Determining the KS→3π amplitude in pp(OR e+e−)→K0K0

The amplitude ratio 〈3π|T|K_S〉/〈3π|T|K_L〉 can be well determined in e⁺e^? (or low energy $\text{p}\text{p}\text{)→K}{}^{\mathrm{o}}\text{K}{}^{\mathrm{o}}$ from the decay time-distribution when each produced kaon→3π, other unknown parameters of the distribution being obtainable from corresponding observations involving known channels like ππ.     

Inclusive production of Ξ+ and Ξ− in K+ p interactions at 32 GeV/c

The inclusive production of $\text{Ξ}{}^{\mathrm{+}}$ and Ξ^? hyperons is investigated in K⁺ p interactions at 32 GeV/c. The production cross sections, 36.4±9 μb for the $\text{Ξ}{}^{\mathrm{+}}$ and 6.5±3 μb for the Ξ^?, are rising strongly with energy similarly to $\text{Λ}$ and Λ production in K⁺ p interactions. The $\text{Ξ}{}^{\mathrm{+}}$ are produced preferentially in the forward direction in the c.m.s., while the Ξ^? are produced dominantly backwards. The average transverse momenta and 〈p_T〉_Ξ^?=0.58±0.09 GeV/c.     

Measurement of the isospin amplitude ∣M012∣ in the reaction γn → ϱ0(pπ−) at 7.5 GeV

The cross-channel isospin amplitude $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ is measured in the single reaction γn → ?⁰(pπ^?) at 7.5 GeV assuming the ?⁰ dominance model. A low-mass enhancement is found for $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}{}^2$ in the range of m(pπ^?) of ～1.2 to ～1.7 GeV. The reaction strongly violates s-channel helicity conservation but is consistent with t-channel helicity conservation. The $\text{∣M}{}_0{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{∣}$ features are found to be very similar to those obtained in previous analyses of πp → π(Nπ) reactions.     

γ production and multiplicity correlations between neutral and charged pions in pp interactions at 69 GeV/c

From 3500 γ's observed in the 4.7 m HBC MIRABELLE at Sepukhov, we obtain the dependence on n_? of the average number of produced π^0,s, 〈n₀〉, and the π⁰π⁰ correlation parameter, $\text{?}{}_2{}^{00}$. We present also the $\text{?}{}_2{}^{\mathrm{??}}$ and $\text{?}{}_2{}^{\mathrm{+0}}$ parameters and information concerning KNO scaling. Various momentum distributions are given. The invariant γ cross sections distributions are compared with corresponding data at other energies.     

Hole mass measurement in p-type InP and GaP by submillimetre cyclotron resonance in pulsed magnetic fields

The first observation of cyclotron resonance in p-type InP is reported. The holes were thermally excited at 110 K and the resonance was observed at 337μm wavelength (HCN laser) using a pulsed magnetic field of 0–350 kG. The effective masses of the light and heavy holes in the 〈111〉 direction were found to be $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.12 ± 0.01 m}{}_0$, and in the 〈100〉 direction $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.12 ± 0.01 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.02 m}{}_0$. We obtain an estimate of the Dresselhaus parameters A = ?5.04, |B| = 3.12, C² = 6.57. We also report the effective masses for p-type GaP in the 〈111〉 direction as $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.18 ± 0.02 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.04 m}{}_0$.     

Production and decay of quark-gluon strings: inclusive distributions of hadrons in p⊥ and x

The dependence of inclusive cross sections of the production of hadrons $\text{p}\text{p}\text{→ hX}$ on p_⊥ (and also on x and √s) is calculated at high energy in the region of small p_⊥ ? 1–2 GeV. The model of production and decay of quark-gluon strings is used under the simplest assumptions about the k_⊥ dependence of the quark distributions in nucleons ～ exp(?γ₁k²_⊥) and about the form of the string fragmentation function $\text{G}\text{?}{}^{\mathrm{<mtext>h</mtext>}}\text{～}\text{exp}\text{[?γ}{}^{\mathrm{<mtext>h</mtext>}}\text{(}\text{p}{}_{\mathrm{\perp }}\text{? z}\text{k}{}_{\mathrm{\perp }}\text{)}{}^2\text{]}$ where γ₁ and γ^h are some constants. The theory reproduces all existing experimental data and yields the “seagull effect” for the dependence of 〈p_⊥〉 on x. Predictions are given for the p_⊥ dependence of the spectra of π^± mesons produced at high energies at SPS and other future colliders.     

Self-adjointness of the minimal Schrödinger operator with potential belonging to L1, loc

Let $\text{0 ?q(x) ∈L}{}_{\mathrm{1,loc}}\text{(}\text{R}{}^{\mathrm{m}}\text{)}$,m? 1.Consider the operatorT₀ = ?Δ+q with domain consisting of all bounded measurable functions $\text{u(x), x ∈}\text{R}{}^{\mathrm{m}}$, having bounded support, for which the distribution ?Δu+qu belongs to $\text{L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The main result of the paper is essential self-adjointness of $\text{T}{}_0\text{in L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential.     

