Thermoelectric measurements on tungsten at ultra low temperatures

Measurements are reported of the thermoelectric ratio G for three zone-refined tungsten samples at temperatures down to 45 mK. For the purest sample $\text{(}\text{R}{}_{\mathrm{300K}}\text{R}{}_{\mathrm{0K}}\text{= 44 000)}$, G behaves simply and in accord with expectations. For two less pure samples $\text{(}\text{R}{}_{\mathrm{300K}}\text{R}{}_{\mathrm{0K}}\text{= 44 000 and 22 000)}$, G behaves anomalously, becoming increasingly more negative with decreasing temperature down to at least 45 mK. This anomalous behavior is tentatively attributed to trace amounts of iron.     

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 mathematical interpretation of Dirac's formalism part b: generalized eigenfunctions in trajectory spaces

Starting with a Hilbert space $\text{L}{}_2\text{(}\text{R}\text{,μ)}$ we introduce the dense subspace $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ where $\text{R}$ is a positive self-adjoint Hilbert–Schmidt operator on $\text{L}$₂(R,μ). For the space $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ a measure-theoretical Sobolev lemma is proved. The results for the spaces of type $\text{R}\text{(}\text{L}{}_2\text{(}\text{R}\text{,μ))}$ are applied to nuclear analyticity spaces $\text{S}{}_{\mathrm{<mtext>X,</mtext><mtext>A</mtext>}}\text{=}\text{?}\text{t>0}\text{e}{}^{\mathrm{<mtext>-t</mtext><mtext>A</mtext>}}\text{(X)}$, where e^?t$\text{A}$ is a Hilbert–Schmidt operator on the Hilbert space X for each t>0. We solve the so-called generalized eigenvalue problem for a general self-adjoint operator $\text{P}$ in X.     

Teopия acиммeтpии штaкoвcкиx пpoфилeй вoдopoдныx линий в плoтнoй плaзмe

The asymmetric Stark profile for spectral lines of hydrogen has been calculated in first approximation in terms of the expansion parameter $\text{n}{}^2\text{a}{}_0\text{R}{}_0$ [a₀=Bohr radius, n= principal quantum numberm $\text{R}{}_0\text{=(}\text{3}\text{4πN}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$=mean distance between charged particles]. Additional terms, which determine the asymmetry, are expressed through the universal functions Λ(β) and χ(β), which are connected with the first moments of the components of the ion-electric field inhomogeneity tensor. Comparison is made with results based on a nearest neighbour approximation. It is shown that the shift of the symmetry centre of the profiles may be the ion-electric field inhomogeneity.     

Measurement of line widths of CO of planetary interest at low temperatures

Self-broadened, air-broadened and CO₂-broadened half-widths of lines R(0) through R(0) in the CO fundamental have been measured at 100°K (self-broadening only), 200°K, 250°K and 300°K using the Ladenburg-Reiche curve-of-growth. The relation $\text{γ}{}^{\mathrm{°}}{}_{\mathrm{m}}\text{(T)}\text{γ}{}^{\mathrm{°}}{}_{\mathrm{m}}\text{(300°K)}\text{=(}\text{300}\text{T}\text{)}{}^{0.75}$, which we found previously for the nitrogen-broadened half-widths of R(0), R(8) and R(16), is shown to be valid for all of the line widths measured in the present study.     

Electron-hole interaction in the presence of excitons

We calculate the effective electron-hole interaction V_re in the presence of an exciton gas, which reads in real space:

$\text{V}{}_{\mathrm{re}}\text{(r)=}\text{?e}{}^2\text{r}\text{{1+}\text{∑}\text{i=1}\text{4}\text{(?1)}{}^{\mathrm{i}}\text{C}{}_{\mathrm{i}}\text{exp}\text{(?Z}{}_{\mathrm{i}}\text{r}\text{a}\text{}}$

The parameters C_i and Z_i are given explicitly for GaAs. For this material, we show the binding energy of the exciton is weakly modified so long as $\text{8πR}{}_0\text{?}{}_{\mathrm{ex}}\text{a}{}_0{}^3\text{kT?1}$. (R₀, exciton Rydberg, a₀ exciyon radius, ?_ex exciton density, T temperature).     

Nonlinear temperature and velocity distributions in the two-dimensional Bénard problem

The nonlinear temperature and velocity profiles of a two-dimensional Boussinesq fluid heated from below are shown to be the sum or terms with periodicity $\text{Λ}\text{cr}\text{n}$, with n = 1, 2, 3; their amplitudes are a function of $\text{? =}\text{(R}{}_{\mathrm{<mtext>a</mtext>}}\text{? R}{}^{\mathrm{<mtext>cr</mtext>}}{}_{\mathrm{<mtext>a</mtext>}}\text{)}\text{R}{}^{\mathrm{<mtext>cr</mtext>}}{}_{\mathrm{<mtext>a</mtext>}}$. The results are in agreement with the observations of Bergé and Dubois.     

