Scaling function for two-point correlations with long-range interactions to order 1/η

The two-point correlation function ? (q, ξ) is calculated in the critical region of momentum space q in terms of a suitable correlation lenght ξ, by means of perturbation expansion to order 1/n, for an n-vector system with long-range interactions decaying as $\text{|}\text{R}\text{/a|}{}^{\mathrm{?(d\; +\; \sigma )}}$, for $\text{|}\text{R}\text{/a|}\text{a}\text{?}\text{1}$, where a is the spacing on a d-dimensional lattice, σ < d < 2σ and 0 < σ ? 2 ? η_SR. The calculations are done in zero field for T ? T_c. Explicit expansions for long-range propagators are developed for $\text{σ « 1}$ and for the neighborhood of σ ? 2 ? η_SR, in terms of which a universal, cut-off independent scaling function is obtained over the whole range of $\text{x = |}\text{q}\text{| ξ}$, and it is shown that the amplitude of the correlation-length dependence of the susceptibility becomes a universal parameter. Both the exponents and the coefficients of the expansion for fixed q as $\text{(T ? T}{}_{\mathrm{<mtext>c</mtext>}}\text{)}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{→0}$ are calculated explicitly. The former are shown to require the validity of the operator-product expansion and explicit logarithmic correction terms are obtained for $\text{d = d}{}^1\text{= 3σ/2}$. For these and other dimensionalities, the coefficients are shown to be finite functions of d and σ. The correction to the Ornstein-Zernike form is given explicitly, with non-integer powers of x that have finite coefficients.     

Inverse solutions to the inelastic scattering problem

Exact inverse solutions to the integral equation $\text{φ(r}{}_{\mathrm{s}}\text{|r}{}_0\text{, k) = ?}{}_{\mathrm{D}}{}^3\text{f (r, ω)g(r|r}{}_0\text{, k)g(r|r, k)d}{}^3\text{r}$, where g(r|r_j, k); j = 0 or s is the free space Green function, are derived in plane and cylindrical coordinates for fixed ω. These solutions allow an inelastic scattering potential f(r, ω) which is of compact support r ? $\text{D}$³ to be recovered from scattering data collected over the surfaces of a plane and cylinder respectively.     

Depolarization in proton inclusive inelastic scattering and in the (d,p) reaction on medium-weight nuclei

The energy-averaged depolarization parameter K_y^y′ has been measured for the inelastic scattering of 18 MeV protons from ⁵⁴Fe, ⁶³Cu and ⁹²Mo at 45°, 90° and 135°, and for 14.35 MeV protons from ⁶³Cu at 45° and 135°. In all cases K_y^y′ varies from approximately unity for scattering with low energy loss to approximately zero for inelastic scattering to high excitation energies. The change from one of these values to the other occurs over a region ≈ 6 MeV wide centered at about 5 MeV excitation. A simple two-component model fits both the K_y^y′ and inelastic crosssection data. K_y^y′ has also been measured for the ⁵⁴Fe($\text{d}$, $\text{p}$)Fe reaction with 16 MeV deuterons incident. Here K_y^y′ changes from approximately the maximum possible value, $\text{2}\text{3}$, to about zero in a 6 MeV region centered at roughly 13 MeV excitation. The ($\text{d}$,$\text{p}$) data can be fitted by an extension of the model used for the proton scattering data.     

The magnetic moment of the 4+, 3.55 MeV level of 18O

The magnetic moment of the 4⁺, 3.55 MeV level of ¹⁸O has been determined to be |g| = 0.62 ± 0.10 in a perturbed angular correlation measurement on nuclei recoiling into gas and vacuum. Analysis of the recoil-into-gas data using the Abragam-Pound model agrees with analysis of the recoil-into-vacuum data using a model for the electronic ensemble described in a previous communication. The value of the g-factor shows the 4⁺ wave function to consist mainly of the$\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}{}^2$ configuration.     

Mobility of an electron in a Guassian random potential

The mobility of an electron in a Gaussian random potential is evaluated. It is shown that the relaxation time of the electron is found to be proportional to $\text{L}{}^2\text{|}\text{p}\text{|}$ for large and small correlation lengths L where |p| is the electron momentum.     

