Is KNO scaling proved or postulated?

Assuming Feynman's scaling law, Koba, Nielson and Olesen had shown that as s → ∞, (i) 〈n^q〉/〈n〉^q → d_q where d_q is independent of s and $\text{(ii)}\text{σ}{}_{\mathrm{n}}\text{(s)/σ}{}^{\mathrm{(s)}}{}_{\mathrm{<mtext>incl</mtext>}}\text{→ (}\text{1}\text{〈n〉)}\text{Ψ(n/〈n〉)}$. The derivation of the latter result is, however, not rigorous and it does not follow, as a necessary consequence, from the scaling law.     

X-ray determination of the mean-square vibrational amplitudes of atoms in nearly perfect CdS crystals

The mean-square amplitudes of Cd and S atoms in CdS were determined for vibrations parallel as well as perpendicular to the c-axis. The results were obtained by measuring the temperature dependence of X-ray integrated intensities for reflections from both basal and prismatic planes in nearly perfect crystals. The analysis of the experimental data is given in detail. The following results were found for T = 295°K: 〈u²_Cd〉_∥ = 2.85±0.04×10^?18cm², 〈u²_s〉_∥ = 1.94 ± 0.08 × 10^?18cm², 〈u²_Cd〉_⊥= 2.39 ± 0.04 × 10^?18cm² and 〈u²_s〉⊥ = 1.63 ± 0.08 × 10^?18cm². The fact that Cd atoms have a larger vibrational amplitude than the S atoms is briefly discussed.     

Variation of average charged particle multiplicity inp-nucleus interactions with energy and the two component description of particle production at high energies

Experimental data on average shower particle multiplicity (〈N _s〉) accumulated onp-nucleus interactions in the wide momentum region of 7.1–8000 GeV/c is investigated. It is observed that 〈N _s〉 is represented exceedingly well as a function of (v _vS). There are two physical processes which represent the experimental data reasonably well in the two momentum regionsviz 7.1–67.9 GeV/c and 67.9–8000 GeV/c. 〈N _s〉=a( _v ^S)/a+b fits the data in the low momentum region, whereas 〈N _s〉=a +b ln (v _vS) fits the experimental data in the high momentum region. The two physical processes are unified and represented by a single equation which is shown to be the consequence of two component theory and collective models.     

The missing mass squared dependence of the average charged particle multiplicity in the reaction K+p → KoX++ from 5–16 GeV/c

The average charged particle multiplicity, 〈n_ch(M_X²)〉, in the reaction K⁺p→K^oX⁺⁺ is studied as a function of the mass squared, M_X², of the recoil system X and also as a function of the K^o transverse momentum, p_T, at incident momenta of 5.0, 8.2 and 16.0 GeV/c. The complete data samples yield distributions which are not independent of c.m. energy squared, s, They exhibit a linear dependence on log (M_X²_X/M_o²)[M_o²=1 GeV²] with a change in slope occurring for M_X²≈s/2, and do not agree with the corresponding distributions of 〈n_ch〉 as a function of s for K⁺ p inelastic scattering. Sub-samples of the data for which K^o production via beam fragmentation, central production and target fragmentation are expected to be the dominant mechanisms show that, within error, the distribution of 〈n_ch(M_X²)〉 versus M_X² is independent of incident momentum for each sub-sample separately. In particular in the beam fragmentation region the 〈n_ch(M_X²)〉 versus M_X² distribution agrees rather well with that of 〈n_ch〉 versus s for inelastic K⁺p interactions. The latter result agrees with recent results on the reactions pp → pX and π^?p → pX in the NAL energy range. Evidence is presented for the presence of different production mechanisms in these separate regions.     

Non-perturbative QCD effects explain the ΔI = 12 rule in the chiral limit

It is shown that in the chiral limit, the enhancement of the $\text{ΔI=}\text{1}\text{2}$ transitions for mesons is explained by the large size of non-perturbative QCD matrix elements. For $\text{〈}\text{s}\text{s〉 = 〈}\text{u}\text{u〉}$ we obtain ∣M(K_S⁰ → 2π⁰) ∣ =(5.2±0.6) × 10^?7m_K in excellent agreement with experiment.     

