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, $\text{R′}{}_{\mathrm{e}}\text{= 3.53}\text{A}\text{?}$.     

Optical absorption by neutral bound excitons

In this note we determine the oscillator strengths for the dipole absorption of neutral bound excitons in direct gap semiconductors, using our previously obtained 35-term Page and Fraser type wave function, and taking into account the detailed electronic structure as well as the electron-hole exchange interaction.The envelope part of the oscillator strengths varies considerably with the electron-hole mass ratio $\text{σ =}\text{m}{}^1{}_{\mathrm{e}}\text{m}{}^1{}_{\mathrm{h}}$, and is maximum for the (D⁰, X)- complex when σ = 0.4. For typical σ-values (σ? 0.1–0.2), . But when σ approaches zero, the overlapping of the electron and the hole envelope wave functions of the (A⁰,X)-complex decreases progressively so that the oscillator strength also decreases and tends to zero.In the case of zinc-blende materials (T_d) and positive spin-orbit coupling at $\text{k}\text{= 0}$, we confirm that the line strength for transitions to or from $\text{J =}\text{1}\text{2}\text{(Γ}{}_6\text{)}$ or $\text{J =}\text{5}\text{2}\text{(Γ}{}_7\text{+ Γ}{}_8\text{)}$ level of the (A⁰, X)-complex is equal to one quarter of the line strength to or from the $\text{J =}\text{3}\text{2}\text{(Γ}{}_8\text{)}$ level.In the case of CdS, where our computed values are only in qualitative agreement with the experimental values, we discuss the use of the phenomenological result of Rashba.     

Hyperfine structure of CH3OH

Hyperfine structure of the (0, 0, 1) - (1, 0, 1) transition of methanol has been investigated by beam absorption and of the (J, 1, 3?) → (J, 1, 3+) transitions for J = 2, 3, and 6 by beam-maser spectroscopy. The best-fit results for the spin-rotation and spin-spin coupling constants $\text{C}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$ and $\text{D}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$, respectively, are in kHz¹: $\text{C}{}_{101}{}^{\mathrm{(1)}}\text{= 2.4(10)}$, $\text{C}{}_{101}{}^{\mathrm{(2)}}\text{= ?0.6(10)}$, $\text{D}{}_{101}{}^{\mathrm{(1)}}\text{= ?13.8(9)}$, $\text{D}{}_{101}{}^{\mathrm{(2)}}\text{= 7.0(9)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(1)}}\text{= ?5.0(10)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(2)}}\text{= ?5.5(10)}$ and ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

The ultraviolet absorption spectrum of thioformaldehyde

The spectra of H₂CS and D₂CS were surveyed over the wavelength region from 230 to 180 nm and four distinct absorptions were identified. These are assigned to transitions from the $\text{X}\text{?}{}^1\text{A}{}_1$ ground state to the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π, π}{}^1\text{)}$, $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$, $\text{D}\text{?}{}^1\text{A}{}_1\text{(n, 3p}{}_{\mathrm{y}}\text{)}$, and $\text{E}\text{?}{}^1\text{B}{}_2\text{(n, 3p}{}_{\mathrm{z}}\text{)}$ electronic states. A vibrational and rotational analysis of the second system was undertaken. The results indicate that the molecule is planar in the $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$ state and that while the CH and CS bond lengths remain near their ground-state values, the HCH angle increases substantially.     

Overtone bands of 14N16O and determination of molecular constants

The wavenumbers of the rotation-vibration lines of ¹⁴N¹⁶O are reported for the (2-0) and (3-0) bands. The full set of spectroscopic constants for the three bands (1-0), (2-0), and (3-0) has been determined with the method developed by Albritton, Schmeltekopf, and Zare for merging the results of separate least-squares fits. The vibrational constants ω_e, ω_ex_e, ω_ey_e, and the vibrational dependence of the rotational constants have been deduced. The apparent spin-orbit constant $\text{A}\text{?}{}_{\mathrm{<mtext>v</mtext>}}$ and its centrifugal correction $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext>}}$ (including the spin-rotation constant) have a vibrational dependence of the following form: $\text{A}\text{?}{}_{\mathrm{v}}\text{=}\text{A}\text{?}{}_{\mathrm{e}}\text{? α}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{) + γ}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{)}{}^2$ and $\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>v</mtext>}}\text{=}\text{A}\text{?}{}_{\mathrm{<mtext>D</mtext><mtext>e</mtext>}}\text{? β}{}_{\mathrm{A}}\text{(v +}\text{1}\text{2}\text{) + δ}{}_{\mathrm{A}}\text{(v +}\text{built+1}\text{2}\text{)}{}^2$; the values of the constants in these two equations have been determined.     

