Alexander Volya
Topics related to the construction, phenomenological determination, and effects of the effective three-body forces within the traditional nuclear shell model approach are discussed. The manifestations of the three-body forces in realistic nuclei in the 0f7/2 and 1s0d shell model valence spaces are explored.
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The tensor-force effects on the evolution of the spin-orbit splittings in the neutron drops are investigated within the framework of the relativistic Hartree-Fock theory. For fair comparisons on the pure mean-field level, the results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A interaction are adopted as meta-data. Through a quantitative analysis, we certify that the $π$-pseudovector ($π$-PV) coupling affects the evolutionary trend through the tensor force embedded. The strength of the tensor force is explored by enlarging the strength $f_π$ of the $π$-PV coupling. It…
The Faddeev equations for the three-body bound state with two- and three-body forces are solved directly as three-dimensional integral equation. The numerical feasibility and stability of the algorithm, which does not employ partial wave decomposition is demonstrated. The three-body binding energy and the full wave function are calculated with Malfliet-Tjon-type two-body potentials and scalar Fujita-Miyazawa type three-body forces. The influence of the strength and range of the three-body force on the wave function, single particle momentum distributions and the two-body correlation functions …
The four-body Yakubovsky equations in a Three-Dimensional approach with the inclusion of the three-body forces is proposed. The four-body bound state with two- and three-body interactions is formulated in Three-Dimensional approach for identical particles as function of vector Jacobi momenta, specifically the magnitudes of the momenta and the angles between them. The modified three dimensional Yakubovsky integral equations is successfully solved with the scalar two-meson exchange three-body force where the Malfliet-Tjon-type two-body force is implemented. The three-body force effects on the en…
The Faddeev equations for the three-body bound state are solved directly as thre e-dimensional integral equations without employing partial wave decomposition. Two-body forces of the Malfliet-Tjon type and simple spin independent genuine three-body forces are considered for the calculation of the three-body binding energy.
The traditional nuclear shell model approach is extended to include many-body forces. The empirical Hamiltonian with a three-body force is constructed for the identical nucleons on the 0f7/2 shell. Manifestations of the three-body force in spectra, binding energies, seniority mixing, particle-hole symmetry, electromagnetic and particle transition rates are investigated. It is shown that in addition to the usual expansion of the valence space within the tranditional two-body shell model, the three-body component in the Hamiltonian can be an important part improving the quality of the theoretica…
The Transfer to the Continuum method has been applied to describe the $^{11}\text{Li}(p,pn)$ and $^{14}\text{Be}(p,pn)$ reactions in inverse kinematics, using structure overlaps computed within a full three-body model for the projectile. Calculations agree with the available experimental data on the unbound $^{10}$Li and $^{13}$Be nuclei.
We calculate the equation of state of nuclear matter in the self-consistent T-matrix scheme including three-body nuclear interactions. We study the effect of the three-body force on the self-energies and spectral functions of nucleons in medium.
The first practical method to evolve many-body nuclear forces to softened form using the Similarity Renormalization Group (SRG) in a harmonic oscillator basis is demonstrated. When applied to He4 calculations, the two- and three-body oscillator matrix elements yield rapid convergence of the ground-state energy with a small net contribution of the induced four-body force.
