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A fully gauge-invariant, Lorentz-covariant, nonlocal, and nonlinear theory, for coupled spin-½ fields, ψ, and vector fields, A, i.e., "electrons" and "photons," is constructed. The field theory is linear in the ψ fields. The nonlinearity in the A fields arises unambiguously from the requirement of gauge invariance. The coordinates are generalized to admit hypercomplex values, i.e., they are taken to be Clifford numbers. The nonlocality is limited to the hypercomplex component of the coordinates. As the size of the nonlocality is reduced toward zero, the theory goes over into the inhomogeneous Dirac theory. The nonlocality parameter corresponds to an inverse mass and induces self-regulatory properties of the propagators. It is argued that in a gauge-invariant theory a graph-by-graph convergence is impossible in principle, but it is possible that convergence may hold for the complete solution, or for sums over classes of graphs.
A general formalism for the scattering of heavy ions, which is especially convenient to study the antisymmetrization effects, is developed. Antisymmetrization effects are investigated by expanding the completely antisymmetrized wave function according to the number of exchanged nucleons. The particle-core model for the scattering of nuclei with loosely bound nucleons is presented. A formula for the additional contribution to the effective potential due to antisymmetrization effects is obtained by calculating the expectation value of the Hamiltonian with intrinsic wave functions. Application of the formalism is illustrated for the 14N + 14N scattering problem and its usefulness is demonstrated.
In view of new high-precision experiments in atomic physics it seems necessary to reexamine nonlinear theories of electrodynamics. The precise calculation of electronic and muonic atomic energies has been used to determine the possible size of the upper limit Emax to the electric field strength, which has been assumed to be a parameter. This is opposed to Born's idea of a purely electromagnetic origin of the electron's mass which determines Emax. We find Emax≥1.7×1020 V/cm.
With the mass asymmetry described by the dynamical collective fragmentation coordinate ξ, and with use of the asymmetric two-center shell model, the fission mass distributions for 226Ra, 236U, and 258Fm (which are typical representatives for triple-, double-, and single-humped distributions) are explained.
We investigate the production of heavy quarks in continuum and bound states in nuclear collisions. Creation rates for free bb and tt quark pairs and for bottomonium and toponium in the ground state are computed at energies of the BNL Relativistic Heavy Ion Collider, CERN Large Hadron Collider (LHC), and Superconducting Super Collider. Central and peripheral heavy-ion collisions are discussed. For top-quark creation we assumed a mass range of 90≤mt≤250 GeV. The creation rate for top quarks in peripheral collisions is estimated to be by a factor 40 to 130 smaller compared with corresponding central collisions. For mt=130 GeV we calculated a creation rate of about 4760 top-quark pairs per day at the LHC (3.5 TeV/nucleon) for Pb-Pb collisions.
The Gottfried sum-rule violation reported by the New Muon Collaboration was interpreted as an indication for a flavor asymmetry of the sea quark in the nucleon. We investigate the alternative possibility that isospin symmetry between the proton and the neutron is breaking. We examine systematically the consequences of this possibility for several processes, namely, neutrino deep inelastic scattering, the charged pion Drell-Yan process, the proton Drell-Yan process, and semi-inclusive deep inelastic scattering, and conclude that a decision between the two alternative explanations is possible.
We discuss the multiplicity distribution of electron-positron pairs created in the strong electromagnetic fields of ultrarelativistic heavy-ion transits. Based on nonperturbative expressions for the N-pair creation amplitudes, the Poisson distribution is derived by neglecting interference terms. The source of unitarity violation is identified in the vacuum-to-vacuum amplitude, and a perturbative expression for the mean number of pairs is given.
We calculate angular correlations between coincident electron-positron pairs emitted in heavy-ion collisions with nuclear time delay. Special attention is directed to a comparison of supercritical and subcritical systems, where angular correlations of pairs produced in collisions of bare U nuclei are found to alter their sign for nuclear delay times of the order of 2 × 10-21 s. This effect is shown to occur exclusively in supercritical systems, where spontaneous positron creation is active.
We investigate the influence of additional nonlinear terms in the Dirac Lagrangian on strongly bound electron states in heavy and superheavy atoms. Upper bounds for the coupling constants are deduced by comparison with precision spectroscopy data in QED. We demonstrate that nonlinear interactions may cause significant modifications of electron binding energies in superheavy quasiatomic systems which would not be visible in ordinary atomic-physics measurements.
