Nijmegen Potentials Research Articles

Hartree-Fock Calculations of 12C Nucleus at Equilibrium and Under Static Compression

Abstract: The ground state features of the semi-doubly magic 12C nucleus (i.e. binding energy, nuclear radius, radial density distribution, and single particle energies) are estimated using ab initio calculations at equilibrium and under high static compression. Nijmegen and Reid soft-core (RSC) potentials are used as input nucleon-nucleon interactions. Within the framework of the constrained spherical Hartree-Fock approximations, we do the calculations in no-core shell-model space, which consists of six major oscillator shells (i.e. 21 single particle orbitals). The sensitivity of the ground state features of the 12C nucleus to the degree of compression and the sensitivity of the equation of state to the two potentials are investigated. We also discovered that the nuclear binding energy calculated using the Nijmegen potential is higher than that calculated using the RSC potential. When utilizing the Nijmegen potential, the curve reaches zero binding energy faster than when using the RSC potential. Besides, in the case of Nijmegen, the spectrum of single-particle energies increases more quickly than in the case of RSC potential under compression. The space between single-particle energy shells is also visible in the energy spectrum. At high compression, the radial density distribution becomes higher than that in the interior zone when the RSC potential is applied. Keywords: Nijmegen potential, RSC potential, Ab-initio calculations model, Radial density distribution, Ground state, 12C nucleus.

LOCV calculation for nuclear and neutron matter with the Nijmegen potential

The lowest order constrained variational (LOCV) formalism is formulated for the Nijmegen soft-core potential, which is fitted by the proton-proton (pp) scattering phase shift. The calculations are performed for the equation of state (EOS) of both nuclear and neutron matter. The state-dependent correlation functions are calculated by the minimization of two-body cluster energy, and the resulting Euler Lagrange equations are solved for this kind of potential. It is shown that LOCV calculations can work with this kind of interaction as well as other interactions in configuration space. The state-dependent correlation functions are calculated by minimization of two-body cluster energy for each channel with various JLSTMT, by using Nijmegen interaction. The correlation functions are compared with those coming from UV14 interaction in LOCV formalism. It is shown that unlike UV14, AV14, and AV18 potentials, the binding energy obtained from Nijmegen in the LOCV framework is −16.81 MeV that is close to the experimental value. Finally, it is recognized our LOCV results with Nijmegen interaction are similar to calculations with different interactions and different many-body methods.

Properties of 4He Nucleus in the Mean Field Approximation with Compression

Constrained spherical Hartree–Fock approximations are used to investigate nuclear system of closed shell $$^{4}{\hbox {He}}$$ nucleus. Two potentials were used: Reid soft core (RSC) and Nijmegen potentials. Moreover, the dependence of the nuclear properties was studied for the degree of compression. It was seen that it is possible to compress the nucleus into a smaller volume. This means that nuclear equation of state becomes softer for the compressed nucleus. Also, the nucleus becomes more bounded using RSC than Nijmegen potential. The $$E_{{\mathrm{HF}}}$$ increases steeply toward zero binding energy under compression for both potentials. In the case of using Nijmegen potential, the curve increases to zero binding energy more than RSC potential. In addition to that the spectrum of single particle increases more rapidly for Nijmegen than for RSC potential under compression. For the compressed nucleus, the energy spectrum also clearly shows the gaps between single-particle energy shells. In addition, it is preserved the ordering of the energy spectrum levels and the gaps among them. Finally, except in the interior region, the radial density distribution remains constant, while it is larger with RSC than with Nijmegen potential. At large compression, it becomes larger than that in the interior region when RSC potential is used.

Ground State Properties of Closed Shell <sup>4</sup>He Nucleus under Compression

This paper addresses the effects of nuclear properties at different potentials. Reid Soft Core (RSC) and Nijmegen potentials were used to study the nuclear system of 4He nucleus. It has been examined with and without large compression. Moreover, the constrained spherical Hartree-Fock (CSHF) approximations are used as a major tool of analysis. The dependence of the ground state properties was investigated to the degree of compression. It was noticed that it is possible to compress the nucleus to a smaller volume and the nucleus becomes more bounded using RSC than Nijmegen potential. It was also shown that the spectrum of single particle levels increases more rapidly for Nijmegen than RSC potential under compression. Finally, the radial density distribution remains constant, except in the interior region, while it is larger with RSC than Nijmegen potential. At large compression, the radial density distribution becomes larger than that in the interior region when RSC potential is used.