We address the connection between the saturating behavior of infinite nuclear matter and the description of finite nuclei based on state-of-the-art chiral two- and three-nucleon forces. We observe that chiral two- and three-nucleon interactions (at N2LO and at N3LO) which have been found to predict realistic binding energies and radii for a wide range of finite nuclei (from p-shell nuclei up to nickel isotopes) are unable to saturate infinite nuclear matter. On the other hand, it has been shown that, when the fits of the cD and cE couplings of the chiral three-nucleon interactions include the …
The present thesis aims at studying the properties of symmetric nuclear and pure neutron matter from a Green's functions point of view, including two-body and three-body chiral forces. An extended self-consistent Green's function formalism is defined to consistently incorporate three-body forces in the many-body calculations. The effect of three-nucleon interactions is included via the construction of a dressed two-body density dependent force. This is obtained performing an average of the leading order three-body terms in the chiral effective field theory expansion. The dressed force correspo…
Nuclear symmetry energy and the role of three-body forces
本研究在LOCV框架下引入基于同位旋依赖参数化的修订三体力，结合AV18两体力，成功再现冷核物质饱和参数，并预测中子星最大质量超过2倍太阳质量。
Three-nucleon (3N) forces are an indispensable ingredient for accurate few-body and many-body nuclear structure and reaction theory calculations. While the direct implementation of chiral 3N forces can be technically very challenging, a simpler approach is given by employing instead a medium-dependent NN interaction V_med that reflects the physics of three-body forces at the two-body normal-ordered approximation. We review the derivation and construction of V_med from the chiral 3N interaction at next-to-next-to-leading order (N2LO), consisting of a long-range $2π$-exchange term, a mid-range $…
We calculate thermodynamic quantities in symmetric nuclear matter within the self-consistent Green's functions method including three-body forces. The thermodynamic potential is computed directly from a diagrammatic expansion, implemented with the CD-Bonn and Nijmegen nucleon-nucleon potentials and the Urbana three-body forces. We present results for entropy and pressure up to temperatures of 20 MeV and densities of 0.32 fm^-3. While the pressure is sensitive to the inclusion of three-body forces, the entropy is not. The unstable spinodal region is identified and the critical temperature assoc…
The effect of a microscopic three-body force on the saturation properties of nuclear matter is studied within the Brueckner-Hartree-Fock approach. The calculations show a decisive improvement of the saturation density along with an overall agreement with the empirical saturation point. With the three-body force the symmetry energy turns more rapidly increasing with density, which allows for the direct URCA process to occur in $β$-stable neutron star matter. The influence of the three-body force on the nuclear mean field does not diminish the role of the ground state correlations.
We propose new effective inter-nucleon forces with a finite-range three-body operator. The proposed forces are suitable for describing the nuclear structure properties over a wide mass number region, including the saturation point of nuclear matter. The forces are applied to microscopic calculations of $Z=N$ ($A\le 40$) nuclei and O isotopes with a method of antisymmetrized molecular dynamics. We present the characteristics of the forces and discuss the importance of the finite-range three-body term.
Within the self-consistent Green's functions formalism, we study the effects of three-body forces on the in-medium spectral function, self-energy and effective mass of the nuclear matter constituents, analyzing the density and momentum dependence.
A one-dimensional system of bosons with short-range repulsion and mid-range attraction is used as a laboratory to explore the evolution of many-body forces by the Similarity Renormalization Group (SRG). The free-space SRG is implemented for few-body systems in a symmetrized harmonic oscillator basis using a recursive construction analogous to no-core shell model implementations. This approach, which can be directly generalized to three-dimensional nuclei, is fully unitary up to induced A-body forces when applied with an A-particle basis (e.g., A-body bound-state energies are exactly preserved)…
In recent years, the Similarity Renormalization Group has provided a powerful and versatile means to soften interactions for ab initio nuclear calculations. The substantial contribution of both induced and initial three-body forces to the nuclear interaction has required the consistent evolution of free-space Hamiltonians in the three-particle space. We present the most recent progress on this work, extending the calculational capability to the p-shell nuclei and showing that the hierarchy of induced many-body forces is consistent with previous estimates. Calculations over a range of the flow …
In the past few years in-medium similarity renormalization group methods have been introduced and developed. In these methods the Hamiltonian is evolved using a unitary transformation in order to decouple a reference state from the rest of the Hilbert space. The evolution by itself will generate, even if we start from a two-body interaction, many-body forces which are usually neglected. In this work we estimate the effect of these residual many-body forces by comparing results obtained with the Hybrid Multi-determinant method, which keeps the Hamiltonian within the two-body sector, with the co…
Three body effects are studied for both asymmetric nuclear matter and pure neutron matter to calculate the nuclear Equation of State . The Brueckner Hartree Fock approximation is used using CD Bonn B and Argonne V18 potentials. A two body density dependent Skyrme potential is added to reproduce the empirical saturation point. Good agreement is obtained in comparison with exact calculation including three body forces.
