Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

The quantal system of Bose particles described by the non-linear Schrödinger equation i?φ/?t = -$\text{1}\text{2}$?²φ/?x² + cφ1φ², with c= cxf∞ and via the ground state with finite particle density, is the 1- dimensional gas of impenetrable bosons studied by M. Girardeau, T.D. Schultz, A. Lenard, H.G. Vaidya and C.A. Tracy. We show that the 2-point (resp. 2n-point) function, or the 1-particle (resp. n-particle) reduced density matrix, of this system satisfies a non-linear differential equation (resp. a system of non-linear partial differential equations) of Painlevé type. Derivation of these equations is based on the link between field operators in a Clifford group and monodromy preserving deformation theory, which was previously established and applied to the 2-dimensional Ising model and other problems. Several related topics are also discussed.     

Squeezing and sub-Poissonian effects up-to fourth order in fifth harmonic generation

The concept of squeezing of the electromagnetic field is investigated in fundamental mode in fifth harmonic generation with the approximation |gt|²?1, where g is coupling constant and t, the interaction time between waves during the process. It has been found that squeezing occurs in amplitude, amplitude-squared, amplitude-cubed and fourth-order amplitude states of the field for selective phase values of field amplitude of fundamental mode. The dependence of squeezing on the photon number has also been investigated and found to be sub-Poissonian in nature. The signal to noise ratio has been studied in different order. It is found that the signal to noise ratio is higher in lower order.     

Stationary solitons of the fifth order KdV-type. Equations and their stabilization

Exact stationary soliton solutions of the fifth order KdV type equation, u_t + αu^pu_x + βu_3x + γu_5x = 0, are obtained for any p (> 0) in case αβ > 0, Dβ > 0, βγ < 0 (where D is the soliton velocity), and it is shown that these solutions are unstable with respect to small perturbations in case p ≥ 5. Various properties of these solutions are discussed. In particular, it is shown that for any p these solitons are lower and narrower than the corresponding γ = 0 solitons. Finally, for p = 2 we obtain an exact stationary soliton solution even when D, α, β, γ are all > 0 and discuss its various properties.     

Absence of the fifth force problem in a model with spontaneously broken dilatation symmetry

A scale invariant model containing dilaton ? and dust (as a model of matter) is studied where the shift symmetry ? → ? + const. is spontaneously broken at the classical level due to intrinsic features of the model. The dilaton to matter coupling “constant” f appears to be dependent of the matter density. In normal conditions, i.e. when the matter energy density is many orders of magnitude larger than the dilaton contribution to the dark energy density, f becomes less than the ratio of the “mass of the vacuum” in the volume occupied by the matter to the Planck mass. The model yields this kind of “Archimedes law” without any especial (intended for this) choice of the underlying action and without fine tuning of the parameters. The model not only explains why all attempts to discover a scalar force correction to Newtonian gravity were unsuccessful so far but also predicts that in the near future there is no chance to detect such corrections in the astronomical measurements as well as in the specially designed fifth force experiments on intermediate, short (like millimeter) and even ultrashort (a few nanometer) ranges. This prediction is alternative to predictions of other known models.     

s- and p-wave neutron spectroscopy. Xe. Intermediate structure in 90Y and the generalized R-matrix theory

The resonance structure observed in the ⁸⁹Y(n, n)⁸⁹Y total cross section measurements in the range of 0.3 to 1.2 MeV incident energy was investigated using the generalized R-matrix theory of nuclear reactions and the doorway interpretation of intermediate structure. The energies and wave functions of the doorway resonances were calculated in a 2-particle and 3p-1h basis of the shell model. The model space and the parameters of the model calculation chosen were consistent with other shell model calculations in the mass-90 region. Several strong p-wave doorways with J^π = 0⁺, 1⁺, and 2⁺ were predicted by the model in the energy range studied. This is due to proximity of p-wave giant resonance. The escape widths Γ^↑ and the spreading widths Γ^↓ for these states were evaluated using the model wave functions and the R-matrix formalism. The calculated energy dependence of the total cross section shows that most of the predicted doorways are in general agreement with the observed anamolies with similar relative strength. More significantly, the underlying p-wave gross structure representing a grand average is of very similar shape in both theory and experiment. As expected in the mass 90-region, the s- and d-wave doorways contribute less significantly to the calculated resonance structure.     

