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.     

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.     

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.     

The Pomeron and the scaling law for partial wave amplitudes

From the scaling law for the s-channel partial wave amplitudes, which guarantees simultaneously t-channel unitarity at threshold t = 4μ² and s-channel unitarity, we derive: (i) The intercept α(0) of the Pomeron is always one, if α(4μ²) > 1. (ii) The total and the elastic cross sections are bounded from below for s → ∞.

where α(4μ²) and δ(4μ²) are the position and the type of te Pomeron singularity (J ? α(4μ²))^{?1?δ(4μ2) at t = 4μ2}. (iii) The type of the Pomeron singularity δ(4μ²) is restricted: either $\text{δ(4μ}{}^2\text{) ?}\text{1}\text{2}$ or $\text{δ(4μ}{}^2\text{) ?}\text{1}\text{2}$.     

Generalized renormalization group equation for period-doubling bifurcations

Given a mapping $\text{x → ?(λ,x)}$, whose bifurcation points accumulate at λ = Λ_∞, it is shown that the iterates $\text{(?α)}{}^{\mathrm{p\times }}\text{[?}{}^{\mathrm{2p}}\text{(Λ}{}_{\mathrm{\infty }}\text{?μ/δ}{}^{\mathrm{p}}\text{, X}{}_{\mathrm{\infty }}\text{+y/(?α)}{}^{\mathrm{p}}\text{)?X}{}_{\mathrm{\infty }}\text{]}$ converge to a function ψ(μ,y)asp→∞, where X_∞ maximizes $\text{?(Λ}{}_{\mathrm{\infty ,x}}\text{)}$. The function ψ is universal up to scaling in μ and y, and satisfies ψ(μ/δ,ψ(μ/δ,?y/α)) = ?α^?1ψ(μ,y). This result generalizes the well-known Feigenbaum universal function g(y) with g(g(?y/α)) = ?g(y/α, which is the special case for μ = 0.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Determination of the spectroscopic quadrupole moments of 131Cs, 132Cs and 136Cs

Nuclear spectroscopic quadrupole moments of the radioactive isotopes ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs have been determined from the hyperfine structure of the $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state by the level crossing method. The results including a Sternheimer correction are: $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{131}\text{Cs}\text{) = ?0.625(6)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = +0.508(7)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = +0.225(10)}\text{b}$. The quadrupole moments of all the Cs isotopes from A = 131 to A = 137 are recalculated. It is shown, that nuclear quadrupole moments of a specific isotope obtained from different atomic P-states only agree within the limits of error after application of the Sternheimer correction. The increase of Q_s with decreasing neutron number conforms with other observations and theoretical calculations stating that for elements around Z = 55 nuclear deformation develops below N = 82. The staggering of the sign of Q_s may be interpreted as consequence of an oblate-prolate degeneracy of the nuclear energy surface. Some magnetic moments have been slightly improved: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = 2.219(7) μ}{}_{\mathrm{<mtext>N</mtext>}}$, $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = 3.705(15)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetism).     

Search for parity-nonconservation effects in deep-inelastic μ-N interaction

The difference of the cross sections for deep inelastic scattering of muons with average momenta 21 GeV/c with right and left helicity at large angles, i.e., with large momentum transfer, has been measured. No statistically-significant dependence of cross sections on the longitudinal polarization of muons has been found, i.e. no parity-nonconservation effects in deep inelastic μN interaction have been observed. The magnitude of the cross-section asymmetry $\text{R =}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉 ? 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}\text{[〈σ}{}_{\mathrm{<mtext>R</mtext>}}\text{〉+ + 〈σ}{}_{\mathrm{<mtext>L</mtext>}}\text{〉]}$ may be represented as R = β〈Q²〉 = (? 4 ± 6) × 10^?3 〈Q², (GeV/c)²〉. The limitations G_o^(μ) = (+ 6 ± 10)G have been obtained for the constant G_o^(μ) of vector-axial interaction $\text{(}\text{G}{}_{\mathrm{<mtext>o</mtext>}}{}^{\mathrm{(\mu )}}\text{2}\text{) [}\text{μ}\text{γα(1 + γ}{}_5\text{)μ] J}{}_{\mathrm{\alpha }}{}^{\mathrm{<mtext>o</mtext>}}$ (hadron, V-A).     

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.     

