Deep inelastic sum rules at fixed hadron energy

Experimentally, it is much easier to measure structure functions at fixed hadron energy E_h, rather than at fixed Q². We prove the sum rules

,

$\text{h}{}_{\mathrm{NS}}\text{=}\text{4}\text{3}\text{(}\text{1}\text{6}\text{π}{}^2\text{?}\text{5}\text{8}\text{),}$

$\text{h}{}_{\mathrm{S}}\text{=}\text{4}\text{16+3n}{}_{\mathrm{<mtext>f</mtext>}}\text{(2π}{}^2\text{+}\text{1}\text{6}\text{π}{}^2\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{?}\text{65}\text{12}\text{?}\text{5}\text{72}\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{).}$

Here s = 2m_pE_h and F_2,3 are the standard functions for scattering of neutrinos on an isoscalar target. K is an unknown constant, and the corrections to the sum rules are O(α_s²), O(α_s^1.75), respectively.     

On the mobility of a very pure semiconductor including the low impurity concentration limit

The low temperature mobility μ limited by charged impurities is calculated by solving the equation for the relaxation rate previously derived. The calculated μ behaves like $\text{μ = 2.03 κ}{}^2\text{(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{?3}}\text{z}{}^{\mathrm{?2}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{?1}}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>?1</mtext><mtext>2</mtext>}}$ In $\text{[38.2κ}{}^2\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{/z}{}^2\text{e}{}^4\text{h}\text{?}\text{n}{}_{\mathrm{s}}\text{]}$ for lowest concentrations n_s<10¹¹cm^?3 for Ge and

$\text{μ = 0.360}\text{h}\text{?}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{κ(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^{\mathrm{<mtext>1</mtext><mtext>?3</mtext><mtext>4</mtext>}}$

for intermediate concentrations n_s ～ 10¹²?10¹⁴cm^?3.     

Electron-exciton inelastic collision cross sections for different semiconductors

The electron-exciton inelastic collision cross sections for the different semiconductors CdS, ZnO, CdSe, Si, Cu₂O, CuCl, CuBr and CuI have been calculated in the Glauber approximation. The transitions 1s–2s, 1s–3s, 1s–2p and 1s–3p have been considered. The calculations are carried out as function of the different available values of $\text{σ =}\text{m}{}^1{}_{\mathrm{e}}\text{m}{}^1{}_{\mathrm{h}}$ where m¹_e and m¹_h are, respectively, the electron a corresponding semiconductors.     

Electric dipole transition cross sections and effective site symmetry of Eu3+ in pseudocentric K5Eu(MoO4)4

The fluorescence and absorption spectra of Eu³⁺ in K₅Eu(MoO₄)₄ have been measured at 300 K and 77 K. The fluorescence lifetime of the ⁵D₀ state is 1.4 ms at 300 K. The largest cross section $\text{σ(}{}^5\text{D}{}_0\text{→}{}^7\text{F}{}_2\text{(4)) = 1.3 × 10}{}^{\mathrm{?21}}\text{cm}{}^2$ and the removal of degeneracies require to replace the nearest neighbour D_3d symmetry of Eu³⁺ by the effective symmetries C₁, C₂ and C_s of the whole unit cell. It is shown that C₁ dominates because of the statistical distribution of K⁺ and Eu³⁺. The corresponding inhomogeneous broadening is observed at 77 K.     

On the transition rate for the two-electron one-phonon transition

By using different gauges, the relativistic rates for the $\text{K}{}_{\mathrm{\alpha \alpha 2}}\text{(1}\text{s}{}^{\mathrm{?2}}\text{→2}\text{s}{}^{\mathrm{?1}}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{) and the}\text{K}{}_{\mathrm{\alpha 2}}{}^{\mathrm{<mtext>h</mtext>}}\text{(1}\text{s}{}^{\mathrm{?2}}\text{→1}\text{s}{}^{\mathrm{?1}}\text{2}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{)}$ transitions are calculated for Ne, Ar, Ca, Fe and Cu. The problem in the use of the single configuration HF model is discussed.     

Dye laser site selection spectroscopy on U6+ luminescent molecular centers in LiF-U3O8 crystals

The polarized excitation and emission spectra of the U⁶⁺ molecular centers giving the most intense emission lines at 18 940 cm^?1 and 19 285 cm^?1 are presented and analyzed in detáil. From the polarization experiments, it is shown that the symmetry of the centers is C_4v and that the symmetries of the observed electronic states are Γ₂, Γ₁ and Γ₅. Finally, an electronic model is proposed which associates the emission and excitation lines of the U⁶⁺ centers in the visible region to transitions between the fundamental state $\text{Γ}{}_1\text{(6p}{}^6\text{,}{}^1\text{S)}$ and the states of the excited configuration $\text{6p}{}^5\text{(}{}^2\text{P}\text{3}\text{2}\text{) 7s}$.     