Observation of a dip-bump structure in differential cross section for pp → nn in the 700–760 MeV/c momentum range

Based on a sample of about 3500 events, we have measured the total and differential cross sections of $\text{p}\text{p}\text{→}\text{n}\text{n}$ in the 700–760 MeV/c incident momentum region. It is found that σ_CE = 10.7 ± 0.2 mb at the average momentum of 730 MeV/c. The differential angular distribution is characterised by a sharp peak and a dip in the forward direction followed by a secondary maximum. The position of the dip corresponds to |t| ≈ m_π². These results are compared with the predictions of the model of Bryan-Phillips. On the other hand, this dip-bump structure can be well understood on a simple picture involving a π exchange and a constant background (for |t| ? 3 m_π²).     

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.     

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.     

On the diffraction of neutrons by magnetic spiral structures

A beam of neutrons of wave vector K incident on a magnetic spiral structure with propagation vector q gives rise to two diffracted beams. These are peaked at $\text{K·q}\text{q}\text{～±}\text{q}\text{2}$, and their intensity varies with the direction of K with the same functional form as is derived in the dynamical theory of X-ray diffraction. In real cases the two lines are broad enough to overlap significantly, giving rise to intrinsic double diffraction effects in a multi-domain crystal. These have been observed experimentally in holmium.     

The elastic behaviour of In-Tl alloys in the vicinity of the martensitic transition

To test further the prediction of collapse of the [110], q|| [11&#x0304;0] acoustic mode at the martensitic phase transition, pulse superposition measurements of ultrasonic wave velocities have been made in indium-thallium alloys containing 25 and 27 at. % thallium. These alloys are f.c.c. at room temperature and transform on cooling to the f.c.t. phase at 196 ± 2°K and 127 ± 2°K, respectively. Results show that $\text{1}\text{2}$(C₁₁ ? C₁₂) goes to zero within experimental error at the transition temperature. The room temperature elastic constants of the tetragonal 11.5 and 15 at. % thallium alloys are also reported.     

Evidence for two narrow pp resonances at 2020 MeV and 2200 MeV

From the study of the reaction $\text{π}{}^{\mathrm{?}}\text{p→p}{}_{\mathrm{F}}\text{p}\text{p}\text{π}{}^{\mathrm{?}}$ using a fast proton (p_F) trigger device in the CERN Omega spectrometer, we find evidence for two narrow $\text{p}\text{p}$ states produced mainly in association with a Δ° (1232) and a N° (1520). The statistical significance of each peak is greater than 6 standard deviations. Masses and natural widths of these resonances are respectively M = 2020 ± 3 MeV, Λ₁ = 24 ± 12 MeV and M₂ = 2204 ± 5 MeV, Λ₂ = 16_?16⁺²⁰ MeV. Our data are consistent with a small production of the narrow ～ 1935 MeV resonance already reported. Production cross sections for these new $\text{p}\text{p}$ resonances are given.     

Differential cross section and analyzing power for backward pions in 2H(p, π+)3H

Cross sections and analyzing powers are presented for the reaction ${}^2\text{H}\text{(}\text{p}\text{, π}{}^{\mathrm{+}}\text{)}{}^3\text{H}$ at 400, 425, 443 and 470 MeV, and laboratory pion angles of 120°, 130°, 140°, 150° and 160°. The cross sections have flat angular distributions, are in contradiction with an earlier experiment which indicated a backward peak at 470 MeV, but are in quantitative agreement with a calculation based on the two-nucleon model.     

The microwave spectrum of MnO3F

The microwave spectrum of MnO₃F has been remeasured and several corrections and new results have been obtained: B₀ = 4129.141 MHz, D_J = 1.12 kHz, D_JK = 1.87 kHz; $\text{α}{}_3{}^{\mathrm{B}}\text{= 8.622}$, $\text{α}{}_5{}^{\mathrm{B}}\text{= ? 11.994}$, $\text{α}{}_6{}^{\mathrm{B}}\text{= 6.042}$, |q₅| = 16.005, and |q₆| = 8.456 MHz.     

