Energies and orbital sizes for some Rydberg and valence states of the nitrogen molecule

Accurate SCF computations are reported on the Rydberg states of N₂ of electron configurations $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$, $\text{---1π}{}_{\mathrm{u}}{}^3\text{3σ}{}_{\mathrm{u}}$, and ---3σ_g2π_g, also on the valence states of the configuration $\text{---1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$. The Rydberg state calculations supplement those of Lefebvre-Brion and Moser. A comparison is made between the $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ states and the parallel set of states of the $\text{1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$ configuration. This comparison shows a sharp difference in the ¹Σ⁺ states of the two configurations, the ¹Σ⁺ state being very high in the latter but relatively low in the former configuration. Recknagel coefficients are given for the several states of the two configurations; as expected, these are much smaller for the $\text{1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ configuration. Also, the ¹Δ state is relatively lower for the latter configuration.     

Inclusive production of Ξ+ and Ξ− in K+ p interactions at 32 GeV/c

The inclusive production of $\text{Ξ}{}^{\mathrm{+}}$ and Ξ^? hyperons is investigated in K⁺ p interactions at 32 GeV/c. The production cross sections, 36.4±9 μb for the $\text{Ξ}{}^{\mathrm{+}}$ and 6.5±3 μb for the Ξ^?, are rising strongly with energy similarly to $\text{Λ}$ and Λ production in K⁺ p interactions. The $\text{Ξ}{}^{\mathrm{+}}$ are produced preferentially in the forward direction in the c.m.s., while the Ξ^? are produced dominantly backwards. The average transverse momenta and 〈p_T〉_Ξ^?=0.58±0.09 GeV/c.     

The infrared part of the C2 Phillips system (2.3–0.9 μm)

Line positions and molecular constants for the 0-0, 1-0, 2-0, 0-1, 2-1, 3-1, 0-2, 1-2, and 4-2 bands of the C₂ Phillips system ($\text{A}{}^1\text{Π}{}_{\mathrm{u}}\text{-X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$) are reported. Among them, five bands have not been reported previously. Rotational perturbations have been observed in the previously unobserved v = 1 level of the $\text{A}{}^1\text{Π}{}_{\mathrm{u}}$ state. This state is perturbed by the $\text{c}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state which was discovered by Ballik and Ramsay. These observations provide new information regarding the perturbing state. In particular, the minimum of the potential energy for the $\text{c}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state has been found to be at 9227.4 cm^?1 instead of 13 310 cm^?1, which was the previous T_e value for this electronic state.     

3Σu−-3Σu+ coupling in the O2B3Σu− predissociation

The role of $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ spin-orbit mixing in the O₂ Schumann-Runge predissociation is investigated. The $\text{2}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state is found to cross the $\text{B}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ state near 2.0 Å with an interaction matrix element of approximately 55 cm^?1. This state contributes to the widths of the Bv ≥ 6 levels, but introduces only small level shift perturbations. When the partial widths due to the ${}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{-}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ interaction are added to the previously calculated widths due to the ⁵Π_u, ³Π_u, and ¹Π_u states, reasonable agreement is obtained with experimental measurements on O¹⁶O¹⁶ and O¹⁸O¹⁸. The possibility of non-Lorentzian line profiles and the dependence of the width on rotational quantum number is investigated. The approximation of the spin-orbit matrix element by its value at the crossing point is shown to be a good approximation for calculating the second difference perturbations.     

Absolute vacuum ultraviolet absorption spectra of some gaseous azabenzenes

Absolute extinction coefficient and oscillator strength of pyridine, pyrimidine, pyrazine, and s-triazine were recorded with moderate resolution in the region of 3.5–9.5 eV. Analogous to ${}^1\text{A}{}_{\mathrm{<mtext>1</mtext><mtext>g</mtext>}}\text{→}{}^1\text{B}{}_{\mathrm{<mtext>2</mtext><mtext>u</mtext>}}$, ¹B_1u, ${}^1\text{E}{}_{\mathrm{<mtext>1</mtext><mtext>u</mtext>}}\text{π → π}{}^1$ transitions of benzene, several $\text{n → π}{}^1$ and Rydberg transitions are presented and discussed.     

Spectrum and structure of the He2 molecule: Characterization of the singlet and triplet states associated with the UAO's 4s, 4dσ, 4dπ, and 4dδ

The emission spectrum of the He₂ molecule has been rephotographed in the ～4000–～5700 Å region and the $\text{4d(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$, $\text{4d(}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^1\text{Π}{}_{\mathrm{u}}\text{,}{}^1\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$, $\text{4s}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^3\text{Π}{}_{\mathrm{g}}$ and $\text{4s}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ}{}^1\text{Π}{}_{\mathrm{g}}$ transitions analyzed. The 4dδj³Δ_u, 4dπj³Π_u, $\text{4dσj}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{4sh}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states have been characterized through v = 2 and the 4dδJ¹Δ_u, 4dπJ¹Π_u, $\text{4dσJ}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{4sH}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states for v = 0. The term levels for these perturbed and l-uncoupled states have been confirmed (a) by analyses of bands with common levels from Δv = 0, ±1 sequences and (b) by analyses of the transitions between the above states from 4d and 4s and the $\text{c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ and $\text{C}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ states associated with 3pσ. Molecular constants are reported which have been partially corrected for the effects of l-uncoupling and the homogeneous perturbations between the state pairs J, H and j, h.     