Interpreting data from polarized proton beams

The reactions pp → pp and pp → Δ⁺⁺n with polarized beam and/or polarized target are currently under investigation at the Argonne ZGS. We discuss how to interpret various measured quantities in terms of amplitudes whose behavior is familiar (as functions of s, t). For pp total cross sections and elastic scattering, Argonne measurements will yield Im ?₂ (s,t = 0) and the rather complicated combination $\text{2|?}{}_5\text{|}{}^2\text{+}\text{Re}\text{(?}{}_1\text{?}{}_2{}^1\text{? ?}{}_3\text{?}{}_4{}^1\text{)}$, where ?_i (i = 1, … 5) are conventional s-channel helicity amplitudes. The forward direction (t = 0) is of special interest. We find that for both pp → pp and pp → Δ⁺⁺n, polarized beam — polarized target experiments plus the rather general (testable) assumption that amplitudes with the same s-channel helicity flip quantum numbers are proportional, are sufficient to fully determine all non-vanishing amplitudes at t = 0. Numerical estimates of some observables, based on calculations in a specific model, are also given.     

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.     

Defect dominated conductivity in Zn3P2

The electrical resistivity and Hall coefficient of Zn₃P₂ have been measured for single crystal and thin polycrystalline film samples which were annealed over a range of equilibrium vapor compositions and temperatures. The room temperature electrical resistivity of single crystal samples annealed at 573 K varied from approximately 10⁵Ω-cm for single crystals heated in equilibrium with zinc to 10 Ω-cm for those annealed in a phosphorus rich ambient. Hall measurements indicate that a variation in carrier concentration is responsible for these changes. The experimentally observed dependence of carrier concentration [h° ], (cm^?3) on phosphorus pressure is given by [h°] = 1.32 · 10¹⁶ [p(P₄)]^0.13 for samples annealed at 573 K. The experimentally determined pressure dependence is in good agreement with a model based on phosphorus interstitials acting as acceptors. The pressure and temperature dependence of the carrier concentration yield the equilibrium constant K_I for the formation of interstitial phosphorus defects according to the reaction

$\text{1}\text{4}\text{P}{}_4\text{→ P′}{}_{\mathrm{i}}\text{+ h°}$

where

$\text{K}{}_{\mathrm{I}}\text{= 10}{}^{\mathrm{42.4\; \pm \; 2}}\text{cm}{}^{\mathrm{?6}}\text{torr}{}^{0.25}\text{[p(P}{}_4\text{)]}{}^{\mathrm{?0.25}}\text{exp(?1.18}\text{ev}\text{kT}\text{)}$

. The accommodation of phosphorus interstitials is discussed in light of the crystal structure of Zn₃P₂.     

A search for monojet events produced by virtual Z0 bosons in e+e− annihalation at petra

A search was performed for the associated production of two different Higgs bosons via a virtual Z⁰ in e⁺e^? annihilation (e⁺e^? → h₁⁰h₂⁰) using the JADE detector at PETRA. This was motivated by the interpretation of the monojet events observed at the CERN p$\text{p}$ collider as anomalous Z⁰ decays into two neutral Higgs bosons (h₁⁰ and h₂⁰), where h₁⁰ is stable and escapes detection while h₂⁰ decays into hadrons. Single- or di-jet events with large momentum imbalance are then expected at PETRA energies. No evidence for such events was found in our data; this excludes h₂⁰ masses in the range of 1 to 21 GeV with 95% CL, if the branching fraction for Z⁰ → h₁⁰h₂⁰ is a larger than one half that for $\text{Z}{}^0\text{→ v}{}_{\mathrm{\mu }}\text{v}{}_{\mathrm{\mu }}$. The possibility that the monojets could originate from supersymmetric higgsino production from Z⁰ decay is also examined.     

Scaling laws for inelastic partial-wave amplitudes and the high-energy behaviour of multiparticle production

t-channel unitarity equations are derived for n-particle overlap functions. Together with s-channel unitarity they lead to scaling laws for the inelastic s-channel partial-wave amplitudes $\text{?}{}_{\mathrm{l}}{}^{\mathrm{(n)}}\text{(s)}$ in the limits $\text{s → ∞, l → ∞ x = l (}\text{μ}\text{√s}\text{)}{}^3\text{=}\text{fixed}$. Assuming the validity of the scaling law in the whole range, allowed by s-channel unitarity — i.e. for $\text{l > L (s) = (α(4μ}{}^2\text{) ? 1) (}\text{s}\text{4μ}\text{)}\text{log}\text{(}\text{s}\text{s}{}_1\text{)}$ we obtain constant production cross sections σ⁽ⁿ⁾(s) at high energies s → ∞ up to s factors.     