Longitudinal polarization transfer in the T→p, →n)3He reaction

The longitudinal polarization of neutrons has been measured for the reaction $\text{T}\text{→p}\text{,}\text{→n}\text{)}{}^3\text{He}$ with the incident proton beam longitudinally polarized. Measurements were performed at 0° for proton energies from 4 to 15 MeV and an angular distribution was measured at 10 MeV. The data determine the polarization transfer coefficient K_z^z′, which is equivalent to the Wolfenstein A′ parameter for nucleon-nucleon scattering. The quantity K_z^z′ at 0° increases from about 0.3 at 3 MeV incident energy to 0.9 at 9 MeV, and then decreases to 0.5 at 15 MeV. The data are computed with R-matrix calculations which reproduce the qualitative shape of the data at 0° and the angular distribution at 10 MeV.     

The 12C(13C, α)21Ne reaction: High-spin states,resonances and coherence widths

Excitation functions were measured for states of ²¹Ne populated by the ${}^{12}\text{C}\text{(}{}^{13}\text{C}\text{, α)}$ reaction over the bombarding energy range E_lab = 18.2–32.0 MeV (18.4–27.0 MeV) at θ_lab = 7°(25°) in in 200 keV steps, and average coherence widths of states and the moment of inertia of the compound nucleus ²⁵Mg were obtained from these excitation functions. A statistical analysis of these data was performed. Angular distributions for states in ²¹Ne to 10 MeV in excitation energy were measured at θ_lab = 7°, 18°, 28° and 43° at bombarding energies from 29.0 to 31.0 MeV in 400 keV steps. These data along with Hauser-Feshbach predictions allow us to suggest spins for some states as well as to suggest possible candidates for rotational bands in ²¹Ne.     

Polarisation in neutron-deutron scattering at 30 MeV

The polarisation asymmetry in elastic$\text{n}\text{?d}$ scattering has been measured at 30 MeV from 45° to 140° c.m. neutron angle with uncertainties less than 0.03.     

The phase φ+− of CP violation in the K0 → π+π− decay

The phase φ_+? is evaluated on the basis of measurements of the K_S-K_L interference in the π⁺π^? decay mode and the mass difference Δm, both reported previously by this group. The result is: φ_{+? = 45.9° ± 1.6°}. This, together with previous results on $\text{|η}{}_{\mathrm{+?}}\text{|, |}\text{η}{}_{00}\text{η}{}_{\mathrm{+?}}\text{|}$ and the charge asymmetry δ in leptonic decay, is compared with the prediction of the superweak model, with good agreement.Finally the result is used to find, on the basis of unitarity, a new upper limit on CP violation in the decay K⁰ → 3π⁰. This limit is |η₀₀₀|^2? 0.21.     

Hybrids: Mixed states of quarks and gluons

We calculate the spectrum of the four ground state hybrid $\text{(}\text{q}\text{qg}\text{)}$ nonets, J^PC = (0, 1, 2)^?+, 1^??, using the MIT bag model to first order in cavity perturbation theory. Quark and gluon self-energies are included by a fit to the s-wave mesons and baryons and to the glueball candidate i(1440). We find a large gluon self-energy which substantially increases our predictions of the glueball and hybrid masses. We discuss the phenomenology of hybrids, including a suggestion that the A₃ (1670) and a second peak at 1850 MeV in the fπ channel may be mixtures of the isovector $\text{q}\text{q}$ d-wave state with the $\text{q}\text{qg}$ s-wave.     

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.     

Investigation of the central component of SrTiO3 by neutron scattering with eV resolution

We studied the energy width and the width in reciprocal space Δq of the central mode of SrTiO₃ above T_c. At T_c+4° we observed an energy width of about 6×10^?7 eV. If the measured Δq is interpreted by a correlation length $\text{Δq}{}^{\mathrm{?1}}\text{= ξ = ξ}{}_0\text{?}{}^{\mathrm{<mtext>?</mtext><mtext>2</mtext><mtext>3</mtext>}}$ we obtain $\text{ξ}{}_0\text{= 75}\text{A}\text{?}$.