A self-consistent calculation of nuclear matrix elements of the neutrinoless double beta decays (0nbb) of 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te and 130Xe is presented in the framework of the renormalized quasiparticle random phase approximation (RQRPA) and the standard QRPA. The pairing and residual interactions as well as the two-nucleon short-range correlations are for the first time derived from the same modern realistic nucleon-nucleon potentials, namely from charge-dependent Bonn potential (CD-Bonn) and the Argonne V18 potential. In a comparison with the traditional approach of using the Miller-Spencer Jastrow correlations matrix elements for the 0nbb-decay are obtained, which are larger in magnitude. We analyze the differences among various two-nucleon correlations including those of the unitary correlation operator method (UCOM) and quantify the uncertainties in the calculated 0nbb-decay matrix elements.
We analyze neutrinoless double $β$-decay ($\nbb$-decay) mediated by heavy particles from the standpoint of effective field theory. We show how symmetries of the $\nbb$-decay quark operators arising in a given particle physics model determine the form of the corresponding effective, hadronic operators. We classify the latter according to their symmetry transformation properties as well as the order at which they appear in a derivative expansion. We apply this framework to several particle physics models, including R-parity violating supersymmetry (RPV SUSY) and the left-right symmetric model (L…
We determine the influence of the three-body force and the medium modification of meson masses on pairing in nuclear and neutron matter. A reduction of the pairing gap is found and increasing with density.
The nucleon spectral function in nuclear matter fulfills an energy weighted sum rule. Comparing two different realistic potential, these sum rules are studied for Green's functions that are derived self-consistently within the $T$ matrix approximation at finite temperature.
A fully self-consistent treatment of short-range correlations in nuclear matter is presented. Different implementations of the determination of the nucleon spectral functions for different interactions are shown to be consistent with each other. The resulting saturation densities are closer to the empirical result when compared with (continuous-choice) Brueckner-Hartree-Fock values. Arguments for the dominance of short-range correlations in determining the nuclear-matter saturation density are presented. A further survey of the role of long-range correlations suggests that the inclusion of pio…
The spectral function of protons in the asymmetric nuclear matter is calculated in the self-consistent T-matrix approach. The spectral function per proton increases with increasing asymmetry. This effect and the density dependence of the spectral function partially explain the observed increase of the spectral function with the mass number of the target nuclei in electron scattering experiments.
Dynamical correlations in asymmetric infinite nuclear matter are investigates in a transport theoretical approach. Self-energies due to short range correlations and their influence on the nucleon spectral functions are described in an approach accounting for a realistic treatment of mean-field dynamics and a self-consistently derived quasi-particle interaction. Landau-Migdal theory is used to derived the short range interaction from a phenomenological Skyrme energy density functional. The spectral functions in asymmetric nuclear matter are found to follow in their gross features closely the pa…
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group. Much of his work was based on Brueckner's formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski-Scott separation method that was an important part of his early work. The core-polarisation and his work related to effective interactions in general are also addressed.
The electromagnetic transitions to various low-lying excited states of 16O, 48Ca and 208Pb are calculated within a model which considers the short-range correlations. In general the effects of the correlations are small and do not explain the required quenching to describe the data.
Recent results concerning the use of the Correlated Basis Function to investigate the ground state properties of medium-heavy doubly magic nuclei with microscopic interactions are presented. The calculations have been done by considering a Short-Range Correlation between nucleons. The possibility of identifying effects produced by Short-Range Correlations in electromagnetically induced phenomena is discussed.
We apply ideas of the parquet-diagram and optimized Fermi-hypernetted chain methods to determine the short-range structure of the pair wave function in neutron matter and compare these with Bethe-Goldstone results and those of low-order variational calculations. It is shown that the induced interaction, describing the exchange of density, spin, and tensor fluctuations, has a profound influence on the short-ranged structure of the pair wave function and, hence, on effective interactions in neutron matter.
