Energy dependence of the C(O, α) reaction

The energy dependence of the ¹²C(¹⁶O, α) reaction was measured at incident energies of E_lab=112−191 MeV. In the range ofE_x(²⁴Mg)=30−56 MeV, the excitation energies of the structures in the inclusive α spectrum were found to vary continuously as a function of incident energy in this region. This fact indicates that these structures do not represent excitations in ²⁴Mg, but rather that they originate from a different process such as a sequential ejectile decay.     

Freeq-Schrödinger equation from homogeneous spaces of the 2-dim Euclidean quantum group

After a preliminary review of the definition and the general properties of the homogeneous spaces of quantum groups, the quantum hyperboloidqH and the quantum planeqP are determined as homogeneous spaces ofF _q (E(2)). The canonical action ofE _q (2) is used to define a naturalq-analog of the free Schrödinger equation, that is studied in the momentum and angular momentum bases. In the first case the eigenfunctions are factorized in terms of products of twoq-exponentials. In the second case we determine the eigenstates of the unitary representation, which, in theqP case, are given in terms of Hahn-Exton functions. Introducing the universalT-matrix forE _q (2) we prove that the Hahn-Exton as well as Jacksonq-Bessel functions are also obtained as matrix elements ofT, thus giving the correct extension to quantum groups of well known methods in harmonic analysis.     

Beam-size effect in time-delayed laser-induced double gratings

We have studied theoretically the effect of the probe-beam size on time-delayed laser-induced double gratings by assuming that the probe beam is described as a Gaussian beam. LettingE _s1 andE _s2 be the Four-Wave Mixing (FWM) signals originating from the diffraction of the probe beam by the gratings, the condition for the occurrence of the FWM signal modulation is that the divergence angle ofE _s1 andE _s2 is larger than half of the intersection angle between the propagation directions ofE _s1 andE _s2. We have also proposed methods to increase the modulation contrast.     

The4He(12C, γ)16O reaction at stellar energies

The capture reaction⁴He(¹²C, γ)¹⁶O (E _c.m.= 1.34–3.38 MeV) as well as the elastic scattering process⁴He(¹²C,¹²C)⁴He (E _c.m.=1.44–3.38 MeV) have been investigated with the use of an intense¹²C beam and a windowless and⁴He recirculating gas target system. The measurements involved two large NaI(T1) crystals in close geometry to an extended gas target, whereby angle-integrated γ-ray yields were obtained. A large area plastic detector was used for the suppression of time-independent background. A search for cascade γ-ray transitions was carried out by coincidence techniques. The measurement of absolute cross sections is also reported. Theoretical fits of the excitation function for the groundstate γ-ray transition requireE1 as well asE2 capture amplitudes, which are of equal importance at stellar energies. This result increases significantly the stellar burning rate of⁴He(¹²C, γ)¹⁶O and leads to¹⁶O as the dominant product at the end of helium burning in massive stars. The observed capture yield to the 6.92 MeV state is dominated by the direct capture mechanism and plays a small role at stellar energies.     

Quantum Non-Gravity and Stellar Collapse

Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects E_BE_{\rm B} (related to the Planck scale) and the much higher scale E_LE_{\rm L} signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: E_LE_{\rm L} is the energy scale below which a special relativistic spacetime emerges, E_BE_{\rm B} is the scale below which this spacetime geometry becomes curved. This implies that the first ‘quantum’ gravitational effect around E_BE_{\rm B} could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of E_LE_{\rm L}. This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole.     

Linking numbers,contacts, and mutual inductances of a random set of closed curves

We establish here a new, general result of integral geometry, concerning closed rigid curves of arbitrary shapes inE ³ and their linking numbersI. It generalizes by a different method, the interesting integral property ofI ² found recently by Pohl and extended by des Cloizeaux and Ball, for two curves. We considern closed curves linked successively to each other and forming a ring. The cyclic product of their linking numbers is integrated over the group of rigid motions of the curves. This integral is shown to factorize over a special algebra of characteristic functions. Each curve possesses two such intrinsic functions. The same algebra is shown to describe a larger class of integral geometry properties: a new theorem is established for a family of displacement integrals involving linking numbers, contact angles, and mutual inductances of the set ofn curves.     

Commutative asymptotic limit of a quasi-SU(2) formulation of general relativity

The notion of local quasi-gauge bundle structure is introduced. We show that general relativity can be recast in a local quasi-SU(2)-bundle framework. In the limit of weak asymptotic gravitational field, this geometrical setup gives rise to spin-2 tensor fields sourcing global charges. If such charges are available, it is shown that the asymptotic geometrical framework is that of aU(1) gauge bundle overS ₂, the commutative geometry of the (Dirac) magnetic monopole.     

