arXiv subjects

Th. A. Rijken

Publications and source records attributed to Th. A. Rijken.

At least 19 recordsLinked to original sources

arXiv2026

Topics in Kadyshevsky Field Theory

In these notes we deal with several field theoretical topics in the framework of the Quantum Field Theory as developed by Kadyshevsky. The main motivation for studying the Kadyshevsky formalism is that in the kadyshevsky graphs, in contrast with the Feynman graphs, the particles remain on the mass shell. This facilitates the use of phenomenological form factors, {\it e.g.} Gaussian ones. In the first part we construct the second quantised quasi-particle formalism, which is employed to develop the functional integral formalism. In the latter we develop the path-integral, the Schwinger-Symanzik equations, generalised Wightman functions, and the Kadyshevsky reduction formulas. In the second part we cover the topics: (i) the relation between the Feynman and Kadyshevsky perturbation theory, and (ii) the Gross-Jackiw method in the Kadyshevsky formalism. The latter method is applied to the kadyshevsky formalism for interaction Lagrangians with derivatives, in particular for pion-nucleon interactions: (i) pseudo-vector $NNπ$-, (ii) vector $NNρ$-, and (iii) gauge-invariant $Δ_{33}Nπ$ coupling.

hep-th↗

arXiv2026

Novel method for evaluating the eigenvalues of the Heun differential equation with an application to the Breit equation

Eigenvalues of the Breit equation, in which only the static Coulomb potential is considered, have been found. Over the past decades several authors have analyzed the Breit equation to obtain numerically or by approximation an estimation of the energy levels. Various approaches have been used and no determination of the energy levels currently exists that is directly based on the second order Heun differential equation derived. The aim of this work is to provide a method of calculation that can be used to numerically calculate the energy levels for various spin states to high accuracy. From the Breit equation, we derive the corresponding second-order Heun differential equation and continued fraction from which the eigenvalues can be determined very accurately. Next, we present a novel method based on the Green function method, which leads to a semi-infinite determinant from which we are able to obtain the numerical values of the eigenvalues by direct calculation. Using suitable numerical methods for the direct calculation of the continued fraction and the semi-infinite determinant, we show that both methods are consistent within 25 digits of accuracy. We show that the correct energy levels for the Dirac equation follow from our results by a suitable mapping of the variables. The results are in total agreement with earlier calculations found in the literature and extend this by several digits of additional accuracy. The condition on the determinant giving the energy levels provides a rich structure that is promising in extending the results of this work.

quant-ph↗

arXiv2025

Massive Spin-2: Field-equations, Propagators, Massless-limit, and Perihelion Precessions

This paper presents the quantization of massive and massless spin-2 particles, using the auxiliary field method. The issue, the so-called vDVZ-discontinuity, whether the perihelion precessions for a massive graviton are in agreement with the data, is studied in the context of this spin-2 theory in tree-approximation. In the context of this setting, it is found, that a massive gravitation model with an imaginary scalar ghost, for a small graviton mass is compatible with the perihelion-precession of Mercury, etc..

physics.gen-ph↗

arXiv2025

Nucleon-Quark Diquark-exchange Interaction

In this note the nucleon-quark diquark-exchange interaction is derived using the Feynman-propagator for axial-vector diquark (D) exchange. The Feynman diquark propagator is derived and the result is a (-)-sign difference w.r.t. quark-antiquark exchange. This is due to the (-)-sign for a closed fermion loop, present in for example vector and axial-vector quark-antiquark exchange, but absent in the case of D-exchange. The calculations in these notes follow closely those for vacuum polarisation in the literature. Taking into account that the diquark D is a color $\left{\bar{3}_c\right\}$-state giving a factor +2. The result is an effective axial-vector diquark propagator. Application to $QN \rightarrow NQ$ gives a repulsive potential, which has been used in mixed nuclear-quark matter calculation.

nucl-th↗

arXiv2025

Constituent Quark-model for BaryonsTh. Harmonic confinement and Two-body Meson-exchange Potentials

