Isospin Dynamics in Heavy Ion Collisions: from Coulomb Barrier to Quark Gluon Plasma
M. Di Toro, V. Baran, M. Colonna, G. Ferini, T. Gaitanos, V. Giordano, V. Greco, Liu Bo, M. Zielinska-Pfabe, S. Plumari, V. Prassa, C. Rizzo, J. Rizzo, H. H. Wolter
备注：
18 pages, 12 figures, lecture at the 2008 Erice School on Nuclear Physics, to appear in Progress in Particle and Nuclear Physics
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this report we present a selection of new reaction observables in dissipative collisions particularly sensitive to the symmetry term of the nuclear Equation of State (Iso-EoS). We will first discuss the Isospin Equilibration Dynamics. At low energies this manifests via the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation with the symmetry term acting as a restoring force. At higher beam energies Iso-EoS effects will be seen in Imbalance Ratio Measurements, in particular from the correlations with the total kinetic energy loss. For fragmentation reactions in central events we suggest to look at the coupling between isospin distillation and radial flow. In Neck Fragmentation reactions important $Iso-EoS$ information can be obtained from the correlation between isospin content and alignement. The high density symmetry term can be probed from isospin effects on heavy ion reactions at relativistic energies (few AGeV range). Rather isospin sensitive observables are proposed from nucleon/cluster emissions, collective flows and meson production. The possibility to shed light on the controversial neutron/proton effective mass splitting in asymmetric matter is also suggested. A large symmetry repulsion at high baryon density will also lead to an "earlier" hadron-deconfinement transition in n-rich matter. A suitable treatment of the isovector interaction in the partonic EoS appears very relevant.
In this work, the Coulomb mixing and the isospin mixing in the ground states of even-even nuclei are evaluated in perturbation theory. The calculation of the isospin mixing is performed by using the connection to isovector monopole resonance properties. The uncertainty in the results that depends on different choices of the Skyrme interactions is shown. While Coulomb mixing turns out to be large in the ground states of heavy nuclei, isospin mixing is very small.
Applying the Hellmann-Feynman theorem to a charged pion gas, the quark and gluon condensates at low isospin density are determined by precise pion properties. At intermediate density around $ f_π^2m_π$, from both the estimation for the dilute pion gas and the calculation with Nambu--Jona-Lasinio model, the quark condensate is strongly and monotonously suppressed, while the gluon condensate is enhanced and can be larger than its vacuum value. This unusual behavior of the gluon condensate is universal for Bose condensed matter of mesons. Our results can be tested by lattice calculations at finit…
Isospin violation effects in nuclei are investigated within a microscopic approach which takes into account the influence of the residual strong interaction on the Coulomb interaction. The renormalization of the off-diagonal Coulomb field acting within a nucleus, by the residual strong interaction is calculated analytically in a simplified RPA. From the expression for the suppression coefficient of the isospin violating part of the Coulomb field, the isospin violating spreading widths of isobaric analog states are derived. The resulting reduction of the width is in agreement with the data on t…
The anomaly in Coulomb energy differences (CED) between the isospin T=1 states in the odd-odd N=Z nucleus 70Br and the analogue states in its even-even partner 70Se has remained a puzzle. This is a direct manifestation of isospin-symmetry breaking in effective nuclear interactions. Here, we perform large-scale shell-model calculations for nuclei with A=66-78 using the new filter diagonalization method based on the Sakurai-Sugiura algorithm. The calculations reproduce well the experimental CED. The observed negative CED for A=70 are accounted for by the cross-shell neutron excitations from the …