Sequence of different types of nonlinear current oscillation in n-GaAs

In_xGa_1– xAs(x}<0.03)/GaAs lasers grown by vapor phase epitaxy using an In/Ga alloy source were characterized by double crystal X-ray (DCX) diffraction and deep level transient spectroscopy (DLTS) measurements. Based on the results obtained from (400), (511), and (¯511) DCX rocking curves, the obvious effect of In incorporation is to give an increase in the full width at half maximum of the rocking curves that correlates with a coherency of the epitaxial layers. From DLTS spectra according to the In content, the most prominent electron deep traps areE 4 (E _c-0.58eV) andE5 (E _c-0.84eV). TheE 4 trap density increases with In content while the change ofE 5 trap density is not monotonic. The trend ofE 5 trap densities versus In content is very similar to that of etch pit densities (EPDs), that is, a minimum in EPD andE 5 trap density is observed at an In content ofx0.003 but beyond this value the densities increase again with In content.     

An interesting representation of lie algebras of linear groups

I have presented a means of getting a representation space of a general linear group ofn dimensions in terms of homogeneous functions ofn,n-dimensional vectors. Except in particular cases, the representation is of the Lie algebra, rather than the group. A general formalism is set up to evaluate the Casimir operators of the Lie algebra of the group in terms of the degrees of homogeneity of the functions (which are eigenfunctions of the Casimir operators) in then variables. It is noticed that the Casimir operators exhibit certain symmetries in these degrees of homogeneity which relate different representations having the same eigenvalues for the Casimir operators. Contour integral formulas that enable one to pass from one such representation to another are presented. An expression for the eigenvalues of a general Casimir operator in terms of the degree of homogeneity is presented.     

Bifurcation phenomena in a periodically driven current filament and a conjecture on the turbulent patterns by computer simulations

Bifurcation routes to chaos in a periodically driven current filament have been studied by computer simulations. By an impact ionization model, theS-shaped currentvoltage curve is perturbed by the dc+ac bias ofE ₀+E _acsin(27f ₀t). The bifurcation maps are described as a function ofE ₀. In the prebreakdown region, the fractal basin boundary, the crisis and the intermittency are discussed, based on the general considerations of the carrier dynamics on the catastrophe manifold. The intermittent burst of the current filament is explained by the destabilization of the weak turbulence generated in the lower branch. In the diffusion-reaction model, the spatio-temporal mode patterns of the transverse carrier profile have revealed the competitive evolution of the hyper-freezing and the firing.     

Weak Hopf Algebras and Singular Solutions¶of Quantum Yang–Baxter Equation

We investigate a generalization of Hopf algebra by weakening the invertibility of the generator K, i.e. exchanging its invertibility KK ^{− 1}= 1 to the regularity . This leads to a weak Hopf algebra and a J-weak Hopf algebra which are studied in detail. It is shown that the monoids of group-like elements of and are regular monoids, which supports the general conjucture on the connection betweek weak Hopf algebras and regular monoids. Moreover, from a quasi-braided weak Hopf algebra is constructed and it is shown that the corresponding quasi-R-matrix is regular . Received: 1 May 2001 / Accepted: 1 September 2001     

Impact of equilibrium radial electric field on energy loss process after pedestal collapse

An impact of the equilibrium radial electric field on energy loss processes after pedestal collapse is numerically investigated using the BOUT++ framework. Using linear stability analysis, the resistive ballooning mode is shown to be stabilized by the radial shear of the equilibrium radial electric field. On the other hand, the energy loss level after the pedestal collapse increases if the equilibrium radial electric field is taken into account. The spatio-temporal and phase diagram analyses show that the equilibrium radial electric field partially cancels the fluctuation-driven toroidally axisymmetric radial electric field and weakens the E × B shearing rate after pedestal collapse, weakening the turbulence suppression by vortex shearing. The equilibrium radial electric field therefore increases turbulence intensity in nonlinear cyclic oscillations among pressure gradient, E × B shearing rate, and turbulence intensity, which gives rise to subsequent bursts of turbulent transport and increases the energy loss level.     

Constraints on finite-range baryonic and leptonic forces from stellar evolution

The contribution to stellar energy loss is considered that would result if finite-range baryonic and.or leptonic forces exist. By requiring that these new interactions do not upset standard models on stellar evolution dynamics upper limits are placed on their strengths. In particular, α_E<4×10⁻²⁶ is found from solar data and α_E<4×10⁻²⁸ from data on red giants for the fine structure constant α_E of a force coupled to the electronic number.     

