Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

The measurement of the rotational relaxation times of OCS from the nutation signals

The time dependence of microwave absorption was measured for the J = 2-1 and J = 3-2 transitions of OCS under on- and off-resonant conditions utilizing Stark and source modulation, respectively. The two effective pressure parameters obtained under the two conditions, which correspond to $\text{(T}{}_2{}^{\mathrm{?1}}\text{+ T}{}_1{}^{\mathrm{?1}}\text{)}\text{4πP}$ and $\text{(2πT}{}_2\text{P)}{}^{\mathrm{?1}}$, respectively, according to the Bloch equation, are different beyond experimental error; the difference $\text{(T}{}_2{}^{\mathrm{?1}}\text{? T}{}_1{}^{\mathrm{?1}}\text{)}\text{2πP}$ is 0.94 ± 0.38 (2.5σ) MHz/Torr for J = 2?1. This difference was also determined to be 1.19 ± 0.30 MHz/Torr from the dependence of the nutation frequency on the microwave power.     

Pressure dependence of dielectric constants of alums

The effect of hydrostatic pressure p on the low frequency dielectric constant ? has been investigated for 31 alums of different composition at 293 K in the pressure range between 0 and 7 kbar. The ?(p)-curves deviate from linearity. For almost all alums with symmetric ions the first-, second-, and third-order pressure derivatives of the dielectric constant obey the following relations:

$\text{(}\text{??}\text{?p}\text{)}{}_{\mathrm{T}}\text{< 0, (}\text{?}{}^2\text{?}\text{?p}{}^2\text{)}{}_{\mathrm{T}}\text{> 0, and (}\text{?}{}^3\text{?}\text{?p}{}^3\text{)}{}_{\mathrm{T}}\text{< 0}$

. The logarithmic volume derivative of the low frequency polarizability, $\text{(}\text{? ln α}\text{? ln V}\text{)}{}_{\mathrm{T}}$, is found to be quasi-invariant also in the isotypic crystal group of alums (Jarman's rule). For the cases, where piezooptical data are available, the optical and infrared contributions to the volume dependence of the polarizability are determined.     

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.     

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.     

Anomalous stoner enhancements in amorphous systems

An n-orbital model describing both elastic impurity scattering and exchange interaction is examined near its instability for itinerant ferromagnetism. At the critical point and at zero temperature, long range spin fluctuations cause anomalous enhancements of the density of states near the Fermi energy with $\text{?(E) - ?(E}{}_{\mathrm{F}}\text{) ∝ |E ? E}{}_{\mathrm{F}}\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ in three-dimensions (3D) and with ln²|E ? E_F| in 2D. An estimation of the conductivity $\text{σ(Ω)}$ in a continuum analog model reveals Ω^{$\text{1}\text{4}$} -and ln²$\text{|Ω}{}_{\mathrm{\tau }}\text{|}$-corrections in 3D and 2D respectively.     

Non-analyticity of the entropy and Nernst's law in random spin systems

It is shown explicitly for a soluble model that a random spin system can have an entropy which is non-analytic at (H = 0, T = 0), with $\text{(}\text{?S}\text{?H}\text{)}{}_{\mathrm{H=0}}$ and/or $\text{(}\text{?}{}^2\text{S}\text{?H}{}^2\text{)}{}_{\mathrm{H=0}}$non-vanishing in the T → 0 limit, while nevertheless Nernst's law is satisfied.     

Strengths and lorentz broadening coefficients for spectral lines in the ν3 and ν2 + ν4 bands of 12CH4 and 13CH4

Line strengths and self- and nitrogen-broadened half-widths were measured for spectral lines in the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ and ¹³CH₄ from 2870–2883 cm^?1 using a tunable diode laser spectrometer. From measurements made over a temperature range from 215 to 297 K, on samples of ¹²CH₄ broadened with N₂, we deduced that the average temperature coefficients n, defined as $\text{b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T) = b}{}_{\mathrm{<mtext>L</mtext>}}{}^0\text{(T}{}_0\text{)(}\text{T}\text{T}{}_0\text{)}{}^{\mathrm{?n}}$, of the Lorentz broadening coefficients for the ν₃ and ν₂ + ν₄ bands of ¹²CH₄ were 0.97 ± 0.03 and 0.89 ± 0.04, respectively. A smaller increase is observed in line half-width with increasing pressure for E-species lines, for both self- and nitrogen-broadening, than for other symmetry species lines over the range of pressures measured, 70 to 100 Torr.     