Aproksymatsiya khvyl'ovoyi funktsiyi ta polyaryzatsiyni kharakterystyky deytrona dlya potentsialiv Neymehens'koyi hrupy

The coefficients of analytic forms for the deuteron wave function in the configuration representation for Nijmegen potentials have been calculated numerically. The obtained wave functions do not contain redundant nodes. The calculated parameters of a deuteron agree well with experimental and theoretical data. The polarization characteristics T20 and Ayy calculated with the use of the obtained wave functions are comparable with earlier results.

D*ΞNbound state in strange three-body systems

The recent update of the strangeness $\ensuremath{-}2$ ESC08c Nijmegen potential incorporating the NAGARA and KISO events predicts a $\mathrm{\ensuremath{\Xi}}N$ bound state, ${D}^{*}$, in the $^{3}S_{1}(I=1)$ channel. We study if the existence of this two-body bound state could give rise to stable three-body systems. For this purpose we solve the bound state problem of three-body systems where the $\mathrm{\ensuremath{\Xi}}N$ state is merged with $N\text{'s}$, $\mathrm{\ensuremath{\Lambda}}\text{'s}$, $\mathrm{\ensuremath{\Sigma}}\text{'s}$, or $\mathrm{\ensuremath{\Xi}}\text{'s}$, making use of the most recent updates of the two-body ESC08c Nijmegen potentials. We found that there appear stable states in the $\mathrm{\ensuremath{\Xi}}NN$ and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Xi}}N$ systems, the $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Lambda}}N$ and $\mathrm{\ensuremath{\Xi}}\mathrm{\ensuremath{\Sigma}}N$ systems being unbound.

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.

LightΞhypernuclei

Arguments in favor of a light $\Xi NN$ hypernucleus with $(I)J^P=(3/2)1/2^+$ are presented, within the uncertainties of our knowledge of the baryon-baryon strangeness $-2$ interactions. If bound, this $\Xi NN$ state, being decoupled from the lowest $N\Lambda\Lambda$ system, would be stable. It will also benefit from additional binding due to the electromagnetic interaction what makes it worthwhile to look for. We show how the equivalent state with $J=3/2$ could never be bound in spite of the attractive interaction of the two-body subsystems. We illustrate our discussion with a full-fledged Faddeev calculation of the $\Xi NN$ system using simple potentials that mimic more elaborate interactions. We also make contact with different recent phenomenological interactions from the literature, like the ESC08 Nijmegen potential or quark-model based potentials.

Elastic electron-deuteron scattering within a relativistic potential model

Elastic electron-deuteron scattering was considered in the point form of relativistic quantum mechanics. Observables of this process and the dependence of the deuteron form factors on the 4-momentum transfer Q up to 8 fm−1 were calculated. The nucleon-nucleon potentials used in the calculations included the Nijmegen potentials NijmI and NijmII, the Bonn potential CD-Bonn, and the Moscow potential involving forbidden states. A parametrization of the nucleon form factors that complies with present-day experimental results was used as input data. The results of the calculations that employ all of the above potential types describe experimental data at least up to Q ≈ 5 fm−1.

Test of the Glauber formula for nucleon-deuteron scattering at intermediate energies

A high-precision test of the Glauber formula for the amplitude of nucleon-deuteron scattering is performed. Nucleon-nucleon amplitudes used in the calculations depend on the spins of interacting particles, phase shifts, and mixing parameters. These amplitudes were derived by using the Nijmegen potentials. The differential cross sections for nucleon-deuteron scattering were calculated for the projectile-nucleon energies of 65, 95, 135, 150, 190, and 250~MeV, and the results of these calculations were compared with experimental data.

Spin-dependent part of interaction cross section and Nijmegen potential

Low energy $\bar{p}d$ interaction is considered taking into account the polarization of both particles. The corresponding cross sections are obtained using the Nijmegen nucleon-antinucleon optical potential with shadowing effects taken into account. Double-scattering effects are calculated within the Glauber approach and found to be about 10-20%. The cross sections are applied to the analysis of the polarization buildup which is due to the interaction of stored antiprotons with a polarized target. It is shown that, at realistic parameters of a storage ring and a target, the filtering mechanism may provide a noticeable polarization in a time comparable with the beam lifetime. The energy dependence of the polarization rate for deuterium target is similar to that for hydrogen one. However, the time of polarization for deuterium is much smaller than that for hydrogen.