We investigate the role of the Coulomb and the vector-isovector $ρ$ potentials in the asymmetry of the neutron and proton pseudospin splittings in nuclei. To this end, we solve the Dirac equation for the nucleons using central vector and scalar potentials with Woods-Saxon shape and $Z$ and $N-Z$ dependent Coulomb and $ρ$ potentials added to the vector potential. We study the effect of these potentials on the energy splittings of proton and neutron pseudospin partners along a Sn isotopic chain. We use an energy decomposition proposed in a previous work to assess the effect of a pseudospin-orbit…
We study the role the proton-electron gas interaction has on the formation of nuclear structures in neutron star crusts. Using a classical molecular dynamics model we study isospin symmetric and asymmetric matter at subsaturation densities and low temperatures varying the Coulomb interaction strength. The effect of such variation is quantified on the fragment size multiplicity, the inter-particle distance, the isospin content of the clusters, the nucleon mobility and cluster persistence, and on the nuclear structure shapes. We find that the proton-electron Coulomb interaction distributes matte…
We study Fermi transitions and isospin mixing in an isotopic chain 70-78 Kr considering various approximations that use the same Skyrme-Hartree-Fock single particle basis. We study Coulomb effects as well as the effect of BCS and quasiparticle random phase approximation (QRPA) correlations. A measure of isospin mixing in the approximate ground state is defined by means of the expectation value of the isospin operator squared in N=Z nuclei (which is generalized to N different from Z nuclei). Starting from strict Hartree-Fock approach without Coulomb, it is shown that the isospin breaking is neg…
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isobaric systems with N/A = 0.5 and 0.58. Our fndings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
The isospin breaking effects due to the Coulomb interaction in weakly-bound nuclei are studied using the Gamow Shell Model, a complex-energy configuration interaction approach which simultaneously takes into account many-body correlations between valence nucleons and continuum effects. We investigate the near-threshold behavior of one-nucleon spectroscopic factors and the structure of wave functions along an isomultiplet. Illustrative calculations are carried out for the T=1 isobaric triplet. By using a shell-model Hamiltonian consisting of an isoscalar nuclear interaction and the Coulomb term…
Effects of the isospin-symmetry breaking (ISB) beyond mean-field Coulomb terms are systematically studied in nuclear masses near the $N=Z$ line. The Coulomb exchange contributions are calculated exactly. We use extended Skyrme energy density functionals (EDFs) with proton-neutron-mixed densities, to which we add new terms breaking the isospin symmetry. Two parameters associated with the new terms are determined by fitting mirror and triplet displacement energies (MDEs and TDEs) of isospin multiplets. The new EDFs reproduce MDEs for the $T=\frac12$ doublets and $T=1$ triplets, and TDEs for the …
We study the effect of isospin degree of freedom on the balance energy (E$_{bal}$) as well as its mass dependence throughout the mass range 48-270 for two sets of isobaric systems with N/Z = 1 and 1.4 at different colliding geometries ranging from central to peripheral ones. Our findings reveal the dominance of Coulomb repulsion in isospin effects on E$_{bal}$ as well as its mass dependence throughout the range of the colliding geometry. Our results also indicate that the effect of symmetry energy and nucleon-nucleon cross section on E$_{bal}$ is uniform throughout the mass range and throughou…
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isotopic systems with N/Z = 1.16 and 1.33 as well as isobaric systems with N/A = 1.0 and 1.4. Our findings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
We study the effect of isospin degree of freedom on balance energy throughout the mass range between 50 and 350 for two sets of isotopic systems with N/Z = 1.16 and 1.33 as well as isobaric systems with N/Z = 1.0 and 1.4. Our findings indicate that different values of balance energy for two isobaric systems may be mainly due to the Coulomb repulsion. We also demonstrate clearly the dominance of Coulomb repulsion over symmetry energy.
We present a new procedure of isospin symmetry breaking of cooper-quartets in nuclear matter using Ginzburg-Landau theory, namely we couple the cooper-quartets to the pion-meson field and $SU(2)$ gluons. The paper also describes phenomena resulting from this approach.