Electronic spectra and vibronic coupling of pyrazine

The absorption and fluorescence spectra of pyrazine have been observed in vapor, solution and crystal, and the vibrational structures have been analyzed in detail. The fluorescence spectrum consists of long progressions of the nontotally symmetric vibration ν₅(b_2g), and the absorption spectrum contains also the progression of the corresponding excited state vibration ν′₅(b_2g. However, the pattern of the latter progression is unusual because of the highly anharmonic nature of the potential of the ¹B^3u state, which may be expressed by a functional form containing a quadratic term in the normal coordinate. All the experimental results suggest that the known vibronic interaction between the ${}^1\text{B}{}_{\mathrm{3u}}\text{(n,π}{}^1\text{)}$ state and the ${}^1\text{B}{}_{\mathrm{1u}}\text{(π, π}{}^1\text{)}$ state through the vibration ν₂(b_2g) is strong. The vibronic coupling and the potential of the ¹B_3u state were found to be very sensitive to solvent.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

Laser-excited phosphorescence spectrum of C3S2 in an Ar matrix

The phosphorescence spectrum of C₃S₂ was observed in a low-temperature Ar matrix with excitation of an Ar⁺ laser. The spectrum consists of a very strong 0-0 band at 18 287 cm^?1 and well-resolved progressions in the ν₂, ν₅, ν₆, and ν₇ vibrations. Side bands were found on the high-energy sides of some transitions. The separation between the main and side bands is 23 cm^?1. Polarization analysis suggests that C₃S₂ is linear symmetric in the Phosphorescent state as in the ground electronic state. On the basis of symmetry considerations and a qualitative evaluation of spin-orbit coupling, the phosphorescent state is assigned to ³Σ_u^? with Σ_u⁺ and Π_u components split by spin-spin interaction. The Σ_u⁺ level is lower than the Π_u one by 23 cm^?1 and the main and side band emissions start from the Σ_u⁺ and Π_u levels, respectively. The Σ_u⁺ component seems to acquire allowed character from a ¹Σ_u⁺ state by spin-orbit coupling and from bent ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}\text{(}{}^1\text{B}{}_2\text{)}$ and ${}^1\text{Δ}{}_{\mathrm{g}}\text{(}{}^1\text{A}{}_1\text{+}{}^1\text{B}{}_2\text{)}$ states by ν₅ vibronic coupling. Mixing of the Σ_u⁺ and Π_u components through ν₅ is responsible for most of the side bands. The ν₅ frequency is estimated to be 160 ± 20 cm^?1 in the ³Σ_u^? state from the intensities of ν₅ progression bands and from the ground-state frequency, 411 cm^?1.     

Energy levels of low lying triplet states of N2 from infrared emission studies

A theoretical model used to describe the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ and B³Π_g states of N₂ is presented. Using recently acquired high resolution spectra of the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{→ B}{}^3\text{Π}{}_{\mathrm{g}}$ (0-0) band, rotational energy levels of the v = 0 vibrational levels of these two states are generated with this model. These levels are in excellent agreement with those obtained using a combination differences technique. The precision of the model generated levels is 0.01 cm^?1. The previously unpublished rotational levels of Dieke and Heath for the $\text{A}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, B³Π_g and C³Π_u states are referenced to the $\text{N}{}_2\text{X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ (v = 0, J = 0) ground level and tabulated here. Estimates of the precision of their work are made.     

Uniaxial stress effects on the 3.4 eV optical structure of silicon by schottky-barrier electroreflectance

The electroreflectance of Si under uniaxial stress has been measured in the 3.0–4.0 eV region at 77 K. The results indicate that the dominant structure in this energy region is attributed to Λ^v₃ → Λ^c₁ (or L^v_3′ → L^c₁ transition. The deformation potentials of these bands are determined to be $\text{D}{}^1{}_1\text{= -7 ± 3 eV,}\text{D}{}^3{}_3\text{= 4 ± 1 eV}\text{and}\text{D}{}^5{}_1\text{= 5 ± 2 eV}$.     

Lifetime of electronic states of CO2+

The radiative lifetimes of the $\text{A}\text{?}{}^2\text{Π}{}_{\mathrm{u}}$ and $\text{B}\text{?}{}^2\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ states of CO₂⁺ were measured by means of the delayed coincidence method. Excitation was performed by a pulsed electron beam incident on CO₂. The results of these measurements are 115 ± 5 nsec for the $\text{A}\text{?}{}^2\text{Π}{}_{\mathrm{u}}$ state and 126 ± 3 nsec for the $\text{B}\text{?}{}^2\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ state.     

