Realistic NN Potentials Research Articles

Spin correlation coefficients in lepton–deuteron elastic scattering and their sensitivity to realistic NN potentials

Spin correlation coefficients in the elastic scattering of leptons on the deuteron, [Formula: see text], are studied in the one-photon-exchange approximation within the limit of zero lepton mass. Numerical estimations for the spin correlation coefficients caused by a polarized beam and a vector polarized target are given. The estimated spin correlation coefficients are analyzed at various values of beam energy and scattering angle. The sensitivity of the obtained results to the choice of realistic NN potential used for the deuteron wave function is investigated. We found a considerable dependence of the results on the realistic deuteron wave functions at incident beam energies greater than 0.4 GeV and backward scattering angles. The estimated results are of particular interest for encouragement of experimental measurements of lepton–deuteron scattering which aim for accurate calculation of the charge radius of the proton to a high degree of precision. These results may also stimulate new generation of measurements of different physical observables very sensitive to the spin structure of the nucleon and light nuclei.

Polarization observables in elastic lepton-deuteron scattering and their sensitivity to realistic NN potentials

Polarization effects in the elastic lepton scattering on the deuteron process are studied in the one-photon-exchange Born approximation within the limit of zero mass of the lepton. Numerical estimations for the spin asymmetries with an unpolarized lepton beam and a tensor polarized target are given. The estimated results are analysed at various lepton beam energies and scattering angles. For the first time, the sensitivity of the results for tensor spin asymmetries to the choice of modern NN potential used for the deuteron wave function (DWF) is investigated. A considerable influence of the results on the realistic and modern DWFs at incident beam energies greater than 0.6 GeV and scattering angles greater than 30 is obtained.

Beam-target double spin asymmetries in the reaction γd → π0d near threshold and the role of D-wave component of the deuteron wave function

We investigate coherent π0-photoproduction on the deuteron near threshold with special emphasis on beam-target double spin asymmetries. We present results for the spin asymmetries $T^{c}_{1M}$ (M = 0, 1) for circular polarized photons and vector polarized deuterons, $T^{c}_{2M}$ (M = 1, 2) for circular polarized photons and tensor polarized deuterons, $T^{l}_{1M}$ (M = 0, ± 1) for longitudinal polarized photons and vector polarized deuterons, and $T^{l}_{2M}$ (M = 0, ± 1, ± 2) for longitudinal polarized photons and tensor polarized deuterons in the γd → π0d reaction near threshold. We also discuss the sensitivity of the estimated results to the D-wave component of the deuteron wave function. The unitary isobar MAID-2007 model is used for the elementary γN → πN amplitude. This model is parameterized in terms of invariant amplitudes and allows one to give a more reliable description of the threshold region. The realistic and high-precision Bonn NN potential (full model) is used for the deuteron wave function. We have found that the D-wave component of the deuteron wave function has a little effect on the $T^{c}_{1M}$ (M = 0, 1) and $T^{l}_{2M}$ (M = 0, 1, 2) spin asymmetries. On the contrary, we have obtained a significant role of the D-wave component on the spin asymmetries $T^{c}_{2M}$ (M = 1, 2), $T^{l}_{1M}$ (M = 0, ± 1), and $T^{l}_{2M}$ (M = − 1,− 2).

Coherent π0-Photoproduction on the Deuteron near Threshold and the Role of D-Wave Component of the Deuteron Wave Function

Near-threshold coherent photoproduction of π0-meson on the deuteron is investigated. Numerical results for the unpolarized differential and total cross sections, the linear photon Σ-asymmetry, the vector T11 and tensor T2M (M = 0, 1, 2) deuteron spin asymmetries, and the spin asymmetry $$\tilde{T}_{20}$$ of the total cross section are presented. The role of D-wave component of the deuteron wave function on these physical observables is studied. The calculations are based on the impulse approximation in which we use the realistic and high-precision Bonn NN potential (full model) for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary γN → πN amplitude that describes well the threshold region. We have found that the D-wave component has a negligible effect on the unpolarized cross sections and the vector deuteron T11-asymmetry at photon lab-energies close to threshold. On the contrary, we have obtained a significant role of the D-wave part of the deuteron wave function on the Σ, T2M, and $$\tilde{T}_{20}$$ spin asymmetries. The results for the unpolarized differential cross section are compared to the experimental data from TAPS and a satisfactory agreement within the uncertainties has been obtained at forward pion angles. At backward pion angles, our results underestimate the experimental data and a disagreement has been found.

