The quark compound bag model: Defining the admixture of six-quark bag in the deuteron

The probability of the six-quark bag part of the deuteron is defined within recently formulated quark compound bag (QCB) model. An upper limit of about 1 % for the admixture of the confined bag in the deuteron is found for the QCB potential supplied by the long range Paris interaction. The six-quark bag corrections to the static multipole moments of the deuteron are estimated to be ?1 % forμ _d and ?6% forQ _d .     

One-dimensional spin glass with oscillating long-range interaction

In this paper a long-range interacgion approximation for spin glasses is proposed as an alternative to the Sherrington-Kirkpatrick model. The one-dimensional model of Ising spins with the interaction κV _O cosQ x exp (?κ|x|), where κ?c?Q (c is the spin concentration) is studied in detail. The long-range approximation enables one to describe the spin configuration in terms of slowly varying in space fields of the type of amplitude (ρ) and phase (ψ); the ψ-dependent part of the Hamiltonian is analogous to the Hamiltonian, describing the weak pinning of the charge density waves by impurities. As a result, the phase variable apears to be gaples in equilibrium thermodynamics and parametrizes different metastable states under quasiequilibrium conditions. In the mean field approximation (MFA) (κ»0) in the vicinity of the transition pointT _c =cV ₀, there is a symmetric cusp of the magnetic susceptibility ξ; at low temperatures the heat capacity is proportional toT, whereas the susceptibility does not depend on temperature. The MFA cannot be applied in the close vicinity ofT _c (|τ?(κ/c)^2/3) and at very low temperaturesT?κV ₀ when a gap appears in the distribution of the molecular fielsh ath≈0.     

The determination by an independent method ofP k electron capture probabilities in133Ba and139Ce decays gamma decay of133Ba

The electron capture decays of¹³³Ba (10.4 y) and¹³⁹Ce (140 d) were investigated with high resolution Ge(Li) detectors. By x-ray — γ-ray coincidences values of the quantityP _k ω _k ? _k for various transitions in the decay of¹³³Ba and¹³⁹Ce are obtained. The factor ω _k ? _k was measured independently by means ofK-conversion electron-K x-ray coincidences and was then used to determineP _k , theK-capture probability. The independent measurement of the product ω _k ? _k , together with recent accurate values of ω _k , provides a new method for the accurate calibration of semiconductor x-ray detectors. In the decay of¹³⁹Ce, a value ofP _k =0.78±0.03 is found (where the error represents twice the standard deviation) from whichQ _ec =326 _?30 ⁺⁷⁰ keV to the¹³⁹La ground-state is found by use of theory. In¹³³Ba decay, values are found ofP _k 1=0.72±0.04 for theEC transition to the 437 keV level in¹³³Cs,P _k 2=0.80±0.07 to the 384 keV level, and from an independent measurement, the ratioP _k 1/P _k 2=0.87±0.07. From these results the ground-state value ofQ _ec =522 _?10 ⁺²⁰ keV is derived from theory for¹³³Ba decay. The gamma spectrum of¹³³Ba also was remeasured. From the present gamma intensities and previous conversion electron intensities, new values forK-shell conversion coefficients are obtained. Previously reported γ-rays at 35 and 391 keV are not confirmed.     

On phase transitions in Schlögl's second model

We study Schlögl's second model, characterized by chemical reactions $$\begin{array}{*{20}c} {2X\underset{{k_2 }}{\overset{{k_1 }}{\longleftrightarrow}}3X,} & {X\underset{{k_4 }}{\overset{{k_3 }}{\longleftrightarrow}}0,} \\ \end{array} $$ ind-dimensional space. The reactions are assumed to be local; local fluctuations are fully taken into account, and particle transport occurs via diffusion. In contrast to previous investigations, we find no phase transition whenk ₄≠0 andd<4. Fork ₄=0,k ₃≠0, and 1≦d<4, we find a second-order phase transition which is in the same universality class as the transition in Schlögl's first model. Only ford≧4 we do find the first-order transition found also by previous authors. These claims are supported by extensive Monte Carlo calculations for various realizations of this process on discrete space-time lattices.     