The properties of symmetric nuclear matter are investigated in the nonlinear relativistic mean field theory of nuclear matter. We consider the constraints imposed by four nuclear ground state properties on the coupling constants and on the equation of state at zero and at finite temperature. We find that the compression constant K(ρ0) as well as the temperature is irrelevant for the stiffness of the equation of state for m*(ρ0)≤0.7. The main point is that the relativistic mean field theory exhibits acausal and unphysical behavior for compressibilities below K(ρ0)=200 MeV. Every set of coupling constants with a negative quartic coupling constant c is unstable against small quantum fluctuations.
We study a relativistic model of the nucleus consisting of nucleons coupled to mesonic degrees of freedom via an effective Lagrangian whose parameters are determined by a fit to selected nuclear ground-state data. We find that the model allows a very good description of nuclear ground-state properties. Because of the relativistic nature of the model, the spin properties are uniquely fixed. We discuss variations of the parametrization and of the data which suggest that the present fit has exhausted the limits of the mean-field approximation, and discuss extensions which go beyond the mean field.
Positron creation in crossed-beam collisions of high-energy, fully stripped heavy ions is investigated within the coupled-channel formalism. In comparison with fixed-target collisions of highly stripped heavy-ion projectiles positron production probabilities are enhanced by more than one order of magnitude. The increase results from the possibility to excite electrons from the negative energy continuum into all bound states. The positron spectrum is shifted towards higher energies because of the absence of electron screening. Rutherford scattering as well as nuclear collisions with time delay are investigated. We also discuss the filling of empty bound states by electrons from pair-production processes.
We present calculations for the impact-parameter dependence of K-shell ionization rates in p¯-Cu and in p¯-Ag collisions at various projectile energies. We show that the effect of the attractive Coulomb potential on the Rutherford trajectory and the antibinding effect caused by the negative charge of the antiproton result in a considerable increase of the ionization probability. Total ionization cross sections for proton and antiproton projectiles are compared with each other and with experimental ionization cross sections for protons.
Binding energies and wave functions of inner-shell electronic states in superheavy quasimolecules with (Zp+Zt)α>1 are calculated. Ionization during a collision of very heavy ions is investigated within a molecular basis generated by the solutions of the two-center Dirac equation. Transitions to vacant bound states as well as direct excitation to the continuum are taken into account. We present theoretical values for the ionization probability as a function of impact parameter, bombarding energy, and combined nuclear charge. Our computed results are compared with recent experimental data. It is suggested that relativistic binding energies of electrons in superheavy quasimolecules can be determined experimentally via the impact-parameter dependence of ionization and the anisotropy of quasimolecular radiation.
This Letter discusses inner-shell excitation in collisions of very heavy ions (Z1+Z2≳140) in the framework of the quasimolecular model. The importance of multistep excitations and of coupling between continuum states is demonstrated. The 1sσ vacancy probabilities resulting from coupled-channels calculations exceed perturbation theory by a factor 3-5, thus giving good agreement with recent experimental results.
Quasimolecular resonance structures in the 12C-12C system are studied in the framework of the coupled channel formalism in the energy range Ec.m.=5-14 MeV. The influence of the coupling of the first excited 2+ state in 12C on the resonance structures is investigated by choosing various types of coupling potentials. The intermediate structures in the reflection and transition coefficients and cross sections can be interpreted with the double resonance mechanism. NUCLEAR REACTIONS 12C(12C, 12C), quasimolecular states, coupling potentials, coupled channel calculations for σ(θ).
On the basis of the two-center shell model a theory is developed for the excitation of loosely bound nucleons in heavy ion collisions. These nucleons move in the two-center shell model potential generated by all the nucleons and are described by molecular wave functions. The model is applied to calculate the cross sections for the elastic and inelastic 13C-13C scattering. The cross sections show intermediate structures caused by the excitation of quasibound resonances in the molecular nucleus-nucleus potential. NUCLEAR REACTIONS 13C(13C,13C) molecular wave functions, dynamical two-center shell model, quasimolecular resonances, radial and Coriolis coupling, coupled channel calculations for σ(θ).
Inner-shell ionization induced by nuclear Coulomb excitation in collisions of very heavy ions
(1978)
K- and L-shell ionization of 238U with Xe and U projectiles is investigated. Internal conversion following nuclear Coulomb excitation which is particularly important for deformed heavy nuclei is compared with direct ionization of inner-shell electrons in superheavy quasimolecules. Both processes exhibit different impact-parameter dependences. As a result of internal conversion, about 0.1-0.3 K holes per central collision are created.