On the recombination mechanism of quarks into a baryon in proton fragmentation

The similarity and difference between our quark cascade model with recombination mechanism and Van Hove's quark fragmentation-recombination model are discussed. Van Hove's fragmentation-recombination model is extended to the model which describesx-dependence of the hadron spectra as well as the baryon multiplicities by using our diffusion equation. The recombination probability in Van Hove's model can be related with the recombination factor λ′ in our diffusion equation. Thex-dependence of the hadron spectra causes another restriction on the recombination probability in Van Hove's model. The inclusive spectra of mesons, proton andΔ ⁺⁺ in proton fragmentation and baryon multiplicities except∑ ^? multiplicity are explained by both our model with recombination mechanism and the model with recombination mechanism a la Van Hove. But the ration(∑ ^?)/n(∑ ^+;) may not be explained by naive quark-parton model with recombination mechanism without considering quark spin.     

Measurement and statistical model analysis of pre-fission neutron multiplicities

The average number of neutrons preceding fission (ν_pre) was measured for the compound systems ¹⁶⁸YB, ¹⁷⁸W, ¹⁸⁸Pt, ¹⁹²Pb, ¹⁹⁸Pb, ²⁰⁰Pb, ²¹⁰Po, ²¹³At and ²⁵¹Es formed by reactions induced by ¹⁶O, ¹⁸O, ¹⁹F, ²⁸Si or ³⁰Si projectiles with energies (E) between 4.9 and 7.2 MeV/A In some cases ν_pre is seen to increase with increasing E above a threshold energy (E_th) whereas the statistical model indicates that it should decrease. For a given projectile, this threshold decreases with increasing fissility, becoming equal to the Coulomb barrier around A_CN∼213 for ¹⁶O projectiles. Below E_th the variation of ν_pre with E is consistent with statistical model predictions. The deviations above E_th have been attributed to dissipative effects not included in the model. Extensive statistical model and Xχ² analyses of the pre-fission data below E_th and of fission and fusion excitation function data, previously measured, were made. The diffuseness parameters of the fusion spin-distributions agreed reasonably well with those suggested by the zero-point motion model. The ratios of level densities at saddle and equilibrium deformations (a_f/a_v) were found to be consistent with a value of unity, and the fission barriers (E_f) consistent with the predictions of the finite-range rotating liquid-drop model. However these values for a_f/a_ν and E_f may not represent the true values. Inclusion of dissipation requires higher values, whilst inclusion of the temperature dependence of E_f in statistical model calculations is shown to result in a reduction in the value of a_f/a_ν. Since reliable theoretical calculations are unavailable for either effect the consistency of the data with the finite range fission barriers can only be demonstrated to within 10–15% and values for a_f/a_ν, have an uncertainty of at least 5%.     

A study of 80,82,84Sr by (α, 2nγ) reactions

The ^AKr(α, 2nγ)^A+2Sr reactions have been studied by in-beam γ-ray spectroscopy for A = 78, 80, and 82. States with spins up to 10⁺ in ^82,84Sr and 6⁺ in ⁸⁰Sr are identified. The Sr nuclei undergo a transition from spherical to deformed ground states as neutrons are removed from the N = 50 shell. The systematics of these nuclei are compared with calculations based upon the shell model and interacting boson model.     

Inclusive two-particle correlations in 40 GeV/c π−p collisions and particle production mechanisms

Inclusive two-particle correlations in rapidity variables between π⁺π^?, π⁺π⁺ and π^?π^? obtained in 40 GeV π^?p collisions are discussed in the framework of the Mueller Regge model and the multiperipheral cluster model. The data show features similar to the data reported at much higher energies from the CERN ISR. This behaviour is more easily understood from the multiperipheral cluster model. Data on transverse momentum correlations in the same reactions can be qualitatively understood from the same model.     