The coloured Jones function

The invariantsJ _K,k of a framed knotK coloured by the irreducibleSU(2) _q -module of dimensionk are studied as a function ofk by means of the universalR-matrix. It is shown that whenJ _K,k is written as a power series inh withq=e ^h , the coefficient ofh ^d is an odd polynomial ink of degree at most 2d+1. This coefficient is a Vassiliev invariant ofK. In the second part of the paper it is shown that ask varies, these invariants span ad-dimensional subspace of the space of all Vassiliev invariants of degreed for framed knots. The analogous questions for unframed knots are also studied.Partially supported by NSF Grant DMS-9123657     

Phase Transition and Level-Set Percolation for the Gaussian Free Field

We consider level-set percolation for the Gaussian free field on ${\mathbb{Z}^{d}}$ , d ≥ 3, and prove that, as h varies, there is a non-trivial percolation phase transition of the excursion set above level h for all dimensions d ≥ 3. So far, it was known that the corresponding critical level h _*(d) satisfies h _*(d) ≥ 0 for all d ≥ 3 and that h _*(3) is finite, see Bricmont et al. (J Stat Phys 48(5/6):1249–1268, 1987). We prove here that h _*(d) is finite for all d ≥ 3. In fact, we introduce a second critical parameter h _** ≥ h _*, show that h _**(d) is finite for all d ≥ 3, and that the connectivity function of the excursion set above level h has stretched exponential decay for all h > h _**. Finally, we prove that h _* is strictly positive in high dimension. It remains open whether h _* and h _** actually coincide and whether h _* > 0 for all d ≥ 3.     

Scattering of fast muons by copper nuclei

The relative probability forK-capturePK ₉₃₆/PK ₅₃₉≦0.05 and forL-capturePL ₉₃₆/PL ₅₃₉=4.4±0.7 yield a total transition energyQ _EC in the energy Intervall 981≦Q _EC ≦1,021keV. The high-energy γ-spectrum and the half-life of¹⁹¹Pt were remeasured.     

Precise atomic masses of147Eu,147Gd,and151Tb derived from their decay properties

Theβ-decay energies of¹⁴⁷Eu,¹⁴⁷Gd, and¹⁵¹Tb were determined by usingγ-spectroscopical methods. The comparison of experimental with calculatedK-capture probabilities yielded theQ _EC values 1.690( _?16 ⁺²¹ )MeV and 2.203( _?13 ⁺¹⁹ )MeV for¹⁴⁷Eu and¹⁴⁷Gd, respectively. By measuring the ratio of positron decay to electron capture for two branches in¹⁴⁷Eu decay, the decay energiesQ _EC=1.702(13) MeV andQ _EC=1.709(18)MeV were derived. Also fromEC/β ⁺ ratios the valuesQ _EC=2.225(75) MeV for¹⁴⁷Gd, andQ _EC=2.566(12)MeV for¹⁵¹Tb were obtained. Earlier discrepancies in the mass adjustment of these isotopes were removed. In course of the present studiesγ-decay properties of¹⁴⁷Eu and¹⁴⁷Gd were reinvestigated.     

Bestimmung der Quantenausbeute der Rubinfluoreszenz bei Anregung durch Einstrahlung in eine der blauen Absorptionslinien

The relative quantum efficiency of ruby is measured, when the crystal is excited both in the blue lines and in the bands near these lines. The ratioQ _line/Q _band=1,6 is obtained. With the absolute value ofQ _band as given byMaiman et al. an absolute quantum efficiency of unity forQ _line is determined.     

Consequences of diffractive heavy flavor production

We calculate the lepton spectrum inpp collisions from the production and semileptonic decay ofΛ _c andΛ _b , and find limits on their production cross sections. Total cross sections in excess of 1 mb forΛ _c and 2 1/2μb forΛ _b violate the experimental fact that (μ/π)?10^?4. Abundant production ofΛ _c has led to speculations on the existence of a large intrinsic charm sea inside the proton. We discuss alternative ways of probing such a structure inside the proton: jets opposite highp _T direct photons and central production of ψ.     

Early scaling in two photon reactions?

We show that the interpretation given by the TPC/2γ collaboration that their results for the photon structure functionF ₂ ^γ (x) indicates precocious scaling forQ ²>0.3 GeV² andx<0.1 is questionable. It appears to be a spurious effect possibly due to the fact that (i) the authors do not include two prong events (important at lowW), and (ii) in presenting the data they have averaged theW dependence in eachQ ² bin. To estimate the pointlike contribution of the offshell photon, we use the quark parton model (QPM) and find that this accounts for the data forQ ²>20 GeV² and all values ofW. This hard component is also responsible for the bulk of the cross section at lowQ ² andW<3 GeV. The soft or hadronic component is shown to dominate only at highW>6 GeV for values ofQ ²≤10 GeV².     