On the validity of the scaling law for partial-wave amplitudes

It is shown that the scaling law for partial-wave amplitudes Im f^l(s) holds for lγ (√s/4μ) (α(4μ²)?1) log s, if the leading Regge singularity α(t) in the t-channel is bounded by

$\text{Re α(t) ? α(4μ}{}^2\text{+}\text{α(4μ}{}^2\text{)?1}\text{2μ}\text{(}\text{t}\text{?2μ)}$

and is smooth near t = 4μ² in the sense of eq. (4).     

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.     

On the oscillatory modes of quarks in baryons

The color bond structure of a quark-antiquark system is extended, in the long-range approximation, self-consistently to the baryonic three-quark bond structure for SU(3)_c and generally to the N-quark bond structure for SU(N)_c. The universal (N-independent) mass square eigenvalues for massless quarks are

$\text{M}{}^2\text{=(H}{}_{\mathrm{N}}\text{)}{}^2\text{?2m}{}_{\mathrm{\rho }}{}^2\text{∑}\text{α=1}\text{3N?3}\text{ν}{}_{\mathrm{\alpha }}\text{+}\text{constant}\text{, ν}{}_{\mathrm{\alpha }}\text{=0,1,2,…}$

.     

Constructing effective actions for N = 1 supersymmetry theories: Symmetry principles and ward identities

The implications of the anomalous superconformal Ward identities for the construction of effective actions describing the low-energy dynamics of supersymmetry theories are investigated. The results apply to any N = 1 supersymmetry theory with an anomaly structure,

$\text{D}{}^{\mathrm{<mtext>\alpha </mtext><mtext>?</mtext>}}\text{V}{}_{\mathrm{<mtext>\alpha </mtext><mtext>\alpha </mtext><mtext>?</mtext>}}\text{+2D}{}_{\mathrm{\alpha }}\text{S=0}$

, where $\text{V}{}_{\mathrm{<mtext>\alpha </mtext><mtext>\alpha </mtext><mtext>?</mtext>}}$ is the supercurrent and the chiral superfield S represents the anomaly.     

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).     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

Centrifugal distortion effects in the microwave spectrum of methylene cyanide

The rotational spectrum of methylene cyanide has been measured up to J = 62 and a total of 82 b-type transitions have been obtained. These data have been analyzed with a semirigid rotor Hamiltonian to give accurate rotational and centrifugal distortion constants. The rotational constants are (in MHz) $\text{A}$ = 20882.7537 ≠ 0.017, $\text{B}$ = 2942.3003. ≠ 0.0031, $\text{C}$ = 2616.7225 ≠ 0.0031 The quartic centrifugal distortion constants are (in MHz)

$\text{Δ}{}_{\mathrm{J}}\text{(1.855455 ≠ 0.014) x 10}{}^{\mathrm{?3}}\text{Δ}{}_{\mathrm{JK}}\text{= (?6.79218 ≠ 0.027) x 10}{}^{\mathrm{?2}}$

$\text{Δ}{}_{\mathrm{K}}\text{(8.621628 ≠ 0.013) x 10}{}^{\mathrm{?1}}\text{δ}{}_{\mathrm{J}}\text{= (4.892607 ≠ 0.016) x 10}{}^{\mathrm{?4}}$

$\text{δ}{}_{\mathrm{K}}\text{= (6.7501 ≠ 0.29) x 10}{}^{\mathrm{?3}}$

The uncertainties are twice the standard deviations in the constants obtained from the least squares analysis, and represent approximately 95% confidence limits.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

Stark effect in the torsio-rotational spectrum of propargyl mercaptan and SH bond moment determination

The Stark effect of rotational and torsio-rotational transitions of propargyl mercaptan has been analyzed. Assuming a dependence of the dipole moment components on the internal rotation angle of the type: $\text{μ}{}_{\mathrm{a}}\text{= μ}{}_{\mathrm{a}}{}^0\text{+ μ}{}_{\mathrm{a}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, $\text{μ}{}_{\mathrm{b}}\text{= μ}{}_{\mathrm{b}}{}^0\text{+ μ}{}_{\mathrm{b}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, and $\text{μ}{}_{\mathrm{c}}\text{= μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{sin}\text{α}$, the following values of the determinable quantities were obtained: $\text{μ}{}_{\mathrm{a}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.718 ± 0.003}\text{D}$, $\text{μ}{}_{\mathrm{b}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.495 ± 0.010}\text{D}$, and $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{= 0.809 ± 0.015}\text{D}$.The SH bond moment was also evaluated from $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}$ and compared with the SH bond moment of similar molecules.     

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.