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We show that information about quasimolecular electronic binding energies in transient atomic systems of Z=Z1+Z2 up to 184 can be obtained from three sources: (1) the impact-parameter dependence of the ionization probability; (2) the ionization probability in head-on collisions as a function of total nuclear charge Z; (3) the delta-electron spectrum in coincidence with K-vacancy formation in asymmetric collisions. Experiments are proposed and discussed.
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 master operators B which cause the entropy production dH/dt = - k-1 dS/dt to become extremal for fixed statistical operators W are constructed and discussed. There are boundaries of the set B of master operators, B = {B | Σ B2vu = b} for which the problem is solvable yielding minimal entropy production, while no solution exists in the set B without any constraints. Operators with maximal entropy production must be extremal points of B.
The temporal development of macroobservables is described within a correlation-functionformalism. The results are exact for a certain class of initial ensembles. The same problem is discussed with the help of the linear-response-formalism. The results agree under certain conditions which should be fulfilled for macroobservables.
For experiments on fission-fragment induced desorption the detection of significant correlations between desorbed ions has been reported [1]. In this paper the method for the detection and quantitative description of these correlations will be described. The statistics of the desorption-process leads to equations for mass-line intensities of ion spectra. Using a time-to-amplitude-converter for flight-time measurements these intensities depend on interdependences of different ions desorbed by the same fission-fragment. The equations allow the computation of correlationcoefficients whose interdependence with desorption probabilities of the respective ions can be shown in Venn-diagrams. Results are given and an interpretation is suggested for fission-fragment desorbed thiamine molecular and fragment ions.
Pion-production cross sections have been measured for the reaction 40Ar+40Ca--> pi ++X at a laboratory energy of 1.05 GeV/nucleon. A maximum in the pi + cross section occurs at mid-rapidity, which is anomalous relative to p+p and p+nucleus reactions and compared to many other heavy-ion reactions. Calculations based on cascade and thermal models fail to fit the data.
In the present paper we develop the essential theoretical tools for the treatment of the dynamics of High Energy Heavy Ion Collisions. We study the influence of the nuclear equation of state and discuss the new phenomena connected with phase transitions in nuclear matter (pion condensation). Furthermore we investigate the possibility of a transition from nuclear to quark matter in High Energy Heavy Ion Collisions. In this context we discuss exotic phenomena like strongly bound pionic states, limiting temperatures, and exotic nuclei.
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.
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〉.
Proton emission in relativistic nuclear collisions is examined for events of low and high multiplicity, corresponding to large and small impact parameters. Peripheral reactions exhibit distributions of protons in agreement with spectator-participant decay modes. Central collisions of equal-size nuclei are dominated by the formation and decay of a fireball system. Central collisions of light projectiles with heavy targets exhibit an enhancement in sideward emission which is predicted by recent hydrodynamical calculations.
Inclusive energy spectra of protons, deuterons, and tritons were measured with a telescope of silicon and germanium detectors with a detection range for proton energies up to 200 MeV. Fifteen sets of data were taken using projectiles ranging from protons to 40Ar on targets from 27Al to 238U at bombarding energies from 240 MeV/nucleon to 2.1 GeV/nucleon. Particular attention was paid to the absolute normalization of the cross sections. For three previously reported reactions, He fragment cross sections have been corrected and are presented. To facilitate a comparison with theory the sum of nucleonic charges emitted as protons plus composite particles was estimated and is presented as a function of fragment energy per nucleon in the interval from 15 to 200 MeV/nucleon. For low-energy fragments at forward angles the protons account for only 25% of the nucleonic charges. The equal mass 40Ar plus Ca systems were examined in the center of mass. Here at 0.4 GeV/nucleon 40Ar plus Ca the proton spectra appear to be nearly isotropic in the center of mass over the region measured. Comparisons of some data with firestreak, cascade, and fluid dynamics models indicate a failure of the first and a fair agreement with the latter two. In addition, associated fast charged particle multiplicities (where the particles had energies larger than 25 MeV/nucleon) and azimuthal correlations were measured with an 80 counter array of plastic scintillators. It was found that the associated multiplicities were a smooth function of the total kinetic energy of the projectile. NUCLEAR REACTIONS U(20Ne,X), E / A=240 MeV/nucleon; U(40Ar,X), Ca(40Ar,X), U(20Ne,X), Au(20Ne,X), Ag(20Ne,X), Al(20Ne,X), U(4He,X), Al(4He,X), E / A=390 MeV/nucleon; U(40Ar,X), Ca(40Ar,X), U(20Ne,X), U(4He,X), U(p,X), E / A=1.04 GeV/nucleon; U(20Ne,X), E / A=2.1 GeV/nucleon; measured sigma (E, theta ), X=p,d,t.