The theory of nucleon transfer in heavy ion reactions is formulated on the basis of the molecular particlecore model for a system consisting of two cores and one extracore nucleon. The extracore nucleon is described by the molecular wave functions of the asymmetric two-center shell model. The cores, which are assumed to be collectively excitable, are treated with vibrator-rotator models. Potentials for shape polarization are contained in the asymmetric two-center shell model and the interaction between the cores. The excitation and transfer of the extracore nucleon is induced by the radial and rotational couplings. The coupled channel equations, which include the recoil effects in first approximation, are derived in a form suitable for numerical calculations of cross sections. NUCLEAR REACTIONS Heavy ion scattering, theory of nucleon transfer, molecular wave functions, two-center shell model, collective and single-particle excitation.
Within an extended semiquantal theory we perform large-sized coupled-channel calculations involving 260 collective levels for Coulomb fission of 238U. Differential Coulomb fission cross sections are studied as a function of bombarding energy and impact parameter for several projectiles. In the Xe + U case, total cross sections are also given. We find a strong dependence on projectile charge number, PCF(180°)∼(Zp)6 in the region 50≤Zp≤92 for a fixed ratio E/ECoul, which might be helpful to separate Coulomb fission experimentally from sequential fission following transfer reactions. Since the cross sections are sensitive to the moment of inertia ⊖ at the saddle point, Coulomb fission can serve as a tool to investigate the dependence of ⊖ on elongation. The fragment angular distribution exhibits deviations from 1/sinθf which are pronounced at low incident energies. Our theory indicates that the recently measured Xe + U fission cross sections contain a major fraction of Coulomb-induced fission at E≤0.85 ECoul. NUCLEAR REACTIONS, FISSION Calculated Coulomb fission cross sections σ(Ep,θp) for 54Xe, 67Ho, 82Pb, 92U→92238U, fragment angular distribution, fission energy spectrum, mean spin value 〈Jf〉.
The theory of direct electron-positron pair production in the collision of heavy ions is formulated in the framework of the quasimolecular model. The pair production process acquires a collective nature for (Z1+Z2)α>1 and can be understood as the shakeoff of the strong vacuum polarization cloud formed in the quasimolecule. The total cross section is, e.g., 76 μb for Pb + Pb at Coulomb barrier energies.
Internal conversion of γ rays from Coulomb-excited nuclear levels cannot be neglected compared with the spontaneous and induced positron production in overcritical electric fields. It is shown that both processes are separable by their different distributions with respect to the ion angle and the positron energy.
Excitations of the atomic shell in heavy-ion collisions are influenced by the presence of a nuclear reaction. In the present Rapid Communication we point out the equivalence between a semiclassical description based on the nuclear autocorrelation function with an earlier model which employs a distribution of reaction times f(T). For the example of U+U collisions, results of coupled-channel calculations for positron creation and K-hole excitations are discussed for two schematic reaction models.
A new spontaneous-symmetry-breaking mechanism is formulated for SU(3), which is used to describe the formation of bags around quarks. The Higgs field is replaced by the scalar product of two colored fermion fields. This model gives mass only to one gluon (equivalent to Aμ8) when spontaneously broken. The consequences of this scheme are discussed, and it is argued that it can explain several puzzling high-energy heavy-ion experiments.
We compare a proximity-type potential for two interacting nuclei with the double-folding method. Both spherical and deformed systems are considered. Special "orientation windows" are found for two deformed nuclei giving rise to nuclear cohesion. If the same nucleon-nucleon interaction is utilized, the proximity and the double-folding potentials agree fairly well for a spherical + deformed system. However, deviations are found in the case of two deformed nuclei.
For the scattering of 28Si on 28Si coupled channel calculations of the elastic scattering and inelastic single excitation of the first 2+ state of 28Si are carried out. The real coupling potentials are calculated in the framework of an adiabatic model. The resulting cross sections reveal structures in agreement with the observed ones and support their interpretation as nuclear molecular resonances.
The energy shift of K electrons in heavy atoms due to the self-energy correction has been calculated. This process is treated to all orders in Zα, where Z denotes the nuclear charge. For the superheavy system Z=170, where the K-shell binding energy reaches the pair-production threshold (E1sb∼2mc2), a shift of +11.0 keV is found. This shift is almost cancelled by the vacuum polarization, leaving a negligible effect for all quantum-electrodynamical corrections of order α but all orders of Zα.
Different collective deformation coordinates for neutrons and protons are introduced to allow for both stretching and γ transitions consistent with experiments. The rotational actinide nuclei 234-238U and 232Th are successfully analyzed in this model. NUCLEAR STRUCTURE 232Th, 234-238U calculated B (E2) values, collective model.