Neutron–19C scattering: Towards including realistic interactions

Low-energy neutron–C19 scattering is studied in the three-body n+n+C18 model using a realistic nn potential and a number of shallow and deep n–C18 potentials, the latter supporting deeply-bound Pauli-forbidden states that are projected out. Exact Faddeev-type three-body scattering equations for transition operators including two- and three-body forces are solved in the momentum-space partial-wave framework. Phase shift, inelasticity parameter, and cross sections are calculated. For the elastic n–C19 scattering in the JΠ=0+ partial wave the signatures of the Efimov physics, i.e., the pole in the effective-range expansion and the elastic cross section minimum, are confirmed for both shallow and deep models, but with clear quantitative differences between them, indicating the importance of a proper treatment of deeply-bound Pauli-forbidden states. In contrast, the inelasticity parameter is mostly correlated with the asymptotic normalization coefficient of the C19 bound state. Finally, in the regime of very weak C19 binding and near-threshold (bound or virtual) excited C20 state the standard Efimovian behaviour of the n–C19 scattering length and cross section was confirmed, resolving the discrepancies between earlier studies by other authors (Mazumdar et al., 2006 [20], Yamashita et al., 2007 [23]).

Exchange Effects in the Radiative Capture Reactions3H(α, γ)7Li and3He(α, γ)7Be

The mirror 3 H(α, γ) 7 Li and 3 He(α, γ) 7 Be reactions have been considered using the algebraic versions of the resonating group model and of the orthogonality conditions model. Exchange effects in interaction of the colliding nuclei and influence of the corresponding exchange terms in matrix elements of the interaction potential on calculated astrophysical S-factors for the reactions have been studied. At the present time one of the most important aims of nuclear reaction theory is to build so called ab initio approaches to description of nuclear reactions, which use realistic NN-potentials and exactly account for all exchange effects caused by the antisymmetry of a wave function of nuclear system. Such approaches are in continuous progress but, nevertheless, turn out to be very complicated procedures, which are, in fact, unrealizable for sufficiently heavy colliding nuclei. Though, there are alternative approaches suitable for heavier systems. They are based on the resonating group model (RGM) [1] or its algebraic version (AVRGM) [2] with effective NN-potentials and, as above mentioned approaches, rigorously allow for the exchange effects. However, complexities rapidly grow even in such approaches at increasing system mass. Thus, a development of reliable approximations within the existing microscopic approaches is rather topical problem of nuclear reaction theory. Such approximations will allow to simplify the calculations significantly and even to make ones realizable for sufficiently complicated systems.

A Λnnthree-body resonance

We solved the Faddeev equations in the Λ nn system J π = ½ + , T = 1). There is no bound state but found a resonance state. Complex Energy Method helps to find the location of the resonance energy in the complex Riemann sheet. We obtained a resonance energy E = 0.25 − 0.40 i MeV using the realistic NN and YN Nijmegen potential. As a preliminary result the recent Nijmegen YN potential (NSC97f) gives 0.60± 0.05 - (0.25 ± 0.05) i MeV. We discuss importance of an irreducible three-body force to make it bound.

Conventional BCS, unconventional BCS, and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.

Investigation of the structure of the few body kaonic nuclei using the method of hyperspherical functions in momentum space

The kaonic clusters KNN and KNNN are studied within the method of hyperspherical functions in the momentum representation. Binding energies and widths of three- and four-body nuclear quasibound states are calculated by employing realistic NN potentials and the energy dependent chiral KN interaction, as well as a phenomenological KN potential. The comparison of the results of calculations obtained in the framework of the variational method, Faddeev, Faddeev-Yakubovsky equations, and method of hyperspherical functions in configuration space are discussed.

Realistic calculations of [formula omitted], [formula omitted], and [formula omitted] quasibound states

Binding energies and widths of three-body K¯NN, and of four-body K¯NNN and K¯K¯NN nuclear quasibound states are calculated in the hyperspherical basis, using realistic NN potentials and subthreshold energy dependent chiral K¯N interactions. Results of previous K−pp calculations are reproduced and an upper bound is placed on the binding energy of a K−d quasibound state. A self-consistent handling of energy dependence is found to restrain binding, keeping the calculated four-body ground-state binding energies to relatively low values of about 30 MeV. The lightest strangeness −2 particle-stable K¯ nuclear cluster is most probably K¯K¯NN. The calculated K¯N→πY conversion widths range from approximately 30 MeV for the K¯NNN ground state to approximately 80 MeV for the K¯K¯NN ground state.