The structure and density dependence of the pairing gap in infinite matter is relevant for astrophysical phenomena and provides a starting point for the discussion of pairing properties in nuclear structure. Short-range correlations can significantly deplete the available single-particle strength around the Fermi surface and thus provide a reduction mechanism of the pairing gap. Here, we study this effect in the singlet and triplet channels of both neutron matter and symmetric nuclear matter. Our calculations use phase-shift equivalent interactions and chiral two-body and three-body interactio…
The density and temperature dependence of nucleonic single particle spectral function in symmetric nuclear matter at finite temperatures and densities beyond normal nuclear matter density is investigated in a model emphasizing short-range correlations and phase space aspects. A simple but self-consistent approach based on quantum transport theory is used. In particular we consider the density and temperature regime occuring e.g. during the core collapse in a supernova explosion and the subsequent formation of a neutron star. Mean-field effects are incorporated by a Skyrme type potential.
Short-range correlations in nuclear and neutron matter are examined through the properties of the correlated wave function obtained by solving the Bethe-Goldstone equation. Tensor correlations are explored through the dominant tensor-driven transition and central correlations through the singlet and triplet S waves. Predictions from a popular meson-theoretic nucleon-nucleon potential employed in the Dirac-Brueckner-Hartree-Fock approach are compared with those from two- and three-body high-quality chiral interactions in Brueckner G-matrix calculations. Short-range correlations in symmetric mat…
Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. It is shown that the correlations give rise to an extra node in the ground-state wave-function in the nucleons, contrary to what happens in non-relativistic calculations with a hard core. The effect of the correlations in the ground state properties of the nuclear matter and neutron matter is studied. The nucleon effective mass and equation of state (EOS) are very sensitive to short range …
We report the results of a calculation of the nuclear matrix element of neutrinoless double-$β$ decay of $^{48}$Ca, carried out taking into account nucleon-nucleon correlations in both coordinate- and spin-space. Our numerical results, obtained using nuclear matter correlation functions, suggest that inclusion of correlations leads to a $\sim$ $20\%$ decrease of the matrix element, with respect to the shell model prediction. This conclusion is supported by the results of an independent calculation, in which correlation effects are taken into account using the spectroscopic factors of $^{48}$Ca…
We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.
We calculate the nuclear matrix elements of the neutrinoless double beta ($0νββ$) decays of $^{76}$Ge and $^{82}$Se for the light-neutrino exchange mechanism. The nuclear wave functions are obtained by using realistic two-body forces within the proton-neutron quasiparticle random-phase approximation (pnQRPA). We include the effects that come from the finite size of a nucleon, from the higher-order terms of nucleonic weak currents, and from the nucleon-nucleon short-range correlations. Most importantly, we improve on the presently available calculations by replacing the rudimentary Jastrow shor…
The Unitary Correlation Operator Method (UCOM) is applied to realistic potentials. The effects of tensor correlations are investigated. The resulting phase shift equivalent correlated interactions are used in the no-core shell model for light nuclei and for mean-field calculations in the Fermionic Molecular Dynamics model for nuclei up to mass A=48.
Continuing our effort to build a consistent power counting for chiral nuclear effective field theory (EFT), we discuss the subleading contact interactions, or counterterms, in the singlet channels of nucleon-nucleon scattering, with renormalization group invariance as the constraint. We argue that the rather large cutoff error of the leading amplitude requires O(Q) of the EFT expansion to be nonvanishing, contrary to Weinberg's original power counting. This, together with the ultraviolet divergences of two-pion exchanges in the distorted-wave expansion, leads to enhancement of the 1S0 countert…
A study of the effects of short-range correlations over the (e,e'p) reaction for low missing energy in closed shell nuclei is presented. We use correlated, quasi-hole overlap functions extracted from the asymptotic behavior of the one-body density matrix, containing central correlations of Jastrow type, up to first-order in a cluster expansion, and computed in the very high asymptotic region, up to 100 fm. The method to extract the overlap functions is checked in a simple shell model, where the exact results are known. We find that the single-particle wave functions of the valence shells are s…
We investigate the effects of fluctuations of the nuclear surface on the harmonic oscillator elastic charge form factor of light nuclei, while simultaneously approximating the short-range correlations through a Jastrow correlation ~factor. Inclusion of surface-fluctuation effects within this description, by truncating the cluster expansion at the two-body part, is found to improve somewhat the fit to the elastic charge form-factor of $^{16}O$ and $^{40}Ca$. However, the convergence of the cluster expansion is expected to deteriorate. An additional finding is that the surface-fluctuation correl…
A recent paper [S. Ohkubo, Phys. Rev. C 95, 044002 (2017)] found that the measured 1S0 phase shifts can be reproduced using a deeply attractive nucleon-nucleon potential. We find that the deuteron would decay strongly via pion emission to the deeply bound state arising in this potential. There- fore the success of a deeply attractive potential in describing phase shifts must be regarded only as an interesting curiosity.