Determination of the isotopic shift of the first resonance line in Cs(I) spectrum for the isotopes 131Cs, 132Cs,and 136Cs

The isotope shifts of the resonance line $\text{λ = 8521}\text{A}\text{?}$ of ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs with respect to ¹³³Cs were determined by a new scanning technique to be $\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{131}\text{Cs}\text{) = +1.70(40)}\text{mK}$, $\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{132}\text{Cs}\text{) = ?0.95(80)}\text{mK}$, $\text{v}\text{?}\text{(}{}^{136}\text{Cs}\text{)-}\text{v}\text{?}\text{(}{}^{133}\text{Cs}\text{) = ?4.0(3.0)}\text{mK}$. In accordance with results from other Cs isotopes and neighbouring elements they show the change 〈δr²〉 in the second radial moment of the nuclear charge distribution to be a factor of 5 to 10 smaller than expected from the model of uniform charge distribution. Integral isotope shifts over the isotopic chains of Xe, Cs, and Ba were analyzed in terms of collective models. Assuming an isotopic shift discrepancy of 0.5 for the nuclear volume shift it was possible to derive deformation parameters $\text{〈β}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in quantitative agreement with those from B(E2) measurements.     

Measurement of the excitation transfer rate between the n = 4 levels of hydrogen and deuterium

In a hydrogen-deuterium plasma of high purity the excitation transfer rate K^DH₄ for the process $\text{H}{}^1\text{(n = 4) +}\text{D}\text{(n = 1)→}\text{H}\text{(n = 1) +}\text{D}{}^1\text{(n = 4)}$ (n is the principal quantum number) has been measured by means of dye-laser fluorescence. Using an adequate numerical model, also the corresponding cross section σ^DH₄ could be determined.     

Reorientational motion of the OH− ion in cubic sodium hydroxide

The rotational motion of the OH^? ion was studied in cubic NaOH at 575 K with quasielastic incoherent neutron scattering. The data are compared to two simple models yielding values for the radius of rotation R, the translational mean square displacement 〈u²〉_H, the rotational jump rate τ^?1 and the rotational diffusion coefficient D_R. The following parameter values are obtained: (a) rotational jump model: $\text{R = 0.95}\text{A}\text{?}$, $\text{〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.052}\text{A}\text{?}{}^2\text{, τ}{}^{\mathrm{?1}}\text{= 2}\text{meV}$, (b) rotational diffusion model: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

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)     

Cross section of ion excitation in ion-ion collision

The “effective Feynman diagram” technique introduced in a previous paper is used to express the cross section of ion excitation in ion-ion collisions $\text{(A + B → A}{}^1\text{+ B)}$ in terms of the corresponding photon resonance absorption $\text{(hv + A → A}{}^1\text{)}$ and Thomson-scattering (hv + B → hv + B) cross sections. The result is checked for the process He⁺ + H(1s) → He⁺ + H(2p) with experiment and very good agreement is obtained.     

Infrared bands of 12C2HD

The rotational structure of about 40 bands of ¹²C₂HD observed in the region 6000?600 cm^?1 has been measured and interpreted with the purpose of determining a comprehensive set of molecular constants for this isotopic variety of acetylene. Combining these data with the results for ¹²C₂H₂ and ¹²C₂D₂, a reevaluation of the equilibrium internuclear distances for the acetylene molecule has been made: $\text{r}{}_{\mathrm{e}}\text{(CH) = 1.06215 ± 17 × 10}{}^{\mathrm{?5}}\text{A}\text{?}$ and $\text{r}{}_{\mathrm{e}}\text{(CC) = 1.20257 ± 9 × 10}{}^{\mathrm{?5}}\text{A}\text{?}$ were obtained. This paper presents all the molecular constants derived in this study.     

A least upper bound on the superconducting transition temperature

It is rigorously shown that the superconducting transition temperature of any material for which the Eliashberg theory is valid must satisfy k_BT_c ? 0.2309 A, where A is the area under its electron-phonon spectral function α²F(ω). This relation is a least upper bound, not just an upper bound, in the sense that there is an optimal situation in which the equality holds. This occurs when the Coulomb pseudopotential parameter $\text{μ}{}^1$ is zero and the spectral function is the Einstein spectrum Aδ(ω ? 1.750 A). These results are generalized in an approximate, but sufficiently accurate, way to the case $\text{μ}{}^1\text{≠ 0}$ to obtain the more useful least upper bound $\text{k}{}_{\mathrm{<mtext>B</mtext>}}\text{T}{}_{\mathrm{<mtext>c</mtext>}}\text{? c(μ}{}^1\text{) A}$ and the corresponding optimal spectrum $\text{Aδ[ω ? d(μ}{}^1\text{)A]}$. Numerical results for the functions $\text{c(μ}{}^1\text{)}$ and d(μ¹) are presented for $\text{0 ? μ}{}^1\text{? 0.20}$. It is shown that the T_c's of many materials (including Nb₃Sn), for which experimental values of A and $\text{μ}{}^1$ are available, do not lie very far below the upper bound.     