Renormalization group improved predictions for quarkonium decay

A method recently suggested to resolve the ambiguity related to scheme dependence in perturbative QCD is applied to calculations of radiative corrections to quarkonium decay. Renormalization group improved predictions are given for the ratio $\text{R=Г(}{}^1\text{S}{}_0\text{→had)/Г(}{}^3\text{S}{}_1\text{→had)}$, as a function of $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$. The values obtained are substantially larger than in conventional schemes. One finds in particular that R>182 for charmonium, and R>174 for bottomium, independently of the value of the quark mass and $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$. It follows that $\text{Г(}\text{n}{}_{\mathrm{c}}\text{→}\text{had}\text{)>6.9}\text{MeV}$ and $\text{Г(}\text{n}{}_{\mathrm{b}}\text{→}\text{had}\text{)>3.6}\text{MeV}$. Values of the wave function at the origin as a function of $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$ are also extracted from the measured gluonic width of the ³S₁ state. An upper bound for $\text{λ}{}_{\mathrm{<mtext>MS</mtext>}}$ is obtained under some assumptions.     

Phase transition in strongly inhomogeneous ferromagnets

A field theoretical model is proposed to describe the critical behaviour of a strongly inhomogeneous spin system with a position dependent concentration of magnetic atoms C(R) and magnetisation M(R). Assuming a finite number of $\text{n}$ Fouriermodes $\text{C}{}_{\mathrm{<mtext>Q</mtext>}}{}_{\mathrm{<mtext>v</mtext>}}\text{v}\text{= 1}$,..., $\text{n}$, to express C(R), the quenched randomness requires to interpret {$\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}\text{Q}{}_{\mathrm{<mtext>v</mtext>}}\text{|}{}^2$} on a set of invariant or marginal lengths. As consequence, M(R) can be described by n Fourier-modes M_Qv, where $\text{n ?}\text{n}$. For short range spin-spin interaction, we find for strong inhomogeneity, i.e. large n, the critical exponent between those of the related homogeneous system and those of the spherical model.     

Franck-condon factors for diatomic molecules and the factorization method

By means of the factorization method, recurrence relations for the matrix elementS$\text{<ψ}{}_{\mathrm{<mtext>v\text{'}</mtext>}}\text{¦r}{}^{\mathrm{N}}\text{¦ψ}{}_{\mathrm{<mtext>v</mtext>}}\text{<}$ for an arbitrary positive integer N are obtained in the framework of α-averaging for the Morse potential. The method of calculating the matrix element$\text{<ψ}{}_{\mathrm{<mtext>v\text{'}</mtext>}}\text{¦R}{}_{\mathrm{<mtext>e</mtext>}}\text{¦ψ}{}_{\mathrm{<mtext>v</mtext>}}\text{<}$ is outlined, provided a dependence of the electronic transition moment R_e on the internuclear distance r can be approximated by the polynomial R_e(r)=a₀+a₁r+a₂r²+…+ainNr^N. Recurrence relations are also obtained for the case of the exponential dependence R_e(r).     

Indirect long-range oscillatory interaction between adsorbed atoms

The oscillatory part of the indirect interaction between two adatoms on a metal surface, separated by a large distance R, is examined for the jellium as well as for the tight-binding model. The asymptotic form of the interaction is derived from the singularity of its Fourier transform at wave number q = 2k_F. For a substrate with a spherical Fermi surface, the interaction energy is proportional to $\text{cos}\text{(2k}{}_{\mathrm{<mtext>F</mtext>}}\text{R)}\text{R}{}^5$. The fall-off is faster than the corresponding oscillatory interaction between two impurities in the bulk, which varies as $\text{cos}\text{(2k}{}_{\mathrm{<mtext>F</mtext>}}\text{R)}\text{R}{}^3$. For substrates with a partially filled surface band, the interaction energy falls off much more slowly. Under simple assumptions, the interaction behaves as $\text{cos}\text{(2k}{}_{\mathrm{<mtext>F</mtext>}}\text{R)}\text{R}{}^2$. Comparisons are made with the numerical calculations by Einstein and Schrieffer. The experimental results of Tsong on Re atoms adsorbed on W using field-ion microscopy is also discussed.     

