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.     

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).     

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.     

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.     

Sequential two-photon spectroscopy of some ion-pair states of IBr

Molecular constants of the first E 0⁺ ion-pair state of IBr vapor have been determined using polarization-labeling spectroscopy applied to the sequential transitions E 0⁺ ← B′ 0⁺ ← X 0⁺, while the second f 0⁺ ion-pair state is reported and characterized for the first time. A least-squares, simultaneous analysis of data for the I⁷⁹Br and I⁸¹Br isotopes gives the following constants (in cm^?1) for I⁷⁹Br:

$\text{E}\text{state}\text{: T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 39487.32(12), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{= 119.518(21), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{ξ}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.2109(12)}$

,

$\text{ω}{}_{\mathrm{<mtext>e</mtext>}}\text{y}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 2.34(22) × 10}{}^{\mathrm{?4}}\text{, B}{}_{\mathrm{<mtext>e</mtext>}}\text{= 2.9701(14) × 10}{}^{\mathrm{?2}}$

,

$\text{α}{}_{\mathrm{<mtext>e</mtext>}}\text{= 5.43(59) × 10}{}^{\mathrm{?5}}\text{,}\text{and}\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 6.8(16) × 10}{}^{\mathrm{?7}}$

.

$\text{F}\text{state}\text{: T}{}_{\mathrm{<mtext>e</mtext>}}\text{= 45382.58(17), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{= 128.805(66), ω}{}_{\mathrm{<mtext>e</mtext>}}\text{ξ}{}_{\mathrm{<mtext>e</mtext>}}\text{= 0.3630(69)}$

,

$\text{ω}{}_{\mathrm{<mtext>e</mtext>}}\text{y}{}_{\mathrm{<mtext>e</mtext>}}\text{= ? 9.7(22) × 10}{}^{\mathrm{?4}}\text{, B}{}_{\mathrm{<mtext>e</mtext>}}\text{= 3.0073(30) × 10}{}^{\mathrm{?2}}\text{,}\text{and}\text{α}{}_{\mathrm{<mtext>e</mtext>}}\text{= 8.52(48) × 10}{}^{\mathrm{?5}}$

. Preliminary data for the first $\text{Ω}\text{= 1}$ ion-pair state, accessed in the sequence $\text{1(}{}^3\text{P}{}_2\text{) ← A(}\text{Ω}\text{= 1) ← X 0}{}^{\mathrm{+}}$, indicate that T_e is ?30 cm^?1 higher in energy than that of the E state.     

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):

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

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

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

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

     

“Forbidden” rotational spectra of symmetric-top molecules: PH3 and PD3

A millimeter-wave spectrometer having a sensitivity of 4 × 10^?10 cm^?1 in the 2-mm region has been constructed for observation of extremely weak millimeter-wave spectra of gases. It has been used to measure J → J, K = 0 ← 3 transitions in PH₃ and J → J, K = 0 ← 3 as well as K = ±1 ← ±4 transitions in PD₃. The B₀ and C₀ spectral constants (in MHz) are: for PH₃, B₀ = 133 480.15 ± 0.12 and C₀ = 117 488.85 ± 0.16; for PD₃, B₀ = 69 471.10 ± 0.03 and C₀ = 58 974.37 ± 0.05. The effective ground-state values obtained for the bond angle and bond length are: for PH₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.420}{}_0$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.34}{}_5$; for PD₃, $\text{r}{}_0\text{(}\text{A}\text{?}\text{) = 1.417}{}_6$ and $\text{α}{}_0\text{(}{}^{\mathrm{o}}\text{) = 93.35}{}_9$. The corresponding zero-point-average values were calculated to be: for PH₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4269}{}_9\text{± 0.0002}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.228}{}_7$; for PD₃, $\text{r}{}_{\mathrm{z}}\text{(}\text{A}\text{?}\text{) = 1.4226}{}_5\text{± 0.0001}$ and $\text{α}{}_{\mathrm{z}}\text{(}{}^{\mathrm{o}}\text{) = 93.256}{}_7\text{± 0.004}$. For both species, the equilibrium values are $\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{) = 1.4115}{}_9\text{± 0.0006}$ and $\text{α}{}_{\mathrm{e}}\text{(}{}^{\mathrm{o}}\text{) = 93.32}{}_8\text{± 0.02}$.     

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

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).     

Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.     

Molecular structure of phosgene as studied by gas electron diffraction and microwave spectroscopy: The rz structure and isotope effect

The r_z structure of phosgene has been determined by a joint analysis of the electron diffraction intensity and the rotational constants as follows: $\text{r}{}_{\mathrm{z}}\text{(}\text{CO}\text{) = 1.1785 ± 0.0026}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(}\text{CCl}\text{) = 1.7424 ± 0.0013}\text{A}\text{?}$, ∠_z;ClCCl = 111.83 ± 0.11°, where uncertainties represent estimated limits of experimental error. The effective constants representing bond-stretching anharmonicity have been obtained from an analysis of the isotopic differences in the r_z structure: $\text{a}{}_3\text{(}\text{CO}\text{) = 2.9 ± 0.9}\text{A}\text{?}{}^{\mathrm{?1}}$, $\text{a}{}_3\text{(}\text{CCl}\text{) = 1.6 ± 0.4}\text{A}\text{?}{}^{\mathrm{?1}}$. The equilibrium bond distances have been estimated from the r_z structure for the normal species and from the anharmonic constants to be $\text{r}{}_{\mathrm{e}}\text{(}\text{CO}\text{) = 1.1756 ± 0.0032}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(}\text{CCl}\text{) = 1.7381 ± 0.0019}\text{A}\text{?}$.     

