Prediction of hyperdeformed nuclear states at very high spins

Calculations based on the generalized cranking-Strutinsky method with the deformed Woods-Saxon potential predict the existence of extremely elongated hyperdeformed nuclear shapes with the axis ratios significantly exceeding2:1. The strongest effect is expected to take place for nuclei around ¹⁶⁶Er, ¹⁶⁸Yb, and ¹⁷⁰Hf (Z = 68, 70, 72; N = 98) for spins as high as the fission limit down to I ∼ 10–20. The chances for observing those states in nature are discussed in detail. Systematic occurrences of the superdeformed and hyperdeformed states also in lighter (A ∼ 70, and A ∼ 100) nuclei are suggested as a consequence of the approximate pseudo-oscillator (or pseudo-SU(3) symmetries of the realistic nuclear mean field.     

Baryon-to-entropy ratio in very high energy nuclear collisions

We compute as a function of rapidity y the baryon number carried by quarks and antiquarks with p _T > p ₀ ≈ 2 GeV produced in Pb+Pb collisions at TeV energies. The computation is carried out in lowest order QCD perturbation theory using structure functions compatible with HERA results. At p ₀ = 2 GeV the initial gluon density is both transversally saturated and thermalised in the sense that the energy/gluon equals to that of an ideal gas with the same energy density. Even at these high energies the initial net baryon number density at y = 0 at τ = 0.1 fin will be more than the normal nuclear matter density but the baryon-toentropy ratio is only (B-B?)/S ～ 1/5000. Further evolution of the system is discussed and the final baryon-to-entropy ratio is estimated.     

Total photoproduction cross section at very high energy

In this paper we apply to the photoproduction total cross section a model we have proposed for purely hadronic processes and which is based on QCD mini-jets and soft gluon re-summation. We compare the predictions of our model with the HERA data as well as with other models. For cosmic rays, our model predicts substantially higher cross sections at TeV energies than models based on factorization, but lower than models based on mini-jets alone, without soft gluons. We discuss the origin of this difference.     

Phase of reflection of very low energy electrons at crystal surfaces

The amplitude coefficients of electron reflection at crystal surfaces are complex numbers, each of which may be characterized by a reflection intensity (the squared modulus of the coefficient) and a phase. The phase of reflection of very low energy (? 10 eV) electron reflection is described on the basis of existing theory, and experimental approaches to phase determination are reviewed. Theoretical properties of the phase are described on the basis of the two-beam dynamical theory of diffraction. The model considered is an idealized substrate crystal with an attached selvedge (surface region). The indirect effect of inelastic scattering (absorption) is included by going to complex values of the electron energy or of the surface-normal component K of the propagation vector. In the absence of a selvedge the phase is determined solely by the band structure of the substrate crystal. If a selvedge is present there are large additional effects on the phase associated with zeros of the amplitude coefficient of reflection on the complex K plane. The experimental approaches considered are: (1) measurement of the kinetic energy distributions of ions produced in the field ion microscope, and (2) measurement of the periodic deviations from the Schottky line in field-assisted thermionic emission and photo-emission. Recent results of phase determination for W (011) surface by method (1) are summarized and compared with theoretical expectations.     

Physics perspectives of heavy-ion collisions at very high energy

The structure of stretchable electronics is based on the buckling of a thin film on a compliant substrate. Under anisotropic biaxial prestrains, this structure may buckle into several patterns, including cylindrical, checkerboard, and undulating patterns. The displacement and energy of each pattern are deduced analytically. By comparing their minimum potential energies, the critical buckling condition of each pattern is determined. After secondary bifurcation, the checkerboard pattern occurs just above the critical prestrains, but the undulating pattern dominates other regions. The buckling amplitude and wavenumber of the undulating pattern are shown under biaxial prestrains. Even if the structure is under equi-biaxial prestrains, it may buckle into an asymmetric undulating pattern.     

Wobbling excitations at high spins in

We found that in ¹⁵⁶Dy and ¹⁶²Yb the lowest odd spin gamma-vibrational states transform to the wobbling excitations after the backbending, associated with the transition from axially-symmetric to nonaxial shapes. The analysis of quadrupole electric transitions determines uniquely the sign of the γ-deformation in both nuclei after the transition point.     

Semi-hard parton rescatterings in nuclear collisions at very high energies

Representing the semi-hard partonic interactions by the exchange of Lipatov's perturbative Pomeron, we express the semi-hard nuclear cross section as a self shadowing cross section. With the help of a generating functional technique, we obtain average numbers of multiple semi-hard partonic collisions without any need of using explicit expressions for the multi-parton distributions. The average number of semi-hard interactions of a given projectile parton against a target nucleus is estimated quantitatively and it is shown to grow very rapidly above one with increasing the c.m. energy.     

Scaling at very high energy and an emulsion experiment at the ISR

With reference to a recent paper of the Bombay-CERN-Cracow collaboration, we show that the ISR emulsion experiment does not disprove scaling.     

The pairing correlations and nuclear shapes at very high angular momenta

The usual Strutinsky shell corrections include the pairing correlations in the BCS approach. At high-spin states the cranked intrinsic wave functions are not symmetric or antisymmetric under time reversal symmetry for general triaxial shapes. On the basis of the Hartree-Fock-Bogoliubov (HFB) approach two generalizations of the Strutinsky procedure are given to describe pairing correlations also for high-spin states and triaxial shapes. The method is applied to the neutron-deficient rare earth nucleus ¹⁵⁰Gd. It is found that pairing has an important effect on the change of nuclear deformation with increasing angular momentum. The proton pairing persists at least up to I ≈ 40.     

Level structure of 99Rh at high spins

High spins states in ⁹⁹Rh were populated via the ⁶⁶Zn(³⁷Cl, 2p2n)⁹⁹Rh reaction at an incident beam energy of 130 MeV. Seventeen new transitions have been observed in the present study and the level scheme has now been extended up to a spin of J∼ 25ħ and an excitation energy of about E _x∼ 10 MeV. The observation of a positive parity E2 cascade based on the 9/2⁺ isomeric level is suggestive of collective behaviour in this nucleus up to high spins. Spherical shell model (within restricted model space) and Cranked shell model calculations were performed to obtain an insight into the observed level structure. The new collective band observed up to a spin of J∼ 25ħ is suggested to be based on (πg _9/2 ³) ⊗ (νg _7/2 ²) quasi-particle excitations. Received: 12 July 1999 / Revised version: 14 September 1999