The gamma decay of high spin states of39K

First will be exhibited, for the stationary case, a connection between the probability, to find a particle in the region of interaction, and the derivative of the scattering phase shift for the momentum. From the idea, that in stationary scattering a resonance is linked with an appreciable increase of this probability, one obtains new and quantitative criteria for the behavior ofδ _l(k). For instance, the nonresonant behavior can be characterised by the condition 2k dδ _l(k)/dk<1. The maximum of probability for the particle to be in the region of interaction, is considered in accordance with the criterium of maximal change of the phase shift, as a function ofk. This characterises the location of the resonance. Wigner's lower limit fordδ _l (k)/dk allows to formulate a resonance condition directly for the cross section. Furthermore will be discussed some connections with the pole approximations of theS-matrix and the “collision lifetime” of Smith.     

Co-energy of surface and grain boundary in Ag film

A model is proposed for calculating the co-energy of surface and grain boundary (GB) by the modified analytical embedded atom method (MAEAM). As example, the energy densities E_d of the two adjacent grains are obtained when their (0 0 1) twist GB meets the free surface (h₁ k₁ 0)/(h₂ k₂ 0) of Ag film. The period along the boundary line on the surface is found and the energy density is calculated for the situations either with or without periodicity. The results show that, the energy value achieved via this model can be stable even for most grains with boundary line smaller than 100 nm. Among the grains with (h k 0) surface, (1 0 0) grains should be favored and grow fastest when they meet (1 1 0) grains.     

Determination of the spectroscopic quadrupole moments of 33 75 As and 29 63 Cu

The HFS-splitting of the 2s-2p and 3d-2p transitions of muonic arsenic and 3d-2p transitions of copper have been measured with high resolution Ge-semiconductor detectors to determine the nuclear quadrupole moments. A coincidence measurement was performed to separate the 2s-2p transition from the background. The nuclear spectroscopic quadrupole moments were found to be:Q _spec=0.314(6) b for ₃₃ ⁷⁵ AsQ _spec=0.220(15) b for ₂₉ ⁶³ Cu. In addition, generalized Barrett moments were determined in a model-independent analysis of muonic transition energies.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).     

The simplified Hubbard model in one and two dimensions

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero couplingU and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function ofU, temperature and band fillingp. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at ?4d<U _c (p)≦?2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order forU>U _c . The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.     

Critical behaviour at the displacive limit of structural phase transitions

For a special critical point at zero temperature,T _c =0, which is called the displacive limit of a classical or of a quantum-mechanical model showing displacive phase transitions, we derive a set of static critical exponents in the large-n limit. Due to zero-point motions and quantum fluctuations at low temperatures, the exponents of the quantum model are different from those of the classical model. Moreover, we report results on scaling functions, corrections to scaling, and logarithmic factors which appear ford=2 in the classical case and ford=3 in the quantum-mechanical case. Zero-point motions cause a decrease of the critical temperature of the quantum model with respect to the classicalT _c , which implies a difference between the classical and the quantum displacive limit. However, finite critical temperatures are found in both cases ford>2, while critical fluctuations still occur atT _c =0 for 0<d≦2 in the classical case and for 1 <d≦2 in the quantum model. Further we derive the slope of the critical curve at the classical displacive limit exactly. The absence of 1/n-corrections to the exponents of the classical model is also discussed.     

Yrast band spectroscopy of132Sm and130Nd

The states in the yrast band of¹³² Sm have been identified for the first time up to J^π=16⁺. The yrast band of¹³⁰Nd has also been extended from J^π=16⁺ to 24⁺. The energy of the first 2⁺ state in¹³²Sm indicates that the quadrupole deformation ε₂ ～ 0.3 and is still increasing as the neutron number N decreases across the samarium isotopes. The results for¹³⁰Nd allow the (h_2/11)² proton crossing frequency to be determined as ω=0.325 ± 0.005 MeV/?. This result is compared with cranked shell model predictions.