The origin and importance of electron-translation effects within a molecular description of electronic excitations in heavy-ion collisions is investigated. First, a fully consistent quantum-mechanical description of the scattering process is developed; the electrons are described by relativistic molecular orbitals, while the nuclear motion is approximated nonrelativistically. Leaving the quantum-mechanical level by using the semiclassical approximation for the nuclear motion, a set of coupled differential equations for the occupation amplitudes of the molecular orbitals is derived. In these coupled-channel equations the spurious asymptotic dynamical couplings are corrected for by additional matrix elements stemming from the electron translation. Hence, a molecular description of electronic excitations in heavy-ion scattering has been achieved, which is free from the spurious asymptotic couplings of the conventional perturbated stationary-state approach. The importance of electron-translation effects for continuum electrons and positrons is investigated. To this end an algorithm for the description of continuum electrons is proposed, which for the first time should allow for the calculation of angular distributions for δ electrons. Finally, the practical consequences of electron-translation effects are studied by calculating the corrected coupling matrix elements for the Pb-Cm system and comparing the corresponding K-vacancy probabilities with conventional calculations. We critically discuss conventional methods for cutting off the coupling matrix elements in coupled-channel calculations.
We calculate the spin polarization of 1sσ vacancies and emitted δ electrons induced by the strong magnetic field (|Bmax|∼1016G) in collisions of very heavy ions (Z1+Z2=178). The electron excitations are determined by the solution of coupled-channel equations within the quasimolecular basis states including the vector potential. The formulation is extended to the many-electron case. Spin polarizations of the order of 5-10% for impact energies below the Coulomb barrier are predicted.
We define a new scalar-tensor theory with an effective gravitational coupling constant depending on a scalar field. The coupling is such that the gravitational interaction decreases with the strength of the scalar field. We show that this is not sufficient to prevent the gravitational collapse of sufficiently massive dense objects.
We compute the energy spectrum of photons which originate from the quark-annihilation process ss¯→γg in quark-gluon plasma. The spectrum peaks at an energy Eγmax∼2ms∼400 MeV in the rest frame of the plasma. We expect one photon from the above process in the energy range of 2ms±0.25ms per hundred quark-gluon plasmas of a size R=3 fm and a lifetime τ=6 fm/c formed in nuclear collisions.
Phenomenological consequences of a hypothetical light neutral particle in heavy ion collisions
(1986)
We discuss the possibility that the line structure observed in the spectrum of the positrons produced in heavy ion collisions is due to the decay of a new neutral elementary particle. We argue that this can be ruled out unless one is willing to accept fine tuning of parameters, or to assume the dominance of nonlinear effects.
By using the analytical superasymmetric fission model it is shown that all ‘‘stable’’ nuclei lighter than lead with Z>40 are metastable relative to the spontaneous emission of nuclear clusters. An even-odd effect is included in the zero point vibration energy. Half-lives in the range 1040–1050 s are obtained for Z>62. The region of metastability against these new decay modes is extended beyond that for α decay and in some cases, in the competing region, the emission rates for nuclear clusters are larger than for α decay.
The great majority of the known nuclides with Z>40, including the so-called stable nuclides, are metastable with respect to several modes of spontaneous superasymmetric splitting. A model extended from the fission theory of alpha decay allows one to estimate the lifetimes and the branching ratios relative to the alpha decay for these natural radioactivities. From a huge amount of systematic calculations it is concluded that the process should proceed with maximum intensity in the trans-lead nuclei, where the minimum lifetime is obtained from parent-emitted heavy ion combinations leading to a magic (208Pb) or almost magic daughter nucleus. More than 140 nuclides with atomic number smaller than 25 are possible candidates to be emitted from heavy nuclei, with half-lives in the range of 1010–1030 s: 5He, 8–10Be, 11,12B, 12–16C, 13–17N, 15–22O, 18–23F, 20–26Ne, 23–28Na, 23–30Mg, 27–32Al, 28–36Si, 31–39P, 32–42S, 35–45Cl, 37–47Ar, 40–49 K, 42-51. . .Ca, 44–53 Sc, 46–53Ti, 48–54V, and 49–55 Cr. The shell structure and the pairing effects are clearly manifested in these new decay modes.
Atomic excitations are used to obtain information on the course of a nuclear reaction. Employing a semiclassical picture we calculate the emission of δ electrons and positrons in deep inelastic nuclear reactions for the example of U+U collisions incorporating nuclear trajectories resulting from two different nuclear friction models. The emission spectra exhibit characteristic deviations from those expected for elastic Coulomb scattering. The theoretical probabilities are compared with recent experimental data by Backe et al. A simple model is used to estimate the influence of a threebody breakup of the compound system upon atomic excitations.