Soft Two-body potentials between the constituent quarks of the nucleon are derived using harmonic oscillator, i.e. gaussian, quark wave-functions. The gaussian wave-functions are very suited for applications with the ESC soft-core interactions, which employ gaussian form factors. In these notes using the Fourier transformation to momentum space the local and non-local contributions of the potentials based on the ESC meson-quark-quark vertices are evaluated. Using the ESC16 parameters translated to the quark-level leads to parameter free two-body and three-body diquark and triquark meson-exchange interactions. Applications to the SU(3) baryon-octet states and the $Δ_{33}$ resonance are performed., within the CQM using a harmonic confinement potential, leading to a satisfactory picture with relativistic constituent quarks. We present two versioins for the $N-Δ$ splitting: (i) model A with the instanton interaction, and (ii) model B with a large color-magnetic interaction from an almost point like OGE. The size of the baryons $\approx$ 1 fm.

nucl-th↗

arXiv2024

Constituent Quark Model and nucleon-Nucleon Potentials

In these notes, while focusing on the meson-nucleon vertices, we give a derivation of the nucleon-nucleon 9NN) potentials from meson-exchange between quarks. To establish such a relation the quark-quark-meson (QQM) interactions are properly defined. Hitherto, the coefficients in the Pauli-spinor expansion of the meson-nucleon-nucleon (NNM) vertices are equated with those of the QQM-vertices. In these notes we employ the description of the nucleon with Dirac-spinors in the SU(6) semi-relativistic "constituent" quark-model (CQM) as formulated by LeYouanc, et al. It appears that the constituent quark model with $m_q= M_N/3$, is able to produce the same ratio's for the central-, spin-spin-, tensor-, spin-orbit-, and quadratic-spin-orbit Pauli-invariants as in the phenomenological NNM-vertices. In order to achieve this, the scalar-, magnetic-vector, and axial-vector interactions require, besides the standard ones, an extra coupling to the quarks without the introduction of new parameters. in the case of the axial-vector mesons an extra coupling to the quarks is necessary, which is related to the quark orbital angular momentum contribution to the nucleon spin. Furthermore, a momentum correlation between the quark that is coupled to the meson and the remaining quark pair, and a (gaussian) QQM form factor, are necessary to avoid "spurious" terms. From these results we have obtained a formulation of the QQ-interactions which is directly related to the NN extended-soft-core (ESC) interactions. This has been applied to mixed quark-nuclear matter in a study of (heavy) neutron stars.

nucl-th↗

arXiv2024

Quark-Quark and Quark-nucleon Potential model Extended-soft-core meson-exchange Interactions

The Quark-quark (QQ) and Quark-nucleon (QN) interactions in this paper are derived from the Extended-soft-core (ESC) interactions. The meson-quark-quark (MQQ) vertices are determined in the framework of the constituent quark model (CQM). These vertices are such that upon folding with the ground-state baryon quark wave functions the one-boson-exchange (OBE) amplitudes for baryon-baryon (BB), and in particularly for nucleon-nucleon (NN), are reproduced. This opens the attractive possibility to define meson-quark interactions at the quark level which are directly related related to the interactions at the baryon level. the latter have been determined by the baryon-baryon data. Application of these "realistic" quark-quark interactions in the quark-matter phase is presumably of relevance for the description of highly condensed matter, as e.g. neutron-star matter.

nucl-th↗

arXiv2024

Nucleon-quark mixed matter and neutron star EOS

The nucleon-quark mixed matter is defined in the Brueckner-Hartree-Fock framework, in which quark densities are determined by equilibrium conditions between nucleon and quark chemical potentials, and nucleon-quark interactions play critical roles for resulting EoSs (equation of state). The two models of EoSs are derived from the nucleon-quark mixed matter (NQMM): The NQMM-A EoSs are based on the simple assumption that nucleons and free quarks occupy their respective Fermi levels and their Fermi spheres overlap from each other. In NQMM-B EoSs, the quark Fermi repulsion effect is incorporated on the basis of quakyonic matter, meaning that the nucleon Fermi levels are pushed up from the quark Fermi sphere by the Pauli exclusion principle. For the NQMM-A EoSs, the neutron-star mass-radius ($MR$) curves are pushed up above the region of $M \sim 2.1M_\odot$ and $R_{2.1M_\odot}\sim$ 12.5 km indicated by the recent observations, as the $qN$ repulsions increase. For the NQMM-B EoSs, the similar results are obtained by the combined contributions from the $qN$ repulsion and the quark Fermi repulsion. In both models of EoSs, the important roles of the $qN$ di-quark exchange repulsions are demonstrated to reproduce reasonable values of $M_{max}$ and $R_{2.1M_\odot}$.