The main goal of the research presented in this dissertation was to develop a theoretical model for relativistic nuclear spectral functions at high missing momenta and removal energies based on the multi-nucleon short-range correlation (SRC) model. The nuclear spectral functions are necessary for the description of high energy nuclear processes currently being studied at different labs such as JLAB, LHC and FNAL. The model followed the effective Feynman diagrammatic approach in order to account for the relativistic effects important in the SRC domain. In addition to the two-nucleon (2N) SRC wi…
Ab initio short-range nuclear matrix elements for neutrinoless double-beta decay
TRIUMF（特柳姆夫实验室）；McGill University（麦吉尔大学）；University of British Columbia（不列颠哥伦比亚大学）；Massachusetts Institute of Technology（麻省理工学院）；Technische Universität Darmstadt（达姆施塔特工业大学）；ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH（极端物质研究所EMMI，GSI重离子研究中心有限公司）
We extend a recent chiral approach to nuclear matter of Lutz et al. [Phys. Lett. B474 (2000) 7] by calculating the underlying (complex-valued) single-particle potential U(p,k_f) + i W(p,k_f). The potential for a nucleon at the bottom of the Fermi-sea, U(0,k_{f0})= - 20.0 MeV, comes out as much too weakly attractive in this approach. Even more seriously, the total single-particle energy does not rise monotonically with the nucleon momentum p, implying a negative effective nucleon mass at the Fermi-surface. Also, the imaginary single-particle potential, W(0,k_{f0}) = 51.1 MeV, is too large. More…
Variational calculations of symmetric nuclear matter and pure neutron matter with the tensor-optimized Fermi Sphere (TOFS) method: many-body effects and short-range correlation
We sketch an approximate method to quantify the number of correlated pairs in any nucleus $A$. It is based on counting independent-particle model (IPM) nucleon-nucleon pairs in a relative $S$-state with no radial excitation. We show that IPM pairs with those quantum numbers are most prone to short-range correlations and are at the origin of the high-momentum tail of the nuclear momentum distributions. Our method allows to compute the $a_2$ ratios extracted from inclusive electron scattering. Furthermore, our results reproduce the observed linear correlation between the number of correlated pai…
We put forward a formalism to calculate the relativistic particle - hole and delta - hole excitation polarization insertion for pion propagator by using the particle - hole - antiparticle representation of nucleon and delta propagators in nuclear matter. The real and the imaginary part of the polarization insertion and the dispersion relation for pion propagator are calculated numerically. We find that the short range correlation enhances the delta - hole excitation but suppresses the particle - hole excitation, it also suppresses the pion condensation. We find that the effect of the short ran…
Short range correlations are introduced using unitary correlation method in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation. The effect of the correlations in the ground state properties of the nuclear matter is studied.
The short-range and tensor correlations associated to realistic nucleon-nucleon interactions induce a population of high-momentum components in the many-body nuclear wave function. We study the impact of such high-momentum components on bulk observables associated to isospin asymmetric matter. The kinetic part of the symmetry energy is strongly reduced by correlations when compared to the non-interacting case. The origin of this behavior is elucidated using realistic interactions with different short-range and tensor structures.
Nuclear matrix elements of the neutrinoless double beta decays of 96Zr, 100Mo, 116Cd, 128Te, 130Te and 136Xe are calculated for the light-neutrino exchange mechanism by using the proton-neutron quasiparticle random-phase approximation (pnQRPA) with a realistic nucleon-nucleon force. The g_pp parameter of the pnQRPA is fixed by the data on the two-neutrino double beta decays and single beta decays. The finite size of a nucleon, the higher-order terms of nucleonic weak currents, and the nucleon-nucleon short-range correlations (s.r.c) are taken into account. The s.r.c. are computed by the tradit…
Semiclassical periodic-orbit theory (POT) is applied to the physics of nuclear structures, with the use of a realistic nuclear mean-field model given by the radial power-law potential. Evolution of deformed shell structures, which are responsible for various nuclear deformations, are clearly understood from the contribution of short classical periodic orbits (POs). Bifurcations of short POs, which imply underlying local dynamical symmetry, play significant role there. The effect of the spin degree of freedom is also investigated in relevance to the pseudospin symmetry in spherical nuclei and t…
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 nucl…
Effects of the short-range tensor interaction on the density-dependence of nuclear symmetry energy are examined by applying an approximate expression for the second-order tensor contribution to the symmetry energy derived earlier by G.E. Brown and R. Machleidt. It is found that the uncertainty in the short-range tensor force leads directly to a divergent high-density behavior of the nuclear symmetry energy.