Pumping of titanium sapphire laser

Two methods of Ti:Sapphire pumping for the generation of tunable laser radiation in the visible region were studied. For coherent pumping, the radiation of the second harmonic of a Nd:YAP laser was used and a maximum output energy ofE _out=4.5 mJ was reached from the Ti:Sapphire laser. For noncoherent pumping, two different lengths of flashlamp pulses were used and a maximum ofE _out=300 mJ was obtained. Preliminary estimations of the wavelength range of tunability were made.     

Nuclear compressibility and its effect on nuclear binding energies from the study of muonic atoms

The variation of nuclear parameter with mass number elicits information about nuclear compressibility. Analysis of muonic x-ray transitions provides an elegant method to investigate the behaviour of the nuclear parameterr ₀. It is observed from the behaviour ofr ₀ that nuclei in the regionA⩽70 are highly compressible while those in the regionA∼210 are almost incompressible. The behaviour ofr ₀ is incorporated into the semi-empirical mass formula through the Coulomb energy term. From the modified mass formula thus obtained binding energies of about 440 spherical nuclei have been calculated. The results suggest that nuclear compressibility imposes certain relationship between excess binding energies (E _exp−E _cal) and neutron. proton number. The present study also points out that shell effects exhibited by nuclear binding energies cannot be accounted for by simply varying the coefficients of the mass formula: on the other hand extra terms are necessary to explain them.     

Dependence of the Thomas-Fermi energy on the nuclear coordinates

LetE(R), respectivelye(R), denote the total energy, respectively the electronic contribution to the energy, in the Thomas-Fermi theory for a system of two fixed nuclei a distanceR apart. We prove thate(R) and –E(R) increase asR does. For the case ofN fixed nuclei, we prove the monotonicity ofe andE under certain displacements of the coordinates of the nuclei. The analogous result for the electronic contribution to the Born-Oppenheimer energy is proved.Research supported by U.S. National Science Foundation under Grant MCS 80-17781     

Role of rational surfaces on fluctuations and transport in the plasma edge of the TJ-II stellarator

It has been shown that transport barriers in toroidal magnetically confined plasmas tend to be linked to regions of unique magnetic topology such as the location of a minimum in the safety factor, rational surfaces or the boundary between closed and open flux surfaces. In the absence ofE×B sheared flows, fluctuations are expected to show maximum amplitude near rational surfaces, and plasma confinement might tend to deteriorate. On the other hand, if the generation ofE×B sheared flows were linked to low order rational surfaces, these would be beneficial for confinement. Experimental evidence ofE×B sheared flows linked to rational surfaces has been obtained in the plasma edge region of the TJ-II stellarator. Presented at the Workshop on the Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June, 2000.     

A study on the156,158,160,162,164,166Dy isotopes

The microscopic structure of the 0⁺ excitations of the^{156,158,160,162,164,166}Dy isotopes has been studied using the Pairing Plus Quadrupole (PPQ) model in the framework of the Random Phase Approximation (RPA). To determine the nature and general trends of the properties of these states depending on the neutron number, their energies, theB(E2) andρ ²(E0) transition values and two-nucleon transfer strengths have been calculated. In addition, the relative summed strengths ofL=0 transitions in the (t,p) and (p,t) reactions have been calculated and compared with experiment.     

Estimate of stellar masses from their QPO frequencies

Kilohertz quasiperiodic oscillations (kHz QPOs) are observed in binary stellar systems. For such a system, the stellar radius is very close to the marginally stable orbit R _ms as predicted by Einstein’s general relativity. Many models have been proposed to explain the origin of the kHz QPO features in the binaries. Here we start from the work of Li et al (Phys. Rev . Lett. 83, 3776 (1999)) who in 1999, from the unique millisecond X-ray pulsations, suggested SAX J1808.4−3658 to be a strange star, from an accurate determination of its rotation period. It showed kHz QPOs eight years ago and so far it is the only set that has been observed. We suggest that the mass of four compact stars SAX J1808.4−3658, KS 1731−260, SAX J1750.8−2900 and IGR J17191−2821 can be determined from the difference in the observed kHz QPOs of these stars. It is exciting to be able to give an estimate of the mass of the star and three other compact stars in low-mass X-ray binaries using their observed kHz QPOs.     

A study of the density of gap states in amorphous semiconductors from thermostimulated conductivity spectra

A theoretical analysis of thermostimulated conductivity spectra _TSC(T) has been applied to determine the density of gap states g(E) in a-Si: H and a-Si: H/a-SiN _x : H multilayer structures. The results for g(E) are consistent with the results deduced from Fritzsche's analytical approach as well as other methods. A comparison has been made between the two different analytical approaches for _TSC(T). We discuss the relationship between the energy of maximum thermostimulated current emission E _m and quasi-Fermi level E _q. We demonstrate that E _q could be a better parameter than E _m in the general theoretical treatment of thermostimulated conductivity.