Heavy Ion Collisions (HIC) represent a unique tool to probe the in-medium nuclear interaction in regions away from saturation. In this work we present a selection of reaction observables in dissipative collisions particularly sensitive to the isovector part of the interaction, i.e. to the symmetry term of the nuclear Equation of State (EoS). At low energies the behavior of the symmetry energy around saturation influences dissipation and fragment production mechanisms. We will first discuss the recently observed Dynamical Dipole Radiation, due to a collective neutron-proton oscillation during t…
Precision Tests of Isospin Symmetry through Coulomb excitation of A = 62 Nuclei
GSI Helmholtzzentrum für Schwerionenforschung（GSI亥姆霍兹重离子研究中心）；Department of Physics, The University of Tokyo（东京大学物理系）；RIKEN Nishina Center（理化学研究所仁科中心）；Instituto de Fisica Corpuscular, CSIC-Universidad de Valencia（瓦伦西亚大学-CSIC粒子物理研究所）；Dipartimento di Fisica e Astronomia, Università di Padova（帕多瓦大学物理与天文学系）；INFN, Sezione di Padova（意大利国家核物理研究所帕多瓦分部）；Departamento de Física Teórica, Universidad Autónoma de Madrid（马德里自治大学理论物理系）；School of Physics, Engineering and Technology, University of York（约克大学物理、工程与技术学院）；College of Education, Yokohama National University（横滨国立大学教育学部）；Center for Nuclear Study, University of Tokyo（东京大学核研究分中心）；Instituto de Estructura de la Materia, CSIC（CSIC物质结构研究所）
We investigate the effect of the inclusion of relativistic Coulomb terms in a confined-isospin-density-dependent-mass (CIDDM) model of strange quark matter (SQM). We found that if we include Coulomb term in scalar density form, SQM equation of state (EOS) at high densities is stiffer but if we include Coulomb term in vector density form is softer than that of standard CIDDM model. We also investigate systematically the role of each term of the extended CIDDM model. Compared with what was reported in Ref.~\cite {ref:isospin}, we found the stiffness of SQM EOS is controlled by the interplay amon…
Recent experimental data have revealed large mirror energy differences (MED) between high-spin states in the mirror nuclei 67Se and 67As, the heaviest pair where MED have been determined so far. The MED are generally attributed to the isospin symmetry breaking caused by the Coulomb force and by the isospin nonconserving part of the nucleon-nucleon residual interaction. The different contributions of the various terms have been extensively studied in the fp shell. By employing large-scale shell model calculations, we show that the inclusion of the g9/2 orbit causes interference between the elec…
Isospin is included in the description of Coulomb excitation of multiple giant isovector dipole resonances. In the excitation of even-even nuclei, a relevant portion of the excitation strength is shown to be associated with 1+ two-phonon states, which tends to be hindered or completely supressed in calculations in which the isospin degree of freedom is not considered. We find that the excitation cross sections is strongly dependent on the ground state isospin.
Two instructive effects concerning fragment production at disintegration of finite nuclei are predicted with the statistical multifragmentation model: (1) a concentration of neutrons in intermediate mass fragments during the phase transition, (2) the break of the spatial symmetry of the fragment's isospin distribution, as well as of the symmetry of the fragment's emission from a statistical source, induced by the external Coulomb field.
