Elastic-constant measurements in solid argon at the melting point

The velocities of ultrasonic waves have been measured in solidified argon in the pressure range up to 6 kb (600 MPa). Shear wave velocities could be measured to temperatures very close to the melting point, such that both liquid and solid phases coexisted, $\text{(T?T}{}_{\mathrm{<mtext>m</mtext>}}\text{)}\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{<10}{}^{-5}$. The measurements show that neither the shear velocity tends to zero nor its derivative with temperature tends to -8 as T→T_m.     

Nuclear magnetic resonance and relaxation in liquid zinc

Measurements of the Knight shift K and the nuclear spin-lattice relaxation rate $\text{(}\text{1}\text{T}{}_{\mathrm{l}}\text{)}$ of Zn⁶⁷ are reported for liquid Zn. Measurements of K extend from 409°C (supercooled) to 700°C; measurements of $\text{(}\text{1}\text{T}{}_{\mathrm{l}}\text{)}$ cover the range 425 – 620°C. The Knight shift shows a weak positive temperature dependence attributed to thermal expansion. The reciprocal enhancement factor of the Korringa relation K(α) is found to increase with temperature from .77 ± .04 to .82 ± .04 in the range 425 – 620°C. The quadrupolar contribution to the relaxation rate was concluded to be very small with an estimated upper limit given by $\text{(}\text{1}\text{T}{}_{\mathrm{l}}\text{)}{}_{\mathrm{Q}}\text{≤ 15 sec.}{}^{\mathrm{-l}}$     

The law of corresponding states for metals

Using the similarity of the effective potentials seen by ions in metals a reduced phonon equation of state is derived. It is shown that the melting point T_m(0) and the atomic volume Ω₀ at T = 0 K and at p = 0 are suitable macroscopic parameters for scaling ? and σ characterizing the interatomic potentials of metals having similar structures. The temperature and pressure dependence of thermodynamical quantities reduced with the above parameters are discussed and the results are compared with the experiment. It is shown that the pressure dependence of the reduced thermodynamic quantities can be described by the pressure dependence of the scaling parameters T_m(p) and Ω₀(p).The general form of the reduced equation of state (containing the electronic contributions as well) obtained gives that the reduced pressure is a universal function of the following reduced variables: the volume, temperature, de Broglie wavelength, Gibbs free energy of electrons $\text{3}\text{5}\text{zE}{}_{\mathrm{fo}}\text{?}$ (E_fo is the Fermi energy at T = 0 K) and depe of the valence z as well. It is shown that $\text{E}{}_{\mathrm{fo}}\text{?}$ is a function of $\text{Ω}{}_{\mathrm{o}}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$ and $\text{(}\text{E}{}_{\mathrm{fo}}\text{/?}\text{)Ω}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ is approximately constant within the same sub-group of the periodic table.     

Specific heat of liquid 3He at 29.4 bar

The specific heat of liquid ³He has been measured from 4 to 300 mK. Even at very low temperature, it deviates from a pure γT behavior. The effective mass $\text{m}{}^1\text{= 5.8m}{}_3$ is in good agreement with previous results, but disagrees with recent measurements around T_A.     

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.     

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.     

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.     

Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field

We study the correlation function 〈σ₀^x(t)σ_n^x(0)〉 of the transverse Ising model in a critical field whose hamiltonian is $\text{1}\text{2}\text{Σ}{}_{\mathrm{l}}\text{{σ}{}_{\mathrm{l}}{}^{\mathrm{x}}\text{σ}{}_{\mathrm{l+1}}{}^{\mathrm{x}}\text{?σ}{}_{\mathrm{l}}{}^{\mathrm{z}}\text{}}$. At an arbitrary temperature T we relate the autocorrelation to a Fredholm determinant. Moreover at T = 0 the correlations are given by a Painlevé V function for all n. The long-time asymptotic behavior of this function is found and the connection problem is studied. This result contains oscillatory terms which are related to the density of states at the Brillouin zone boundary.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

Connections between thermodynamic quantities and vacancy and diffusion characteristics in binary metallic solid solutions

With the use of the similarity of interatomic potentials relations concerning vacancy and diffusion characteristics in disordered regular solid solutions have been derived. It has been shown that the vacancy concentration is constant along ifT_c(x) = T_A + (T_B ? T_A)x + 2ΔT_x(1?x), (T_A and T_B are the melting points of pure components A and B respectively, and ΔT is proportional to the excess enthalpy of mixing, x is the concentration of the atoms B) which is proportional to the binding energy of the crystal. The validity conditions of several empirical rules known in the literature are also analyzed. It has been found that the generalization of the well-known rule for self- and impurity diffusion in pure metals has the following form In $\text{D}{}_0{}^{\mathrm{z}}\text{(x) ～ p}\text{Q}{}^{\mathrm{z}}\text{(x)}\text{T}{}_{\mathrm{c}}\text{(x)}$ (Z = AorB) where p is a constant for alloys having identical structures (D₀^z(x) and Q^z(x) denote the preexponential factors and the activation energies respectively). The results calculated from the relations derived were compared with experimental data for tracer diffusion in the systems AgAu, CuNi (having slight deviation from regularity), Pb-Tl (showing ordering phenomena) and AlZn (clustering effects) and a good agreement was found.     

