The E-B band system of diatomic iodine

Sequential pump and probe pulses are used to excite state-selected E ← B ← X transitions in I₂ vapor, and the E ← B bands recorded by polarization-labeling spectroscopy at relatively high dispersion. Molecular constants and Dunham expansion coefficients Y_n,0 (n = 0–7), Y_n,1 (n = 0–3), and Y_n,2 (n = 0, 1) for the E state are obtained in the range 0 ≤ v_E ≤ 96, based on a global least-squares fit of 1050 assigned rotational transitions. Definite evidence is cited to show that the EO_g⁺ ion-pair state correlates diabatically with the ground state $\text{I}{}^{\mathrm{?}}\text{(}{}^1\text{S}{}_0\text{) + I}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{)}$ of the separated ions.     

A spectroscopic study of the D(0u+) ion-pair state of Br2 by the optical-optical double-resonance technique

An optical-optical double-resonance technique has been applied to study the D(0_u⁺) ion-pair state of Br₂ in a one-photon resonant three-photon absorption. The OODR transition proceeds through the high vibrational level of the B³Π(0_u⁺) state, which compromises a large Franck-Condon shift required for the excitation of Br₂ from the X¹Σ_g⁺ state to the D(0_u⁺) state. Dunham parameters of the D(0_u⁺) state, based on a global least-squares fit of 407 transitions (v′ = 0–16, J′ = 17–115), are Y₀₀ = 49928.443(41), Y₁₀ = 134.467(19), Y₂₀ = ?8.71(27) × 10^?2, Y₃₀ = ?3.36(10) × 10^?3, Y₀₁ = 4.2382(15) × 10^?2, Y₁₁ = ?1.061(36) × 10^?4, Y₂₁ = ?2.00(27) × 10^?6, and Y₀₂ = ?1.93(11) × 10^?8 for ⁷⁹Br₂ (all in cm^?1, and 3σ in parentheses). The single rovibronic fluorescence spectrum of the D(0_u⁺) state shows a transition terminating on the X¹Σ_g⁺ ground state, and establishes the absolute v′ numbering on the basis of the Franck-Condon factor calculations. The v′ = 2 and 3 levels of the D(0_u⁺) state are strongly perturbed due to the heterogeneous interaction with the 1_u state correlating with the same ionic products of the D(0_u⁺) state at the dissociation limit, $\text{Br}{}^{\mathrm{?}}\text{(}{}^1\text{S) +}\text{Br}{}^{\mathrm{+}}\text{(}{}^3\text{P}{}_2\text{)}$.     

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

On the multiplicity of hadrons in QCD jets

A three-loop calculation is presented for the jet multiplicity of produced slightly-off-shell gluons for a pure Yang-Mills theory. Planar and non-planar graphs are found to be equally important in an axial gauge. If the three-loop calculation is indicative of what happens at higher orders $\text{n}\text{(Q}{}^2\text{) ∝}\text{exp}\text{{[(}\text{2C}{}_{\mathrm{<mtext>A</mtext>}}\text{πb}\text{) 1}\text{n}\text{Q}{}^2\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{}}$ where C_A = 3 and $\text{b =}\text{(33 ? 2n}{}_{\mathrm{<mtext>f</mtext>}}\text{)}\text{12π}$ in QCD.     

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.     

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

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.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

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

The uniform and the strong topology on realizations of the algebra of polynomials

It is shown that under quite general assumptions on the operators A₁,…,A_n (unbounded, symmetric) and on the domain $\text{D}$ on the realization $\text{P}\text{(A}{}_1\text{,…,A}{}_{\mathrm{n}}\text{)}$ of the algebra of polynomials $\text{P}\text{(x}{}_1\text{,…,x}{}_{\mathrm{n}}\text{)}$, the strongest locally convex topology τ_st coincides with the uniform topology τ_$\text{D}$ as well as with the strong operator topology τ_s. In the case n = 2 some conditions are given, under which these general assumptions are fulfilled.     

Revised molecular constants,RKR potential,and long-range analysis for the B3Π(0u+) state of Cl2, and rotationally dependent Franck-Condon factors for Cl2 (BX1Σg+)

Literature data for the line frequencies of the B³Π(0_u⁺) ← X¹Σ_g⁺ transition of Cl₂ are fitted directly by least squares to obtain new molecular constants. The constants from individual bands are merged to obtain single-valued estimates of the rotational constants for each vibrational level of the B state. The results are combined with recent data from the B → X system in emission to obtain new RKR turning points for the B and X states, and Franck-Condon factors for the B-X system. The new constants are also used to provide revised long-range parameters for Cl₂(B) which differ from those of earlier work. In particular, the coefficient C₅ of the leading term in the inverse-power long-range potential is now found to be $\text{C}{}_5\text{= 1.16(2) × 10}{}^5\text{A}\text{?}{}^5\text{cm}{}^{\mathrm{?1}}$. Theoretical results for the variation of centrifugal distortion parameters for levels near dissociation are tested for D_v and H_v, and an extrapolation based on this behavior is used to facilitate determination of reliable B_v and G(v) values for the highest observed B-state levels.     

