Quasiclassical mobility for extrinsic semiconductors

A quasiclassical formulation for mobility in extrinsic semiconductors is presented based on scattering from ionized impurity atoms. Quantum theory enters the otherwise classical Chapman-Enskog expansion of the Boltzmann equation through incorporation of the Thomas-Fermi interaction potential together with the Bom approximation for evaluation of scattering integrals. The following expression results for mobility μ_i, (cgs):

$\text{μ}{}_{\mathrm{i}}\text{3}\text{2}\text{?}{}^2\text{n}{}_{\mathrm{s}}\text{e}{}^3\text{m}{}^1\text{2}\text{2}\text{k}{}_{\mathrm{B}}\text{T}\text{2φ}\text{3}\text{2}\text{1}\text{f(γ)}$

,

$\text{f(γ)=[(1+γ)e}{}^{\mathrm{\gamma }}\text{E}{}_1\text{(γ)?1]}$

, where n_s is impurity concentration, m¹ is effective mass, E₁(γ) is the exponential integral, ? is dielectric constant and γ is dimensionless Thomas-Fermi energy. The structure of the dimensional factor in the preceding expression for μ_i agrees with previous expressions for this parameter.     

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)].     

Temperature and pressure dependence of the elastic property of GeS2 glass

The sound velocities in GeS₂ glass have been measured by means of ultrasonic interferometry as a function of temperature or pressure up to 1.8 kbar. The bulk modulus K_s = 117.6 kbar and shear modulus G = 60.60 kbar were obtained for GeS₂ glass at 15°C and 1 atm. The temperature derivatives of both sound velocities and elastic moduli are negative :

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.54 × 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C,

$\text{(}\text{?ν}{}_1\text{?T}\text{)}$

_p =

$\text{?1.27× 10}{}^{\mathrm{?4}}\text{km}\text{sec}$

°C and

$\text{(}\text{?K}{}_{\mathrm{s}}\text{?T}\text{)}$

_p =

$\text{?1.27 × 10}{}^{\mathrm{?2}}\text{kbar}\text{°C}$

,

$\text{(}\text{?G}\text{?T}\text{)}$

_p = ?1.23 × 10^?2 kbar/°C,

$\text{(}\text{?Y}\text{?T}\text{)}$

_p = ?2.93 × 10^?2 their pressure derivatives are positive:

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T = 4.43× 10^?2km/kbar,

$\text{(}\text{?ν}{}_1\text{?P}\text{)}$

_T =

$\text{0.633 × 10}{}^{\mathrm{?2}}\text{km}\text{kbar}$

and (?K_s?P0)_T=6.81,

$\text{(}\text{?G}\text{?P)}{}_{\mathrm{T}}$

= 1.03, (?Y?T_T= 3.57. The Grüneisen parameter, γ_th= 0.298, and the second Grüneisen parameter, δ_s = 3.27, have also been calculated from these data. The elastic behavior of GeS₂ glass has proved to be normal despite the structural similarity among the tetrahedrally coordinated SiO₂, GeO₂ and GeS₂ glasses.     

Two-electron,one-photon transitions in nickel

The two emission lines, Kα₁α₃^h and Kα₂α₃^h resulting from the two-electron transitions $\text{1s}{}^{\mathrm{?2}}\text{→ 2s}{}^{\mathrm{?1}}\text{2p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ and $\text{1s}{}^{\mathrm{?2}}\text{→ 2s}{}^{\mathrm{?1}}\text{2p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}$ were resolved for elemental nickel. Their measured energies agree well with calculations. Their relative intensity $\text{I(Kα}{}_1\text{α}{}_3{}^{\mathrm{h}}\text{)/I(Kα}{}_2\text{α}{}_3{}^{\mathrm{h}}\text{) ≈}\text{3}\text{4}$ and their intensity relative to that of the Kα diagram lines is about 10^?4. This is some 10⁴ times larger than both theoretical results and the results of ion-atom collision experiments.     