We consider the transition from quark to hadronic matter which may result during the cooling/expansion of the quark-gluon plasma formed in energetic collisions of weakly isospin-asymmetric ions. This transition involves the energy density of u and d quark matter and the one of nearly isospin-symmetric nuclear matter. Within bag models, the former entails knowledge of the bag pressure, a poorly constrained quantity. The bag pressure at high density can be fixed imposing equality of quark and nucleonic energy densities at the (assumed known) transition point. We find this value to be very model …
A hidden local symmetry formalism with a two-photon counterterm approach is performed based on the relativistic continuum quantum many-body theory. The underlying electromagnetic under-screening as well as screening effects between the electric charged point-like electrons and composite protons are discussed by analyzing the in-medium isospin mixing of Lorentz vector with scalar due to electromagnetic photon. Besides the usual screening results, the main conclusion is that an effective oscillatory instantaneous Coulomb potential between the like-charged collective electrons contributes a very …
For nuclei with N = Z, the isospin degree of freedom is important and, for deformed systems, rotational bands of different isospin may be expected at low excitation energies. We have investigated, in a simple model space, the influence of the isospin-breaking Coulomb interaction on the degree of chaoticity of these rotational bands. The statistical measures used rely on an analysis of level-spacing distributions, which are extremely difficult to measure experimentally. We show, however, that the overlap intergrals between states of similar frequency reflect well the degree of chaoticity. This …
Isospin symmetry of atomic nuclei is explicitly broken by the charge-dependent interactions, primarily the Coulomb force. Within the nuclear density functional theory, isospin is also broken spontaneously. We propose a projection scheme rooted in a mean field theory, that allows the consistent treatment of isospin breaking in both ground and exited nuclear states. We demonstrate that this scheme is essentially free from spurious divergences plaguing particle-number and angular-momentum restoration approaches. Applications of the new technique include excited high-spin states in medium-mass N=Z…
We develop the isospin-invariant Skyrme-EDF method by considering local densities in all possible isospin channels and proton-neutron (p-n) mixing terms as mandated by the isospin symmetry. The EDF employed has the most general form that depends quadratically on the isoscalar and isovector densities. We test and benchmark the resulting p-n EDF approach, and study the general properties of the new scheme by means of the cranking in the isospin space. We extend the existing axial DFT solver HFBTHO to the case of isospin-invariant EDF approach with all possible p-n mixing terms. Explicit expressi…
The influence of the isospin-independent, isospin- and momentum-dependent equation of state (EoS), as well as the Coulomb interaction on the pion production in intermediate energy heavy ion collisions (HICs) is studied for both isospin-symmetric and neutron-rich systems. The Coulomb interaction plays an important role in the reaction dynamics, and strongly influences the rapidity and transverse momentum distributions of charged pions. It even leads to the $π^-/π^+$ ratio deviating slightly from unity for isospin-{\it symmetric} systems. The Coulomb interaction between mesons and baryons is als…
The one- plus two-body isospin nonconserving nuclear interactions are included in the prediction of ground state energies of fp shell nuclei using spectral distribution theory. This in turn is used to calculate the linear term in the isobaric mass-multiplet equation and the predictions are then compared to experimental values after the addition of the Coulomb contribution. The agreement is found to be reasonable as observed for sd shell nuclei earlier. One also sees that in this method the contribution to the linear term comes almost completely from the one body isovector Hamiltonian and that …
The isovector and isotensor energy differences between yrast states of isobaric multiplets in the lower half of the $pf$ region are quantitatively reproduced in a shell model context. The isospin non-conserving nuclear interactions are found to be at least as important as the Coulomb potential. Their isovector and isotensor channels are dominated by J=2 and J=0 pairing terms, respectively. The results are sensitive to the radii of the states, whose evolution along the yrast band can be accurately followed.
Although SU(2) isospin symmetry is generally assumed in the basic theory of the strong interaction, a number of significant violations have been observed in scattering and bound states of nucleons. Many of these violations can be attributed to the electromagnetic interaction but the question of how much of the violation is due to it remains open. A schematic model based on clustering of quarks in the interior of the confinement region of the two-nucleon system is introduced and evaluated. In this model the Coulomb interaction is the source of all isospin breaking. It draws on a picture of the …
The statistical mechanics of quarks and gluons are investigated within the context of the canonical ensemble. Recursive techniques are developed which enforce the exact conservation of baryon number, total isospin, electric charge, strangeness, and color. Bose and Fermi-Dirac statistics are also accounted for to all orders. The energy, entropy and particle number densities are shown to be significantly reduced for volumes less than 5 cubic fm.
We show that the extensively studied equation of state (EOS) of strongly coupled QED plasma fits the recent lattice EOS data of gluon plasma remarkably well, with appropriate modifications to take account of color degrees of freedom and running coupling constant. Hence we conclude that the quark gluon plasma near the critical temperature is a strongly coupled color-Coulombic plasma.
