Impact parameter analysis of the reaction π−p→pπ+π−π− at 9 and 12 GeV/c with very fast secondary proton

The results on the impact parameter for the reactions π^?p→pπ⁺π^?π^?, pK⁺K^?π^?, with a fast secondary forward proton are given at 9 and 12 GeV/c. For the reaction π^?p→pπ⁺π^?π^? our results corresponding to the small |u| region (|u| < 1 GeV²) are compared to the existing data for the small |t| region. We show that small |u| events are more central than small |t| events.     

Elastic pp scattering in the cern sps energy region

The pronounced dip-bump structure with a sharp minimum at |t| = 1.5 (GeV/c)², recently observed in elastic $\text{p}$p scattering at P_L = 50 GeV/c at the CERN SPS, is explained by the quark multiple scattering model with a realistic wavefunction for the proton and the antiproton. It is predicted that a second dip will appear around |t| = 7 (GeV/c)² at P_L = 50 GeV/ c and at higher energies.     

Measurements of elastic scattering in alpha-alpha and alpha-proton collisions at the CERN intersecting storage rings

We measured the elastic scattering of $\text{αα}\text{at}\text{s}\text{= 126}\text{GeV}$ and of αp at $\text{s}\text{= 89}\text{GeV}$. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV². At small |t| = 0.05?0.07 GeV², this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α_tot(αα) = 250 ± 50 mb and an integrated elastic cross section σ_e1(αα) = 45 ± mb. Another method of estimating σ_tot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV², and for 0.05 < |t| < 0.18 GeV² behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σ_tot(αp) = 130 ± 20 and σ_e1(αp) = 20 ± 4mb. Results on pp elastic scattering at $\text{s}\text{= 63}\text{GeV}$ agree with previous ISR experiments.     

A measurement of e+e− → pp for (1975 ⩽ s ⩽ 2250) MeV

The $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{p}$ cross section has been measured in the energy interval (1975 ? 2E ? 2250) MeV for |cosθ| < 0.7. The measurement is based on ～ 100 events, thus improving by a factor 3 on the previous existing statistics in this energy interval. The form factor |G|² is given as a function of energy under the assumption |G_E| = |G_M|. We also give the first measurement of the differential cross section, averaged over the energy interval, and estimate the ratio G_M|/|G_E| from it.     

Inequalities for the Schattenp-norm. IV

We prove some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA,B, andX are operators such thatA +B ≧ |X| andA +B ≧ |X*|, then ∥AX +XB∥ _p ^p + ∥AX* +X*B∥ _p ^p ≧2 ∥X∥ _2p ^2p for 1 ≦p<∞, and max (∥AX +XB∥, ∥AX* +X*B∥) ≧ ∥X∥². Also, for any three operatorsA,B, andX, $$|| |A|X - X|B| ||_2^2 + || |A*|X - X|B*| ||_2^2 \leqq ||AX - XB||_2^2 + ||A*X - XB*||_2^2 .$$      

Calculation of the t2g antibonding molecular orbital in |VF6|4, comparison with E.S.R. investigations on KZnF3: V2+

Using the L.C.A.O.-M.O. framework we have calculated the coefficient λ_π which defines the t_2g antibonding orbital of the |VF₆|^4? cluster in the KZnF₃ host lattice, for the ⁴A_2g ground state. An approximate Hamiltonian, analogous to the one early used by Sugano and Shulman for |NiF₆|^4?, gives a good agreement between the calculation and the estimation of λ_π from E.S.R. measurements.     

Regge cuts and large-|t| pp scattering

It is shown that recent measurements of the large-|t| pp elastic-scattering differential cross section at FNAL and CERN-ISR agree with earlier predictions based on the dominance of a pomeron pole(P) with αp(t) = 1.067 + 0.10 t, and a P ? P cut, out to the largest measured |t| values (12 GeV²). Some of the problems raised by this success are discussed.     

Soft π−p and pp elastic scattering in the energy range 30 to 345 GeV

Differential cross sections for π^?p and pp elastic scattering have been measured at incident momenta ranging from 30 to 345 GeV and in the t range 0.002 (GeV/c)² ? |t| ? 0.04 (GeV/c)². From the analysis of the data, the ratio ? (t = 0) of the real to the imaginary parts of the forward scattering amplitude was determined together with the logarithmic slope b of the diffraction cone.The results on the real parts confirm the validity of the forward dispersion relations at high energies. Using the dispersion relations, it was shown that the experimental data on ?_{π?p(t = 0)} require a continuous rise of the total πp cross sections, at least up to the energy of 2000 GeV, thus revealing a close similarity in high-energy behaviour of πp and pp interactions.The results on the slope parameters from this experiment together with the analysis of the available world data demonstrate that the existing experimental data are consistent with the hypothesis of a universal shrinkage of the hadronic diffraction cone at high energies. The value of the asymptotic shrinkage parameter α_p^′ was found to be independent of the kind of the incident hadron and of the momentum transfer in the t range |t| ? 0.2 (GeV/c)² : 2α_{p^′ = ± 3 (GeV/c)^?2}.     