The emission spectra of H35Cl+, H37Cl+, D35Cl+, and D37Cl+ in the region 2700–4100 Å

The $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}$ emission spectrum of HCl⁺ has been measured and analyzed for four isotopic combinations. These analyses extend previous work and provide rotational constants for the v = 0–2 levels of the ground state and for the v = 0–9 levels of the excited state. RKR potentials have been determined for both states, although the upper state could not be fitted precisely to such a model. Calculated relative intensities based on these potentials demonstrated that the electronic transition moment must change rapidly with lower state vibrational quantum number. Although considerable caution should be exercised in applying the concept of equilibrium constants to the $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}$ state, the following are the best estimates of these constants (in cm^?1) for the $\text{X}{}^2\text{Π}$ state of H³⁵Cl⁺: B_e = 9.9406, ω_e = 2673.7, A_e = ? 643.7, and $\text{r}{}_{\mathrm{e}}\text{= 1.315}\text{A}\text{?}$. For the $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}$ state of H³⁵Cl: T_e = 28 628.08, B_e ～ 7.505, ω_e ～ 1606.5, and $\text{r}{}_{\mathrm{e}}\text{= 1.514}\text{A}\text{?}$.     

Rotationally resolved spectra of two van der Waals states of I + Cl

Three-step optical resonance is used to execute state-selected transitions from the ground state of ICl to two van der Waals states, $\text{b(}\text{Ω}\text{= 1)}$ and $\text{b′(}\text{Ω}\text{= 2)}$, both of which correlate with the second dissociation limit, $\text{I}\text{(}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) +}\text{Cl}\text{(}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$, of ICl. Since the B(0⁺) state also belongs to this limit, three out of five states converging to I + Cl¹ are now accounted for. Principal constants of these states are: b′(2): T_e = 18275.84, ω_e = 31.093, ω_ex_e = 1.672, ω_ey_e = 0.0070, B_e = 0.034834, α_e = .001587, and D_e = 164.09 cm^?1; b(1): T_e = 18273.30, ω_e = 26.75, ω_ex_e = 0.882, B_e = 0.03579, q = 0.00084, and D_e = 166.63 cm^?1. In both states the equilibrium distance is near 4.2 Å, slightly greater than the sum of van der Waals contact radii, $\text{r}{}_{\mathrm{<mtext>I</mtext>}}\text{+ r}{}_{\mathrm{<mtext>Cl</mtext>}}\text{= 3.95}\text{A}\text{?}$. The large value of q in the b(1) state indicates that, in the basis set $\text{|j}{}_{\mathrm{a}}\text{j}{}_{\mathrm{b}}\text{j}\text{Ω}\text{〉}$ (a = I, b = Cl, j = j_a + j_b) the b(1) and b′(2) states belong to j = 1 and j = 2 “complexes,” respectively.     

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 theorems on the level order in potential models

We study the potentials of the form U(r)=?r^?1+λV(r), $\text{(}\text{d}\text{d}\text{r}\text{)(}\text{r}{}^2\text{d}\text{V}\text{d}\text{r}\text{)?0}$, and show that the energy levels satisfy the inequalities $\text{E(N}{}_{\mathrm{c}}\text{, l)?E(N}{}_{\mathrm{c}}\text{, l+1)}$ to first order in λ, where N_c denotes the coulombic principal quantum number and l the angular momentum. Similarly for potentials $\text{U(r)=r}{}^2\text{+λV(r), (}\text{d}\text{d}\text{r}{}^2\text{)}{}^2\text{V(r)?0}$, we prove to first order in λ that $\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{)?}\text{E}\text{?}\text{(N}{}_{\mathrm{H}}\text{,}\text{l}\text{+2)}$, where NH denotes the harmonic oscillator quantum number. In the latter case, we give also quantitative restrictions on the relative positions at the lth and (l+1)th states.     

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 $\text{B}{}_{\mathrm{e}}\text{= 19.9738(42) × 10}{}^{-3}\text{, α}{}_{\mathrm{e}}\text{= 5.602(84) × 10}{}^{-5}\text{, γ}{}_{\mathrm{e}}\text{= 1.02(41) × 10}{}^{-7}\text{, D}{}^{\mathrm{e}}{}_{\mathrm{J}}\text{= 3.040(74) × 10}{}^{-9}\text{cm}{}^{-1}\text{, and r}{}_{\mathrm{e}}\text{= 3.6470(5)}\text{A}\text{?}$.     

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.     

Thermochemistry of azide salts and the azide ion using direct minimisation equations to obtain the lattice energy of the univalent azide salts

The opportunity to test a new equation for the computation of the lattice energy and at the same time examine a disparity in the literature data for the enthalpy of formation of the azide ion, $\text{ΔH}{}^{\mathrm{\theta }}{}_{\mathrm{?}}\text{(}\text{N}{}_3{}^{\mathrm{?}}\text{) (}\text{g}\text{)}$ was the motivation for this study. The results confirm our earlier calculation and show the new equation to be reliable. Thermodynamic data produced in the study take values: $\text{ΔH}{}^{\mathrm{\theta }}{}_{\mathrm{?}}\text{(}\text{N}{}_3{}^{\mathrm{?}}\text{)(}\text{g}\text{) = 144}\text{kJ mor}{}^{\mathrm{?1}}$ΔH^θ_hyd(N₃^?) = ?315 KJ mol^?1 or ΔH^θ_hyd(N₃^?) = ?295 KJ mol^?1U_POT(NaN₃) = 732 kJ mol^?1U_POT(KN₃) = 659 kJ mol^?1U_POT(RbN₃) = 637 kJ mol^?1U_POT(CsN₃) = 612 kJ mol^?1U_POT(TIN₃) = 689 kJ mol^?1. The lattice energies of azides whose enthalpies of formation are documented have been calculated as well as the enthalpy of formation of the azide radical.