Brueckner calculations including a microscopic three-body force have been extended to isospin asymmetric nuclear matter. The effects of the three-body force on the equation of state and on the single-particle properties of nuclear matter are discussed with a view to possible applications in nuclear physics and astrophysics. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs isospin asymmetry $β=(N-Z)/A$ is fulfilled in the whole asymmetry range $0\leβ\le 1$ up to high densities. The three-body force provides a strong enhance…
The use of leading order effective field theory (EFT) to describe neutron-deuteron scattering leads to integral equations that have unusual behaviour: when only two-body interactions are included, the scattering amplitude does not approach a limit when the cutoff used to solve the equations is removed. It has recently been shown that this cutoff dependence can be eliminated by the careful inclusion of a three-body force. In this paper we show that the cutoff dependence is just a reflection of the fact that the aforementioned integral equations admit an infinite number of solutions amongst whic…
The calculation of the spreading width of a compound nuclear reaction caused by a symmetry breaking $K$-body force acting in an $A$-body system ($K << A$, usually $K=2$) involves the determination of the local average square matrix element in $A$-body space. This problem is reduced to finding the global mean square matrix element $v^2$ in $K$-body space. The result is a compact formula for the spreading width which contains $v^2$ as an input. Our method is based on the dilute gas approximation for excitons close to the Fermi edge. The relative strength of the contributions of operators with di…
We study the impact of three-body forces on the response functions of cold neutron matter. These response functions are determined in the random phase approximation (RPA) from a residual interaction expressed in terms of Landau parameters. Special attention is paid to the non-central part, including all terms allowed by the relevant symmetries. Using Landau parameters derived from realistic nuclear two- and three-body forces grounded in chiral effective field theory, we find that the three-body term has a strong impact on the excited states of the system and in the static and long-wavelength l…
Exactness of the normal-ordered two-body truncation of three-nucleon forces
研究低能核物理中正规序哈密顿量二体截断的准确性原因，证明在含单双激发的耦合簇方法下该截断对零程三体力精确，为正规序二体近似提供了分析基础。
Benchmarking $Λ$NN three-body forces and first predictions for A=3-5 hypernuclei
本文对ΛNN三体力的两种分波分解方法进行基准测试，并首次定量评估其对A=3-5超核分离能的贡献。
We review the nuclear forces currently in use, i.e., the high-precision NN potentials of the 1990's and the nuclear two- and many-body forces based upon chiral effective field theory (EFT). We argue that the EFT approach is superior to any of the older schemes. Since accurate chiral forces are available now, the stage is set for microscopic nuclear structure to move into a new exciting era.
We review recent progress in implementing high-precision chiral two- and three-body forces in nuclear many-body systems beyond light nuclei. We begin with applications to finite nuclei, which we study through the nuclear shell model and self-consistent mean field theory. We then turn our attention to infinite nuclear matter treated within the framework of Landau's theory of normal Fermi liquids.
Three-body forces acting on a $Λ$ hyperon in a nuclear medium are investigated, with special focus on the so-called hyperon puzzle in neutron stars. The hyperon-nucleon two-body interaction deduced from SU(3) chiral effective field theory is employed at next-to-leading order. Hyperon-nucleon three-body forces are approximated using saturation by decuplet baryons and are transcribed to density-dependent effective two-body interactions. These together are taken as input in a Brueckner-Bethe-Goldstone equation with explicit treatment of the $ΛN\leftrightarrowΣN$ and $ΛNN\leftrightarrowΣNN$ couple…
Using the complex energy method, the problem of nucleon-deuteron scattering is solved with a simple three-body force having a separable form. Our results are compared with the results of modern direct two-variable calculations and a good agreement is found. This forms a firm base for other applications of the complex energy method.
The exchange of a single pion does not contribute to $Nα$ scattering, due to the isoscalar nature of the target. Therefore peripheral $Nα$ scattering may be used to probe existing models for the two-pion exchange component of the $NN$ potential. In a recent work we have considered this possibility using an effective $Nα$ interaction based on two-body forces only. In the present communication we discuss the role played by the two-pion exchange three-nucleon force, since its range is comparable to the two-pion exchange potential (TPEP).