Low temperature phase diagrams for quantum perturbations of classical spin systems

We consider a quantum spin system with Hamiltonian $$H = H^{(0)} + \lambda V,$$ whereH ⁽⁰⁾ is diagonal in a basis ∣s〉=? _x ∣s _x 〉 which may be labeled by the configurationss={s_x} of a suitable classical spin system on ? ^d , $$H^{(0)} |s\rangle = H^{(0)} (s)|s\rangle .$$ We assume thatH ⁽⁰⁾(s) is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitation, whileV is a finite range or exponentially decaying quantum perturbation. Mapping thed dimensional quantum system onto aclassical contour system on ad+1 dimensional lattice, we use standard Pirogov-Sinai theory to show that the low temperature phase diagram of the quantum spin system is a small perturbation of the zero temperature phase diagram of the classical HamiltonianH ⁽⁰⁾, provided λ is sufficiently small. Our method can be applied to bosonic systems without substantial change. The extension to fermionic systems will be discussed in a subsequent paper.     

Formation and diffusion of self-interstitial atoms in silicon crystals under hydrostatic pressure: Quantum-chemical simulation

A theoretical modeling of the formation of Frenkel pairs and the diffusion of a self-interstitial atom in silicon crystals at normal and high (hydrostatic) pressures has been performed using molecular dynamics, semiempirical quantum-chemical (NDDO-PM5, PM6), and ab initio (SIESTA) methods. It is shown that, in a silicon crystal, the most stable configuration of a self-interstitial atom in the neutral charge state (I ⁰) is the split configuration 〈110〉. The shifted tetrahedral configuration (T ₁) is stable in the singlet and triplet excited states, as well as in the charge state Z = +2. The split 〈110〉 interstitial configuration remains stable under hydrostatic pressure (P ≤ 80 kbar). The activation barriers for diffusion of self-interstitial atoms in silicon crystals are determined to be as follows: ΔE _a (Si)(〈110〉 → T ₁) = 0.59 eV, ΔE _a (Si)(T ₁ → T′₁) = 0.1 eV, and ΔE _a (Si)(T ₁ → 〈110〉) = 0.23 eV. The hydrostatic pressure (P ≤ 80 kbar) increases the activation barrier for diffusion of self-interstitial atoms in silicon crystals. The energies of the formation of a separate Frenkel pair, a self-interstitial atom, and a vacancy are determined. It is demonstrated that the hydrostatic pressure decreases the energy of the formation of Frenkel pairs.     

The hyperfine structure of they 8 p-multiplet of 4f 7(8 S) 6s 6p in EuI

The hyperfine splitting constants of the 4f ⁷ 6s 6p y ⁸ P _7/2 level of Eul were determined using the level crossing method. These values and those for the hyperfine splittings of the other 4f ⁷ 6s 6p levels are compared to theoretical values calculated with eigenfunctions of Smith and Collins. For the quadrupole coupling constants a better agreement between theory and experiment is obtained if different 〈r ^?3〉 _p -parameters are assumed for 4f(⁸ S) 6s 6p(³ P) and for 4f ⁷(⁸ S) 6s 6p(¹ P).     

A Monte Carlo program for QCD event simulation ine +e− annihilation at LEP energies

We present a Monte Carlo program for event simulation of Quantum Chromodynamics ine ⁺e^? annihilation, which includes multi-emission of quanta treated in the leading-logarithm approximation. Some difficulties of currentO(α _s ) phenomenology, associated with the treatment of divergences, are eliminated, without essentially altering the results of the analysis of the data from PETRA. At the same time a direct extension is provided of current QCD phenomenology to LEP energies, where multi-emission effects cannot be ignored. Detailed predictions for hadrons within the LEP energy interval are reported. With respect to conventionalO(α _s ) calculations, some new predicted features are: i) an average hadron multiplicity rising faster than logW, whereW is the c.m. energy, ii) a slower increase of the average hadron transverse momentum, 〈p _T ² 〉∝αα _s (W ²)W instead of the ∝α _s (W ²)W ² behaviour expected in theOα _s ) approximation. Implications for detector design and pattern recognition at LEP are also discussed.     