Spin-dependent part of pp̄ interaction cross section and Nijmegen potential

Low energy pp̄ interaction is considered taking into account the polarization of both particles. The corresponding cross sections are calculated using the Nijmegen nucleon-antinucleon optical potential. Then they are applied to the analysis of the polarization buildup which is due to the interaction of stored antiprotons with polarized protons of a hydrogen target. It is shown that, at realistic parameters of a storage ring and a target, the filtering mechanism may provide a noticeable beam polarization in a time comparable with the beam lifetime.

In-mediumTmatrix for nuclear matter with three-body forces: Binding energy and single-particle properties

We present spectral calculations of nuclear matter properties including three-body forces. Within the in-medium $T$-matrix approach, implemented with the CD-Bonn and Nijmegen potentials plus the three-nucleon Urbana interaction, we compute the energy per particle in symmetric and neutron matter. The three-body forces are included via an effective density dependent two-body force in the in-medium $T$-matrix equations. After fine tuning the parameters of the three-body force to reproduce the phenomenological saturation point in symmetric nuclear matter, we calculate the incompressibility and the energy per particle in neutron matter. We find a soft equation of state in symmetric nuclear matter but a relatively large value of the symmetry energy. We study the the influence of the three-body forces on the single-particle properties. For symmetric matter the spectral function is broadened at all momenta and all densities, while an opposite effect is found for the case of neutrons only. Noticeable modification of the spectral functions are realized only for densities above the saturation density. The modifications of the self-energy and the effective mass are not very large and appear to be strongly suppressed above the Fermi momentum.

Photon-induced neutron polarization from the2H(γ,n→)1Hreaction within theNN-force model with an intermediate dibaryon

A model for the $\mathit{NN}$ force, which is induced by the formation of an intermediate dibaryon dressed with \ensuremath{\sigma}- and other meson fields, has been developed by the present authors in previous years. This model is applied to the deuteron photodisintegration processes with the main focus on the \ensuremath{\gamma}-induced polarization ${P}_{y}^{'}$ of the neutron at energies below ${E}_{\ensuremath{\gamma}}\ensuremath{\lesssim}$ 30 MeV. The inclusion of the intermediate dibaryon leads to a model of the $\mathit{NN}$ force completely different to the conventional $\mathit{NN}$ potential models at short distances. Here the model is tested on the nucleonic level through comparison to rather similar predictions from the conventional $\mathit{NN}$ potential model both for the total and differential cross sections and also for the spin polarization of the ejected neutrons. The predictions of the present model are at least of the same quality than those for the Nijmegen potential; the visible differences with experimental data for ${P}_{y}^{'}$ still remain. However, in combination with the previous results a consistent description can be achieved simultaneously for many observables.

Exclusive electrodisintegration of the deuteron within the point form of relativistic quantum mechanics

The process of exclusive deuteron electrodisintegration is considered within the point form of relativistic quantum mechanics. Relevant calculations are performed on the basis of the Nijmegen and Moscow nucleon-nucleon potentials, the latter involving forbidden states. Final-state interaction is taken into account. For either type of the potentials used, the results of the calculations describe well experimental data at final-neutron momenta p n of up to 500 MeV/c.

Microscopic 8-quark study of the antikaon-nucleon-nucleon systems

We study the possibility of binding eight quarks in a molecular hadronic system composed of two nucleons and an antikaon, with the quantum numbers of a hexaquark flavor, in particular, with strangeness $\ensuremath{-}1$, isospin $1/2$, parity -, baryonic number 2, and two possible spins, 0 or 1. We discuss the possible production of this hadron in the experiments which are presently investigating hot topics like the ${\ensuremath{\Theta}}^{+}$ pentaquark or the ${K}^{\ensuremath{-}}$ deeply bound in nuclei. The ${K}^{\ensuremath{-}}\ifmmode\bullet\else\textbullet\fi{}N$ interactions and the coupling to other channels are computed microscopically from a confining and chiral invariant quark model resulting in local plus separable Gaussian potentials. The $N\ifmmode\bullet\else\textbullet\fi{}N$ interactions used here are the state of the art Nijmegen potentials. The binding energy and the decay rate of the ${K}^{\ensuremath{-}}\ifmmode\bullet\else\textbullet\fi{}N$ and ${K}^{\ensuremath{-}}\ifmmode\bullet\else\textbullet\fi{}N\ifmmode\bullet\else\textbullet\fi{}N$ systems are computed with configuration space variational methods.