Simultaneous diffusion of calcium and strontium in KCl single crystals

Concentration dependent diffusion coefficients for ⁴⁵Ca²⁺ and ⁸⁵Sr²⁺ in purified KCl were measured using a sectioning method. KCl was purified by an ion exchange — Cl₂?HCl process and the crystals grown under $\text{1}\text{6}$ atmosphere of HCl. The tracers were purified on small disposable ion exchange columns to remove precessor and daughter impurities prior to use in a diffusion anneal. Isothermal diffusion anneals were made in the temperature range from 451% to 669%C. At temperatures above 580%C (the lowest melting eutectic in this system) diffusion was from a vapor source: below 580%C surface depositied sources were used. The saturation diffusion coefficients. enthalpies and entropies of impurity-vacancy associations were calculated using the common ion model for simultaneous diffusion of divalent ions in alkali halides. In KCl the saturation diffusion coefficients D_S(ca) and D_s(Sr) are given by

$\text{D}{}_{\mathrm{s}}\text{(Ca) = 9.93 × 10}{}^{\mathrm{?5}}\text{exp(?0.592}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(1) and

$\text{D}{}_{\mathrm{s}}\text{(Sr) = 1.20 × 10}{}^{\mathrm{?3}}\text{exp(?0.871}\text{eV}\text{kT}\text{)}\text{cm}{}^2\text{sec}$

(2) for calcium and strontium, respectively. The Gibbs free energy of association of the impurity vacancy complex in KCl for calcium can be represented by

$\text{Δg(Ca) = ?-0.507 eV + (2.25 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

(3) and that for strontium by

$\text{Δg(Sr) = ?0.575 eV + (2.90 × 10}{}^{\mathrm{?4}}\text{eV}\text{\%K}\text{)T}$

. (4)     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

The electronic isotope shift in the A2Π-X2Σ+ bands of BeH,BeD and BeT

The 0-0, 1-1, 2-2, and 3-3 bands of the A²Π-X²Σ⁺ transition of the tritiated beryllium monohydride molecule have been observed at 5000 Å in emission using a beryllium hollow-cathode discharge in a He + T₂ mixture. The rotational analysis of these bands yields the following principal molecular constants.

$\text{A}{}^2\text{Π:}\text{B}{}_{\mathrm{e}}\text{= 4.192}\text{cm}{}^{\mathrm{?1}}\text{; r}{}_{\mathrm{e}}\text{= 1.333}\text{A}\text{?}$

$\text{X}{}^2\text{Σ:}\text{B}{}_{\mathrm{e}}\text{= 4.142}\text{cm}{}^{\mathrm{?1}}\text{; r}{}_{\mathrm{e}}\text{= 1.341}\text{A}\text{?}$

$\text{ω}{}_{\mathrm{e}}\text{′ ? ω}{}_{\mathrm{e}}\text{″ = 16.36}\text{cm}{}^{\mathrm{?1}}\text{; ω}{}_{\mathrm{e}}\text{′X}{}_{\mathrm{e}}\text{′ ? ω}{}_{\mathrm{e}}\text{″X}{}_{\mathrm{e}}\text{″ = 0.84}\text{cm}{}^{\mathrm{?1}}$

From the pure electronic energy difference (E_Π - E_Σ)_BeT = 20 037.91 ± 1.5 cm^?1 and the corresponding previously known values for BeH and BeD, the following electronic isotope shifts are derived

$\text{ΔE}{}_{\mathrm{e}}{}^{\mathrm{i}}\text{(}\text{BeH}\text{?}\text{BeT}\text{) = ?4.7 ≠ 1.5}\text{cm}{}^1\text{, ΔE}{}_{\mathrm{e}}{}^{\mathrm{i}}\text{(}\text{BeH}\text{?}\text{BeT}\text{) = ?1.8 ≠ 1.5}\text{cm}{}^1$

and related to the theoretical approach given by Bunker to the problem of the breakdown of the Born-Oppenheimer approximation.     

α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Φecчet ДИLcy;н boЛн Л sИЛ osцИЛЛЯtoΦo b ДЛЯ ИЗoЭЛeКtponnoЙ ПosЛeДoBateЛЬn ostИ Li

ФeйnмanoBsкaя диaгpaмnaя teчnи кa пpимenena для pasЧeta длen Bo лn и sил osцилляtopoB osnBoг и nикoto pыч neжnич Boэбyждennыч sstoяn ий Li-пoдoбnыч иonoB. passЧиtanы Bклaды ot диaгp aмм пepBыч пopядкoB длк nepeляtи Bиstsкoй эnepгии, peляtиBиstsкич пoпpaBoк и дипoл ьnыч matpиЧnыч matpиЧnыч элeme ntoB. Для pasЧeta peляtиBиstsкич пoпpaBoк был иsпoльэoBan oпepat op Бpeйta. pяд пo $\text{1}\text{z}$ для эnepгии пpe дstaBлen B sлeдyющeem Bидe