A measurement of the KL0p elastic cross section for 3 ⩽p⩽13 GeV/c and 0.1⩽|t|⩽1.3 GeV2

The cross section for the K_L⁰p elastic scattering has been measured for the first time. The incident momentum and momentum transfer ranges are 3 ?p? 13 GeV/c, 0.1 ? |t| ? 1.3 GeV². The results are compared to those of other experiments related to ours by isotopic spin conservation, finding agreement with some and discrepancies with others. The differential cross sections have been parametrized in the form Ae^bt. The coefficients show little or no dependence on energy, with A ? 9.8 mb · GeV^?2and b ? 4.7 GeV^?2. The effective linear trajectory has been determined and gives α₀ = 0.95 ± 0.15, α′ = ?0.35 ± 0.48 GeV^?2, in good agreement with dominance by pomeron exchange.     

Eikonal description of nucleon-nucleon polarizations

Nucleon-nucleon elastic polarization data are analyzed within an eikonal framework in the range 6?plab?45 GeV/c and |t| 2.5 GeV/V². The isovector component is found to be dominated by a nearly exchange degenerate ρ-A₂ contribution while the isoscalar part requires both a lower lying Regge-pole exchange and an asymptotic pomeron contribution.     

Measurement of elastic scattering in antiproton-proton collisions at 52.8 GeV centre-of-mass energy

We measured the differential cross section for p?p and pp elastic scattering in the momentum-transfer range 0.01 <|t| < 1.0 GeV² at the CERN Intersecting Storage Rings with center-of-mass energy $\text{s}\text{= 52.8}\text{GeV}$. Fitting the differential cross section with an exponential [Aexp (bt)], we found $\text{b}\text{p}\text{p = 13.92 ± 0.59}\text{GeV}{}^{\mathrm{?2}}$ for |t| < 0.05 GeV², whilst for |t| > 0.09 GeV², $\text{b}\text{p}\text{p = 10.68 ± 0.26}\text{GeV}{}^{\mathrm{?2}}$. Using the optical theorem, we obtained for the total cross section $\text{σ}{}_{\mathrm{<mtext>tot</mtext>}}\text{(}\text{p}\text{p)= 44.86 ± 0.78}\text{mb}$ and, by integrating the differential cross section, we obtained for the total elastic cross section $\text{σ}{}_{\mathrm{<mtext>el</mtext>}}\text{(}\text{p}\text{p) = 7.89 ± 0.28}\text{mb}$. Calculations of σ_tot combining elastic-rate and total-rate measurements are also given. All of these measurements were also performed for pp scattering at the same energy, and the results for both reactions are compared.     

The pomeron in elastic meson-baryon scattering

We show that a pomeron (P) trajectory with α_P(t) ≈ 1.07 + 0.22t provides a simple and satisfactory fit to π^±p and K^±p elastic scattering data (as well as pp and $\text{p}$p considered in an earlier publication) for |t| < 1.2 GeV², including the rising total cross sections. The destructive term needed to explain the diffraction minimum in pp may be explained as a weak P ? P cut effect provided that the Gribov vertices are given suitable structure, and the prediction is then made that similar minima should be observed in meson-baryon scattering at FNAL somewhere in the region 1.5 < |t| < 2.5 GeV². The P ? P cut does not seem to be related (at least directly) to the unitarization effects which must eventually make σ_tot ～ log²s (but not until s > 10⁸GeV²). Thus the “effective” J-plane singularity structure, at currently available energies seems to be much simpler than it can be asymptotically.     

The experimental study of Ba 6pjnk |M| = 0, 1 autoionizing series

The spectra of the Ba 6pnk autoionizing Stark states with |M| = 0, 1, converging to the 6p_1/2⁺ and 6p_3/2⁺ ionization thresholds, are measured as a function of the electric field strength F. Several 6p_jnk Stark manifolds with n = 13–15 have been systematically studied in order to explore their characteristics of configuration interaction. Experimental results are analyzed by fitting them to the Lorentzian profile, from which the positions and widths are determined. Different spectroscopic properties between the Ba 6p_1/2nk and 6p_3/2nk autoionizing Stark states are investigated. Comparison between the Ba 6p_jnk autoionizing Stark states with |M| = 0 and those with |M| = 1 are made.     