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

N2+ bound quartet and sextet state potential energy curves

Potential energy curves for the ${}^4\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{u}}$, ${}^4\text{Π}{}_{\mathrm{g}}$ and ${}^6\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{g}}$ states of N⁺₂ that dissociate to N (${}^4\text{S}{}^0$) and $\text{N}{}^{\mathrm{+}}\text{(}{}^3\text{P)}$, have been determined from a complete active space self-consistent field calculation. The ${}^6\text{Σ}{}^{\mathrm{+}}{}_{\mathrm{g}}$ state is found to be significantly bound (D_e = 2.68 eV) with a minimum at 1.72 Å.     

The origin of 3.55 eV emission band of RbCl:Tl

Fluorescence spectra of KCl:Tl, RbCl:Tl and NH₄Cl:Tl under A band excitation at room temperature (300 K) and liquid nitrogen temperature (77 K) have been re-examined in order to ascertain the origin of the 3.55 eV emission band of RbCl:Tl. The emission band at RT is found to show two components and the weaker component becomes dominant at LNT. The observations are explained in terms of Patterson's model of two local environments for Tl⁺ ion. One of them is a Tl⁺ having local CsCl like environment. The 3.55 eV emission band at 300 K is assigned to electronic transition in the Tl⁺ having local CsCl like environment.     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%     

The spectrum of HeNe+

Discharges through mixtures of helium and neon show two band groups near 4250 and 4100 Å as first observed by Druyvesteyn. These bands, assigned to the HeNe⁺ ion by Tanaka, Yoshino, and Freeman, have been studied under high resolution and have been fairly completely analyzed. The upper state of the transition is a very weakly bound state resulting from $\text{He}{}^{\mathrm{+}}\text{(}{}^2\text{S) +}\text{Ne}\text{(}{}^1\text{S}{}_0\text{)}$. There are two lower states resulting from the two components of $\text{Ne}{}^{\mathrm{+}}\text{(}{}^2\text{P) +}\text{He}\text{(}{}^1\text{S}{}_0\text{)}$. The upper of these two (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) is also very weakly bound while the lower of the two, the ²Σ⁺ ground state, has a dissociation energy of 0.69 eV and an r_e value of 1.30 Å. All bands in both band groups show four branches designated R_ff, Q_ef, Q_fe, and P_ee. From their analysis the rotational constants in the various vibrational levels of the three electronic states have been determined. While no spin splitting in the B²Σ⁺ state has been found the ground state X²Σ shows a very large spin splitting and the $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state a very large $\text{Ω-type}$ doubling. The vibrational numberings in all these states were established by the study of the spectrum of ³HeNe⁺. At the same time the hyperfine structure observed in all lines of ³HeNe⁺ confirmed the nature of the upper state B²Σ⁺ as resulting from He⁺ + Ne, i.e., by charge exchange from the ground state. The ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ component of the ²Π state has not been observed, presumably because of low intensity.     

Magnetic circular dichroism of transition metal ions in solids—II K2NaGaF6: Cr3+

The absorption and MCD spectra of the ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}$, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{a}}$ and ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{1g}}{}^{\mathrm{b}}$ spin-allowed transitions of Cr³⁺ in K₂NaGaF₆ are reported. It is shown that transitions to the ${}^4\text{T}{}_{\mathrm{1g}}$. states are induced by T_1u vibratio the other spin-allowed transition, ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^4\text{T}{}_{\mathrm{2g}}$, there are three competing intensity mechanisms: electric dipole induced by T_1u vibrations, electric dipole induced by T_2u vibrations and magnetic dipole, and an estimate is made of the relative importance of these. The magnetic dipole ${}^4\text{A}{}_{\mathrm{2g}}\text{→}{}^2\text{E}{}_{\mathrm{g}}$ zero-phonon line is observed to be accompanied by a vibrational sideband for which the coupling is predominantly with T_2u vibrations. Other weak transitions are observed in MCD spectra and their origin briefly discussed.     

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: $\text{R = 0.99}\text{A}\text{?}\text{, 〈u}{}^2\text{〉}{}_{\mathrm{H}}\text{= 0.046}\text{A}\text{?}{}^2\text{, D}{}_{\mathrm{R}}\text{= 0.72}\text{meV}$.     

Analysis of the B′3Σu− → B3Πg (0,0) emission band of molecular nitrogen

The (0,0) band of the $\text{B′}\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{→ B}{}^3\text{Π}{}_{\mathrm{g}}$ emission (Infrared Afterglow) system of molecular nitrogen has been recorded with a resolution of 0.046 cm^?1 and a line position accuracy of 0.007 cm^?1. Six hundred and seventy-two lines are tabulated into a line list for the 1.53 μm (low-resolution) emission feature. Of these, 482 are assigned as members of the 27 branches of the B′ → B transition, while 150 are identified with the 1PG (3,6) band. Molecular constants for the v = 0 levels of the $\text{B′}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{?}}$ and B³Π_g states have been computed and tabulated.