The eigenvalue problem of a short-range potential is revisited in view of the increased interest in simple models imitating the nuclear forces. This is in order to conduct calculations of vibronic energies in fermion-boson coupled systems.
In the present work short range correlations are introduced for the first time in a relativistic approach to the equation of state of the infinite nuclear matter in the framework of the Hartree-Fock approximation using an effective Hamiltonian derived from the $σ-ω$ Walecka model. The unitary correlation method is used to introduce short range correlations. The effect of the correlations in the ground state properties of the nuclear matter is discussed.
In this work we report on the effects of short-range correlations upon the matrix elements of neutrinoless double beta decay. We focus on the calculation of the matrix elements of the neutrino-mass mode of neutrinoless double beta decays of 48Ca and 76Ge. The nuclear-structure components of the calculation, that is the participant nuclear wave functions, have been calculated in the shell-model scheme for 48Ca and in the proton-neutron quasiparticle random-phase approximation (pnQRPA) scheme for 76Ge. We compare the traditional approach of using the Jastrow correlation function with the more co…
This contribution gives a short review of recent theoretical advances in most topics of nuclear cluster physics concentrating, however, around {$α$} particle clustering. Along the route, the point of view will be critical mentioning not only progress but also failures and open problems.
A linear correlation is found between the magnitude of nucleon-nucleon short-range correlations and the nuclear binding energy per nucleon with pairing energy removed. By using this relation, the strengths of nucleon-nucleon short-range correlations of some unmeasured nuclei are predicted. Discussions on nucleon-nucleon pairing energy and nucleon-nucleon short-range correlations are made. The found nuclear dependence of nucleon-nucleon short-range correlations may shed some lights on the short-range structure of nucleus.
The present paper is aimed to developing an effective field theory in the GeV region to describe consistently both elastic and inelastic NN-scattering in a fully covariant way. In this development we employ our novel s-channel mechanism of NN-interaction at intermediate and short ranges assuming a formation of the six-quark bag dressed with basic meson fields such as $π$, $σ$, $ρ$ and $ω$ in the intermediate state. The peripheral part of the interaction is governed by t-channel one- and two-pion exchanges described fairly well by chiral perturbation theory. The $σ$-meson dressing should be esp…
The evaluation of short range contributions to neutrinoless double beta decay has been challenged due to critics of the ansatz of the nuclear matrix element calculations. We comment on the critics and uncertainties of these calculations and the effect on the derived limits.
Computational difficulties aside, nonequilibrium Green's functions appear ideally suited for investigating the dynamics of central nuclear reactions. Many particles actively participate in those reactions. At the two energy extremes for the collisions, the limiting cases of the Green's function approach have been successful: the time-dependent Hartree-Fock theory at low energy and Boltzmann equation at high. The strategy for computational adaptation of the Green's function to central reactions is discussed. The strategy involves, in particular, incremental progression from one to three dimensi…
We extend a recent chiral approach to nuclear matter by including the most general (momentum-independent) NN-contact interaction. Iterating this two-parameter contact-vertex with itself and with one-pion exchange the emerging energy per particle exhausts all terms possible up-to-and-including fourth order in the small momentum expansion. The equation of state of pure neutron matter, $\bar E_n(k_n)$, can be reproduced very well up to quite high neutron densities of $ρ_n=0.5\fmd$ by adjusting the strength of a repulsive $nn$-contact interaction. Binding and saturation of isospin-symmetric nuclea…
Calculations of the $^{16}$O$(e,e'pN)$ cross sections to the ground state and first excited levels of the $^{14}$C and $^{14}$N nuclei are presented. The effects of nuclear fragmentation have been obtained in a self-consistent approach and are accounted for in the determination of the two-nucleon removal amplitudes. The Hilbert space is partitioned in order to compute the contribution of both long- and short-range effects in a separate way. Both the two-proton and the proton-neutron emission cross sections have been computed within the same models for the reaction mechanism and the contributio…
