Nonergodicity and dynamical approach to the anharmonic oscillator

General lower bounds for the time average C^AA(∞)≡lim_T→∞(1/T)∝^T₀ C^AA(t) dt of the correlation C^AA(t)≡A(t)A(0)−A² of an arbitrary variable A are derived, which depend only on the temperature derivatives of the canonical averages of A and the Hamiltonian of the system. The bounds may be used to give good estimations for C^AA(∞) which is different from zero when A is nonergodic. It is important to take care of these terms when dynamical theories made for interacting systems are applied to isolated systems. We show explicitely that our recently developed dynamical approach to phonon systems with quartic anharmonicity yields excellent results for the corresponding isolated system, the anharmonic single well oscillator, when nonvanishing time averages are taken into account.     

Measurements of the spin correlation parameters Axx and Ayy for p-p scattering at 46.9 MeV

The A_xx and A_yy spin correlation coefficients of proton-proton scattering have been measured at E_lab = 46.9 MeV and θ_c.m. = 90° with the same experimental techniques already used at Saclay from 11 to 26 MeV and at Grenoble at 37.2 MeV. For A_xx the deviation from the predictions of the energy-dependent phase-shifts analysis of Livermore is significant (≈ 3.7 standard deviations) but not as large as for the 47.5 MeV Tokyo measurement. For A_yy the agreement is very good.     

Calculation of the ground state properties of even-even Sn isotopes

We investigate the ground-state properties of even-even Sn isotopes using the Skyrme-Hartree-Fock (SHF) and Skyrme-Hartree-Fock-Bogolyubov (SHFB) methods with SKM* and SLy4 force parameters. We focus on isotopes of even-even Sn because these isotopes are vital to the structural studies of unstable nuclei taking place at the electron radioactive-ion collider at RIKEN. In the present paper, we calculate the binding energies per particle, the rms nuclear charge radii, the rms nuclear proton density radii, and the rms nuclear neutron density radii, for even-even Sn isotopes, using the SHF and SHFB methods. We compare our results with experimental data and with the results of relativistic mean-field theory. Notably, we fit our calculated binding energies per particle to experimental results, using the aforementioned SHF methods with SKM* and SLy4 parameters     

Measurements of interaction cross sections and radii of He isotopes

Secondary beams of ³He, ⁴He, ⁶He, and ⁸He were produced through the projectile fragmentation of an 800 MeV/nucleon ¹¹B primary beam. Interaction cross sections (σ_I) of all He isotopes of 790 MeV/nucleon on Be, C, and Al targets were measured by a transmission-type experiment. The interaction nuclear radii of He isotopes R_I(He) = (σ_I/π)^1/2 − R _I(T) where R_I(T) is the radius of the target nucleus, have been deduced to be R_I(³He) = 1.59 ± 0.06 fm, R_I(⁴He) = 1.40 ± 0.05 fm, R_I(⁶He) = 2.21 ± 0.06 fm, and R_I(⁸He) = 2.52 ± 0.06 fm.     

Total neutron cross sections and the nuclear Ramsauer effect (II). En = 0.5–42 MeV

Investigation at fourteen energies from 0.5 to 42 MeV and A 27 shows that a simple expression describes the σ_T(A,E) surface in the energy and mass number region mentioned above. For E 10 MeV the expression can be interpreted by the nuclear Ramsauer effect, while for E < 10 MeV a better approximation for the black-nucleus formula seems to be useful. The constant amplitude of oscillations suggests a weak volume absorption and a strong surface absorption.     

Elastic proton-proton scattering: Excitation functions from 0.45 to 2.5 GeV

Excitation functions of the differential cross sections dσ/dgw, analyzing powers A_N and spin correlation parameters A_NN, A_SS and A_SL have been measured with internal targets at the Cooler Synchrotron COSY. Data were taken continously during the acceleration and deceleration of the internal beam for kinetic energies between 450 and 2500 MeV and scattering angles 30° σ_cm 90°. Details of the experimental method are presented. The results provide excitation functions and angular distributions of high precision and internal consistency. No evidence for narrow structures are found. Upper limits on the coupling of narrow resonances to elastic scattering in the mass range √s = 2.2…2.8 GeV are deduced. The data have significant impact on phase shift solutions.     

1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Existence and stability of propagating fronts for an autocatalytic reaction-diffusion system

We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B → 2B) and a cubic (A + 2B → 3B) autocatalysis. The parameters of this system are in the ratio D = D_B/D_A of the diffusion constants of the reactant A and the autocatalyst B, and the relative activity k of the cubic reaction. First, for all values of D > 0 and k ≥ 0, we prove the existence of a family of propagating fronts (or travelling waves) describing the advance of the reaction. In particular, in the quadratic case k = 0, we recover the results of Billingham and Needham [Phil. Trans. R. Soc. London A 334 (1991) 1–24]. Then, if D is close to 1 and k is sufficiently small, we prove using energy functionals that these propagating fronts are stable against small perturbations in exponentially weighted Sobolev spaces. This extends part of the results that are known for the scalar equation to which our system reduces when D = 1.     