Resonant paramagnetic enhancement of the thermal and zero-point Nyquist noise

The interaction between a very thin macroscopic solenoid, and a single magnetic particle precessing in a external magnetic field B₀, is described by taking into account the thermal and the zero-point fluctuations of stochastic electrodynamics. The inductor belongs to a RLC circuit without batteries and the random motion of the magnetic dipole generates in the solenoid a fluctuating current I_dip(t), and a fluctuating voltage ε_dip(t), with spectral distribution quite different from the Nyquist noise. We show that the mean square value 〈I_dip²〉 presents an enormous variation when the frequency of precession approaches the frequency of the circuit, but it is still much smaller than the Nyquist current in the circuit. However, we also show that 〈I_dip²〉 can reach measurable values if the inductor is interacting with a macroscopic sample of magnetic particles (atoms or nuclei) which are close enough to its coils.     

Widths of 4f antiprotonic levels in the oxygen region

It is shown that the widths of the 4f antiprotonic levels in ¹⁴N, ^16,17,18O, ¹⁹F and ²³Na are all well described in terms of the lower moments of t-matrices based on the Dover-Richard N N̄ potential. However, the lowest S-wave moment 〈t_s〉 - related to the NN̄ scattering length — is by itself not sufficient with the higher moment 〈r²t_s〉 and the P-wave moment 〈t_p〉 both playing important roles.     

New bounds for dilepton production from heavy neutral leptons

Bounds on 〈E_?ⁿ〉/〈E₊ⁿ〈, 〉E₊E_?〈/〉E₂²〈 and 〈E₊E_?〉/〈E₊〉〈E_?〉 are direved for the processes ν_μN → μ^?μ⁺(e⁺) + X and μN → μ^?μ⁺ + X if dileptons are mediated by a $\text{spin}\text{-}\text{1}\text{2}$ heavy neutral lepton L₀. The bounds are shown to be independent of the production mechanism and mass of L₀. Useful conditional bounds are obtained relating the bounded quantities, which give information about the structure of the weak current responsible for L₀ decay.     

Vibrational properties of the adsorbed monolayer on face-centered cubic crystals

Calculations of mean-square displacements 〈u²〉 of the atoms in adsorbed monolayers on fcc crystals are presented and compared with LEED experimental results. This text is restricted to the case of a C(2 × 2) adsorbed layer on a (100) surface [experimental case of Ni(100) with adsorbed sulfur, sodium, cesium or oxygen]. 〈u²〉's perpendicular to and parallel to a (100) surface are calculated for the adsorbed atoms and the atoms of the first surface layer of the crystal. The values obtained are compared with those for a clean (100) surface and the volume of the crystal. Every possibility for force constants between adsorbate and substrate atoms is examined. It is shown that the measurement of 〈u²〉 perpendicular to the (100) surface yields the adsorbate-substrate force constants and that 〈u²〉 parallel to the (100) surface yields the adsorbate-adsorbate force constants.     

Die Isotopieverschiebung von151Eu,152Eu,153Eu,154Eu und die Kernmomente der radioaktiven Isotope152Eu und154Eu

The isotope shift of the stable¹⁵¹Eu,¹⁵³Eu, and the radioactive¹⁵²Eu,¹⁵⁴Eu isotopes and the hyperfine splitting of the¹⁵²Eu isotope was investigated using a digital recording Fabry-Perot-spectrometer. From isotope shift measurements on the line λ 5 765 Å (4f ⁷ 6s 6p z⁶P_7/2-4f ⁷ 6s² a⁸S_7/2) the relative isotope shift was derived:¹⁵¹Eu:0;¹⁵²Eu: 0.923(8);¹⁵³Eu: 1;¹⁵⁴Eu: 1.197(8). The results show that there is a strong increase in the change of the mean square nuclear charge radius δ〈r²〉 when only one neutron is added to the 88 neutrons of the¹⁵¹Eu nucleus, whereas the change of δ〈r²〉 between¹⁵²Eu and¹⁵³Eu is of the same order of magnitude as that between¹⁵³Eu and¹⁵⁴Eu. From the hyperfine splitting of the radioactive isotope¹⁵²Eu in the line δ 6865 Å (4f ⁷ 6s 6p z ¹⁰ P _9/2-4f ⁷ 6s² a⁸S_7/2) the sign of the magnetic dipole moment μ_I(¹⁵²Eu) was found to be negative, and with this result and earlier experimental data the signs of the nuclear quadrupole momentsQ(¹⁵²Eu) andQ (¹⁵⁴Eu) could be determined to be positive.     