On the difference between pp and pp topological cross sections up to 100 GeV/c

New 100 GeV/c$\text{p}$p data are used to find moments of the difference between the $\text{p}$p and pp topological cross sections. The mean multiplicity for annihilations at 100 GeV/c is estimated to be 9.06 ± 0.56, and the value of the quantity 〈n〉/D to be 2.75 ± 0.33. It is shown that $\text{R}{}_{\mathrm{n}}\text{= {σ}{}_{\mathrm{n}}\text{(}\text{p}\text{p) ? σ}{}_{\mathrm{n}}\text{(pp)}/σ}{}_{\mathrm{n}}\text{(pp)}$ appears at 100 GeV/c to have acquired an asymptotic form, R_n = s^?αβⁿ, with α and β constant.     

Magnetic properties of odd-odd deformed nuclei

Magnetic moments and Ml transition probabilities depend on the parameters $\text{g}{}_{\mathrm{R}}\text{, g}{}_{\mathrm{\Omega }}{}_{\mathrm{<mtext>p</mtext>}}\text{,}\text{and}\text{g}{}_{\mathrm{\Omega }}{}_{\mathrm{<mtext>n</mtext>}}$ in odd-odd deformed nuclei. The parameter g_R can be obtained from an intraband branching ratio and a magnetic moment. Available data are analyzed and compared with predictions of the unified model.     

Cosmological bounds on a left-right symmetric model

The right-handed neutrino cross sections of the processes ν_L + ? → ν_R + ? and ν_R + ? → ν_R + ?, where ? is a relativistic lepton, are calculated in the SU(2)_L × SU(2)_R × U(1) model. According to a cosmological criterion the parameters of the model are bounded. In particular we obtain the bound $\text{M}{}_{\mathrm{<mtext>W</mtext>}}{}_{\mathrm{<mtext>R</mtext>}}\text{? 30 M}{}_{\mathrm{<mtext>W</mtext>}}{}_{\mathrm{<mtext>L</mtext>}}$, assuming the neutrinos are Dirac four-component particles.     

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 $\text{m}{}^1{}_{\mathrm{<mtext>L</mtext>}}\text{= 0.18 ± 0.02 m}{}_0$, $\text{m}{}^1{}_{\mathrm{<mtext>H</mtext>}}\text{= 0.56 ± 0.04 m}{}_0$.     

O(18) revived: Splitting the spinor

We propose an O(18) theory which is perturbatively unifiable and which accounts for the absence of right-handed families in the low-energy world. The theory predicts a fourth left-handed family as well as four right-handed families at energies near the weak scale. It also implies the existence of eight light neutrinos, all of which contribute to the width of the Z⁰. Cosmological arguments suggest that four of these neutrinos should have masses between 2 and 35 GeV, and that the other four should be much lighter. They also suggest the existence of a doubly charged scalar φ⁺⁺ and a singly charged scalar φ⁺. Dramatic signatures include the production of four right-handed charged leptons and eight right-handed quarks, $\text{Z}{}^0\text{→ v′}{}_{\mathrm{<mtext>R</mtext>}}\text{+}\text{v}\text{′}{}_{\mathrm{<mtext>R</mtext>}}\text{→ v}{}_{\mathrm{<mtext>R</mtext>}}\text{γ +\_}\text{v}{}_{\mathrm{<mtext>R</mtext>}}\text{γ}$, and e⁺e^? → φ⁺⁺ + φ^??. The lightest right-handed charged quark should be surprinsingly long-lived $\text{(τ?10}{}^{\mathrm{?2}}\text{sec}\text{)}$ for a particle of mass ? 100 GeV.     

Valence band parameters and free exciton reduced mass of zinc telluride derived from free exciton magnetoreflectance

Reflectance spectra were measured on ZnTe in magnetic fields up to 18 T for B ? [100] and B ? [110]. The experiments yield renormalized valence band parameters $\text{γ}{}^1{}_2\text{= 0.83 ± 0.08}$ and $\text{γ}{}^1{}_3\text{= 1.30 ± 0.12}$, corresponding to bare parameters γ₂ = 0.95 ± 0.09 and γ₃ = 1.48 ± 0.14. From the free exciton Rydberg energy $\text{R}{}^1{}_0\text{= 12.8}\text{meV}$ we derive a reduced exciton polaron mass m₀ 0.080 ± 0.005 and a bare reduced mass m₀ 0.074 ± 0.005, corresponding to $\text{γ}{}^1{}_1\text{= 3.9 ± 0.7}$ and γ₁ = 4.4 ± 0.7 for an electron effective polaron mass $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.116 m}{}_0$. We further calculate the exciton diamagnetic shift rate according to existing low-field theories modified by a variational calculation taking into account polaron effects and valid up to γ ? 1. The difference between experiment and theory is 10% and the agreement is considered satisfactory.