Rotation-inversion spectrum of methylaminoethane

Microwave spectral assignments have been made for the ground and several excited vibrational states of the normal and amino d₁ species of methylaminoethane. The inversion-rotation spectrum is consistent with a trans rotameric form with an amino inversion barrier of ～5.2 kcal mole^?1. The dipole moment of 8.88 ± 0.02 Debye has components |μ_a| = 0.00 ± 0.03, |μ_b| = 0.25 ± 0.03, and $\text{|〈 ± μ}{}_{\mathrm{c}}\text{? 〉| = 0.84 ± 0.01}$ Debye. The normal species N¹⁴ nuclear quadrupole coupling constants are (in MHz) 2.82 ± 0.09, 0.88 ± 0.13, and ?3.70 ± 0.09 for χ_aa, χ_bb, and χ_cc, respectively.     

Study of K−p→K1(890)n at 13 GeV

The results of a wire chamber spectrometer experiment studying $\text{K}$¹ (890) production in the reaction K^?p→ K^?π⁺n at 13 GeV are presented. Strong forward structure is observed for |t|< m²_π in the s-channel density matrix elements and differential cross section. These features are similar to those observed in π^?p→?⁰n data and are characteristics of π exchange. In contrast in the intermediate, |t| ～ 0.2 GeV², and large momentum transfer regions $\text{K}$¹ (890) production is demonstrated by the natural parity ??A₂ exchange contribution.     

Hierarchy of mean multiplicities in pn and π+n interactions at 195 GeV/c

The dependence of the average charged multiplicity, 〈n_X〉, of the system X on |t| and M²_X is studied for the reactions p(π⁺)n→p_fast(p⁺_fast) + X and p(π⁺)n→p_slow + X at 195 GeV/c. For a fixed M²_X, 〈n_X〉 changes significantly among these reactions, yielding a systematic hierarchy of mean multiplicities. The results indicate that a proton emits on the average less charged particles than a pion and more than a neutron.     

The model of the optical switching center and the polarization anomalies in absorption spectra of cupric oxide after fast particles irradiation

We consider the model of the optical switching center—a system with the following properties: it has two (or more) metastable states |1〉, |2〉, separated by a potential barrier U; it can switch from one state to another by absorbing the photons with energy ?ω∼U; the transition |1〉→|2〉 is allowed only for a certain light wave polarization p₁ and the transition |2〉→|1〉—for other polarization p₂; these polarizations p₁, p₂ are orthogonal. The optical properties of this system are studied and are found to exhibit unconventional polarization dependence. In particular, the absorption spectrum observed in natural (unpolarized) light can display new features, that are absent in the spectra, obtained in two independent polarizations. We discuss these results in connection with the (yet unexplained) experimental findings [N.N. Loshkareva, Yu.P. Sukhorukov, B.A. Gizhevskii, A.S. Moskvin, T.A. Belykh, S.V. Naumov, A.A. Samokhvalov, Phys. Solid State 40 (1998) 383], where the similar anomalous polarization dependence of the absorption spectra of cupric monoxide CuO after the fast particle bombardment is reported.     

Stabilization of solutions to nonlinear parabolic equations of the p-Laplace type

In the first part of the paper, we study the stabilization of solutions to nonlinear parabolic equations of the p-Laplace type in L ²(? ⁿ ) for 2n/(n + 2) < p ? n. The proof is based on estimates uniform in time in L ²(? ⁿ , |x| ^s ) for p < n. For p = n, a similar estimate holds with |x| ^s replaced by (ln(2+|x|)) ^s . In the second part of the paper, we prove a uniform stabilization criterion for bounded solutions. This criterion generalizes a widely known result independently proved by Zhikov and Kamin in 1976 for linear parabolic equations.     

A measurement of the KL0p → KS0p reaction between 4 and 14 GeV/c in the range 0.1 ⩽|t|⩽ 2 GeV2

We present experimental data on the K_L⁰p → K_S⁰p reaction between 4 and 14 GeV/c in the range 0.1 ? |t| ? 2 GeV². This experiment has been performed at the CERN PS, using spark chambers and a large aperture magnet. The results show a break of slope at t = ?0.3 GeV². The ω trajectory deduced from the data has an intercept α(0) = 0.5 and a slope α′ = 0.88. A comparison with various models shows that the non-flip amplitude is dominant.     

Study off o (995) resonance in the π0π0 decay channel

A high-statistics study of the π⁰π⁰-system produced in the π^- p→π⁰π⁰ n reaction at 38GeV/c has been carried out at the IHEP accelerator using the GAMS-2000 multiphoton spectrometer. A partial-wave analysis which includesS, D ₀, D_? andD ₊ waves has been performed in the |t|-range up to 1 (GeV/c)². TheS ^*/f ₀(980) resonance is seen as a dip in theS-wave amplitude at small |t|. A distinct peak with a mass of 997±5MeV and a width of 48±10MeV is observed in theS-wave at |t|>0.3 (GeV/c)². The production cross sections are measured.