A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ has the following exact asymptotic form for large k (k ? p_F; p_F, the Fermi momentum): $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉 =}\text{4}\text{9}\text{(}\text{αr}{}_{\mathrm{s}}\text{π}\text{)}{}^2\text{×(}\text{p}{}_{\mathrm{<mtext>F</mtext>}}{}^8\text{k}{}^8\text{) g?(0) + ?}$, where g?(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

Multiplicity distribution in antiproton-proton interactions

In a compilation of $\text{p}\text{p}$ interactions we present evidence for KNO scaling in the primary momentum region up to 7 GeV/c. The average multiplicity in $\text{p}\text{p}$ interactions and annihilations has a logarithmic increase with energy. The reduced statistical momenta of multiplicity distribution $\text{c}{}_{\mathrm{q}}\text{=}\text{〈n}{}^{\mathrm{q}}\text{〉}\text{〈n〉}{}^{\mathrm{q}}$ are energy independent and for all final states have practically the same values as in proton-proton interactions. In annihilations the c_q to appear to be different from those in pp interactions and the KNO scaling function is also different.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

Charge properties of the hadronic system in vp and νp interactions

Charge properties of the hadronic systems from νp and $\text{ν}\text{p}$ scattering in BEBC are studied in the framework of the quark-parto model (QPM). The average charges $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ and $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ of a quark jet and a d-qua jet, respectively, are determined according to two different methods. The difference $\text{〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{\nu }}\text{? 〈Q}{}_{\mathrm{<mtext>jet</mtext>}}\text{〈}{}^{\mathrm{<mtext>\nu </mtext>}}$ is in agreement with e QPM value of 1. Scaling of charge and energy flow in the angular variable λ is demonstrated. The ratios $\text{ΔQ}{}^{\mathrm{<mtext>\nu </mtext>}}\text{/ΔQ}{}^{\mathrm{\nu }}$ of charge flows in νp a $\text{ν}\text{p}$ scattering are in accord with the QPM in both hemispheres.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).     

Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

Information on the dynamics of the reaction KN → K1N from KLN interactions

If $\text{K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{is a K}{}^1$ resonance decaying into K_S,L (the short- and long-lived kaon) and a neutral system S^o of pions, one can isolate the C-even and C-odd, crossed-channel contributions to $\text{KN → K}{}^1\text{N}$ by using the reactions $\text{K}{}_{\mathrm{L}}\text{N → K}{}_{\mathrm{S}}{}^1\text{,}{}_{\mathrm{L}}\text{N}$ whether S^o is a C-eigenstate, or a mixture of C-even and C-odd states. Applications to the production of K¹(890) and the Q-meson are discussed, and simple numerical predictions made for Q_S,L production. Q-production data indicate approximate t-channel helicity conservation for the ω and P' exchanges at vertices involving a spin change, in similarity to the belief for the pomeron. Q_S,L production data can give information also on Q-decays.     

Transverse momenta of partons and dimuons in QCD

Intrinsic (primordial) transverse momenta of quarks and gluons are calculated as well as those arising from recoil (bremsstrahlung) effects, using only the well-known parton distributions as input. The intrinsic k_T's lie typically in the range of 150–250 MeV. Recent approaches using heuristic integro-differential equations for k_T distributions of partons are shown to disagree with the results obtained by rigorous QCD calculations. The transverse momenta of dimuon pairs produced in pp → μ⁺μ^? + X at the ISR can be solely explained by dynamical recoil effects, i.e., $\text{q}\text{q}\text{→(μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{)}\text{g and gq}\text{→(μ}{}^{\mathrm{+}}\text{μ}{}^{\mathrm{?}}\text{)}\text{q}$, and no significant intrinsic transverse parton momenta are required. These dimuon transverse momenta show a pronounced energy dependence which could be easily tested at the CERN ISR. The only disagreement occurs for the average dimuon 〈p_T²〉, but not for 〈p_T〉, observed in pN collisions. Possibilities to resolve this problem are discussed. Our results are also compared with previous theoretical analyses.     

Anomalous shape of cyclotron resonance line in n-GaP in high magnetic fields

Cyclotron resonance in n-GaP has been observed at 119 μm in pulsed magnetic fields up to 410 kG. From the experiments with the magnetic field parallel to the 〈100〉, 〈110〉 and 〈111〉 axes, it is concluded that the transverse effective mass for electron is and that the anisotropy factor of the conduction band is K = 7.9^+3.2_?2.0. An anomalous shape of the absorption curve was found in the magnetic field directions parallel to the crystal axes 〈110〉 and 〈111〉.