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.     

Rotational constants of the E O+g state of I2 determined by polarization spectroscopy

The resonant 2-photon E(O⁺_g) ← B(O⁺_g) ← X(O⁺_g) transition of I₂ vapor has been studied by polarization spectroscopy, leading to a rotational analysis of the ν = 0–15 vibrational levels of the E state. The principal constants determined are $\text{B}{}_{\mathrm{e}}\text{= 19.9738(42) × 10}{}^{-3}\text{, α}{}_{\mathrm{e}}\text{= 5.602(84) × 10}{}^{-5}\text{, γ}{}_{\mathrm{e}}\text{= 1.02(41) × 10}{}^{-7}\text{, D}{}^{\mathrm{e}}{}_{\mathrm{J}}\text{= 3.040(74) × 10}{}^{-9}\text{cm}{}^{-1}\text{, and r}{}_{\mathrm{e}}\text{= 3.6470(5)}\text{A}\text{?}$.     

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.     

Fourier spectrometry: Rovibrational analysis of an infrared 1Π → 1Σ system of yttrium monoiodide

The infrared spectrum of yttrium monoiodide has been excited in an electrodeless microwave discharge and explored between 2500 and 12 000cm^?1 with a high-resolution Fourier transform spectrometer. A unique system is observed (ν₀₀ = 9905.520 cm^?1), which we attribute to a ${}^1\text{Π}\text{→}{}^1\text{Σ}$ transition and an extensive analysis is made. Rovibrational constants are obtained for both states mainly from a simultaneous multiband fitting. This procedure is applied to the whole set of 2231 observed line wavenumbers in the 1-0, 0-0, and 0–1 bands, yielding a final weighted standard deviation of 0.0038 cm^?1. Furthermore, a partial analysis of the 2-0 and 3-1 bands is performed. The following equilibrium constants are derived (cm^?1):

$\text{ω′}{}_{\mathrm{e}}\text{=192.210 ω′}{}_{\mathrm{e}}\text{x′}{}_{\mathrm{e}}\text{=0.463}$

$\text{B′}{}_{\mathrm{e}}\text{=0.0399133 α′}{}_{\mathrm{e}}\text{=0.0001150}$

$\text{ω″}{}_{\mathrm{e}}\text{=215.815 ω″}{}_{\mathrm{e}}\text{x″}{}_{\mathrm{e}}\text{=0.514}$

$\text{B″}{}_{\mathrm{e}}\text{=0.0422163 α″}{}_{\mathrm{e}}\text{=0.0001125}$

High-order constants D_v and H_v are also calculated for the various vibrational levels (v′ = 0, 1, 2, 3; v″ = 0, 1).     

High resolution Fourier spectroscopy of P2 infrared emission spectrum: Analysis of two new systems b3Πg → w3Δu and A1Πg → W1Δu

The investigation of the emission infrared spectrum of P₂ was performed with a high resolution Fourier spectrometer. Two new electronic systems were attributed to b³Π_g → w³Δ_u and A¹Π_g → W¹Δ_u transitions. The molecular parameters are obtained by a complete fitting procedure. The main equilibrium constants of the new states are (in cm^?1):

$\text{ω}{}^3\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 243228.07 ω}{}_{\mathrm{e}}\text{= 591.3 ω}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.5}$

$\text{B}{}_{\mathrm{e}}\text{= 0.256040 δ}{}_{\mathrm{e}}\text{= 0.001409 D}{}_{\mathrm{e}}\text{= 19.0 X 10}{}^{\mathrm{?8}}$

$\text{W}{}^1\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 31096.64 W}{}_{\mathrm{e}}\text{= 627.206 W}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.331}$

$\text{B}{}_{\mathrm{e}}\text{= 0.2628 δ}{}_{\mathrm{e}}\text{= 0.0014 D}{}_{\mathrm{e}}\text{= 23 X 10}{}^{\mathrm{?8}}$

     

The near-ultraviolet and visible bands of antimony monofluoride

The near-ultraviolet and visible emission bands of the SbF molecule have been photographed at high dispersion and rotational analyses performed. The principal molecular constants (in cm^?1) obtained for ¹²¹SbF and ¹²³SbF are

$\text{X}{}_2\text{1:}{}^{121}\text{B}{}_{\mathrm{e}}\text{=0.2803;}{}^{123}\text{B}{}_{\mathrm{e}}\text{=0.2796;α}{}_{\mathrm{e}}\text{=1.93×10}{}_{\mathrm{?3}}$

$\text{a2:}{}^{121}\text{B}{}_{\mathrm{e}}\text{=0.2806;}{}^{123}\text{B}{}_{\mathrm{e}}\text{=0.2801;α}{}_{\mathrm{e}}\text{=1.87×10}{}_{\mathrm{?3}}$

$\text{B0}{}^{\mathrm{+}}\text{:}{}^{121}\text{B}{}_0\text{=0.2800;}{}^{123}\text{B}{}_0\text{=0.2791,}$