Calculations of the Triton Binding Energy with a Lorentz Boosted Nucleon-Nucleon Potential

We study the binding energy of the three-nucleon system in relativistic models that use two different relativistic treatments of the potential that are phase equivalent to realistic NN interactions. One is based on a unitary scale transformation that relates the non-relativistic center-of-mass Hamiltonian to the relativistic mass (rest energy) operator and the other uses a non-linear equation that relates the interaction in the relativistic mass operator to the non-relativistic interaction. In both cases Lorentz-boosted interactions are used in the relativistic Faddeev equation to solve for the three-nucleon binding energy. Using the same realistic NN potentials as input, the solution of the relativistic three-nucleon Faddeev equation for 3 H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.

Microscopic calculations of reaction cross sections for pA elastic scattering from stable and unstable nuclei

Parameter-free optical model potential results for reaction cross sections of proton elastic scattering are presented. The applications cover the 10-1000 MeV energy range and consider both stable and unstable nuclei. The study is based on in-medium g-matrix full-folding optical model approach with the appropriate relativistic kinematic corrections needed for the higher energy applications. The effective interactions are based on realistic NN potentials supplemented with a separable non-Hermitian term to allow optimum agreement with current NN phase-shift analyzes, particularly the inelasticities above pion threshold. The target ground-state densities are obtained from Hartree-Fock-Bogoliubov calculations based on the finite range, density dependent Gogny force. Reaction cross sections are evaluated for proton scattering from various stable and unstable even-even nuclei. The results are compared with measurements and their systematics is analyzed.

THE ppK− SYSTEM STUDIED WITH A CHIRAL SU(3) BASED $\bar{K}N$ POTENTIAL

We have investigated the prototype of [Formula: see text]-nuclear systems, ppK−, with a realistic NN potential and effective local [Formula: see text] potentials based on chiral SU (3) dynamics. Including estimates of theoretical uncertainties, we find that ppK− is not deeply bound, with a total binding energy = 19 ± 3 MeV and mesonic decay width between about 40 and 70 MeV. The [Formula: see text] component in the ppK− compound is of a similar structure as the [Formula: see text] two-body quasibound state embedded in the πΣ continuum.

Reaction cross sections for proton scattering from stable and unstable nuclei based on a microscopic approach

Reaction cross sections for proton-nucleus elastic scattering are investigated within a nonrelativistic microscopic approach for the nucleon-nucleus optical model potential. Applications were made for nucleon energy ranging between 10 MeV and 1 GeV, considering both stable and unstable target nuclei. The study is based on an in-medium g-matrix folding optical model approach in momentum space, with the appropriate relativistic kinematic corrections needed for the higher energy applications. The effective interactions are based on realistic NN potentials supplemented with a separable non-Hermitian term to allow optimum agreement with current NN phase-shift analyses, particularly the inelasticities above pion production threshold. The target ground-state densities are obtained from Hartree-Fock-Bogoliubov calculations based on the finite range, density-dependent Gogny force. The evaluated reaction cross sections for proton scattering are compared with measurements and their systematics is analyzed. A simple function of the total cross sections in terms of the atomic mass number is observed at high energies. At low energies, however, discrepancies with the available data are observed, being more pronounced in the lighter systems.

Nonlocal nucleon-nucleon interaction JISP

The J-matrix inverse scattering formalism is described and a new type of nucleon-nucleon interaction JISP is constructed within its framework. Interaction for each partial NN scattering is represented by a small matrix in the oscillator basis, which allows its direct use in multiparticle shell-model calculations and in calculations within the resonating group approximation. The JISP reproduces np scattering data and deuteron characteristics with an accuracy of modern realistic NN potentials (x2/datum = 1.05). The generalization of this interaction which takes into account violation of charge independence of nucleon-nucleon forces is proposed and pp scattering phases calculated with this new charge-dependent interaction CD-JISP are discussed.

Nuclear Structure in the UCOM Framework: From Realistic Interactions to Collective Excitations

The Unitary Correlation Operator Method (UCOM) provides a means for nuclear structure calculations starting from realistic NN potentials. The dominant short-range central and tensor correlations are described explicitly by a unitary transformation. The application of UCOM in the context of the no-core shell model provides insight into the interplay between dominant short-range and residual long-range correlations in the nuclear many-body problem. The use of the correlated interaction within Hartree-Fock, many-body perturbation theory, and Random Phase Approximation gives access to various nuclear structure observables throughout the nuclear chart.