The past decade has provided a much clearer picture of the structure of high-momentum components in nucleons, associated with hard, short-distance interactions between pairs of nucleons. Recent Jefferson Lab data on light nuclei suggest a connection between these so-called 'short-range correlations' and the modification of the quark structure of nucleons in the nuclear environment. In light of this discovery that the detailed nuclear structure is important in describing the nuclear quark distributions, we examine the potential impact of the isospin-dependent structure of nuclei to see at what …
Employing four different parametrization of the pairing plus multipolar type of effective two-body interaction and three different parametrizations of Jastrow-type of short range correlations, the uncertainties in the nuclear transition matrix elements $M_{N}^{(0ν)}$ due to the exchange of heavy Majorana neutrino for the $0^{+}\rightarrow 0^{+}$ transition of neutrinoless double beta decay of $^{94}$Zr, $^{96}$Zr, $^{98}$Mo, $^{100}$Mo, $^{104}$Ru, $^{110}$Pd, $^{128,130}$Te and $^{150}$Nd isotopes in the PHFB model are estimated to be around 25%. Excluding the nuclear transition matrix elemen…
A relativistic and quantum mechanical framework to compute nuclear transparencies for pion photo- and electroproduction reactions is presented. Final-state interactions for the ejected pions and nucleons are implemented in a relativistic eikonal approach. At sufficiently large ejectile energies, a relativistic Glauber model can be adopted. At lower energies, the framework possesses the flexibility to use relativistic optical potentials. The proposed model can account for the color-transparency (CT) phenomenon and short-range correlations (SRC) in the nucleus. Results are presented for kinemati…
The hole spectral function is calculated in nuclear matter to assess the relevance of nucleon-nucleon short range correlations. The calculation is carried out within the Brueckner scheme of many-body theory by using several nucleon-nucleon realistic interactions. Results are compared with other approaches based on variational methods and transport theory. Discrepancies appear in the high energy region, which is sensitive to short range correlations, and are due to the different many-body treatment more than to the specific N-N interaction used. Another conclusion is that the momentum dependenc…
An overview is given of the theoretical work on nucleon spectral functions in finite nuclei. The consequences of the observed spectral strength distribution are then considered in the context of the nuclear-matter saturation problem. Arguments are presented suggesting that short-range correlations are mainly responsible for the actual value of the observed charge density in 208Pb and by extension for the empirical value of the saturation density of nuclear matter. This observation combined with the general understanding of the spectroscopic strength suggests that a renewed study of nuclear mat…
The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizeable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an \textit{ab-initio} description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi s…
A brief review is given concerning the status of the theoretical work on nucleon spectral functions. A recent concern about the validity of the concept of spectroscopic factors as deduced from (e,e'p) reactions at higher Q^2, is discussed in some detail. The consequences of the observed spectral strength are then considered in the context of nuclear saturation. It is argued that short-range correlations are mainly responsible for the actual value of the observed charge density in 208Pb and by extension for the empirical value of the saturation density of nuclear matter. This observation combin…
A short overview of the direct reaction mechanism and the models used for the analysis of such processes is given. Nuclear reactions proceeding through the direct mechanism and involved in solar hydrogen burning are discussed. The significance of these nuclear reactions with respect to the solar neutrino problem is investigated.
Quark-model descriptions of the nucleon-nucleon interaction contain two main ingredients, a quark-exchange mechanism for the short-range repulsion and meson-exchanges for the medium- and long-range parts of the interaction. We point out the special role played by higher partial waves, and in particular the 1F3, as a very sensitive probe for the meson-exchange part employed in these interaction models. In particular, we show that the presently available models fail to provide a reasonable description of higher partial waves and indicate the reasons for this shortcoming.
Ab-initio Quantum Monte Carlo (QMC) calculations of nuclei from deuterium to 40Ca, obtained using four different phenomenological and local chiral nuclear potentials, are analyzed using the Generalized Contact Formalism (GCF). We extract spin- and isospin-dependent "nuclear contact terms" for each interaction in both coordinate and momentum space. The extracted contact terms, that count the number of short-range correlated (SRC) pairs with different quantum numbers, are dependent on the nuclear interaction model used in the QMC calculation. However, the ratios of contact terms for a nucleus A …