Proton-rich nuclei possess unique properties in the nuclear chart. Due to the presence of both continuum coupling and Coulomb interaction, phenomena such as halos, Thomas-Ehrman shift, and proton emissions can occur. Experimental data are difficult to be obtained therein, so that theoretical calculations are needed to understand nuclei at drip-lines and guide experimentalists for that matter. In particular, the $^{16}$Ne and $^{18}$Mg isotopes are supposed to be one-proton and/or two-proton emitting nuclei, but associated experimental data are either incomplete or even unavailable. Consequentl…
The isospin distribution of particles and fragments in collisions 96Ru+96Ru, 96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at beam energy 400 AMeV is studied with isospin dependent QMD model. We find that the rapidity distribution of differential neutron-proton counting in neutron rich nucleus-nucleus collisions at intermediate energies is sensitive to the isospin dependent part of nuclear potential. The study of the N/Z ratio of nucleons, light charged particles (LCP) and intermediate mass fragments (IMF) shows that the isospin dependent part of nuclear potential drives IMF to be more isospin symmetric…
Influence of configuration-interaction on isospin impurities and isospin symmetry breaking corrections to superallowed $0^+\rightarrow 0^+$ beta decays
University of Warsaw（华沙大学）；The University of Manchester（曼彻斯特大学）；Akal University（阿卡尔大学）；Osaka University（大阪大学）
The structure of the second 2$^+$ resonance in $^{6}$Li is investigated with special emphasis on its isospin 0 components. The wave functions are computed in a three-body model ($α$+$n$+$p$) using the hyperspherical adiabatic expansion method combined with complex scaling. In the decay into three free particles the symmetry conserving short-range interaction dominates at short distance whereas the symmetry breaking Coulomb interaction dominates at intermediate and large distances resulting in substantial isospin mixing. We predict the mixing and the energy distributions of the fragments after …
The isospin dependence of incompressibility is investigated in the Skyrme Hartree-Fock (SHF) and relativistic mean field (RMF) models. The correlations between the nuclear matter incompressibility and the isospin dependent term of the finite nucleus incompressibility is elucidated by using the Thomas-Fermi approximation. The Coulomb term is also studied by using various different Skyrme Hamiltonians and RMF Lagrangians. The symmetry energy coefficient of incompressibility is extracted to be K_τ=-(500\pm50) MeV from the recent experimental data of isoscalar giant monopole resonances (ISGMR) in …
We investigate isospin-symmetry breaking effects in the sd-shell region with large-scale shell-model calculations, aiming to understand the recent anomalies observed in superallowed Fermi beta-decay. We begin with calculations of Coulomb displacement energies (CDE's) and triplet displacement energies (TDE's) by adding the T=1,J=0 isospin nonconserving (INC) interaction into the usual isospin-invariant Hamiltonian. It is found that CDE's and TDE's can be systematically described with high accuracy. A total number of 122 one- and two-proton separation energies are predicted accordingly, and loca…
The fusion process of $^{48}$Ca induced reactions is studied with the two-step model. In this model, the fusion process is devided into two stages: first, the sticking stage where projectile and target come to the touching point over the Coulomb barrier from infinite distance, and second, the formation stage where the di-nucleus formed with projectile and target evolve to form the spherical compound nucleus from the touching point. By the use of the statistical evaporation model, the residue cross sections for different neutron evaporation channels are analyzed. From the results, optimum react…
The question of isospin-symmetry breaking in nuclei of the $sd$ shell is addressed. We propose a new global parameterization of the isospin-nonconserving (INC) shell-model Hamiltonian which accurately describes experimentally known isobaric mass splittings. The isospin-symmetry violating part of the Hamiltonian consists of the Coulomb interaction and effective charge-dependent forces of nuclear origin. Particular attention has been paid to the effect of the short-range correlations. The behavior of $b$ and $c$ coefficients of the isobaric-mass-multiplet equation (IMME) is explored in detail. I…
It is generally believed that isospin would diminish in its importance as we go towards heavy mass region due to isospin mixing caused by the growing Coulomb forces. However, it was realized quite early that isospin could become an important and useful quantum number for all nuclei including heavy nuclei due to neutron richness of the systems~\cite{robson}. Lane and Soper~\cite{lane} also showed in a theoretical calculation that isospin indeed remains quite good in heavy mass neutron rich systems. In this paper, we present isospin based calculations~\cite{jain,swati} for the fission fragment d…
We make a complete dynamical study of Isotopic spin conservation effects on the multiplicity distributions of both hard and soft pions emitted in a quark gluon plasma undergoing a non-equilibrium phase transition.