The B2Σ+ → A2Πi system of silicon nitride,SiN

The 440-nm violet-degraded ${}^2\text{Σ →}{}^2\text{Π}$ bands of SiN, which were previously assigned to a $\text{“K” → A}$ system, have been reanalyzed. These bands are shown to be Δv = 0, ±1 sequence bands of the B²Σ⁺ → A²Π system of SiN. The first reliable value of T_e(A²Π) = 994.4(1) cm^?1 has been obtained, and this determines the location of the D²Π and L²Π states with respect to the ground state. The B²Σ⁺, v = 7 and D²Π, v = 3 levels are shown to be mutually perturbing. A detailed study has been made of the perturbed X²Σ⁺, v = 8 level. The 6–8 band of the B → X system has been photographed at high resolution. A deperturbation of this band confirms T_e(A²Π), and provides the first experimental verification of the inverted nature of the A state.     

Franck-Condon factors and r-centroids for the (D1Π−X1Σ+) transition of SiS molecule using R-K-R-V potential

Turning points of the vibrating SiS molecule in the D¹Π and X¹Σ⁺ electronic states are evaluated using R-K-R-V method. Franck-Condon (FC) factors and r-centroids are computed for the $\text{(}\text{D}{}^1\text{Π?}\text{X}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$ transition of the molecule using wavefunctions appropriate to R-K-R-V potential energy curves. The results of the FC-factors vary in accordance with the estimated intensities and also satisfy the vibrational sum rule. The sequence difference Δr remains approximately constant in the computed r-centroids.     

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.     

An inequality for the trace of matrix products

In this paper we consider a product of n complex m×m matrices A_k (k=1,…,n) with singular values ∝^(k)_i ordered in decreasing magnitude. Using the spectral resolution for the operators $\text{A}{}^{\mathrm{dagger;}}{}_{\mathrm{k}}\text{A}{}_{\mathrm{k}}$, it is shown that $\text{|}\text{Tr}\text{A}{}_1\text{…A}{}_{\mathrm{n}}\text{|≤}\text{∑}\text{i=1}\text{m}\text{Φ}\text{i=1}\text{n}\text{α}{}^{\mathrm{(k)}}{}_{\mathrm{i}}\text{.}$This inequality is an extension of an inequality of von Neumann in the simple case that n=2. The necessary and sufficient condition for the equality sign to hold is established. Application of Hölder's inequality leads to further inequalities which can be useful in statistical mechanics.     

The A′(3Π2) state of ICl

Although $\text{A′(}{}^3\text{Π}{}_2\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$ is forbidden in near case c molecules the A′ ← X transition can be efficiently accomplished by the three-step sequence $\text{A′(}{}^3\text{Π}{}_2\text{) ← D′(2) ← A(}{}^3\text{Π}{}_1\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$. Transitions to a range of levels of A′, v_A′ = 2–38, have been recorded by this means, using J-selective polarization-labeling spectroscopy. Principal constants of the A′ state of I³⁵Cl are T_e = 12682.05, ω_e = 224.57, ω_eχ_e = 1.882, ω_ey_e = ?0.0107, B_e = 0.08653, and α_e = 0.000675 cm^?1. The A′ state is therefore similar in its physical characteristics to two other (relatively) deep states, $\text{A(}{}^3\text{Π}{}_1\text{)}$ and $\text{B(}{}^3\text{Π}{}_0\text{+)}$, of the 2431 configuration.     

The spectrum of HeAr+

Two band groups near 1450 Å, first observed by Tanaka, Yoshino, and Freeman (J. Chem. Phys.62, 4484–4496 (1975)) in discharges through mixtures of helium and argon and assigned by them to the HeAr⁺ ion, were studied under high resolution. Like the similar spectrum of HeNe⁺ previously investigated, the spectrum of HeAr⁺ is a charge transfer spectrum. The upper state B²Σ⁺ of both band groups is derived from $\text{He}{}^{\mathrm{+}}\text{(}{}^2\text{S) +}\text{Ar}\text{(}{}^1\text{S)}$ while the two lower states $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and X²Σ⁺ are derived from $\text{He}\text{(}{}^1\text{S) +}\text{Ar}{}^{\mathrm{+}}\text{(}{}^2\text{P)}$. All three states are very weakly bound, the two lower states even more weakly than the upper state. Unlike HeNe⁺ most of the HeAr⁺ bands are violet shaded. In the longward band group each band shows only three branches while in the shortward group there are four. The former observation shows that the $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state behaves like a ²Σ^? state with γ_v ≈ 0. The B, D, γ, p, and ΔG values of all states were evaluated. While the B_v values of upper and lower states are nearly equal, the D_v values are quite different and this difference accounts for the violet shading of most of the bands even when B′_v is slightly smaller than B″_v; it also accounts for some of the extraheads and linelike features in the rotational structure. As in HeNe⁺ the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ component of ²Π was not observed.