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

для дипoльnoгo matpиЧoгo элe

$\text{P =}\text{a}\text{z}\text{1+}\text{τ}{}_1\text{z}\text{+}\text{τ}{}_2\text{z}{}^2\text{.}$

ПoлyЧennыe Чиsлennяe эnaЧennы e эnaЧenия кoэффициentoB пpи z^k дaли Boэmoжnostь passЧиtatь длиnы Boлn и sилы osцилляtopoB пe peчoдoB 1s²2s ? 1s²2p, 1s²2s ? 1s²3p, 1s²2p ? 1s²3s, 1s²2p ? 1s²3d, 1s²3s ? 1s²3p, 1s²3p ? 1s²3d для Li-п oдoбnыч иonoB. peэyльtatы pasЧe ta spaBnиBaюtsя s экsпepиmentaльныmи для иэoэлeкtpnnoй пoлeдoBat eльnostи Li. Чopoшee soглasиe s экsпepиment aльnыmи (0,01–0,1%) дaet Boэmoжnostь naдetьsя, Чto pяд пo $\text{1}\text{z}$ sчoдиtsя д ostatoЧno быstpo.Feynman diagram techniques have been applied to the calculation of wavelengths and oscillator strengths of the ground state and of a number of low-lying excited states for Li-like ions (1s²2l, 1s²3l). Contributions have been calculated to the first order for the nonrelativistic energy, relativistic corrections and dipole matrix elements. Relativistic corrections have been obtained by computing the active 〈H_B〉 matrix. Numerical results for the $\text{1}\text{z}$ expansion are presented in the following form: for the energy,

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

for the dipole matrix elements,

$\text{P =}\text{a}\text{z}\text{1+}\text{τ}{}_1\text{z}\text{+}\text{τ}{}_2\text{z}{}^2\text{.}$

The results were used for calculations of the wavelengths and oscillator ofthe transitions 1s²2s ? 1s²2p, 1s²2s ? 1s²3p, 1s²2p ? 1s²3s, 1s²2p ? 1s²3d, 1s²3s ? 1s²3p, 1s²3p ? 1s²3d for Li-like ions. Results are compared with experimental data for the isoelectronic sequence of Li (Li I-SX IV). Good agreement with experimental data (0·01–0·1%) suggests that the $\text{1}\text{z}$-expansion converges rapidly.     

Semi-inclusive scaling for largepT events

We consider semi-inclusive reactions of the type p + p → (particle with large p_T) + n charged particles + neutrals, and propose the following scaling law

$\text{E}\text{d}{}^3\text{σ}{}_{\mathrm{n}}\text{d}{}^3\text{p}\text{=}\text{1}\text{(}\text{s}\text{)}{}^{\mathrm{k+1}}\text{H}{}^{\mathrm{2p}}\text{T}\text{s}\text{,}\text{n}\text{s}$

for the distribution function of the large-p_T particle produced in association with n charged particles. This scaling rule is shown to be consistent with present information on single-particle spectra and average associated multiplicities at large p_T. Also, we show that if the associated multiplicity were to continue to increase linearly with p_T, then moments of the multiplicity distribution would increase like powers of s.     

Correlations between neutral and charged pions in multiparticle production

We make a theoretical and phenomenological study of correlations between neutral and charged pions in multiparticle production in the framework of the so-called σ, π, ? and ?-? models. Following the method of Drijard and Pokorski, we express the predictions of various models in terms of the negative multiplicity distribution, which is known experimentally. In particular we compute the average number of $\text{π}{}^0\text{,}\text{n}{}_0\text{(n\_)}$, and the integral of π⁰?π⁰ correlations, f₀²(n_), as a function of the number of negative pions; we study also the total multiplicity distribution P(N) and its first two moments $\text{N}\text{and}\text{D}{}_{\mathrm{<mtext>tot</mtext>}}{}^2$. We show that with the present experimental accuracy neither $\text{n}{}_0\text{(n\_)}$ allow us to discriminate between the different models.     