An SO(10) model with 54 + 126 + 10 higgs

We find an absolute minimum of an SO(10) symmetric potential with SU(3) × U(1) invariance. By fixing the higher scales M_R(〈126〉) ? M_x(〈54〉), the model is consistent with the experimental knowledge about matter stability and the value of sin²θ_w. We determine the spectrum of scalar particles and show that their tree-diagram contributions to nucleon decay amplitudes are proportional to 1/M_x².     

Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.     

Magnetic ordering of Fe atoms in icosahedral Al70−x BxPd30−y Fey quasicrystals

Novel icosahedral quasicrystals, in which Fe atoms possess a magnetic moment, have been found in Al_70?x B_xPd_30?y Fe_y compounds with 5<x<10 and 10<y<20. The compounds have ferromagnetic properties, and their Curie temperature ranges between 280 and 340 K, the saturation magnetization σ _s(5 K)≈7.5 emu/g. It follows from Mössbauer spectra that only a fraction of Fe atoms (12 to 15%) are magnetically ordered at 4.2 K, and the mean saturation field 〈H _hf〉=96 kOe. The isomer shift values confirm that the atomic volume of magnetic Fe sites is larger than that of nonmagnetic Fe sites. The magnetic properties of these quasicrystals can be interpreted in terms of large magnetic clusters with a size of 185 to 290 Å. This size correspond to about 4×10⁴ “unit cells,” hence the magnetic state can be described in terms of bulk parameters. The localized magnetic moment of Fe atoms is tentatively ascribed to bonding between Fe and B, similarly to that in the amorphous Fe_～50B_～50 alloy.     

New qualitative results of the atomic theory

The polarizability α of many atoms and positive ions is related to their energy gap Δ and valence m by the expression αΔ² ? m (in atomic units). The parameter Δ corresponds to a dipolar transition from the ground state to the first excited P state without a change in the principal quantum number n. This relation holds for univalent (m = 1) Na, K, Rb, Cs, Fr and bivalent (m = 2) Mg, Ca, Zn, Sr, Cd, Ba, Yb, Hg atoms. The above relation agrees with the experiment for positive ions Mg⁺ and Ca⁺ (m = 1) and Al⁺ and Ga⁺ (m = 2). The polarizability has been found for atoms and ions of the type Zn⁺, In⁺, Tl⁺, for which experimental data are unavailable. A method of calculating α for ions of the types C⁺⁺, Al⁺⁺, Si⁺⁺ and Si⁺⁺⁺, P⁺⁺⁺, As⁺⁺⁺ has been suggested based on the approximate relation α ?(2/3〈r²〉₀)²/m with the parameter 〈r²〉₀ expressed in terms of the valence m, the charge number q of the atomic or ionic residue, and the ionization potential \({J_q} = \frac{{{q^2}}}{{2v_s^2}}\) as \({\left\langle {{r^2}} \right\rangle _0} = \frac{m}{{2{q^2}}}\nu _s^2\left( {1 + 5\nu _s^2} \right)\). The hydrogen dependence of 〈r²〉₀ on the parameter ν_s has been derived by analytical continuation from the integer values ν_s = 1 and 2. A variational estimate of the van der Waals constant characterizing the interaction of two spherically symmetric atoms at large distances has been given.     

Effects of QCD multi-jet contributions in electron-positron annihilation

By means of a recently proposed Monte Carlo procedure for computing QCD multi-jet finals states in the leading-logarithm approximation, we calculate the effects of multi-emission on the hadronic final state in electron-positron annihilation. In particular, we present quantitative predictions for the growth with energy of the average multiplicity, which increases faster than log W, and for the average transverse momentum, for which ee find 〈p_T²〉 ∝ α_s(W²) W, in contrast with the ∝ α_s(W²) W² behaviour expected in lowest perturbative order calculations.     

Classical Motion in Force Fields with Short Range Correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy 〈p ²(t)〉/2 and mean-squared displacement 〈q ²(t)〉 is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, 〈p ²(t)〉～t ^2/5 independently of the details of the potential and of the space dimension. The stochastically accelerated particle motion is then superballistic in one dimension, with 〈q ²(t)〉～t ^12/5, and ballistic in higher dimensions, with 〈q ²(t)〉～t ². These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: 〈p ²(t)〉～t ^2/3 and 〈q ²(t)〉～t ^8/3 in all dimensions d≥1.