$\text{A0}{}^{\mathrm{+}}\text{:}{}^{121}\text{B}{}_0\text{=0.2385;}{}^{123}\text{B}{}_0\text{=0.2378,}$

$\text{A}{}_2\text{2:}{}^{121}\text{B}{}_{\mathrm{e}}\text{=0.2411;}{}^{123}\text{B}{}_{\mathrm{e}}\text{=0.2405;α}{}_{\mathrm{e}}\text{=1.65×10}{}_{\mathrm{?3}}$

$\text{A}{}_3\text{1:}{}^{121}\text{B}{}_{\mathrm{e}}\text{=0.2414;}{}^{123}\text{B}{}_{\mathrm{e}}\text{=0.2409;α}{}_{\mathrm{e}}\text{=1.70×10}{}_{\mathrm{?3}}$

     

The rotational analysis of the 1Π-X 1Σ+ system at 649.5 nanometers of zirconium oxide

A red-degraded band head, normally badly overlapped by the gamma system, $\text{A}{}^3\text{Φ}\text{- X′}{}^3\text{Δ}$, of zirconium oxide, appears in emission spectra of zirconium arcs and in absorption spectra of S-type stars and of frozen rare gas matrices containing zirconium. The emission band has been examined at high-resolution with the aid of separated zirconium isotopes. Identification of the band as 0-0 of a ${}^1\text{Π}\text{- X}{}^1\text{Σ}{}^{\mathrm{+}}$ system of zirconium oxide is confirmed by rotational analysis where the following constants (cm^?1) are obtained for ⁹⁰Zr¹⁶O:

$\text{B}{}_0\text{′(R,P) = 0.40142 D}{}_0\text{′(R,P) = 3.51 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{′(Q) = 0.40166 D}{}_0\text{′(Q) =3.52 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{″ = 0.42263 D}{}_0\text{″ =3.19 × 10}{}^{\mathrm{?7}}$

$\text{ν}{}_0\text{= 15383.81s}$

The Λ-type doubling in the ¹Π state and the question of whether $\text{X}{}^1\text{Σ}{}^{\mathrm{+}}$ or $\text{X′}{}^3\text{Δ}$ is the true ground state of ZrO are discussed.     

Oscillator strengths in the Cameron system of carbon monoxide

Relative oscillator strengths in the Cameron system of CO(a³Π ← X¹Σ) have been observed in absorption for six bands (υ′ = 0–5, υ″ = 0) with the result, normalized to the absolute (0, 0) band measurement of Hasson and Nicholls, $\text{?}{}_{00}\text{= (1.62±0.07) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{10}\text{= (1.96±0.09) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{20}\text{= (1.41±0.04) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{\mathrm{3\; 0}}\text{= (0.72±0.03) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{40}\text{= (0.31±0.02) × 10}{}^{\mathrm{?7}}$, $\text{?}{}_{50}\text{= (0.14±0.01) × 10}{}^{\mathrm{?7}}$. The density of CO was modulated with a motor-driven vacuum valve and synchronous fluctuations (?1 per cent) in the transmitted intensity detected with a lock-in amplifier. Peak pressure in the 21 cm absorption cell was approximately 10 torr. A curve of growth analysis was used to correct saturation effects by less than 3 per cent.     

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

Ground-state molecular constants of bideuterated methane

A rotational analysis of the satellite bands of the β system of ZrO gives the splittings in the triplet states. For the lowest triplet state X′³Δ, these splittings are:

$\text{δF}{}_{\mathrm{1,2}}\text{= 287.9 ± 0.1 cm}{}^{\mathrm{?1}}\text{,}$

$\text{δF}{}_{\mathrm{2,3}}\text{= 337.6 ± 0.4 cm}{}^{\mathrm{?1}}\text{.}$

     

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.     

Positron production by muon neutrinos BEBC filled with a neon-hydrogen mixture

For e⁺ energy > 0.3 GeV and 10 GeV < visible energy < 100 GeV we find that: (i) $\text{? = (v}{}_{\mathrm{\mu }}\text{+}\text{Ne}\text{→ μ}{}^{\mathrm{?}}\text{e}{}^{\mathrm{+}}\text{)/(v}{}_{\mathrm{\mu }}\text{+}\text{Ne}\text{→ μ}{}^{\mathrm{?}}\text{) = (0.41 ± 0.15)\%}$; (ii) 1.2 ± 0.5 neutral strange particles are produced per μ^?e⁺ event; (iii) the lifetime of possible positron-parent particles is < 3 × 10^?10 s (90% C.L.); (iv) the cross section for direct e⁺ production via the neutral current is < 0.2 times that via the charged current (90% C.L.); (v) the cross section for producing heavy leptons, L⁺, decaying into e⁺ … is < 0.7 × 10^?3 times that for μ^?production, implying M(L⁺) > 10 GeV.     