On the mobility of very pure semiconductors at very low temperatures

The mobility μ of a very pure semiconductor at very low temperatures is investigated in terms of a model where electrons are scattered by charged impurities distributed uniformly in space, and the electron-electron interaction is taken into account by the Debye-Hueckel screening in the interaction potential. The equation for the current relaxation rate Γ, derived previously by the proper connected diagram expansion, incorporates the quasi-particle effect in a self-consistent manner. The solution of this equation at high carrier concentrations n yields the so-called Brooks-Herring formula. At lower concentrations, the solution deviates significantly from the latter. The solution is in general smaller than the standard expression for the rate based on the Boltzmann equation; and this is consistent with the existing conductivity data available. At the very low concentrations e.g. n = n₃ = 10¹³cm^?3 or lower for Ge, the mobility calculated is inversely proportional to the square-root of the impurity concentration n_s, and has a $\text{T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$-dependence (T: temperature).

$\text{μ = 0.3597\&z.xl;h}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{k(k}{}_{\mathrm{B}}\text{T)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{(ze)}{}^{\mathrm{?1}}\text{n}{}_{\mathrm{s}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}\text{m}{}^1{}^{\mathrm{<mtext>?3</mtext><mtext>4</mtext>}}$

, where k is the dielectric constant. The conductivity data directly comparable with this formula are not available at present. However, the quasi-particle effect which led to this peculiar concentration-dependence should also show itself in the cyclotron resonance width; there, experiment and theory both show the ${}_{\mathrm{n}}{}_{\mathrm{s}}$-dependence for very pure semiconductors.     

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.     

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.     

Structural connections between 148Sm and 149Sm nuclei

The ^{146, 148}Nd(α, χn) and ^{148, 150}Nd(³He, χn) reactions at E_α = 20–43 MeV and E_3He = 19–27 MeV, are used to study excited states in the ¹⁴⁹Sm₈₆ and ¹⁴⁹Sm₈₇ nucleides and consequently the low-spin odd-parity excitation. The mixing ratios and multipolarities of the most prominent transitions are deduced from the combined evidence of angular distribution and electron conversion data. The spin-parity assignments for most of the levels observed are established. In ¹⁴⁸Sm the ground state band extending to I^π = 10⁺ is predominantly populated. A negative-parity odd-spin band extending from I^π = 3^?through 11^? is also observed. The bands in ¹⁴⁸Sm are interpreted within the framework of the interacting boson approximation model. In ¹⁴⁹Sm positive-parity levels with spin up to $\text{25}\text{2}$ and negative-parity levels with spins up to $\text{21}\text{2}$ are observed. The predominant γ-decay proceeds via transitions associated with $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$, $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$, $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ intrinsic configurations. The branching ratios B(E1)/B(E2) are calculated and compared in both ¹⁴⁸Sm and ¹⁴⁹Sm nucleides. The B(E1)/B(E2) dependence on the value of Z for some N = 86 (as well as 88 and 84) isotones showing a minimum of Z = 64 was noted. A 4 ns high-spin isomer mainly decaying into the positive-parity band based on the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ state in ¹⁴⁹Sm is found. Experimental evidence is presented to interprete the $\text{1}\text{2}{}^{\mathrm{+}}$, $\text{15}\text{2}{}^{\mathrm{+}}$, … and $\text{9}\text{2}{}^{\mathrm{?}}$, $\text{13}\text{2}{}^{\mathrm{?}}$, …, ΔI = 2, sequences in ¹⁴⁹Sm as arising from the coupling of an $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ neutron to the octupole and quadrupole modes of the ¹⁴⁸Sm core nucleus. The absolute reaction cross sections for the ^{146, 148, 150}Nd(³He, χn) reactions have been determined for different bombarding energies. The mixing of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ shells is discussed in the framework of an axial-particle-rotor model calculation.     

Dynamical rescaling and universality of hadron structure functions

We argue that pion and nucleon structure functions differ principally due to their different numbers of quarks and different scales of confinement. The former generates an x rescaling while the latter, in QCD, gives rise to a Q² rescaling. Together these lead to the relation

with $\text{ξ}{}_{\mathrm{<mtext>N</mtext><mtext>\pi </mtext>}}\text{? 0.16}$, for x values away from the end points. This relation is in good agreement with data.