Upper bound on the slope parameter

We find the axiomatic upper bound on the slope parameter of the scattering amplitude, which is logarithmically divergent with respect to energies in the region 0 < t < 4m²_π. This upper bound is realized in Regge-pole theory. We also obtain explicitly the numerical upper bound on the slope parameter of the linear Regge trajectory.     

On new predictions of the vector-meson dominance model for the reactions πN → ϱ0N and γN → πN

It is shown that the assumption of pole vector-meson dominance for the Ball invariant amplitude having a π-meson pole is sufficient for reproducing the longitudinal amplitude of ?⁰-production by the photoproduction amplitude at |t| < 0.1 (GeV/c)². The strong k²-dependence of the Ball invariant amplitude without the π-meson pole has been found by the deviations of theoretical predictions obtained in the VDM framework for the longitudinal ?⁰-production amplitude from the experimental data in the region |t| > 0.1 (GeV/c)². A natural explanation of the k²-dependence in the one-pion exchange model with absorption is given. The problem of A₂-exchange is discussed.     

Physics (and technique) of gas jet experiments

Recently gas jet targets have been used for the study of small momentum transfer p-p and p-d elastic and inelastic scattering. In these experiments, which were performed at Serpukhov in the USSR and at the Fermilab in the USA, the gas jet is introduced in the main ring of the accelerator. We review the techniques associated with these measurements and summarize the published results which cover 4-momentum transfers 0.001< |t|< 0.12 (GeV/c)^?2 and incident energies 8<E< 400 GeV. Elastic scattering data have yielded precise values for the slope of the nuclear scattering amplitude and for the ratio of the real to imaginary part as a function of energy. The implications of these data on the understanding of high energy hadronic interactions are discussed in some detail. We also present and discuss information on the diffractive dissociation of the proton to low mass states, obtained from inelastic scattering using the gas jet target.     

Semi-phenomenological bounds for the pion-pion coupling constant

Upper and lower bounds on the Chew-Mandelstam ππ coupling constant λ are derived as functions of the D-wave scattering length a₂. The only information used is the axiomatic analyticity domain of the ππ scattering amplitude, and the crossing and unitarity properties. For a₂ = 7 × 10^?4, one obtains ?0.164<λ<0.162. This is compared with previous bounds.     

Quasielastic versus inelastic and deep inelastic lepton scattering in nuclei at x > 1

We have made a thorough investigation of the nuclear structure function W_2A in the region of 0.8 < x < 1.5 and Q² < 20 GeV², separating the quasielastic and inelastic plus deep inelastic contributions. The agreement with present experimental data is good giving support to the results for both channels. Predictions are made in yet unexplored regions of x and Q² to assert the weight of the quasielastic or inelastic channels. We find that at Q² < 4 GeV² the structure function is dominated by the quasielastic contributions for x < 1.5, while for values of Q² > 15 GeV² and the range of x studied the inelastic channels are over one order of magnitude bigger than the quasielastic one. The potential of the structure function at x > 1 as a source of information on nuclear correlations is stressed once more.     

A limit parity admixtures in the atomic 2s → 1s transitions

From a measurement of the intensity of the atomic 2s→1s transition in Tm (Z = 69) a limit of F² < 10^?8 was derived for the square of the parity admixing amplitude in the 2s state, not inconsistent with predictions of neutral current models.     

Quantum Tunneling and Caustics under Inverse Square Potential

We examine the quantization of a harmonic oscillator with inverse square potential V(x)=(mω²/2) x²+g/x² on the line −∞<x<∞. We find that, for 0<g<3?²/(8m), the system admits a U(2) family of inequivalent quantizations allowing for quantum tunneling through the infinite potential barrier at x=0. These are a generalization of the conventional quantization applied to the Calogero model in which no quantum tunneling is allowed. The tunneling renders the classical caustics which arise under the potential anomalous at the quantum level, leading to the possibility of copying the profile of an arbitrary state from one side x>0, say, to the other x<0.     

Measurement of the real part of the forward scattering amplitude in K±p elastic scattering between 0.9 and 2.6 GeV/c

The differential cross section for K^±p elastic scattering has been measured in the forward meson direction (0.0008 < t < 0.1 GeV²) in an electronics experiment at incident momenta between 0.9 and 2.06 GeV/c. The high statistics and absolute normalisation of the data allow a good determination of the real part of the forward nuclear scattering amplitude by means of the Coulomb-nuclear interference effect.     