Strong indirect evidence exists for the existence of attractive forces between nuclei making surface contact. Experimentally, the recent observations of spontaneous positron production in heavy-ion collisions can only be understood if nuclei stick together for times long compared to the collision time. We show that any such tendency for nuclei to attract implies the existence of nuclear molecules with entirely new kinds of collective modes. We present a simple model for these modes and apply it to 238U-238U.
Strange particle abundances in small volumes of hot hadronic gas are determined in the canonical ensemble with exact strangeness and baryon number conservation. Substantial density and baryon number dependence is found. A p¯d experiment is examined and applications to p¯-nucleus annihilations are considered.
The nucleons taking part in heavy ion reaction are considered as a three-component fluid. The first and second components correspond to the nucleons of the target and the projectile, while the thermalized nucleons produced in the course of the collision belong to the third component. Making use of the Boltzmann equation, hydrodynamical equations are derived. An equation of state for anisotropic nuclear matter obtained from a field theoretical model in mean field approximation is applied in a one dimensional version of the three-component fluid model. The speed of thermalization is analyzed and compared to the results of cascade and kinetic models. NUCLEAR REACTIONS Relativistic heavy-ion reactions, hydrodynamic description.
The collision process is described by hydrodynamical equations. The escape of nucleons which do not take part in the thermal equilibrium is considered by including drain terms in these equations. The energy spectra of the escaped nucleons and of nucleons evaporated after the breakup of the fluid are compared. NUCLEAR REACTIONS Relativistic heavy ion reactions, nuclear hydrodynamics, nucleon spectra.
We have investigated the channeling process of charged particles in a bent crystal. Invoking simple assumptions we derive a criterion, which determines whether channeling occurs or not. We obtain the same criterion using the Dirac equation. It is shown that the centrifugal force acting on the particle in the bent crystal significantly alters the effective transverse potential. The cases of axial and planar channeling are considered. The channeling probability and the dechanneling probability due to tunneling of the particle under the barrier in the effective transverse potential are estimated. These probabilities depend on the specific scaling parameter characterizing the process. Using the quasiclassical theory of synchrotron radiation we have calculated the contribution to the radiation spectrum, which arises due to the curvature of the channel. This contribution becomes significant to TeV electrons or positrons. Some practical consequences of our results are briefly discussed.
The components of the nuclear inertia tensor, functions of the separation distance R and of the radius of the light fragment R2, BRR(R,R2), BRR2(R,R2), and BR2R2(R,R2) are calculated within the Werner-Wheeler approximation, by using the parametrization of two intersected symmetric or asymmetric spheres. Analytical relationships are derived. When projected to a path R2=R2(R), the reduced mass is obtained at the touching point. The two one-dimensional parametrizations with R2=const, and the volume V2=const previously studied, are found to be particular cases of the present more general approach. Illustrations for the cold fission, cluster radioactivity, and α decay of 252Cf are given.
The experimental cold-fission yields for the system 233U(nth, f) are analyzed as function of the effective total excitation energy (TXE). The nuclear level density effect is taken into account at higher TXE, in order to benefit by the lower experimental data uncertainty as well as to avoid the quantitative account of the level densities close to fragment ground states. In this way the odd-even staggering which appears in the yields extrapolated at zero excitation energy by using the level densities, vanishes. We conclude that the cold nuclear fragmentation theory including the dynamical model describes well the experimental data.
An alternative theoretical description of axial electron channeling in the multi-GeV region has been developed. We solve a kinetic equation to evaluate an electron distribution function in axially oriented single crystals. Based on the single-string model, the required matrix elements for radiation and scattering by lattice vibrations are calculated employing solutions of the Dirac equation in cylindrical coordinates. Results obtained for 150-GeV electrons propagating along the <110> axis of germanium are in good agreement with experimental observations.
The time dependent Hartree-Fock approximation is used to study the dynamical formation of long-lived superheavy nuclear complexes. The effects of long-range Coulomb polarization are treated in terms of a classical quadrupole polarization model. Our calculations show the existence of "resonantlike" structures over a narrow range of bombarding energies near the Coulomb barrier. Calculations of 238U + 238U are presented and the consequences of these results for supercritical positron emission are discussed. NUCLEAR REACTIONS 238U + 238U collisions as a function of bombarding energy, in the time-dependent Hartree-Fock approximation. Superheavy molecules and strongly damped collisions.
Proton spectra have been calculated for the reaction 12C(85 MeV/nucleon) + 197Au using a three-dimensional hydrodynamical model with viscosity and thermal conductivity and final thermal breakup. The theoretical results are compared to recent data. It is shown that the predicted flow effects are not observable as a result of the impact parameter averaging inherent in the inclusive proton spectra. In contrast, angular distributions of medium mass nuclei (A>3) in nearly central collisions can provide signatures for flow effects.