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 ene…
We have calculated and compared the three-body force effects on the properties of nuclear matter under the gap and continuous choices for the self-consistent auxiliary potential within the Brueckner-Hartree-Fock approach by adopting the Argonne $V18$ and the Bonn B two-body potentials plus a microscopic three-body force (TBF). The TBF provides a strong repulsive effect on the equation of state of nuclear matter at high densities for both the gap and continuous choices. The saturation point turns out to be much closer to the empirical value when the continuous choice is adopted. In addition, th…
The method of screening and renormalization for including the Coulomb interaction in the framework of momentum-space integral equations is applied to the three- and four-body nuclear reactions. The Coulomb effect on the observables and the ability of the present nuclear potential models to describe the experimental data is discussed.
Implementation of chiral two-nucleon forces to nuclear many-body methods with Gaussian-wave packets
针对手征有效场理论未应用于高斯波包核多体方法的问题，本文提出计算手征两核力两体矩阵元的形式体系，可视化矩阵元并分析力的贡献，为团簇现象的从头算研究奠定基础。
We present calculations for symmetric nuclear matter using chiral nuclear interactions within the Self-Consistent Green's Functions approach in the ladder approximation. Three-body forces are included via effective one-body and two-body interactions, computed from an uncorrelated average over a third particle. We discuss the effect of the three-body forces on the total energy, computed with an extended Galitskii-Migdal-Koltun sum-rule, as well as on single-particle properties. Saturation properties are substantially improved when three-body forces are included, but there is still some underlyi…
We study the effect of the nucleon-nucleon-lambda (NN$Λ$) three-body force on neutron stars. In particular, we consider the NN$Λ$ force recently derived by the Jülich--Bonn--Munich group within the framework of chiral effective field theory at next-to-next-to-leading order. This force, together with realistic nucleon-nucleon, nucleon-nucleon-nucleon and nucleon-hyperon interactions, is used to calculate the equation of state and the structure of neutron stars within the many-body non-relativistic Brueckner-Hartree-Fock approach. Our results show that the inclusion of the NN$Λ$ force leads to a…
We explore the effects of a microscopic nuclear three-body force on the threshold baryon density for kaon condensation in chemical equilibrium neutron star matter and on the composition of the kaon condensed phase in the framework of the Brueckner-Hartree-Fock approach. Our results show that the nuclear three-body force affects strongly the high-density behavior of nuclear symmetry energy and consequently reduces considerably the critical density for kaon condensation provided that the proton strangeness content is not very large. The dependence of the threshold density on the symmetry energy …
The inclusion of the three-nucleon forces (3NFs) in \textit{ab initio} many-body approaches is a formidable task, due to the computational load implied by the treatment of their matrix elements. For this reason, practical applications have mostly been limited to contributions where 3NFs enter as effective two-nucleon interactions. In this contribution, we derive the algebraic diagrammatic construction (ADC) working equations for a specific Feynman diagram of the self-energy that contains a fully irreducible three-nucleon force. This diagram is expected to be the most important among those prev…
Classifying the strengthes of three-body forces 3BFs with the condition that observables must be cut-off independent, i.e. renormalised at each order, leads to surprising results with relevance for example for thermal neutron capture on the deuteron. Details and a better bibliography in Ref. [1].
In the present work we are going to add a correction to the BHF potential calculation by introducing a two- body density dependent potential that acts as a three body interaction. Adding the result of this potential to the BHF potential would give us new saturation curves which coincide with the results obtained from the experiment. We compute the energy per particle versus density curves for symmetric nuclear matter, pure neutron matter and the symmetry energy using modern nucleon nucleon potentials like CD Bonn.
Available data on large-angle nucleon-deuteron elastic scattering $Nd\to dN$ below the pion threshold give a signal for three-body forces. There is a problem of separation of possible subtle aspects of these forces from off-shell effects in two-nucleon potentials. By considering the main mechanisms of the process, we show qualitatively that in the quasi-binary reaction $N+d\to (NN)+N$ with the final spin singlet NN-pair in the S-state the relative contribution of the 3N forces differs substantially from the elastic channel. It gives a new testing ground for the problem in question.