Measurement of np elastic scattering at high energies and very small momentum transfers

The np elastic differential cross section has been measured for incident neutron momenta 100–400 GeV/c in the |t| range 6 · 10^?6 ? 5 · 10^?1 (GeV/c)². The np data of this experiment provide a first direct measurement of the hadronic amplitude for |t| < 10^?2 (GeV/c)², which is consistent with the extrapolations from higher |t| values. Our data for |t| < 10^?4 (GeV/c)² are consistent with a rise which can be attributed to Schwinger scattering, caused by the interaction of the neutron magnetic moment with the proton.     

Photon statistics in resonance fluorescence from laser deflection of an atomic beam

There is a simple relationship between the photon statistics in resonance fluorescence and the statistics of the momentum transferred to an atom by a plane traveling wave. We use this relation and the theory of atomic motion in resonant radiation to derive expressions for the mean <n> and the variance <(Δn)²> of the number of photons emitted in a given time by a two-level atom in a coherent exciting field. We find, in addition to the sub-poissonian statistics [<(Δn)²> less than <n>] previously reported for the case of resonant excitation, that super-poissonian photon statistics [<(Δn)²> greater than <n>] occur in resonance fluorescence for certain off-resonance cases. It is suggested that the sub-poissonian and the super-poissonian emission statistics might be demonstrated in a simple photodeflection experiment.     

Messung von Plattenschwingungen sehr kleiner Amplitude durch Lichtstrommodulation

An optical method detecting extreme small mechanical amplitudes of vibrating plates was developed. The two components of the plane vibration were measured with an uncertaintyΔa<10^?8 cm, the flexural vibration was measured with an uncertaintyΔa<10^?6 rad. The method is based on the modulation of a small light beam by a vibrating boundary (measuring plane vibrations) or on the modulation of a vibrating light beam by a fixed boundary (measuring flexural vibrations). The possible amplitude resolution power was calculated to beΔa<10^?10 cm. Examples of amplitude distributions of thin vibrating quartz plates are given.     

Rigorous lower and upper bounds for the slope parameter

It is proved within the framework of axiomatic field theory that the logarithmic derivative of the absorptive part of the scattering amplitude with respect to momentum transfer is bounded from above by $\text{(15}\text{log}\text{s)}\text{[4√t(2 ? √t)]}$ for a sequence of s→+∞, and from below either in the s-channel by const. × s^?5 log^?4s or in the u-channel by const. × u^?5 log^?4u for at least one sequence of s or u →+∞, respectively. In the particular case of the s?u even-symmetric amplitude, a stronger lower bound is obtained; namely, const. × s^?5 log^?4s for at least one sequence of s→+∞. Here s, t, and u are the usual Mandelstam variables, and all bounds are obtained in the forward and the unphysical regions: 0?t<4 (in units of pion mass).It is observed that the Regge amplitude β(t)s^α(t) of high-energy scattering gives the same energy dependence as the above upper bound, and, furthermore, that the slope of the Regge trajectory is bounded from above by $\text{15}\text{[4√t(2 ? √t)]}\text{for}\text{0 < t < 4}$.     

Measurement of the real part of the K−n forward scattering amplitude between 1.2 and 2.6 GeV/c

The differential cross sections of the combined elastic and break-up K^?d reaction have been measured at 1.21, 1.42 and 2.61 GeV/c incident K^? momentum. The measurements have been performed at the CERN PS using multiwire proportional chambers. The values of the invariant momentum transfer t explored (0.0005<|t|<0.1 GeV²) include the Coulomb-nuclear interference region. The differential cross sections have been analysed in the framework of the Glauber impact-parameter formalism. The observed interference effects have been used to derive the ratio of the real to imaginary part of the forward K^?n nuclear amplitude.     

Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order

We use an effective field theory for short-range forces (SREFT) to analyze systems of three identical bosons interacting via a two-body potential that generates a scattering length, a, which is large compared to the range of the interaction, ?. The amplitude for the scattering of one boson off a bound state of the other two is computed to next-to-next-to-leading order (N²LO) in the ?/a expansion. At this order, two pieces of three-body data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium-4 atoms, which are assumed to interact via the TTY potential. We generate N²LO predictions for atom-dimer scattering below the dimer breakup threshold using the bound-state energy of the shallow Helium-4 trimer and the atom-dimer scattering length as our two pieces of three-body input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N²LO phase- shift predictions will receive higher-order corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the “deep” trimer of Helium-4 atoms displays poor convergence.     

Vibrational resonance in fractional-order overdamped multistable systems

We investigated the vibrational resonance in fractional-order overdamped multistable systems theoretically and numerically. For a given fractional order p, our results show that the response amplitude exhibits a series of peaks as the frequency or the amplitude of the high frequency input varies. However, when the low-frequency input increases, the response amplitude exhibits unimodal resonance for 1?<?p?<?2. Additionally, for different values of p, whether the response amplitude changes monotonically depends on the degree of spatial potential asymmetry. The mechanism by which p affects the resonance behavior is analyzed. Our results indicate that the value of p affects the resonance behavior by either altering the conditions under which the response amplitude attains its extreme values, or by altering the oscillating frequency of the response amplitude with varying systematic parameters.     

Temperature dependent time delay of the voltage response to supercritical current pulses in superconducting aluminium

Current pulses larger than the critical current I_c are passed through narrow superconducting aluminium strips. The time delay between the start of the pulse and the onset of the voltage response is measured as a function of current amplitude for various temperatures (0.84<T/T_c<0.98). We find the delay time to be dependent on the temperature as (1 - T/T_c)^α with α changing from a value of - 0.5 for I/I_c close to 1 to a value of - 1.0 for I/I_c larger than 3.     

Dynamical violation of the Zweig rule and the energy dependence of π−p→ ϕn

The large magnitude and rapid decrease with energy of σ(π^?p→?n) in the momentum range < 6 GeV/c indicate a dynamical breaking of the Zweig rule. We provide an explicit box diagram amplitude for this process. Zweig's rule is obeyed exactly at all vertices. The size and rapid fall of the cross section are explained in terms of s channel thresholds and duality cancellations in the intermediate states of the box.     

Temperature dependence of the rotational life times in solid H2

We have studied the temperature dependence of the nuclear transverse and longitudinal relaxation times in solid H₂ for ortho concentrations 10^-3 < X < 10^-2 between 0.4 K and the triple point, 13.9 K. We find a striking temperature dependence in T₂ over the whole temperature range. This new effect is ascribed to a coupling between molecular rotation and lattice vibrations, which is brought into evidence by the narrow width of the spectral density of the rotational fluctuations at low X.     

Phase amplitude decoupling in modulated structures

We examine under what conditions phase and amplitude modulations are decoupled in a modulated structure, within a Landau Ginzburg approach. For the general case of a pth order commensurability, the condition for phase amplitude decoupling depends on the leading anharmonic terms in the Landau Ginzburg free energy. For a 2Mth order leading anharmonic term, the case p = 2M is a border line case. For p > 2M, phase and amplitude are decoupled near the disordered-incommensurate transition temperature, while they are not for p < 2M. In the latter case decoupling occurs at lower temperatures. We discuss the case of deuterated thiourea, which exhibits a commensurate pinning for p = 9 at T = 191 K.     

Calculations of mass and moment of inertia for neutron stars

Masses and moments of inertia for slowly-rotating neutron stars are calculated from the Tolman-Oppenheimer-Volkoff equations and various equations of state for neutron-star matter. We have also obtained pressure and density as a function of the distance from the centre of the star. Generally, two different equations of state are applied for particle densities n > 0.47 fm^?3 and n < 0.47 fm^?3.The maximum mass is, in our calculations for all equations of state except for the unrealistic non-relativistic ideal Fermi gas, given by 1.50 M_⊙ < M < 1.82 M_⊙, which agrees very well with “experimental results”. Corresponding results for the maximum moment of inertia are 9.5 × 10⁴⁴ g · cm² < I < 1.58 × 10⁴⁵ g · cm², which also seem to agree very well with “experimental results”. The radius of the star corresponding to maximum mass and maximum moment of inertia is given by 8.2 km < R < 10.0 km, but a smaller central density ρ_c will give a larger radius.