Alpha-like four-nucleon correlations in the ground state of 48Cr

The ground-state structure of ⁴⁸Cr is investigated by multiple α-like cluster model. The original model with only J = T = 0 α-like cluster is extended so as to deal with the contribution of J > 0 α-like units. The model reproduces the observed ground-state energy of ⁴⁸Cr well and explains the characteristic variation of the ground-state energies from ⁴⁴Ti to ⁴⁸Cr caused by many-body correlations. The properties of the ⁴⁸Cr ground state which originate in the α-like four-nucleon correlations are revealed by the model.     

Some tests of fragmentation models in exclusive channels inK − p reactions at 32 GeV/c

Experimental data for exclusive channels of multiplicity 4–8 in 32 GeV/cK ^? p reactions are compared with predictions of the Lund model. This leads to the following insights: — Evidence is obtained for azimuthal correlations betweenK ⁺ K ^? pairs and p pairs supporting the Lund fragmenttation scheme. — The disagreement of the observed behaviour of leading protons andK ^? with the model predictions indicates that the fate of the valence quarks is not well described by the model. The data support the idea of valence quark separation as advocated by dual models.     

Lepton flavor violation decays τ −→μ − P 1 P 2 in the topcolor-assisted technicolor model and the littlest Higgs model with T-parity

The new particles predicted by the topcolor-assisted technicolor (TC2) model and the littlest Higgs model with T-parity (called LHT model) can induce the lepton flavor violation (LFV) couplings at tree level or one loop level, which might generate large contributions to some LFV processes. Taking into account the constraints of the experimental data on the relevant free parameters, we calculate the branching ratios of the LFV decay processes τ ^?→μ ^? P ₁ P ₂ with P ₁ P ₂=π ⁺ π ^?, K ⁺ K ^? and $K^{0}\bar{K}^{0}$ in the context of these two kinds of new physics models. We find that the TC2 model and the LHT model can indeed produce significant contributions to some of these LFV decay processes.     

On the Q 2 dependence of nuclear structure functions

The recent high statistics NMC data on the Tin to Carbon structure function ratio seems to indicate, for the first time, a significant Q ² dependence, especially at small values of Bjorken x, x < 0.05, and Q ² > 1 GeV². A purely log(Q ²)-type dependence of the structure functions, which is consistent with the free nucleon data, yields a fairly flat ratio with little or no Q ² dependence. In view of this seeming contradiction, we re-examine the applicability of such a model to nuclear structure functions in such a kinematical regime. We find that the model is consistent with all data, within experimental errors, without any need for introducing additional Q ² dependences or higher twist contributions. The model correctly reproduces the Q ² dependence of the Carbon structure function as well. We also critically examine the Q ² dependence of the corresponding spin dependent structure functions.     

Rotational variation of predissociation linewidth in the Schumann-Runge bands of 16O2

Extensive high resolution photoabsorption measurements have been performed on most of the experimentally accessible rotational lines in the Schumann-Runge band system of ¹⁶O₂. Predissociation linewidths are inferred from these measurements for as many lines as possible from the (1-0) to (19-0) bands. A model of the predissociation is developed, which includes the interactions of the B³Σ^-_u state with repulsive ⁵Π_u, ³Π_u, ¹Π_u and ³Σ⁺_u states, and molecular parameters for these interactions are determined by least-squares fitting the model to the experimental vibrational widths for the (1-0) to (18-0) bands. These parameters are then used, in conjunction with the model, to predict the variation of predissociation linewidth with rotation for each Schumann-Runge band. The experimental linewidths are found to exhibit systematic variation with rotation for most of the bands studied, and agreement with the model predictions of rotational variation is excellent. Polynomial fits to the model rotational linewidths are also presented in order to facilitate atmospheric modelling applications.     