The equation of state of symmetric nuclear matter has been investigated within Brueckner approach adopting the charge-dependent Argonne $V_{18}$ two-body force plus a microscopic three-body force based on a meson-exchange model. The effects on the equation of state of the individual processes giving rise to the three-body force are explored up to high baryonic density. It is found that the major role is played by the competition between the strongly repulsive $(σ, ω)$ exchange term with virtual nucleon-antinucleon excitation and the large attractive contribution due to $(σ, ω)$ exchange with $…
We parameterize the recently proposed generalized Skyrme effective force (GSEF) containing extended density dependence. The parameters of the GSEF are determined by the fit to several properties of the normal and isospin-rich nuclei. We also include in our fit a realistic equation of state for the pure neutron matter up to high densities so that the resulting Skyrme parameters can be suitably used to model the neutron star with the "canonical" mass ($\sim 1.4 M_\odot$). For the appropriate comparison we generate a parameter set for the standard Skyrme effective force (SSEF) using exactly the s…
In this paper we present an evolution of our derivation of the shell-model effective Hamiltonian, namely introducing effects of three-body contributions. More precisely, we consider a three-body potential at next-to-next-to-leading order in chiral perturbation theory, and the induced three-body forces that arise from many-body correlations among valence nucleons. The first one is included, in the derivation of the effective Hamiltonian for one- and two-valence nucleon-systems, at first order in the many-body perturbation theory. Namely, we include only the three-body interaction between one or…
A multi-component formalism is developed to describe three-body systems with nonstatic pairwise interactions and non-nucleonic degrees of freedom. The dressed-bag model for $NN$ interaction based on the formation of an intermediate six-quark bag dressed by a $σ$-field is applied to the $3N$ system, where it results in a new three-body force between the six-quark bag and a third nucleon. Concise variational calculations of $3N$ bound states are carried out in the dressed-bag model including the new three-body force. It is shown that this three-body force gives at least half the $3N$ total bindi…
We report quantum Monte Carlo calculations of single-$Λ$ hypernuclei for $A<50$ based on phenomenological two- and three-body hyperon-nucleon forces. We present results for the $Λ$ separation energy in different hyperon orbits, showing that the accuracy of theoretical predictions exceeds that of currently available experimental data, especially for medium-mass hypernuclei. We show the results of a sensitivity study that indicates the possibility to investigate the nucleon-isospin dependence of the three-body hyperon-nucleon-nucleon force in the medium-mass region of the hypernuclear chart, whe…
In order to improve the description of the N-d vector analyzing powers Ay and iT11 (the so-called Ay puzzle) a spin-orbit three-body force has been introduced. The L.S term in the NN potential has been modified including a two-parameter three-body function depending on the hyperradius ρ. The modification has been performed in channels where the pair nucleons (i,j) are coupled to spin Sij=1 and isospin Tij=1. Calculations have been done in the energy region from Elab=648 keV up to Elab=10 MeV. A noticeable improvement in the description of the polarization observables has been obtained
The need for the three-body forces (3BF) for reproduction of physical properties of light nuclei has been evident for some time. These 3BF are doing quite well for light nuclei, but there seems to be scope for other 3BF which may arise from other physical considerations not included so far. Here we discuss a QCD motivated new 3BF which should be included in studies of nuclei, in particular the light one3s. We perform variational Monte Carlo calculations including this new 3BF and discuss improvements brought in thereby for light nuclei.
Working in the framework of the ab-initio no-core shell model, we derive two-body effective interactions microscopically for specific harmonic-oscillator basis spaces from the realistic Argonne V8' nucleon-nucleon potential. However, our two-body effective interaction is only the dominant part of the A-body (A >= 3) effective interaction, which also contains three-, four- and, in general, up to A-body components. We model these multi-body components as a simple two-parameter, basis-space-dependent interaction. We then investigate the coupling needed to provide accurate descriptions of selected…
Faddeev calculations have been performed for nucleon-deuteron photodisintegration of 3He(3H) and proton-deuteron radiative capture. The bulk of the results is based on the AV18 nucleon-nucleon force and the Urbana IX three-nucleon force together with explicit exchange currents or applying the Siegert approach. Three-nucleon force effects are predicted for both processes and supported by most of the data.