nucl-th↗

arXiv2023

Quark phases in neutron stars consistent with implications of NICER

The analyses for the NICER data imply $R_{2.0M_\odot}=12.41^{+1.00}_{-1.10}$ km and $R_{1.4M_\odot}=12.56^{+1.00}_{-1.07}$ km, indicating the lack of significant variation of the radii from $1.4 M_\odot$ to $2.0 M_\odot$. This feature cannot be reproduced by the hadronic matter due to the softening of equation of state (EoS) by hyperon mixing, indicating the possible existence of quark phases in neutron-star interiors. % Two models are used for quark phases: In the quark-hadron transition (QHT) model, quark deconfinement phase transitions from a hadronic-matter EoS are taken into account so as to give reasonable mass-radius ($MR$) curves by adjusting the quark-quark repulsions and the density dependence of effective quark mass. % In the quarkyonic model, the degrees of freedom inside the Fermi sea are treated as quarks and neutrons exist at the surface of the Fermi sea, where $MR$ curves are controlled mainly by the thickness of neutron Fermi layer. % The QHT and quarkyonic EoSs can be adjusted so as to reproduce radii, tidal deformabilities, pressure and central densities inferred from the NICER analysis better than the nucleonic matter EoS, demonstrating the clear impacts of quark phases. Then, the maximum mass for the quakyonic-matter EoS is considerably larger than that for the QHT-matter EoS.

nucl-th↗

arXiv2021

Quark-quark interaction and quark matter in neutron stars

Hyperon ($Y$) mixing in neutron-star matter brings about a remarkable softening of the equation of state (EoS) and the maximum mass is reduced to a value far less than $2M_{\odot}$. One idea to avoid this "hyperon puzzle in neutron stars" is to assume that the many-body repulsions work universally for every kind of baryons. The other is to take into account the quark deconfinement phase transitions from a hadronic EoS to a sufficiently stiff quark-matter EoS. In the present approach, both effects are handled in a common framework. As well as the hadronic matter, the quark matter with the two-body quark-quark interactions are treated within the Brueckner-Bethe-Goldstone theory beyond the mean field frameworks, where interaction parameters are based on the terrestrial data. The derived mass-radius relations of neutron stars show that maximum masses reach over $2M_{\odot}$ even in the cases of including hadron-quark phase transitions, being consistent with the recent observations for maximum masses and radii of neutron stars by the NICER measurements and the other multimessenger data.

nucl-th↗

arXiv2020

Possible lightest $Ξ$ Hypernucleus with Modern $ΞN$ Interactions

Experimental evidence exists that the $Ξ$-nucleus interaction is attractive. We search for $NNΞ$ and $NNNΞ$ bound systems on the basis of the AV8 $NN$ potential combined with either a phenomenological Nijmegen $ΞN$ potential or a first principles HAL QCD $ΞN$ potential. The binding energies of the three-body and four-body systems (below the $d+Ξ$ and $^3{\rm H}$/$^3{\rm He}+Ξ$ thresholds, respectively) are calculated by a high precision variational approach, the Gaussian Expansion Method. Although the two $ΞN$ potentials have significantly different isospin ($T$) and spin ($S$) dependence, the $NNNΞ$ system with quantum numbers $(T=0, J^π=1^+$) appears to be bound (one deep for Nijmegen and one shallow for HAL QCD) below the $^3{\rm H}$/$^3{\rm He}+Ξ$ threshold. Experimental implications for such a state are discussed.

nucl-th↗

arXiv2017

Neutron-star radii based on realistic nuclear interactions

The existence of neutron stars with $2M_\odot$ requires the strong stiffness of the equation of state (EoS) of neutron-star matter. We introduce a multi-pomeron exchange potential (MPP) working universally among 3- and 4-baryons to stiffen the EoS. Its strength is restricted by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The EoSs are derived using the Brueckner-Hartree-Fock (BHF) and the cluster variational method (CVM) with the nuclear interactions ESC and AV18. The mass-radius relations are derived by solving the Tolmann-Oppenheimer-Volkoff (TOV) equation, where the maximum masses over $2M_\odot$ are obtained on the basis of the terrestrial data. Neutron-star radii $R$ at a typical mass $1.5M_\odot$ are predicted to be $12.3\!\sim\!13.0$ km. The uncertainty of calculated radii is mainly from the ratio of 3- and 4-pomeron coupling constants, which cannot be fixed by any terrestrial experiment. Though values of $R(1.5M_\odot)$ are not influenced by hyperon-mixing effects, finely-observed values for them indicate degrees of EoS softening by hyperon mixing in the region of $M\!\sim\!2M_\odot$. If $R(1.5M_\odot)$ is less than about 12.4 km, the softening of EoS by hyperon mixing has to be weak. Useful information can be expected by the space mission NICER offering precise measurements for neutron-star radii within $\pm 5\%$.