Exclusive pi - and charged-particle production in collisions of Ar+KCl is studied at incident energies from 0.4 to 1.8 GeV/u. Complete disintegration of both nuclei is observed. The correlation between pi - and total charge multiplicity shows no islands of anomalous pion production. For constant numbers of proton participants the pi - multiplicity distributions are Poissons. For central collisions <n pi -> increases smoothly and to first order linearly with the c.m. energy. Disagreement with the firestreak model is found. Pacs numbers: 25.70.Hi, 24.10.Dp
Angular and energy distributions of fragments emitted from fast nucleus-nucleus collisions (Ne--> U at 250, 400, and 800 MeV/N) are calculated with use of nuclear fluid dynamics. A characteristic dependence of the energy spectra and angular distributions on the impact parameter is predicted. The preferential sideward emission of reaction fragments observed in the calculation for nearly central collisions seems to be supported by recent experimental data.
This paper reports calculations of the influence of a reaction time T>10-21 s in deep-inelastic Xe-Pb collisions on the energy spectrum of δ electrons ejected in the same collision. It is shown that the lifetime of the superheavy composite system causes pronounced oscillations of width ε=h/T in the electron distribution, which survive the inclusion of multistep excitations and the folding with a lifetime distribution function. This effect may serve as an atomic clock for deep-inelastic collisions.
In heavy ion collisions, the molecular single-particle motion may cause specific structures in the energy dependence of the cross sections which arise by the promotion of nucleons at level crossings according to the Landau-Zener excitation mechanism. In order to examine this effect in asymmetric heavy ion collisions, we have calculated level diagrams of the two-center shell model for the target projectile combinations 13C + 16O and 12C + 17O and analyzed with respect to inelastic excitation and neutron transfer. We select certain reactions as possible candidates for showing enhanced cross sections for nucleon excitation and transfer due to real and avoided level crossings near the Fermi level.
Dynamics of Coulomb fission
(1980)
A general formalism is described for the treatment of Coulomb fission, within the framework of the semiquantal theory. We develop a model for the fission probabilities of levels excited in Coulomb excitation. This model contains penetration of the double-humped fission barrier, competition from gamma and neutron emission, and the spreading of the collective states into noncollective compound states. For 74184W + 92238U, the fission probability at θc.m.=180° is increased by a factor of 3.9, 3.3, and 2.0 at E/ECoul=0.77, 0.85, and 0.935, respectively, compared to the simplified sharp cutoff model used in earlier model calculations. The enhancement comes from barrier penetration. The damping of the fission probability due to spreading into noncollective compound states is small. Prompt Coulomb fission (near the distance of closest approach) is studied in a one-dimensional model. The results clearly imply that prompt fission is negligible. We have also studied the sudden approximation for collective rotational levels in connection with Coulomb fission. At high spins (I≈20), it leads to significant errors. Contrary to the basic assumption of the sudden approximation that the nuclear symmetry axis remains fixed during the collision, it is shown that Coulomb excitation results in a strong alignment of the nuclear symmetry axis perpendicular to the beam axis at small internuclear distances. NUCLEAR REACTIONS, FISSION Semiquantal theory of prompt and asymptotic Coulomb fission, study of double-humped barrier penetration, damping effects, neutron and γ emission. Calculated σ(Ep, θc.m.=180°).
Phase transitions in nuclear matter A method for the description of spin-isospin phase transitions in nuclear matter is developed. It allows a complete description of the pion condensation phase transition in the framework of the Landau-Migdal Fermi liquid theory. The equation of the order parameter is derived and the condensation energy is calculated. We study the influence of pion condensation on the nuclear equation of state and the temperature dependence of pion condensation. NUCLEAR STRUCTURE Description of pion-condensed ground state by Green's function technique.