Activation energy of field emission flicker noise power due to adsorbed potassium on tungsten

The temperature dependence of the field emission flicker noise spectral density functions has been investigated for potassium adsorbed on tungsten (112) planes by a probe hole technique. By integration of the spectral density functions $\text{W(?) = B}{}_{\mathrm{i}}\text{?}{}^{\mathrm{?ge}}\text{i}$ the noise power $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ for different frequency intervals Δ? is obtained. From the exponential temperature dependence of $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ noise power “activation energies” q_Δ? are determined. Plots of these energies versus coverage show a similar “oscillating” behaviour as recently found for $\text{W(?}{}_{\mathrm{j}}\text{)}$ or which indicates phase transitions of the adsorbed potassium submonolayers. The noise activation energies are discussed in terms of existing models and a comparison is made between the experimental q values and surface diffusion energies E_d as determined by conventional methods.     

A new proof of the invariance principle in scattering theory

For free and interacting Hamiltonians, H₀ and H = H₀ + V(r) acting in L²(R³, dx) with V(r) a radial potential satisfying certain technical conditions, and for ? a real function on R with ?′ > 0 except on a discrete set, we prove that the Moller wave operators

exist and are independent of ?. The scattering operator

$\text{S = (Ω}{}^{\mathrm{+}}\text{)1Ω}{}^{\mathrm{?}}$

is shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. $\text{V(r) =}\text{sin}\text{r}\text{r}$ and many others.     

A measurement of the Ω− lifetime

In an experiment at the CERN-SPS charged-hyperon beam, a sample of $\text{2500 Ω}{}^{\mathrm{?}}\text{→ ΛK}{}^{\mathrm{?}}$ decays has been collected at Ω^? momenta of 98.5 and 115 GeV/c. The Ω^? lifetime is found to be $\text{τ}{}_{\mathrm{\Omega }}\text{= (0.822 ± 0.028) × 10}{}^{\mathrm{?10}}\text{s}$.     

On the nature of threshold electric field in quasi-one-dimensional commensurate charge-density-waves

The theory of nonlinear conductivity of commensurate charge-density-waves based on the soliton-tunneling mechanism is proposed. The well known empirical expression $\textcolor{red}{}\text{(}\text{E}\text{)=}\textcolor{red}{}{}_{\mathrm{N}}\text{+;(1?}\text{E}{}_{\mathrm{T}}\text{E}\text{)}\textcolor{red}{}{}_0\text{·}\text{exp}\text{(-}\text{E}{}_0\text{/(}\text{E}\text{?}\text{E}{}_{\mathrm{T}}\text{))θ(}\text{E}\text{?}\text{E}{}_{\mathrm{T}}\text{)}$ is obtained within the frames of self-consistent investigation taking into account the coherant Coulomb interaction of charged solitons. The threshold field $\text{E}$_T is the deconfinement field of bound soliton-antisoliton pairs. The universality relation $\text{E}{}_{\mathrm{T}}\text{ε(0)=}\text{const}$ ($\text{E}$(0) -static dielectric susceptibility) is also obtained. The phenomenological treatment of localized free charges explains the dependence $\text{E}$_T～²_i (;_i-impurity concentration).     

Inclusive π electroproduction in the deep inelastic region

Using 20.5 GeV electrons on protons, we measured inclusive π⁰'s (of transverse momentum, p_T, from 0 to 1.4 GeV/c) produced by virtual photons of energy, ν, from 4 to 16.5 GeV and four-momentum squared, q², from ?1.8 to ?8.5 (GeV/c)². Comparing with charged pion data, we find , supporting the quark model. Photon knockout of a quark is favored as the interpretation of these data because of scaling in z = E_π/ν and similarity in z-dependence of other pion production data. Consistent with this interpretation are the dependence of 〈p_T〉 on q², the azimuthal dependence, and fits to the constituent interchange model. We also observe a possible p_T^?4 dependence at large |q²| over a limited p_T range.     

A Mössbauer study of amorphous Fe40Ni40B20

Amorphous Fe₄₀Ni₄₀B₂₀ (VITROVAC 0040) alloy has been investigated using ⁵⁷Fe Mössbauer Spectroscopy. The Curie temperature T_c is found to be well defined and is 695 ± 1 K. The quadrupole splitting just above T_c is 0.64 mm sec^?1. The crystallization temperature is 698 ± 2 K, close to but definitely above T_c. The average hyperfine field H_eff(T) of the glassy state shows a temperature dependence of $\text{H}{}_{\mathrm{<mtext>eff</mtext>}}\text{(0)[1 ? B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{? C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{(T/T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{? …]}$ indicative of the existence of spin wave excitations. The values of $\text{B}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{C}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ are found to be 0.40 and 0.06, respectively, for T/T_c ? 0.72. At temperatures close to T_c, H_eff(T) varies as (1 ? T/T_c)^β where β is one of the critical exponents and its value is found to be 0.29 ± 0.02.     