Infrared diode laser spectroscopy of the CF radical

The fundamental bands of the CF radical in the $\text{X}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{X}{}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ electronic states were observed by using an infrared tunable diode laser as a source. Zeeman modulation could be used in detecting lines not only in the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state, but also in ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, because the CF radical deviates considerably from Hund's case (a). From the least-squares analysis of the observed spectra, the following molecular constants were obtained: B_e = 1.416 704 (37) cm^?1, α_e = 0.018 419 (50) cm^?1, $\text{r}{}_{\mathrm{e}}\text{= 1.271 977 (17)}\text{A}\text{?}$, D_e = 6.68 (15) × 10^?6cm^?1, p₀ = 0.008 580 (21) cm^?1, p₁ = 0.008 52 (11) cm^?1, and $\text{ν}{}_0\text{= 1286.1281 (5)}\text{cm}{}^{\mathrm{?1}}$, with three standard errors in parentheses.     

Analysis of the I = 0 s-wave for ππ and KK̄ scattering

We show that if one uses a coupled channel parametrisation for the I = 0 S-wave in processes $\text{ππ → ππ, ππ →}\text{K}\text{K}\text{?}$ and KK? → KK? (the last deduced from a $\text{p}\text{?}\text{p → ππ + K}{}_1{}^0\text{K}{}_1{}^0\text{experiment}$) taking properly into account the analytic structure of these waves, then it is possible to fit simultaneously all cross-sections for the above processes, in the ranges $\text{700 < s s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1900}\text{MeV}$ for the first fit, $\text{2M}{}_{\mathrm{<mtext>K</mtext>}}\text{< s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1500}\text{MeV}$ for the second, $\text{2M}{}_{\mathrm{<mtext>K</mtext>}}\text{< s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1170}\text{Mev}$ for the last. None of the three usually claimed resonances ?, S¹, ?′ show up in the corresponding eigenphase analysis.     

Paзлoжeниe пo 1Z для чapтpи-фoкoвcкoй и кoppeляциoннoй энepгии, peлятивиcтcкич пoпpaвoк, дипoльнoгo мaтpичнoгo элeмeнтa

Energies and dipole matrix elements have been calculated for He, Li, Be, B, C, N, O, F, and Ne-like ions (configurations 1s²2sⁿ¹2pⁿ²?1s²2s^n1?12pⁿ²⁺¹). The Hartree-Fock energy, the correlation energy, and relativistic corrections were taken into account. Relativistic corrections were obtained by computing the entire quantity H_B. Numerical results are presented for energies of the terms in the form

$\text{E=E}{}_0\text{Z}{}^2\text{+ ΔE}{}_1\text{Z + ΔE}{}_2\text{+}\text{1}\text{Z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{Z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{Z}{}^3\text{)}$

, and for the fine structure of the terms in the form

$\text{〈1s}{}^2\text{2s}{}^{\mathrm{n1}}\text{2p}{}^{\mathrm{n2}}\text{LSJ|H}{}_{\mathrm{Б}}\text{|1s}{}^2\text{2s}{}^{\mathrm{n1\prime }}\text{2p}{}^{\mathrm{n2\prime }}\text{L′S′J〉=(?1)}{}^{\mathrm{L+S\prime +J}}\text{LSJ}\text{S′L′1}\text{×}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{[E}{}^{\mathrm{(0)}}\text{(Z ? B)+}\text{E}{}_{\mathrm{c0}}\text{]+(?1)}{}^{\mathrm{L\; +\; S\prime \; +\; J}}\text{LSJ}\text{S′L′2}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{E}{}_{\mathrm{cc}}$

. Dipole matrix elements are required for calculation of oscillator strengths or transition probabilities. For the dipole matrix elements, two terms of the expansion in $\text{1}\text{Z}$ have been obtained. Numerical results are presented in the form P(a, a′) = (a/Z)[1 + (τ/Z)].     

Chemical diffusion in nonstoichiometric chromium sulfide,Cr2+yS3

Using the re-equilibration kinetic method the chemical diffusion coefficient in nonstoichiometric chromium sesquisulfide, Cr_2+yS₃, has been determined as a function of temperature (1073–1373 K) and sulphur vapour pressure (10?10⁴ Pa). It has been found that this coefficient is independent of sulphur pressure and can be described by the following empirical equation: $\text{D}\text{?}\text{Cr}{}_{\mathrm{2+y}}\text{S}{}_3\text{=50.86}\text{exp(-39070 cal/mole/}\text{RT)}\text{(cm}{}^2\text{s}{}^{\mathrm{?1)}}$. It has been shown that the mobility of the point defects inCr_2+yS₃ is independent of their concentration and that the self-diffusion coefficient of chromium in this sulfide has the following function of temperature and sulphur pressure: . (cm²s^?1).     