Quasi-particle interaction in nuclear matter from chiral pion–nucleon dynamics

Based on a recent chiral approach to nuclear matter we calculate the in-medium interaction of nucleons at the Fermi surface | p → 1 , 2 | = k f . The isotropic part of this quasi-particle interaction is characterized by four density-dependent (dimensionful) Fermi-liquid parameters: f 0 ( k f ) , f 0 ′ ( k f ) , g 0 ( k f ) and g 0 ′ ( k f ) . In the approximation to 1 π-exchange and iterated 1 π-exchange (which as such leads already to a good nuclear matter equation of state) we find a spin–isospin interaction strength of g 0 ′ ( 2 m π ) = 1.14 fm 2 , compatible with existing empirical values. The consistency relations to the nuclear matter compressibility K and the spin/isospin asymmetry energies serve as a check on our perturbative calculation. In the next step we include systematically the contributions from 2 π-exchange with virtual Δ ( 1232 ) -isobar excitation which have been found important for good single-particle properties and spin-stability of nuclear matter. Without any additional short-distance terms (contributing proportional to k f 2 ) the spin-dependent Fermi-liquid parameters g 0 ( k f 0 ) and g 0 ′ ( k f 0 ) come out far too large. Estimates of these short-distance parameters from realistic NN-potentials go in the right direction, but sizeable enhancement factors are still needed to reproduce the empirical values of g 0 ( k f 0 ) and g 0 ′ ( k f 0 ) . This points towards the importance of higher order iterations subsumed in the induced interaction. We consider also the tensor part of the quasi-nucleon interaction at the Fermi surface. In comparison to the leading 1 π-exchange tensor interaction we find from the 2 π-exchange corrections almost a doubling of the isoscalar tensor strength h 0 ( k f ) , whereas the isovector tensor strength h 0 ′ ( k f ) is much less affected. These features are not changed by the inclusion of the chiral πNΔ-dynamics. The l = 1 tensor Fermi-liquid parameters h 1 ( k f ) and h 1 ′ ( k f ) follow a similar pattern.

Spin-isospin stability of nuclear matter

We calculate the density-dependent spin-isospin asymmetry energy $J({k}_{f})$ of nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $J({k}_{f})$ originate from one-pion exchange, iterated one-pion exchange, and irreducible two-pion exchange with no, single, and double virtual \ensuremath{\Delta}-isobar excitation. We find that the approximation to $1\ensuremath{\pi}$-exchange and iterated $1\ensuremath{\pi}$-exchange terms (which leads already to a good nuclear matter equation of state by adjusting an emerging contact term) is spin-isospin stable, since $J({k}_{f0})\ensuremath{\simeq}24\phantom{\rule{0.3em}{0ex}}\mathrm{MeV}>0$. The inclusion of the chiral $\ensuremath{\pi}N\ensuremath{\Delta}$ dynamics, necessary in order to guarantee the spin stability of nuclear matter, keeps this property intact. The corresponding spin-isospin asymmetry energy $J({k}_{f})$ stays positive even for extreme values of an undetermined short-distance parameter ${J}_{5}$ (whose possible range we estimate from realistic NN potentials). The largest positive contribution to $J({k}_{f})$ (a term linear in density) comes from a two-body contact term with its strength fitted to the empirical nuclear matter saturation point.

Kirson-Babu-Brown core polarization diagrams and low-momentum shell model effective interactions

The Kirson-Babu-Brown (KBB) induced interaction approach is applied to the derivation of the sd-shell nucleon effective interactions. We start from a low-momentum NN interaction Vlow-k obtained by integrating out the high-momentum components of modern realistic NN potentials beyond a decimation momentum λ. Then a large class of core polarization diagrams are summed up to all orders by way of the KBB self-consistent equations. It is found that the solution of these equations is simplified by the use of Vlow-k, which is energy independent, and by treating them in terms of the Green's fuctions in the particle-particle and the particle-hole channels. The effective interactions calculated with the all-order KBB core polarizations and those with the polarization in second-order perturbation theory are found to be rather similar to each other, typical difference between them being less than 10%.

Spin-asymmetry energy of nuclear matter

We calculate the density-dependent spin-asymmetry energy $S(k_f)$ of isospin-symmetric nuclear matter in the three-loop approximation of chiral perturbation theory. The interaction contributions to $S(k_f)$ originate from one-pion exchange, iterated one-pion exchange, and (irreducible) two-pion exchange with no, single, and double virtual $\Delta$-isobar excitation. We find that the truncation to $1\pi$-exchange and iterated $1\pi$-exchange terms (which leads already to a good nuclear matter equation of state) is spin-unstable, since $S(k_{f0})<0$. The inclusion of the chiral $\pi N\Delta$-dynamics guarantees the spin-stability of nuclear matter. The corresponding spin-asymmetry energy $S(k_f)$ stays positive within a wide range of an undetermined short-range parameter $S_5$ (which we also estimate from realistic NN-potentials). Our results reemphasize the important role played by two-pion exchange with virtual $\Delta$-isobar excitation for the nuclear matter many-body problem. Its explicit inclusion is essential in order to obtain good bulk and single-particle properties.