from 3 to 300 GeV/c, have been considered. Correlations have been introduced by two different approaches leading to the same results. The commonly used approximation, consisting in treating nuclear effects only by a product of one-body densities, is carefully analyzed and it is shown that the effects of realistic correl…
Microscopic optical potentials for nucleon-nucleus (NA) scattering obtained from the full folding of the effective g matrices, solutions of the Bruckner-Bethe-Goldstone equation, with the densities of the target, are applied to the case of neutron-nucleus scattering. Given that the optical potentials are specified in all two-body angular momentum, spin and isospin channels available to the NA scattering, the only difference in this model description of proton and neutron scattering observables for a given nucleus is in the inclusion of the Coulomb interaction. A priori microscopic optical mode…
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…
Total cross sections for neutron scattering with energies between 10 and 600 MeV and from nine nuclei spanning the mass range from 6Li to 238U have been analyzed using a simple function of three parameters. The values of those parameters with which neutron total cross section data are replicated vary smoothly with energy and target mass and may themselves be represented by functions of energy and mass.
A model of a fluid of skyrmions coupled to a scalar and to the $ø$ meson mean fields is developed. The central and spin-orbit potentials of a skyrmion generated by the fields predict correct energy levels in selected closed shell nuclei. The effect of the meson fields on the properties of skyrmions in nuclei is investigated.
Quantum Hadrodynamics in mean field approximation describes the effective nucleon-nucleus potential (about -50 MeV deep) as resulting from a strong repulsive vector (about 400 MeV) and a strong attractive scalar (about -450 MeV) contribution. This scalar-vector Lorentz structure implies a significant lowering of the threshold for $p\bar{p}$ photoproduction on a nucleus by about 850 MeV as compared to the free case since charge conjugation reverses the sign of the vector potential contribution in the equation of motion for the $\bar{p}$ states. It also implies a certain size of the photon induc…
Comparisons are made between results of calculations for intermediate energy nucleon-nucleus scattering for 12C, 16O, 40Ca, 90Zr, and 208Pb, using optical potentials obtained from global Dirac phenomenology and from a microscopic Schrödinger model. Differential cross sections and spin observables for scattering from the set of five nuclei at 65 MeV and 200 MeV have been studied to assess the relative merits of each approach. Total reaction cross sections from proton-nucleus and total cross sections from neutron-nucleus scattering have been evaluated and compared with data for those five target…
The optical model potentials for nucleon-nucleus elastic scattering at $65$~MeV are calculated for $^{12}$C, $^{16}$O, $^{28}$Si, $^{40}$Ca, $^{56}$Fe, $^{90}$Zr and $^{208}$Pb in first order multiple scattering theory, following the prescription of the spectator expansion, where the only inputs are the free NN potentials, the nuclear densities and the nuclear mean field as derived from microscopic nuclear structure calculations. These potentials are used to predict differential cross sections, analyzing powers and spin rotation functions for neutron and proton scattering at 65 MeV projectile …
The influence of the underlying nucleon-nucleon collision geometry on evaluations of the nuclear overlap function ($T_{AB}$) and number of binary collisions ($N_{coll}$) is studied. A narrowing of the spatial distribution of the hard-partons with large light-cone fraction $x$ in nucleons leads to a downward correction for $N_{coll}$ and $T_{AB}$, which in turn, results in an upward correction for the nuclear modification factor $R_{AB}$. The size of this correction is estimated for several experimentally motivated nucleon-nucleon overlap functions for hard-partons. It is found to be significan…
We have used the event generator LUCIAE to analyse NA35 data of the $\bar p$ and $\barΛ$ yields, the ratio $\barΛ/\bar p$, and the transverse mass distributions of $\bar p$ and $\barΛ$ in pp and central sulphur-nucleus collisions at 200A GeV. The NA35 data could be reproduced reasonably if one assumes that the s quark pair suppression factor and concerns in nucleus-nucleus collisions are larger than the nucleon-nucleon collision. It seems to indicate that NA35 data might imply the reduction of strangeness suppression in ultrarelativistic nucleus-nucleus collisions comparing to the nucleon-nucl…
The experimental discovery that the nucleus is approximately transparent to low energy pions is reviewed. The consequences of this for nuclear deep inelastic scattering and Drell-Yan interactions are discussed. I argue that low energy nucleus data imply that there is little nuclear enhancement of the pion cloud of a nucleon, and try to interpret this in terms of nucleon-nucleon correlations.
Basing on the thickness (profile) function, previously obtained for the realistic Fermi type distribution of nucleons in nuclei, calculations are made of the microscopic eikonal phases of the nucleus-nucleus scattering and the total reaction cross- sections. In so doing, the phase is deduced to the one-dimensional integral provided that the Gaussian density distribution for the projectile nucleus and an arbitrary shape of the thickness density for the target nucleus are used. The problems of obtaining parameters of the "point" nucleon density are considered. A possibility of approximating the …
Feshbach's projection formalism in the particle-hole model space leads to a microscopic description of scattering in terms of the many-body self-energy. To investigate the feasibility of this approach, an optical potential for O-16 is constructed starting from two previous calculations of the self-energy for this nucleus. The results reproduce the background phase shifts for positive parity waves and the resonances beyond the mean field. The latter can be computed microscopically for energies of astrophysical interest using Green's function theory.
The Microscopic Otical Model Potential is evaluated within a relativistic scheme which provides a natural and consistent relation between the spin-orbit part and the central part of the potential. The Dirac-Brueckner-Hartree-Fock (DBHF) approach provides such a microscopic relativistic scheme, which is based on a realistic nucleon-nucleon interaction and reproduce the saturation properties of symmetric nuclear matter without any adjustable parameter. Its solution using the projection technique within the subtracted T-matrix (STM) representation provides a reliable extension to asymmetric nucle…
We study the efficacy of a new ab initio framework that combines the symmetry-adapted (SA) no-core shell-model approach with the resonating group method (RGM) for unified descriptions of nuclear structure and reactions. We obtain ab initio neutron-nucleus interactions for $^4$He, $^{16}$O, and $^{20}$Ne targets, starting with realistic nucleon-nucleon potentials. We discuss the effect of increasing model space sizes and symmetry-based selections on the SA-RGM norm and direct potential kernels, as well as on phase shifts, which are the input to calculations of cross sections. We demonstrate the…