Cluster Model Analysis of Pion Elastic and Inelastic Scattering from 12C

Angular distributions of differential cross sections for the ¹²C(π ^±, π ^±)¹²C and ¹²C(π ^±, π ^±)¹²C^* reactions at pion kinetic energy ranging from 50 to 260 MeV have been analyzed with the 3α-particle model of ¹²C. The model provides good fits to a wide range of data. Differential cross sections for inelastic transitions to the (2^?+?; 4.44 MeV) and (3^???; 9.64 MeV) states in ¹²C are computed and the deformation lengths δ ₂ and δ ₃ are extracted. It is found that the extracted deformation lengths are sensitive to the nuclear model used and similar to the corresponding values found with other probes and nuclear models.     

QCD jets ine + e −-annihilation and the transition into hadrons

A model has been developed describing QCD jets in the leading logarithmic approximation (LLA) and the subsequent transition into hadrons via a chain decay model. Besides of the production of mesons, the model is also able to describe baryon production. Agreement with recent data frome ⁺ e ^?-annihilation is found. This includes average multiplicities, average transverse momenta and transverse momentum distributions, longitudinal momentum distributions as well as particle production ratios π^α:K ^π : p(0070), charge compensation probabilities and energy flux correlations. The model is compared to similar models developed by other authors.     

Oxygen vacancy model for the E1′ center in SiO2

An (oxygen)^- vacancy model of the E₁^≈ center in alpha quartz, featuring an asymmetric relaxation of the two silicons adjacent to the oxygen vacancy, is presented and analyzed. This model is shown to be consistent with both theoretical calculations and experimental hyperfine data, in contrast with any model previously proposed for the E₁^≈ center.     

A satellite-borne experiment to study the fifth force

An experiment with a satellite-borne torsion balance capable of measuring the fifth force which couples to baryon number or lepton number with a strengtr gravity and range ~ 10⁹ cm is described.     

A relativistic quark model for mesons based on numerical solutions of the Bethe-Salpeter equation

A study is made to determine if the results of the nonrelativistic quark model can be reproduced by a fully relativistic model of deeply bound $\text{spin}\text{-}\text{1}\text{2}$ quarks. It is found that the relativistic model does not reproduce the nonrelativistic results, even when the quarks have nonrelativistic momenta. However, the model is rather successful in accounting for the known properties of mesons.Numerical solutions to the Bethe-Salpeter equation are obtained for pseudoscalar and vector bound states of equal mass quark-antiquark pairs, with either a scalar, pseudoscalar, or neutral vector exchange interaction. The interaction function corresponds to single particle exchange, with the addition of either one or two regulating terms. It is found that the second regulator allows the internal quark momentum to be nonrelativistic, but that the spinor structure of the wave function remains highly relativistic.Only the scalar interaction can account for the observed spectrum of states. The pseudoscalar interaction yields a vector state of lower mass than the pseudoscalar state, and the vector interaction leads to a vector state which lies approximately one quark mass above the pseudoscalar state. The λ quark is taken as slightly heavier than the p and n, and the perturbation treatment of the mass difference leads to a quadratic mass formula.The decay amplitudes for π, K → μν are calculated, and it is found, independent of parameters, that $\text{?}{}_{\mathrm{\pi }}\text{≈ ?}{}_{\mathrm{K}}$ for either a scalar or vector interaction, in agreement with experiment and in contrast with the nonrelativistic model. The amplitudes for ?^o, ω, φ → e⁺e^?, μ⁺μ^? are also calculated, but in this case the ratios (again parameter independent) are in minor discrepancy with experiment.The question of the additivity of quark amplitudes is examined by calculating (with significant restrictions) the magnetic moments of the vector mesons and the amplitudes for magnetic transitions such as ω → π^oγ. The magnetic moments of the vector mesons have the same (trivial) ratios to each other as in the nonrelativistic model, but they are strongly enhanced over the sum of the quark magnetic moments. The amplitude for magnetic transitions, however, is related to the quark magnetic moments in approximately the same ratio as in the nonrelativistic model.The model is also used to obtain parameter dependent predictions for the masses and decay amplitudes. These predictions are not experimentally correct, but are generally well within an order of magnitude for a wide range of the parameters.The most significant defect discovered of the model is the presence of ghost states (the daughters of the vector mesons, with J^PC = 0^+?) with masses of about 2 BeV.