Spectra of the protonated rare gases

Hollow-cathode discharges in the rare gases mixed with small amounts of H₂ have been examined. Earlier results of Brault and Davis on the spectrum of ArH⁺ have been extended, and a new spectrum of KrH⁺ has been found. On the other hand, no emission spectra of HeH⁺, NeH⁺, or XeH⁺ were observed. Principal results for ⁸⁴KrH⁺ are (in cm^?1)

$\text{ω}{}_{\mathrm{e}}\text{=2494.7 B}{}_{\mathrm{e}}\text{=8.381}$

$\text{ω}{}_{\mathrm{e}}\text{χ}{}_{\mathrm{e}}\text{=48.5 α=0.267}$

     

Forbidden lines of the ν3 band of 13CH4: Ground-state constants

The ν₃ fundamental vibration-rotation band of carbon-13 enriched methane (¹³CH₄) was recorded using a high-resolution vacuum infrared grating spectrograph. Forbidden transitions of this band are reported for the first time. Of the nearly 900 transitions identified, 560 are forbidden transitions and 347 of the forbidden transitions have 11 ≤ J ≤ 18. Pairs of forbidden and allowed transitions having the same upper-state energy levels were used to calculate 550 independent differences between ground-state term values. From these data, a least-squares analysis was used to calculate the following values for ground-state structure constants and their standard deviations (in cm^?1):

$\text{β}{}^{\mathrm{O}}\text{hc}\text{= 5.240820 ± 0.000056}$

,

$\text{λ}{}^{\mathrm{O}}\text{hc}\text{=?(1.0856 ± 0.0015) × 10}{}^{\mathrm{?4}}$

,

$\text{?}{}^{\mathrm{O}}\text{hc}\text{= ?(1.4174 ± 0.0034) × 10}{}^{\mathrm{?4}}$

,

$\text{η}\text{hc}\text{= ?(1.73 ± 0.37) × 10}{}^{\mathrm{?11}}$

. The 550 values for the ground-state combination differences retained for analysis can be reproduced with an overall standard deviation of 0.0155 using the stated values for the structure constants. The note added in proof refines the above constants by including the newly observed microwave data.     

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 $\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{) +}\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{)}\text{is 34 700 cm}{}^{\mathrm{?1}}$.     

Two emission systems of BS

Two new systems of emission bands near 2100 and 3100 Å have been produced by a microwave discharge in B₂S₃ vapor. From the known X²Σ⁺ and A²Π_i states of BS, these systems have been assigned as E²Σ⁺ → X²Σ⁺ and E²Σ⁺ → A²Π_i. Constants in cm^?1 for the new state are

$\text{E}{}^2\text{∑}{}^{\mathrm{\pm }}\text{: T}{}_{\mathrm{e}}\text{= 47 929.3, B}{}_{\mathrm{e}}\text{= 0.671 (λ}{}_{\mathrm{e}}\text{= 1.752 A), α}{}_{\mathrm{e}}\text{= 0.008}$

,     

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)     

QED distributions for hard photon emission in e+e− → μ+μ−γ

The hard photon emission in e⁺e^? → μ⁺μ^?γ is investigated to order α³. Formulas for a number of distributions are obtained, when neglecting terms of order (m_e/?)² and (m_μ/?)². Both charge-even and charge-odd contributions are calculated. The total contribution to the charge asymmetry parameter

$\text{? =}\text{[}\text{d}\text{σ(θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{?}\text{d}\text{Oσ(π?θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{]}\text{[}\text{d}\text{σ(θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{+}\text{d}\text{σ(π ? σ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{]}$

does not exceed 5% for the c.m.s. energy 2? = 3 GeV.     

Analysis of the Raman spectrum of SF6

The Raman active fundamentals ν₁(A1g), ν₂(Eg), ν₅(F2g), and the overtone 2ν₆ of SF₆ have been investigated with a higher resolution and the band origins were estimated to be: ν₁ = 774.53 cm^?1, ν₂ = 643.35 cm^?1, ν₅ = 523.5 cm^?1, and 2ν₆ = 693.8 cm^?1. Raman and infrared data have been combined for estimation of several anharmonicity constants. The ν₆ fundamental frequency is calculated as 347.0 cm^?1. From the analysis of the ν₂ Raman band, the following rotational constants of both the ground and upper states have been calculated:

$\text{B}{}_0\text{= 0.09111 ± 0.00005}\text{cm}{}^{\mathrm{?1}}\text{; D}{}_0\text{= (0.16±0.08)10}{}^{\mathrm{?7}}\text{cm}{}^{\mathrm{?1}}$

;

$\text{B}{}_2\text{= 0.09116 ± 0.00005}\text{cm}{}^{\mathrm{?1}}\text{; D}{}_2\text{= (0.18±0.04)10}{}^{\mathrm{?7}}\text{cm}{}^{\mathrm{?1}}$

.