Nuclear orientation study of the excited states of 129I populated in the decay of 129gTe and 129mTe

From the angular distributions of γ-rays emitted by oriented ^129gTe and ^129mTe nuclei implanted in iron by isotope separator, unique spin assignments could be made for the excited states of ¹²⁹I at 487.4 keV $\text{(}\text{5}\text{2}{}^{\mathrm{+}}\text{)}$, 696.0 keV $\text{(}\text{11}\text{2}{}^{\mathrm{+}}\text{)}$, 729.6 keV $\text{(}\text{9}\text{2}{}^{\mathrm{+}}\text{)}$, 768.9 keV $\text{(}\text{7}\text{2}{}^{\mathrm{+}}\text{)}$, 1050.4 keV $\text{(}\text{7}\text{2}{}^{\mathrm{+}}\text{)}$ and 1111.8 keV $\text{(}\text{5}\text{2}{}^{\mathrm{+}}\text{)}$. In addition, E2/M1 amplitude ratios for the following ¹²⁹I γ-rays (energies are in keV) are derived: δ(459.6) = ?(0.076^+0.037_?0.148); δ(487.4) = 0.50^+0.17_?0.10 or δ^? = 0.35^+0.15_?0.09; δ(556.7) = 0.06±0.02 or δ^? = ?(0.10±0.02); δ(624.4) = 0.10±0.26 or δ^? > 0.4; the 696.0 keV γ-ray is pure E2; δ(729.6) = ?(0.34±0.06) or δ^?1 = 0.55±0.05; δ(741.1) = ?(0.27±0.10) or δ^?1 = ?(0.43±0.12); δ(817.2) = 0.46±0.04 or δ^?1 =0.20±0.03 if $\text{I}{}^{\mathrm{\pi }}\text{(845}\text{keV}\text{) =}\text{7}\text{2}{}^{\mathrm{+}}$; δ(1022.6) = ?(0.02 ±0.02) or δ^?1 = ?(0.23±0.02); $\text{δ(1084) = 0.56}{}^{\mathrm{+0.04}}{}_{\mathrm{?0.14}}$; δ(1111.8) = 0.06±0.05 or δ^?1 = ?(0.08±0.05). The anisotropy of the 531.8 keV γ-ray excludes $\text{1}\text{2}{}^{\mathrm{+}}$ as a possible spin assignment for the 559.6 keV level, so that no $\text{1}\text{2}{}^{\mathrm{+}}$ level is fed in the decay from ¹²⁹Te. Anisotropies for the 209, 250.7, 278.4 and 281.1 keV γ-rays are also measured. Comparison of the level scheme is made with theoretical predictions from both the pairing-plus-quadrupole model and the intermediate coupling unified model.     

Turbulent diffusion for the radial twist map

An analytical tool is given to study the statistical properties of the radial twist map, X_n+1 = X_n + α(Y_n+1) and Y_n+1 = Y_n + Af (X_n), with arbitrary rotation number α(Y) and arbitrary periodic force f(X). The case for which f(X) = sin 2 πX and with arbitrary α is treated in the region of large A. The turbulent diffusion coefficient D for the chaotic orbit relaxes as $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ to $\text{A}{}^2\text{4}$, except for the case of the standard map, where the eventual value of D is different from $\text{A}{}^2\text{4}$.     

Homogeneously broadened far-infrared absorption line due to the E → 2A transition of excited chromium ions in ruby

By use of far-infrared laser spectroscopy, we have found that for a high-quality ruby crystal at low temperature, the absorption line due to the electronic transition between the excited states $\text{E}\text{(}{}^2\text{E)}$ and $\text{2}\text{A}\text{(}{}^2\text{E) of Cr}{}^{\mathrm{3+}}$ ions is homogeneously broadened. From the linewidth (0.011 cm^-1) the lifetime of the 2ā level against emission of 29 cm^-1 phonons is obtained.     