Ab initio study of the photodissociation of ammonia

An ab initio SCF and CI treatment of the electronic spectrum of ammonia in both the pyramidal and planar conformation is reported which employs an [8, 6, $\text{1}\text{4}$, 1] AO basis of near Hartree-Fock quality; the ground state CI energy obtained for the equilibrium conformation is ?56.4241 a.u. In addition, further calculations have been carried out at the SCF level to study various photodissociation reactions of NH₃. The calculated CI transition energies are seen to agree with corresponding experimental values to within 0.0–0.3 eV, usually in the 0.1-eV range. Photodissociation to the $\text{NH}{}_2\text{(}{}^2\text{B}\text{?}{}_1\text{) +}\text{H}\text{(}{}^2\text{S)}$ products is confirmed thereby to proceed via the $\text{A}\text{?}\text{1a″}{}_2\text{→ 3s}$ state of ammonia, but contrary to earlier speculation it is found that the transformation between reactant and products is already satisfactorily described at the SCF or orbital level, i.e., a Rydberg 3s of NH₃ is seen to be gradually converted into a pure hydrogenic 1s species as dissociation proceeds. In addition the photolysis of NH₃ to NH₂$\text{(}{}^2\text{A}{}_1\text{) +}\text{H}\text{(}{}^2\text{S)}$ is argued to occur via the $\text{C}\text{?}\text{1a″}{}_2\text{→ 3pz}{}^1\text{A′}{}_1$ state and as such is seen to be a symmetry allowed process, in contrast to the previous assignment involving the $\text{B}\text{?}\text{1a″}{}_2\text{→ 3px}$, $\text{y}{}^1\text{E″}$ species. Finally an attempt is made to analyze the mechanisms of various NH + H₂ photodissociation processes with the help of SCF calculations and symmetry arguments for various higher-lying excited states of ammonia.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

Molecular Rydberg transitions: Cyanogen chloride

The electronic absorption spectrum of cyanogen chloride has been investigated in the range 2200-1250 Å. The first s-Rydberg transitions, $\text{X}\text{?}{}^1\text{Σ}{}^{\mathrm{+}}\text{→}{}^3\text{Π}{}_1$ and $\text{X}\text{?}{}^1\text{Σ}{}^{\mathrm{+}}\text{→}{}^1\text{Π}{}_1$ have been assigned, and analyzed to yield exchange and spin-orbit coupling parameters. The relative intensities of these two transitions have been shown to accord with an intermediate coupling situation. The $\text{π → π}{}^1$ intravalence excitations, leading to ^1.3(Σ^?, Δ and Σ⁺) states, have been discussed. It has been shown that one or both of the ¹Σ^? and ¹Δ states have bent geometries and that the ¹Σ⁺ state is located (tentatively) at 79 755 cm^?1. Two $\text{σ → π}{}^1\text{π → σ}{}^1$ states have been assigned, one at 56 340 cm^?1, the other at 74 450 cm^?1. The latter assignment is tentative, being largely based on observed vibronic interferences between the $\text{X}\text{?}{}^1\text{Σ}{}^{\mathrm{+}}\text{→}{}^1\text{Π}{}_1$ transition and the 74 450 cm^?1 transition. A considerable amount of vibrational oscillator strength and quantum defect data is presented.     

Neutron-proton shell model multiplets in 88Y and 90Y from a study of the (α, nγ) reaction

The non-selective nature of the (α, nγ) reaction has been used to complement information from charged-particle reactions on the level structure of ⁸⁸Y and ⁹⁰Y. The γ-ray spectra were recorded with a 25 cm³ Ge(Li) detector at 90° to the beam using primarily targets of ⁸⁵Rb₂CO₃ and ⁸⁷Rb₂CO₃ and α-particle energies of 11.8, 12.2 and 13.0 MeV. The resulting transitions were accommodated in level schemes that involved primarily the following shell model configurations: $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$, $\text{(π}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^1$, $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$, $\text{(π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$ in ⁸⁸Y and $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1$, $\text{π}\text{g}\text{(}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1$,$\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2)</mtext>}}\text{)}{}^1$ in ⁹⁰Y.     

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase (h?h_ch_c), $\text{χ ～ (h?h}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{In}{}^{\mathrm{<mtext>-4</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h?h}{}_{\mathrm{c}}$ and R_c ～ (h ? h_c)^{$\text{2}\text{3}$}. In${}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h ? h}{}_{\mathrm{c}}$. Far from commensurability $\text{(h?h}{}_{\mathrm{c}}\text{) χ～ (a+h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, $\text{R}{}_{\mathrm{c}}\text{～ (a + h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.