nucl-th↗

arXiv2017

Effects of hyperonic many-body force on $B_Λ$ values of hypernuclei

The stiff equation of state (EoS) giving the neutron-star mass of $2M_{\odot}$ suggests the existence of strongly repulsive many-body effect (MBE) not only in nucleon channels but also in hyperonic ones. As a specific model for MBE, the repulsive multi-pomeron exchange potential (MPP) is added to the two-body interaction together with the phenomenological three-body attraction. For various versions of the Nijmegen interaction models, the MBE parts are determined so as to reproduce the observed data of $B_Λ$. The mass dependence of $B_Λ$ values is shown to be reproduced well by adding MBE with the strong MPP repulsion assuring the stiff EoS of hyperon-mixed neutron-star matter, when $P$-state components of the adopted interaction model lead to almost vanishing contributions. The nuclear matter $Λ\!N$ $G$-matrix interactions are derived and used in $Λ$ hypernuclei on the basis of the averaged-density approximation (ADA). The $B_Λ$ values of hypernuclei with $9 \le A \le 59$ are analyzed in the framework of Antisymmetrized Molecular Dynamics with use of the two types of $Λ\!N$ $G$-matrix interactions including strong and weak MPP repulsions. The calculated values of $B_Λ$ reproduce the experimental data finely within a few hundred keV. The values of $B_Λ$ in $p$-states also can be reproduced well, when ADA is modified to be suitable also to weakly-bound $Λ$ states.

nucl-th↗

arXiv2015

Hyperon-mixed neutron star with universal many-body repulsion

Neutron stars with large masses $\sim 2M_{\odot}$ require the hard stiffness of equation of state (EoS) of neutron-star matter. On the other hand, hyperon mixing brings about remarkable softening of EoS. In order to solve this problem, a multi-pomeron exchange potential (MPP) is introduced as a model for the universal many-body repulsion in baryonic systems on the basis of the Extended Soft Core (ESC) baryon-baryon interaction. The strength of MPP is determined by analyzing the nucleus-nucleus scattering with the G-matrix folding model. The interactions in $Λ\!N$, $Σ\!N$ and $Ξ\!N$ channels are shown to be consistent with experimental indications. The EoS in neutron-star matter with hyperon mixing is obtained from ESC in addition of MPP, and mass-radius relations of neutron stars are derived. The maximum mass is shown to reach $2M_{\odot}$ even in the case of including hyperon mixing on the basis of model-parameters determined by terrestrial experiments.

nucl-th↗

arXiv2015

Extended-soft-core Baryon-Baryon ESC08 model III. S=-2 Hyperon-hyperon/nucleon Interaction

This paper presents the Extended-Soft-Core (ESC) potentials ESC08c for baryon-baryon channels with total strangeness S=-2. The potential models for S=-2 are based on SU(3) extensions of ESC potential models for the S=0 and S=-1 sectors, which are fitted to experimental data. Flavor SU(3)-symmetry is broken only kinematically by the masses of the baryons and the mesons. For the S=-2 channels no experimental scattering data exist, and also the information from hypernuclei is rather limited. Nevertheless, in the fit to the S=0 and S=-1 sectors information from the so called NAGARA event and the $Ξ$-well-depth has been used as constraints to determine the free parameters in the simultaneous fit of the $NN \oplus YN \oplus YY$ data. Therefore, the potentials for the S=-2 sector are determined mainly by the NN-, YN-data, and SU(3)-symmetry.Various properties of the potentials are illustrated by giving results for scattering lengths, effective ranges, bound states, elastic and inelastic phase parameters, and total cross sections. Notably is the prediction of a bound state D$^*$ in the $ΞN(^3S_1,I=1)$-channel with a binding energy $B_E=1.56$ MeV. This state is deuteron-like, i.e. a member of the $\{10^*\}$-decuplet. As for the normal deuteron $D= pn(^3S_1-^3D_1)$ the strong tensor force is responsible for this state. The features of $Ξ$ hypernuclei predicted by ESC08c are studied on the basis of the G-matrix approch. The well-depth $U_Ξ= -7.0$ MeV, and the $Ξ-ΛΛ$ conversion width is $Γ_Ξ^c= 4.5$ MeV.