Theoretical analysis of the centrifugal distortion contributions to the rotational spectra of 2Π diatomics

The centrifugal distortion contributions to the rotational energies of diatomic molecules are derived from the resolution of the vibration-rotation wave equation. The unknown radial dependence of the fine structure constants is taken into account by means of a Taylor expansion around the equilibrium distance. Hence, one obtains the expressions of the centrifugal corrections associated with each fine structure constant in terms of the equilibrium values of its radial derivatives. The case of ²Π states is examined in detail. The dependence of the centrifugal distortion effects upon the choice of the coupling scheme representation is exhibited and a ²Π energy matrix containing the centrifugal constants of any order is proposed. Such a matrix is appropriate to fit the data for any value of the rotational quantum number. The theoretical expressions of the energy levels are related to the experimental data and the correlations between the spin-orbit centrifugal and spin-rotation contributions are put in evidence. It is shown that very compact formulas can be derived allowing a straightforward evaluation of the successive radial derivatives of the spin-orbit function in terms of the spectroscopic data $\text{A}{}^{\mathrm{(1)}}\text{? ?α}{}_{\mathrm{A}}\text{(}\text{w}{}_{\mathrm{e}}\text{B}{}_{\mathrm{e}}\text{)}$; $\text{A}{}^{\mathrm{(2)}}\text{? ?(1 +}\text{α}{}_{\mathrm{B}}\text{w}{}_{\mathrm{e}}\text{2B}{}_{\mathrm{e}}{}^2\text{)A}{}^{\mathrm{(1)}}$; …. Application of these results to the case of several molecules is considered and discussed.     

A new electronic band system of PbO

The chemiluminescence spectrum of atomic Pb reacting with O₃ under single-collision conditions includes a series of 55 bands in the regions 450–850 nm. A vibrational analysis is obtained which shows emission is to the ground state of PbO from excited electronic states not previously analyzed. Forty-nine of the bands are assigned to the a(1)-X(0⁺) transition and the remaining six are tentatively identified as the forbidden b(0^?)-X(0⁺) transition. Both the a and b states are believed to be Hund's case (c) components of the ³Σ⁺ states arising from the configuration $\text{σ}{}^2\text{π}{}^3\text{π}{}^1$. The vibrational parameters of the a state are ν₄ = 16 029 ± 8, ω_e′ = 478.7 ± 1.9, and ω_ex_e′ = 2.292 ± 0.128 cm^?1, where the uncertainties represent two standard deviations of the least-squares fit. Emission is also observed from the PbO B state produced in the reaction of metastable Pb atoms with O₃. Using pulsed laser excitation, an attempt is made to determine radiative lifetimes. We find for the PbO A(0⁺) state τ = 3.74 ± 0.3 μsec, and for the PbO B(1) state τ = 2.58 ± 0.3 μsec, while for the a(1) state τ is estimated to be greater than 10 μsec. From the vibrational analysis, energy conservation arguments place a lower limits to the ground state dissociation energy of $\text{D}{}_0{}^0\text{(}\text{PbO}\text{) ≥ 3.74 ± 0.03}\text{eV}$ (86.2 ± 0.7 kcal/mole). For the Pb + O₃ reaction we find less than 1% of the products are PbO¹ molecules that emit in the visible. Correlations are made with the low-lying states of other Group IV chalconides based on the assignment of the PbO $\text{a}{}^3\text{Σ}{}^{\mathrm{+}}\text{(1)}$ state and the correspondence between the low-lying triplet states of PbO and CO.     

On the electronic spectrum of the Mo2 molecule observed after flash photolysis of Mo(CO)6

Absorption and emission spectra of Mo₂ were investigated using flash photolysis of the Mo(CO)₆ molecule. Tentative vibrational and rotational analyses of the ⁹⁸Mo₂ spectra were performed. For the ground state, ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ type was proposed with ω_e = 477.1 cm^?1, $\text{r}{}_{\mathrm{e}}\text{= 1.929}\text{A}\text{?}$, and D₀(Mo₂) = 95 ± 15 kcal mole^?1. The results were compared with theoretical calculations for Mo₂ and experimental results for Cr₂ obtained previously. It seems reasonable that the transition metal diatomic molecules of this type have a high bond order.     

Space-time symmetries and the gravitational-neutrino field equations in general relativity

We consider a neutrino field with geodesic rays in interaction with a gravitational field admitting a Killing vector field n^μ. It is found that for solutions of the Einstein-Weyl field equations the neutrino field ξ^A and the neutrino flux vector l^μ are restricted by the equations: $\text{L}{}_{\mathrm{n}}\text{ξ}{}^{\mathrm{<mtext>A\; =\; ?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{is}\text{ξ}{}^{\mathrm{A}}$ and $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= 0}$, whereas s is a real constant. In the case of pure radiation neutrino fields these equations become: $\text{L}\text{ξ}{}^{\mathrm{A}}\text{=}\text{case1}\text{2}\text{(p ? is)ξ}{}^{\mathrm{A}}$, $\text{L}{}_{\mathrm{n}}\text{l}{}^{\mathrm{\mu }}\text{= pl}{}^{\mathrm{\mu }}$, where p and s are in general real functions of the coordinates.