Two-body and three-body halo nuclei

We have extracted the nuclear asymptotic normalization coefficients (ANC) for the virtual transitions B→A+N via some transfer reactions and the radioactive nuclear beam experiments. With these coefficients, root-mean-square (rms) radii for the valence particle in some possible halo nuclei have been calculated. The values of rms radii extracted with ANC approach are nearly model-independent, hence are a good quantity for the investigation of nuclear halo. In addition, we have also calculated the rms radii for the two valence neutrons in some three-body systems in terms of the relationship between the radii of valence particle, core nucleus and nuclear matter. With two conditions for nuclear halo formation, we have examined these extracted rms radii. The results show that 11Be(1/2+, g.s), 12B(1-, 2.621 MeV), 13C(1/2+, 3.089 MeV), 14C(0-, 6.903 MeV), 14C(1-, 6.094 MeV), 15C(1/2+, g.s) and 19C(1/2+, g.s) with the valence particle in the 2s ground or excited state are the neutron halo nuclei, whereas 17F(1/2+, 0.495 MeV) and 21Na(1/2+, 2.423 MeV) are the proton halo nuclei in the excited state. For three-body systems, except the well-established two-neutron halo nuclei 6He and 11Li, 14Be and 17B might be the two-neutron halo nuclei as well.     

Nuclear charge radii of (21-32)Mg

Charge radii of all magnesium isotopes in the sd shell have been measured, revealing evolution of the nuclear shape throughout two prominent regions of assumed deformation centered on (24)Mg and (32)Mg. A striking correspondence is found between the nuclear charge radius and the neutron shell structure. The importance of cluster configurations towards N=8 and collectivity near N=20 is discussed in the framework of the fermionic molecular dynamics model. These essential results have been made possible by the first application of laser-induced nuclear orientation for isotope shift measurements.     

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries A_UL and A_UT of the proton in semi-inclusive pion leptoproduction γ^*(q)p→πX. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q² at fixed x_bj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L^z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.     

He particle emission in fast neutron induced reactions

Cross sections for some (n, ³He + dp + n2p) and (n, + 2n2p + n³He + pt + dd + dnp) reactions induced by fast neutrons produced via breakup of 53 MeV deuterons on a Be target (E_n = 4–50 MeV; I_max at 22.5 MeV; FWHM = 15.8 MeV) were measured for isotopes of the elements I, La, Nd, Tb, Ho, Yb, W and Au by the activation technique using high-resolution γ-ray spectroscopy, wherever necessary chemical separation, and in several cases enriched isotopes as targets. Furthermore, ³He/ emission cross-section ratios were measured for Co, Ag, In, Cs, La, Ta, Au and Bi using a quadrupole mass spectrometer. The cross sections decrease as a function of increasing (N−Z)/A of the target nucleus. For target elements with Z 44, the ³He/ emission cross-section ratio increases with increasing Z; for elements with Z > 44, however, the trend is reversed. Hauser-Feshbach calculations suggest that the ³He/ emission cross-section ratios are not explainable by the statistical model.     

Perovskite-like system (Sr,La)(Fe,Ga)O3−δ: structure and ionic transport under oxidizing conditions

The maximum solid solubility of gallium in the perovskite-type La_1−xSr_xFe_1−yGa_yO_3−δ (x=0.40–0.80; y=0–0.60) was found to vary in the approximate range y=0.25–0.45, decreasing when x increases. Crystal lattice of the perovskite phases, formed in atmospheric air, was studied by X-ray diffraction (XRD) and neutron diffraction and identified as cubic. Doping with Ga results in increasing unit cell volume, while the thermal expansion and total conductivity of (La,Sr)(Fe,Ga)O_3−δ in air decrease with gallium additions. The average thermal expansion coefficients (TECs) are in the range (11.7–16.0)×10⁻⁶ K⁻¹ at 300–800 K and (19.3–26.7)×10⁻⁶ K⁻¹ at 800–1100 K. At oxygen partial pressures close to atmospheric air, the oxygen permeation fluxes through La_1−xSr_xFe_1−yGa_yO_3−δ (x=0.7–0.8; y=0.2–0.4) membranes are determined by the bulk ambipolar conductivity; the limiting effect of the oxygen surface exchange was found negligible. Decreasing strontium and gallium concentrations leads to a greater role of the exchange processes. As for many other perovskite systems, the oxygen ionic conductivity of La_1−xSr_xFe_1−yGa_yO_3−δ increases with strontium content up to x=0.70 and decreases on further doping, probably due to association of oxygen vacancies. Incorporation of moderate amounts of gallium into the B sublattice results in increasing structural disorder, higher ionic conductivity at temperatures below 1170 K, and lower activation energy for the ionic transport.     