Convergence of the Born series with low-momentum interactions

The non-perturbative nature of nucleon–nucleon interactions as a function of a momentum cutoff is studied using Weinberg eigenvalues as a diagnostic. This investigation extends an earlier study of the perturbative convergence of the Born series to partial waves beyond the 3S 1– 3D 1 channel and to positive energies. As the cutoff is lowered using renormalization-group or model-space techniques, the evolution of non-perturbative features at large cutoffs from strong short-range repulsion and the iterated tensor interaction are monitored via the complex Weinberg eigenvalues. When all eigenvalues lie within the unit circle, the expansion of the scattering amplitude in terms of the interaction is perturbative, with the magnitude of the largest eigenvalue setting the rate of convergence. Major decreases in the magnitudes of repulsive eigenvalues are observed as the Argonne v 18 , CD-Bonn or Nijmegen potentials are evolved to low momentum, even though two-body observables are unchanged. For chiral EFT potentials, running the cutoff lower tames the impact of the tensor force and of new non-perturbative features entering at N 3LO. The efficacy of separable approximations to nuclear interactions derived from the Weinberg analysis is studied as a function of cutoff, and the connection to inverse scattering is demonstrated.

Does - - Form a Quasi-Bound State?

We have investigated the possible existence of a quasi-bound state for the Σ-Σ-α system in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T = 2, since for an inert α particle there is no strong conversion to Ξ-N-α or Λ-Λ-α possible. A Σ-α optical potential based on Nijmegen model D and original Σ-Σ interactions of the series of Nijmegen potentials NSC97 as well a simulated Gaussian type versions thereof are used. Our investigation of the Σ-Σ-α system leads to a quasi bound state where, depending on the potential parameters, the energy ranges between −1.4 and −2.4 MeV and the level width is less than 0.4 MeV.

Existence ofΛΛ4H: A variational Monte Carlo search

A variational Monte Carlo (VMC) calculation for the binding energy B{sub {lambda}}{sub {lambda}} of the lightest hypernucleus {sub {lambda}}{sub {lambda}}{sup 4}H has been performed in the four-body {lambda}{lambda}pn model. A range of input {lambda}{lambda} potentials of moderate strength produce a particle-stable {sub {lambda}}{sub {lambda}}{sup 4}H for the simulated NSC97e and f {lambda}N potentials, whereas the phenomenological Minnesota {lambda}N potential needs a much stronger {lambda}{lambda} potential to bind. The VMC results for B{sub {lambda}}{sub {lambda}} agree with the prediction of the stochastic variational model but contradict the recent Faddeev-Yakubovsky calculation. As reported earlier, B{sub {lambda}}{sub {lambda}} is sensitive to the triplet {lambda}N channel for a given {lambda}{lambda} potential. The B{sub {lambda}}{sub {lambda}} of {sub {lambda}}{sub {lambda}}{sup 4}H in the three-body {lambda}{lambda}d cluster model is consistent with but slightly lower than the Faddeev calculation. The VMC method predicts a stable {sub {lambda}}{sub {lambda}}{sup 4}H system in both models and thus offers the possibility of identifying {sub {lambda}}{sub {lambda}}{sup 4}H in a future extension of E906 or of a related experiment at KEK, provided the simulated potentials are true representations of realistic Nijmegen potentials.

The structure of nuclear systems derived from low momentum nucleon–nucleon potentials

Various nuclear structure observables are evaluated employing low-momentum nucleon–nucleon (NN) potentials V low- k derived from the CD-Bonn and Nijmegen NN interactions V NN. By construction, the high momentum modes of the original V NN are integrated out in V low- k , with the requirement that the deuteron binding energy and low energy phase shifts of V NN are exactly reproduced. Using this interaction, we evaluate the bulk properties (binding energy and saturation density) of nuclear matter and finite nuclei, in particular their dependence on the cut-off parameter. We also study the pairing gap and the residual interaction in nuclear matter in terms of the Landau parametrization. At low and medium densities, the HF and BHF binding energies for nuclear matter calculated with the V low- k 's derived from the CD-Bonn and Nijmegen potentials are nearly identical. The pairing gaps and Landau parameters derived from V low- k are remarkably close to those given by the full-space V NN. The V low- k interactions, however, fail to reproduce the saturation property of nuclear matter at higher densities if the cut-off for the high momentum modes is assumed density independent.