Subject index for volume 88

The emission and excitation spectra of the aromatic thioketone xanthione have been measured in Shpolskii matrices at 15 K. Under these conditions a sharp and rich vibrational structure is observed in the lowest triplet and the first and second excited singlet states. The phosphorescence excitation spectrum places the origin of the T₁ ← S₀ transition at 15 143 cm^?1, while that of the $\text{S}{}_1\text{(n, π}{}^1\text{) ← S}{}_0$ absorption is tentatively assigned to the band at 16 093 cm^?1. The phosphorescence spectrum, which shows only a weak CS stretch vibrational band, is dominated by ring vibrations. In accordance with the previous analysis of ODMR measurements, it is suggested that T₁ and T₂ states are energetically very close, thereby resulting in a lowest triplet state of heavily mixed n, $\text{π}{}^1\text{-π}$, $\text{π}{}^1$ character. No mirror-image relationship is found between the relatively strong S₂ → S₀ fluorescence and the excitation spectrum of the $\text{S}{}_2\text{(π, π}{}^1\text{) ← S}{}_0$ transition. The latter is dominated by a long, pronounced 336-cm^?1 progression.     

Polarization spectroscopy of the E0g+-B0u+ band system of Br2

The E-B (0_g⁺-0_u⁺) band system of Br₂ has been investigated at Doppler-limited resolution using polarization labeling spectroscopy. Merged E state data for the three naturally occurring isotopes in the range v_E = 0–16, expressed in terms of the constants for ⁷⁹Br₂, are (in cm^?1) Y_0,0 = 49 777.962(54), Y_1,0 = 150.834(22), Y_2,0 = ?0.4182(28), Y_3,0 = 6.6(11) × 10^?4, Y_0,1 = 4.1876(28) × 10^?2, Y_1,1 = ?1.607(16) × 10^?4, and Y_0,2 = 1.39(39) × 10^?8. The bond distance is $\text{r}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.194}\text{A}\text{?}$, and the diabatic dissociation energy to $\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{) +}\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{)}\text{is 34 700 cm}{}^{\mathrm{?1}}$.     

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.     

Analysis of the 2770-Å emission system in I2

A weak emission spectrum of I₂ near 2770 Å is reanalyzed and found to to minate on the A(1u³Π) state. The assigned bands span v″ levels 5–19 and v′ levels 0–8. The new assignment is corroborated by isotope shifts, band profile simulations, and Franck-Condon calculations. The excited state is an ion-pair state, probably the 1g state which tends toward $\text{I}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{I}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_1\text{)}$. In combination with other results for the A state, the analysis yields the following spectroscopic constants: T″_e = 10 907 cm^?1, $\text{D}$″_e = 1640 cm^?1, ω″_e = 95 cm^?1, $\text{R″}{}_{\mathrm{e}}\text{= 3.06}\text{A}\text{?}$; T′_e = 47 559.1 cm^?1, ω′_e = 106.60 cm^?1, $\text{R′}{}_{\mathrm{e}}\text{= 3.53}\text{A}\text{?}$.     

Measurement of the background energy content of Nd-glass picosecond pulses with saturable absorbers

The background energy content of a mode-locked Nd-glass laser is determined with photodetectors and saturable absorbers. By comparing the signal height of a fast detector with the readout of an integrating energy meter the noise energy E_u2 outside the rise-time of the fast detector is measured. The background energy E_u1 within the rise-time is analysed by transmission measurements through two subsequent absorber cells. The obtained mean background to pulse energy (and intensity) ratios of ( and indicate a high degree of mode-locking.     

The electronic spectrum of gaseous SnS

Observations of the spectrum of SnS excited in chemiluminescence have led to the characterization of two low-lying excited states of SnS, $\text{a}\text{Ω}\text{1(}{}^3\text{Σ}{}^{\mathrm{+}}\text{)}$, with T_e = 18 143.9 cm^?1, and $\text{A0}{}^{\mathrm{+}}\text{(}{}^3\text{Π}\text{)}$, with T_e = 22 021.3 cm^?1. Extended rotational analyses of the perturbed bands observed in the absorption spectrum enable assignments to be suggested for the components $\text{Ω}\text{0}{}^{\mathrm{+}}$ and 1 of ³Σ^? and $\text{Ω}\text{1}$ of ³Π.