The role of polarization of Xe by di- and monovalent cations in Xe NMR studies in zeolite A

We consider the role of polarization in the adsorption of Xe in zeolites of type A by direct comparative analysis of the adsorption isotherms, distributions of occupancies, and ¹²⁹Xe NMR chemical shifts of Xe_n in cages containing Ca_xNa_{12 −2x} ions per alpha cage (x = 0, 1, 2, 3, 5). We find that the qualitative trends in the adsorption isotherms, and in the progressions of Xe_n chemical shifts (for n = 0–8 in cages with x = 0, 1 Ca²⁺ ions and for n = 0–5 in cages with x = 2, 3 Ca²⁺ ions) upon increasing the level of Ca²⁺ ion for Na⁺ ion substitution could only be accounted for by including polarization of the Xe atom by the zeolite framework and its ions. This system, which permits observation of individual Xe_n peaks and of directly comparable adsorption isotherms in several cage types, provides a good model system for the interpretation of the more general case in which only the overall average ¹²⁹Xe NMR chemical shift is observed in open network zeolites, arising from free exchange of Xe among cavities of variable occupancy and variable cation distribution.     

Spectroscopic study of BixEu1−xVO4 and BiyGd1−yVO4 mixed oxides

The mixed oxides Bi_xEu_1−xVO₄ and Bi_yGd_1−yVO₄ crystallize in a zircon-type structure, for 0 <x < 0.6 and 0 < y < 0.64, and in a fergusonite-type structure, for 0.94 < x < 1 and 0.93 < y < 1. A process of competition between the dominant and the constrained effects of the lone-pair 6s² of Bi³⁺ is discussed. The diffuse reflectance spectroscopic studies of these mixed oxides are presented. The observed broad bands are attributed to charge transfer processes and the sharp peaks in the Bi_xEu_1−xVO₄ spectra are ascribed to intra-configurational 4f – 4ftransitions of the Eu³⁺ ion. The broad absorption shift in BiLnVO₄ (Ln : Eu and Gd) compounds to the longer wavelengths range, when Bi is introduced in the LnVO₄ lattice, is ascribed to charge transfer processes in a Bi-VO₄ center and are interpreted assuming a Jahn-Teller effect in the excited state of Bi³⁺. The concept of an internal pressure of Bi³⁺ ions is also used to explain the broad A-band shifts.     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.     

Correlation lengths and E8 mass spectrum of the dilute A3 lattice model

The exact perturbation approach is used to derive the elementary correlation lengths ξ_i and related mass gaps mi of the two-dimensional dilute A_L lattice model in regimes 1 and 2 for L odd from the Bethe ansatz solution. In regime 2 the A₃ model is the E₈ lattice realisation of the two-dimensional Ising model in a magnetic field at T = T_c The calculations for the A₃ model in regime 2 start from the eight thermodynamically significant string types found in previous numerical studies. These string types are seen to be consistent in the ordered high field limit. The eight masses obtained reduce with the approach to criticality to the ES masses predicted by Zamolodchikov, thus providing a further direct lattice determination of the Es mass spectrum.     

Thick skin in neutron/proton-rich sodium isotopes

Nucleon (both neutron and proton) density distributions of the chain of sodium isotopes are calculated using a semi-phenomenological model of nuclear density which incorporates correctly the asymptotic behaviour and the behaviour near the centre. The experimental charge root-mean-square radii and the single neutron and proton separation energies, required as input, are used. The calculated interaction cross-sections using these densities in the Glauber model agree well with the experiment. The calculated neutron rms radii r _n and the nuclear skin thickness ( r _n - r _p) closely agree with the corresponding experimental values and also are consistent with the Relativistic Hartree-Bogoliubov (RHB) calculations. Received: 24 April 2001 / Accepted: 28 June 2001     

Molecular structure of nuclei

Cluster structures of nuclei are discussed, with emphasis on nuclear clustering in unstable nuclei. The subjects we discuss are alpha condensed states, clustering in Be and B isotopes, and clustering in ³²Mg and ³⁰Ne. The subject of alpha cluster condensation comes from the clustering nature of dilute nuclear matter. We discuss that recent heavy-ion central collision experiments give us nice evidence of the clustering in dilute nuclear matter. We then present a new prediction of the existence of the “alpha cluster condensed states” in the self-conjugate 4n nuclei around the breakup threshold energy into n alpha-particles. As for the clustering in neutron-rich Be, we discuss the comparison between the antisymmetrized molecular-dynamics results and the recent experimental data, which shows that the clustering feature manifests itself very clearly in neutron-rich Be isotopes both in the ground and excited states. Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. We report our recent study about the possible relationship between the clustering and the breaking of the neutron magic number N = 20 in ³²Mg and ³⁰Ne. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: horiuchi@ruby.scphys.kyoto-u.ac.jp     

New evidence for a subshell gap at N=32

An 879.9(2) keV γ-ray transition has been identified following the β decay of ⁵⁸V and assigned as the 2⁺₁→0⁺₁ transition in ⁵⁸Cr₃₄. A peak in the energies of the first excited 2⁺ states for the even–even chromium isotopes is now evident at ⁵⁶Cr₃₂, providing empirical evidence for a significant subshell gap at N=32. The appearance of this neutron subshell closure for neutron-rich nuclides may be attributed to the diminished π1f_7/2–ν1f_5/2 monopole proton–neutron interaction as protons are removed from the 1f_7/2 single-particle orbital.