nucl-th↗

arXiv2015

Extended-soft-core Baryon-Baryon Model Esc08 II. Hyperon-Nucleon Interactions

The YN results are presented from a new version of the Extended-soft-core (ESC) potential model for Baryon-baryon (BB) scattering. The potentials consist of local- and non-local-potentials due to (i) One-boson-exchange (OBE), (ii) Pomeron and Odderon exchanges, (iii) Two pseudoscalar-exchange (PS-PS), and (iv) Meson-Pair-exchange (MPE). The OBE- and MPE-vertices are regulated by gaussian form factors, producing moderate size potentials in the origin. In addition to the mentioned ingredients of the ESC-model, also the possible short range repulsion due to the quark Pauli-principle in the BB-channels is included in the analysis. The NN, YN, and the S=-2 YY scattering is treated in a unified way using flavor SU(3) symmetry. With the ESC08-model a simultaneous fit is performed for the combined NN and YN data, using single sets of parameters. The achievement is a fit with (i) $χ^2/NN_{data}= 1.081$, and (ii) $χ^2/YN_{data}=1.08$.

nucl-th↗

arXiv2014

Momentum-space Lippmann-Schwinger-Equation, Fourier-transform with Gauss-Expansion-Method

In these notes we construct the momentum-space potentials from configuration-space using for the Fourier-transformation the Gaussian-Expansion-Method (GEM). This has the advantage that the Fourier-Bessel integrals can be performed analytically, avoiding possible problems with the oscillations in the Bessel functions for large r, in particular for $p_f \neq p_i$. The mass parameters in the exponentials of the Gaussian base-functions are fixed using the geometric progression recipe of Hiyama-Kamimura. The fitting of the expansion coefficients is linearly and very fast. Application to nucleon-nucleon is given in detail for the recent Extended-soft-core model ESC08c. The NN phase shifts obtained by solving the Lippmann-Schwinger equations agree very well with those obtained in configuration-space solving the Schrödinger equations.

nucl-th↗

arXiv2014

Extended-soft-core Baryon-Baryon Model ESC08 I. Nucleon-Nucleon Scattering

The Nijmegen extended-sft-core ESC08c model for the baryon-baryon (BB) interactions of the SU(3) flavor-octet of baryons ($N, Λ, Σ$, and $Ξ$) is presented. In this first of a series of papers, the NN results are reported in detail. In the spirit of the Yukawa-approach to the nuclear force problem, the interactions are studied from the meson-exchange picture viewpoint, using generalized soft-core Yukawa-functions. These interactions are supplemented with (i) multiple-gluon-exchange, and (ii) structural effects due to the quark-core of the baryons. The extended-soft-core (ESC) meson-exchange interactions consist of local- and non-local-potentials due to ((i) One-boson-exchanges (OBE, which are the members of nonets of pseudoscalar , vector, scalar, and axial-vector mesons, (ii) diffractive (i.e. multiple-gluon) exchanges, (iii) two pseudoscalar exchange (PS-PS), and (iv) meson-pair-exchange (MPE). The OBE- and MPE-vertices are regulated by gaussian form factors producing potentials with a soft behavior near the origin. The assignment of the cut-off masses for the BBM-vertices is dependent on the SU(3)-classification of the exchanged mesons for OBE, and a similar scheme for MPE. The simultaneous fit of the ESC-models to the NN- and YN-scattering data achieved excellent results for the NN, YN, and favorable properties for the $ΛΛ$ and $ΞN$ systems. In the case of ESC08c, the version of this paper, the results are: (i) For the selected 4313 pp and np scattering data ($ 0 \leq T_{lab} \leq 350$ MeV), the model achieved $χ^2/N_{data} = 1.08$. (ii) The deuteron binding energy and all NN low energy parameters are fitted very nicely. (iii) The YN-data are described also very well with $χ^/N_{data} = 1.09$. (iv) The model predicts a bound $ΞN(^3S_1,I=1)$ states with binding energy 1.56 MeV.

nucl-th↗