Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

http://inspirehep.net/record/1347138/files/arXiv:1503.00732.pdf

Quantum field theory in a magnetic field: From quantum chromodynamics to graphene and Dirac semimetals

Chiral magnetic and vortical effects in high-energy nuclear collisions—A status report

The interplay of quantum anomalies with magnetic field and vorticity results in a variety of novel non-dissipative transport phenomena in systems with chiral fermions, including the quark-gluon plasma. Among them is the Chiral Magnetic Effect (CME) -- the generation of electric current along an external magnetic field induced by chirality imbalance. Because the chirality imbalance is related to the global topology of gauge fields, the CME current is topologically protected and hence non-dissipative even in the presence of strong interactions. As a result, the CME and related quantum phenomena affect the hydrodynamical and transport behavior of strongly coupled quark-gluon plasma, and can be studied in relativistic heavy ion collisions where strong magnetic fields are created by the colliding ions. Evidence for the CME and related phenomena has been reported by the STAR Collaboration at Relativistic Heavy Ion Collider at BNL, and by the ALICE Collaboration at the Large Hadron Collider at CERN. The goal of the present review is to provide an elementary introduction into the physics of anomalous chiral effects, to describe the current status of experimental studies in heavy ion physics, and to outline the future work, both in experiment and theory, needed to eliminate the existing uncertainties in the interpretation of the data.

/pdf/chiral-magnetic-and-vortical-effects-in-high-energy-nuclear-3jne6v5ikj.pdf

Chiral Magnetic and Vortical Effects in High-Energy Nuclear Collisions --- A Status Report

I review the origin and properties of electromagnetic fields produced in heavy-ion collisions The field strength immediately after a collision is proportional to the collision energy and reaches &#x7e; at RHIC and &#x7e; at LHC I demonstrate by explicit analytical calculation that after dropping by about one-two orders of magnitude during the first fm/c of plasma expansion, it freezes out and lasts for as long as quark-gluon plasma lives as a consequence of finite electrical conductivity of the plasma Magnetic field breaks spherical symmetry in the direction perpendicular to the reaction plane, and therefore all kinetic coefficients are anisotropic I examine viscosity of QGP and show that magnetic field induces azimuthal anisotropy on plasma flow even in spherically symmetric geometry Very strong electromagnetic field has an important impact on particle production I discuss the problem of energy loss and polarization of fast fermions due to synchrotron radiation, consider photon decay induced by magnetic field, elucidate dissociation via Lorentz ionization mechanism, and examine electromagnetic radiation by plasma I conclude that all processes in QGP are affected by strong electromagnetic field and call for experimental investigation

https://downloads.hindawi.com/journals/ahep/2013/490495.pdf

Particle production in strong electromagnetic fields in relativistic heavy-ion collisions

We compute the electromagnetic fields generated in heavy-ion collisions by using the HIJING model. Although after averaging over many events only the magnetic field perpendicular to the reaction plane is sizable, we find very strong electric and magnetic fields both parallel and perpendicular to the reaction plane on the event-by-event basis. We study the time evolution and the spatial distribution of these fields. Especially, the electromagnetic response of the quark-gluon plasma can give non-trivial evolution of the electromagnetic fields. The implications of the strong electromagnetic fields on the hadronic observables are also discussed.

Event-by-event generation of electromagnetic fields in heavy-ion collisions

We study the event-by-event generation of flow vorticity in the BNL Relativistic Heavy Ion Collider $\mathrm{Au}+\mathrm{Au}$ collisions and CERN Large Hadron Collider $\mathrm{Pb}+\mathrm{Pb}$ collisions by using the hijing model. Different definitions of the vorticity field and velocity field are considered. A variety of properties of the vorticity are explored, including the impact parameter dependence, the collision energy dependence, the spatial distribution, the event-by-event fluctuation of the magnitude and azimuthal direction, and the time evolution. In addition, the spatial distribution of the flow helicity is also studied.

Vorticity in heavy-ion collisions

The hot and dense matter generated in heavy-ion collisions contains intricate vortical structure in which the local fluid vorticity can be very large. Such vorticity can polarize the spin of the produced particles. We study the event-by-event generation of the so-called thermal vorticity in Au+Au collisions at energy region $\sqrt{s}=7.7--200$ GeV and calculate its time evolution, spatial distribution, etc., in a multiphase transport model. We then compute the spin polarization of the $\mathrm{\ensuremath{\Lambda}}$ and $\overline{\mathrm{\ensuremath{\Lambda}}}$ hyperons as a function of $\sqrt{s}$, transverse momentum ${p}_{T}$, rapidity, and azimuthal angle. Furthermore, we study the harmonic flow of the spin, in a manner analogous to the harmonic flow of the particle number. The measurement of the spin harmonic flow may provide a way to probe the vortical structure in heavy-ion collisions. We also discuss the spin polarization of ${\mathrm{\ensuremath{\Xi}}}^{0}$ and ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}}$ hyperons, which may provide further information about the spin polarization mechanism of hadrons.

Thermal vorticity and spin polarization in heavy-ion collisions

The quark-gluon matter produced in relativistic heavy-ion collisions may contain local domains in which parity ($\mathcal{P}$) and combined charge conjugation and parity ($\mathcal{C}\mathcal{P}$) symmetries are not preserved. When coupled with an external magnetic field, such $\mathcal{P}$- and $\mathcal{C}\mathcal{P}$-odd domains will generate electric currents along the magnetic field---a phenomenon called the chiral magnetic effect (CME). Recently, the STAR Collaboration at the BNL Relativistic Heavy Ion Collider (RHIC) and the ALICE Collaboration at the CERN Large Hadron Collider (LHC) released data of charge-dependent azimuthal-angle correlators with features consistent with the CME expectation. However, the experimental observable is contaminated with significant background contributions from elliptic-flow-driven effects, which makes the interpretation of the data ambiguous. We show that the collisions of isobaric nuclei, $_{44}^{96}\mathrm{Ru}+_{44}^{96}\mathrm{Ru}$ and $_{40}^{96}\mathrm{Zr}+_{40}^{96}\mathrm{Zr}$, provide an ideal tool to disentangle the CME signal from the background effects. Our simulation demonstrates that the two collision types at $\sqrt{{s}_{NN}}=200$ GeV have more than $10%$ difference in the CME signal and less than $2%$ difference in the elliptic-flow-driven backgrounds for the centrality range of 20--60%.

Wei-Tian Deng

Papers

Event-by-event generation of electromagnetic fields in heavy-ion collisions

Vorticity in heavy-ion collisions

Thermal vorticity and spin polarization in heavy-ion collisions

Testing the chiral magnetic effect with isobaric collisions

Electric fields and chiral magnetic effect in Cu + Au collisions