Transverse emission of preequilibrium nucleons, light clusters (complex particles) and charged pions from the isotopic $^{112,124}$Sn+$^{112,124}$Sn reactions at a beam energy of 400\emph{A} MeV, to extract the high-density behavior of nuclear symmetry energy, are investigated within an isospin and momentum dependent transport model. Specifically, the double ratios of neutron/proton, triton/helium-3 and $π^{-}/π^{+}$ in the squeeze-out domain are analyzed systematically, which have the advantage of reducing the influence of the Coulomb force and less systematic errors. It is found that the tra…
We study the in-medium masses of the charmonium states $J/ψ$ and $η_{c}$ in the nuclear medium using QCD sum rule approach. These mass modifications arise due to modifications of the scalar and the twist-2 gluon condensates in the hot hadronic matter. The scalar gluon condensate, $<\frac{α_{s}}π G^a_{μν} {G^a}^{μν}>$ and the twist-2 tensorial gluon operator, $<\frac{α_{s}}π G^a_{μσ} {{G^a}_ν}^σ>$ in the nuclear medium are calculated from the medium modification of a scalar dilaton field introduced to incorporate trace anomaly of QCD within the chiral SU(3) model used in the present investigati…
Some isospin dynamics results in heavy ion collisions from low to relativistic energies obtained through transport approaches, largely inspired by David M.Brink, are reviewed. At very low energies, just above the Coulomb barrier, the stimulating implications of the prompt dipole radiation in dissipative collisions of ions with large isospin asymmetries are discussed. We pass then to the very rich phenomenology of isospin effects on heavy ion reactions at intermediate energies (few AGeV range). We show that it can allow a ``direct'' study of the covariant structure of the isovector interaction …
Pseudospin symmetry in nuclei is investigated by solving the Dirac equation with Woods-Saxon scalar and vector radial potentials. We relate the pseudospin interaction with a pseudospin-orbit term in a Schroedinger-like equation for the lower component of the Dirac spinor. We show that this term gives a large contribution to the energy splittings of pseudospin partners, so that the near pseudospin degeneracy arises from a significant cancellation among the different terms in that equation. This is a manifestation of the dynamical character of this symmetry in the nucleus. We analyze the isospin…
Inspired by Laughlin's theory of the fractional quantum Hall effect, we explore the topological nature of the quark-gluon plasma and the nucleons in the context of the Clifford algebra. In our model, each quark is transformed into a composite particle via the simultaneous attachment of a spin monopole and an isospin monopole. This is induced by a novel kind of meson endowed with both spin and isospin degrees of freedom. The interactions in the strongly coupled quark-gluon system are governed by the topological winding number of the monopoles, which is an odd integer to ensure that the overall …
Hypernuclei $ ^4_Y He$, $ ^4_Y H$, $ ^4_{YY} He$, $ ^4_{YY} H$, where $Y=Λ$, $Σ_0$, $Σ_+$, $Σ_-$, A=4 are considered using the relativistic twelve-quark equations in the framework of the dispersion relation technique. Hypernuclei as the systems of interacting quarks and gluons are considered. The relativistic twelve-quark amplitudes of hypernuclei, including $u$, $d$, $s$ quarks are constructed. The approximate solutions of these equations are obtained using a method based on the extraction of leading singularities of the amplitudes. The poles of the multiquark amplitudes allow us to determine…
A general expression of the hard thermal loop gluon propagator is given for a variety of abelian gauge fixing conditions (Coulomb gauge, axial gauge, covariant gauge, temporal gauge ...) The current --- current interaction energy, in particular the Coulomb energy, is shown to be independent of the gauge fixing condition (not only of the parameter).