A detailed analysis of the effect of tensor correlations on one- and two-body densities and momentum distributions of complex nuclei is presented within a linked cluster expansion providing reliable results for the ground state properties of nuclei calculated with realistic interactions.
In Faddeev calculations of ^3Hwe study the dependence of the binding on the three nucleon force. We adopt the 2 pi -exchange Tucson-Melbourne three-nucleon force and investigate phenomenologically the dependence on the strength of the individual three-body force operators (a -, b -, c - and d -terms). While the a -term provides a tiny contribution the b - and d -terms provides a tiny contribution the b - and d -terms are important to gain the experimental binding energy. We find two solutions for the c -term, one around the value used in the Tucson-Melbourne model and a new one close to zero, …
We present an ab-initio calculation of the longitudinal electron scattering response function off 4He with two- and three-nucleon forces and compare to experimental data. The full four-body continuum dynamics is considered via the Lorentz integral transform method. The importance of the final state interaction is shown at various energies and momentum transfers q. The three-nucleon force reduces the quasi-elastic peak by 10% for q between 300 and 500 MeV/c. Its effect increases significantly at lower q, up to about 40% at q=100 MeV/c. At very low q, however, data are missing.
In a recent paper we studied the behavior of the pairing gaps $Δ_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations employed realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. In this contribution, after a detailed description of the numerical method we employed in the solution of the BCS equations, we will show a preliminary analysis of the Cooper pair wavefunctions.
In the past decades, it has been shown that the three-body force is necessary for a fully microscopic understanding of nuclear many-body systems, and thus efficient schemes for storing and utilizing three-body matrix elements have been developed. However, three-body matrix elements still demand a lot of memory and/or storage and it readily exceeds the limitation of the state-of-the-art supercomputers. We explore the possibility of mimicking the effects of three-body forces in medium-mass region, especially lower $pf$ shell, by density-dependent effective nucleon-nucleon interactions combining …
We explore skewed parton distributions for simple, model wave-functions in a truncated two-body Fock space. Consideration of non-Gaussian wave functions is our main emphasis, from which we observe the distributions are bimodal (there can be two distinct peaks) in the Fock-space diagonal overlap region (x > xi). We demonstrate that this behavior arises from convoluting two light-front wave functions to form the skewed parton distribution. Furthermore, the factorization Ansaetze, which have been used often, are shown not to hold. At high t, we can write the skewed parton distribution in terms of…
The quantum anomaly can be written alternatively into a form violating conservation laws or as non-gauge invariant currents seen explicitly on the example of chiral anomaly. By reinterpreting the many-body averaging, the connection to Pauli-Villars regularization is established which gives the anomalous term a new interpretation as arising from quantum fluctuations by many-body correlations at short distances. This is exemplified by using an effective many-body quantum potential which realizes quantum Slater sums by classical calculations. It is shown that these quantum potentials avoid the qu…
The cancellation between off-shell two body forces and three body forces implies a tremendous simplification in the study of three body resonances in two meson-one baryon systems. While this can be done by means of Faddeev equations we provide an alternative and simpler derivation using just the chiral Lagrangian and the field re-parametrization invariance.
We provide a calculation of N-body (N>2) nucleon interactions at short distances in holographic QCD. In the Sakai-Sugimoto model of large N_c massless QCD, N baryons are described by N Yang-Mills instantons in 5 spacetime dimensions. We compute a classical short distance interaction hamiltonian for N 'tHooft instantons. This corresponds to N baryons sharing identical classical spins and isospins. We find that genuine N-body nuclear forces turn out to vanish for N>2, at the leading order. This suggests that classical N-body forces are always suppressed compared with 2-body forces.
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