Surface cyclotron resonance in Si under uniaxial stress

The cyclotron resonance of inversion-layer electrons on (100)p-type Si is found to depend sensitively on an externally applied compressive stress. At low temperatures (T ? 10 K) we observe a considerable increase of the cyclotron mass m¹_c with stress S along the [001] direction. The effect is most strongly observed at low electron densities n_s. For $\text{S～1.5 × 10}{}^9\text{dyne}\text{cm}{}^2$ and n_s～2 × 10¹¹cm^-2 we obtain $\text{m}{}^1{}_{\mathrm{c}}\text{～0.4 m}{}_0$ instead of the expected 0.2m₀. Along with this change of $\text{m}{}^1{}_{\mathrm{c}}$ a strong narrowing of the resonance is noted. Raising the temperature gives an additional n_s- dependent increase of $\text{m}{}^1{}_{\mathrm{c}}$.     

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.     

Depinning by thermal fluctuations of the charge density wave in Peierls Fröhlich state

It is shown that the thermal fluctuations depin the charge density wave of the Peierls Fröhlich state pinned by impurities at absolute zero temperature. The critical temperature, T_d, of this depinning is estimated as $\text{T}{}_{\mathrm{d}}\text{= 0.55√}\text{m}{}^1\text{mγ}{}_0$ where m¹ and γ₀ are the mass of the collective mode and the pinning frequency at T = 0.     

Absorption spectra of Ni2+ in (NH4)2Mg(SO4)2·6H2O and Co2+ in Na2Zn(SO4)2·4H2O

Optical absorption spectra of Ni²⁺ in (NH₄)₂Mg(SO₄)₂·6H₂O and Co²⁺ in Na₂Zn(SO₄)₂·4H₂O single crystals have been studied at room and liquid nitrogen temperatures. From the nature and position of the observed bands, a successful interpretation could be made assuming octahedral symmetry for both the ions in the crystals. The splitting observed for ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band in Ni²⁺ and ${}^4\text{T}{}_{\mathrm{2g}}\text{(F)}$ band in Co²⁺ at liquid nitrogen temperature have been explained as due to spin-orbit interaction. The extra band observed at 16,325 cm^-1 in the case of Ni²⁺ at low temperature has been interpreted to be the superposition of vibrational mode of SO^2-₄ radical on ${}^3\text{T}{}_{\mathrm{1g}}\text{(F)}$ band. The observed band positions in both the crystals have been fitted with four parameters B, C, Dq and ζ.     

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.     

Neutral mesons with heavy quarks and mixing angles in the six-quark model

In the framework of the six-quark model, based on the gauge group SU(2)_L × U(1) we have obtained expressions for the amplitudes of $\text{K}{}^0\text{?}\text{K}{}^0\text{,}\text{D}{}^0\text{?}\text{D}{}^0\text{,}\text{B}{}^0\text{?}\text{B}\text{B}{}_{\mathrm{S}}{}^0\text{?}\text{B}{}_{\mathrm{S}}{}^0\text{,}\text{T}{}^0\text{?}\text{T}{}^0\text{and}\text{T}{}_{\mathrm{c}}{}^0\text{?}\text{T}{}_{\mathrm{C}}{}^0$ transitions at final 4-momenta of external lines Feynman box diagrams. We have estimated the correctness of using the approximation of extremely small 4-,omenta of valence quarks, composing K⁰-like mesons. The constraints for the parameters of the unitary matrix of weak charged currents have been found at arbitrary value of the t-quark mass. Estimates of numerical values for the mixing parameters and for the parameters of CP violation for neutral systems similar to $\text{K}{}^0\text{?}\text{K}{}^0$ are given.     

On the dynamics of itinerant electron magnets in the paramagnetic state

It is shown how disordered local-moment states, in a metal such as Fe, may be stabilized by constraining magnetic fields. Effective interaction parameters between moments are defined in terms of spin density functional theory. On removing the constraints the moments initially precess but then decay rapidly, the latter process leading to an energy width of S(q, ω) at large q of order $\text{(k}{}_{\mathrm{B}}\text{T}{}_{\mathrm{C}}\text{W)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, where T_C is the Curie temperature and W is the width of the d-band. T he consequences for neutron scattering experiments are discussed and the rather different case of Ni is considered.     

Intensities and pressure-broadened widths of CO2 R-branch lines at 15 μm from tunable laser measurements

Intensities and half-widths of individual lines, over the temperature range 200–325°K in the 15 μm bands of ¹²C¹⁶O₂, have been determined with a tunable diode laser spectrometer. Measurements were made on pure CO₂ and on dilute CO₂-in-N₂ mixtures on the R-branches of the 01¹0-00⁰0 and 02²0-01¹0 transitions. Intensities are approximately equal to those listed in the AFGL compilation. The pressure-broadened half-widths follow the general relationship $\text{b}{}_{\mathrm{L}}{}^0\text{(T) = b}{}_{\mathrm{L}}{}^0\text{(T}{}_0\text{) [}\text{T}{}_0\text{T}\text{]}{}^{\mathrm{n}}$ where n varies considerably from line to line but is always greater than $\text{1}\text{2}$.     

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.