The assumption of an exact isospin symmetry would imply equal strengths for mirror E1 transitions (at least, in the long-wavelength limit). Actually, large violations of this symmetry rule have been indicated by a number of experimental results, the last of which is the 67As - 67Se doublet investigated at GAMMASPHERE. Here, we examine in detail various possible origins of the observed asymmetry. The coherent effect of Coulomb-induced mixing with the high-lying Giant Isovector Monopole Resonance is proposed as the most probable process to produce a large asymmetry in the E1 transitions, with co…
The recent experimental observation of isospin symmetry breaking (ISB) in the ground states of the $T=3/2$ mirror pair $^{73}$Sr - $^{73}$Br is theoretically studied using large-scale shell model calculations. The large valence space and the successful PFSDG-U effective interaction used for the nuclear part of the problem capture possible structural changes and provide a robust basis to treat the ISB effects of both electromagnetic and non-electromagnetic origin. The calculated shifts and mirror-energy-differences are consistent with the inversion of the $I^π$= 1/2$^{-}, 5/2^{-}$ states betwee…
For mirror nuclei with masses A=42-95, the effects of isospin nonconserving nuclear forces are studied with nuclear shell model using the Coulomb displacement energy and triplet displacement energy as probes. It is shown that the characteristic behavior of the displacement energies can be well reproduced if the isovector and isotensor nuclear interactions with J=0 and T=1 are introduced into the f7/2 shell. These forces, with their strengths being found consistent with the nucleon-nucleon scattering data, tend to modify nuclear binding energies near the N=Z line. At present, no evidence is fou…
We study the effects of adding the Coulomb interactions to the harmonic oscillator (HO) approximation of the heavy parton propagating through the quark-gluon plasma (the extension to QCD of the Molliere theory). We explicitly find the expression for the transverse momentum distribution of the gluon radiation of the heavy quark propagating in the quark gluon plasma in the framework of the Moliere theory, taking into account the BDMPSZ radiation in the harmonic oscillator (HO) approximation, and the Coulomb logarithms described by the additional logarithmic terms in the effective potential. We s…
We examine isospin breaking in the nucleon wave functions due to the $u - d$ quark mass difference and the Coulomb interaction among the quarks, and their consequences on the nucleon electroweak form factors in a nonrelativistic constituent quark model. The mechanically induced isospin breaking in the nucleon wave functions and electroweak form factors are exactly evaluated in this model. We calculate the electromagnetically induced isospin admixtures by using first-order perturbation theory, including the lowest-lying resonance with nucleon quantum numbers but isospin 3/2. We find a small ($\…
We study electromagnetic as well as strong isospin breaking effects in the isospin mass splittings of light pseudoscalar and vector mesons. To this end we employ a coupled system of quark Dyson-Schwinger and meson Bethe-Salpeter equations whose interaction kernels contain gluon, pion and photon exchange interactions. In bound states, QCD-induced isospin breaking is manifest on different levels. On the one hand, a different explicit up- and down-quark mass directly affects the propagators of the constituent quarks. On the other hand, it leads to different interaction kernels within the isospin …
Recent high-precision mass measurements of $^{9}$Li and $^{9}$Be, performed with the TITAN Penning trap at the TRIUMF ISAC facility, are analyzed in light of state-of-the-art shell model calculations. We find an explanation for the anomalous Isobaric Mass Multiplet Equation (IMME) behaviour for the two $A$ = 9 quartets. The presence of a cubic $d$ = 6.3(17) keV term for the $J^π$ = 3/2$^{-}$ quartet and the vanishing cubic term for the excited $J^π$ = 1/2$^{-}$ multiplet depend upon the presence of a nearby $T$ = 1/2 state in $^{9}$B and $^{9}$Be that induces isospin mixing. This is contrary t…
