Shimon Levit

Properties of highly excited nuclei

Abstract A prescription is proposed for calculating the contribution of unbound states in nuclear Hartree-Fock calculations at finite temperature. The method is based on the remark that a static Hartree-Fock calculation at finite temperature describes a hot nucleus in equilibrium with an external nucleon vapor. Properties of the hot nucleus including continuum effects are obtained by extracting the contribution of the external gas, which we calculate from a second Hartree-Fock calculation. We show that for a one-body potential this subtraction procedure yields standard formulae for partition functions in terms of phase shifts. Numerical calculations are performed in 56 Fe and 208 Pb. The resuls indicate that continuum contributions are large beyond temperatures of the order of 4 MeV. We also find the existence of a critical temperature, of the order of 10 MeV, beyond which solutions of the equations can no longer be found.

Statistical properties and stability of hot nuclei

Abstract Results of temperature-dependent Hartree-Fock calculations for equilibrated hot nuclei are presented, extending to the highest temperatures at which the nuclei remain stable. A subtraction procedure developed earlier for isolating the properties of the nucleus from the nucleus + vapor system is applied. The temperature dependence of various quantities characterizing hot nuclei is investigated. The influence of different effective interactions in the Hartree-Fock equations is examined. Special attention is devoted to the study of the high-temperature stability limit of hot nuclei. This limit in nuclei with the Coulomb interaction artificially switched off (i.e. uncharged nuclei) is shown to correspond to the critical temperature of the liquid-gas phase transition expected on the basis of hot nuclear matter calculations. In realistic charged nuclei the Coulomb repulsion causes a nucleus to become electrostatically unstable and to fall apart at much lower temperatures than its uncharged partner. The approach to and the temperature of this Coulomb instability are very sensitive to the choice of the nuclear interaction. Studying this instability in compound nuclei with different charge-to-mass ratio provides a sensitive measure of the temperature dependence of the nuclear surface properties as well as of certain features of the nuclear equation of state.

Phenomenology of shape transitions in hot nuclei

Abstract A phenomenological description of the temperature-driven shape transitions in heavy nuclei is presented. The general framework of the Landau theory is used to establish the free energy and entropy dependence on the deformation and the temperature-energy variables. This information is used to discuss the equilibrium quantities as well as the fluctuation effects around equilibrium shapes. Calculations are presented for the entropy, energy and the level density in the context of a typical example of a heavy nucleus undergoing shape transition. The results show considerable deviations from the standard dependences which are obtained using the assumption of a fixed nuclear shape.

Coulomb instability in hot compound nuclei approaching liquid-gas transition

Abstract Coulomb repulsion causes an instability in a hot compound nucleus when its temperature is raised beyond a certain limiting value. We investigate this Coulomb instability using a finite-temperature version of the liquid-drop model. We demonstrate the relation between this instability and the liquid-gas phase transition occurring in hot nuclear matter. The instability temperature T lim depends on the critical temperature T c of the transition and is always below it. The value of T lim is, however, not universal and depends also on the mass and the charge of a compound nucleus. T lim is very sensitive to the basic characteristics of the hot nuclear matter: its equation of state and the temperature dependence of its surface tension.

Landau theory of shape transitions in hot rotating nuclei

Abstract A unified framework of the Landau theory of phase transitions in statistical systems is applied to the description of the shape transitions in hot rotating nuclei. Assuming the temperature dependence of the coefficients of the Landau expansion is consistent with the underlying microscopic theory we derive and discuss the most general features of these transitions which are expected to have a universal character. For nuclei with prolate ground states we find rapid changes of the equilibrium shape from almost prolate to oblate when the excitation energy E ∗ increases in the vicinity of a certain critical value and for a fixed angular momentum J. The rate of these shape transitions depends strongly on the magnitude of J and is faster for smaller J. In the terminology of statistical mechanics the transition is first order when J is less than a certain critical Jc and second order for J > Jc. On the phase diagram of E ∗ versus J the lines of the first and second order transitions meet at an analog of a tricritical point where large fluctuations around the equilibrium shape are expected. The general theory is illustrated by calculations of the properties and the phase diagram of the 166Er nucleus.

Development of a large high-performance 2-D array of GaAs-AlGaAs multiple quantum-well modulators

We present the development of an ultrafast two-dimensional (288 /spl times/ 132 elements) reflection modulator array based on GaAs-AlGaAs multiple quantum-wells embedded in an asymmetric Fabry-Perot structure. The array has low operation voltage (< 4 V), low insertion loss, and high contrast ratio at /spl sim/846 nm. This array was hybridized to 0.25 /spl mu/m complementary metal-oxide-semiconductor driver providing 256 gray levels resolution at frame rate of 50 kHz (driver limited). Major progress in reducing the severe nonuniformity problem of the cavity resonance wavelength in such devices to less than 3.4 nm variation across a 4-in wafer was achieved.

Limiting temperature and limits of statistical particle emission in hot nuclei

Abstract A hot liquid-drop model which describes equilibrated highly excited nuclei is considered. The model includes the neutron and the proton components of the nuclear liquid and is used to calculate the upper limiting temperature of nuclear stability. Stability of hot nuclei against nonequilibrim particle emission is also investigated. The behaviour of both stability limits is presented for wide regions of the ( N , Z ) nuclear chart.

A new semi-classical theory for multiple Coulomb excitation

Abstract A uniform semi-classical approach based on the classical limit of Feynmans path-integral representation is applied for the case of multiple Coulomb excitation. The resulting excitation probabilities are compared with those obtained from the conventional semi-classical treatment and also with the results of the full quantum mechanical coupled channels treatment.

The geometric content of the interacting boson model for molecular spectra: A testground for the nuclear IBM

Abstract The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic hamiltonian onto an exactly solvable geometrical hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low-lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operators in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM.

Mean field solution of QCD2 in the large-N limit☆

Abstract Two-dimensional QCD in the large- N limit is formulated as a Hartree-Fock problem and solved numerically on a lattice. Calculation of single-particle wave functions and the one-body density matrix displays the structure of baryons. Insight into the Skyrme model is provided by showing that in the limit of small quark mass, the baryon is accurately approximated by a spatially varying chiral rotation of the vacuum wave function, where the chiral angle satisfies the sine-Gordon equation. The meson spectrum is calculated in the random phase approximation. The same mean field theory is also applied to chiral and non-chiral Gross-Neveu models, where it agrees with known analytical results.