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.     

Density of states in dirty type II superconductors near Tc

We have determined the behavior of the density of states in the mixed state of superconducting alloys for T → T_c. The local density of states tends towards the BCS expression with the order parameter playing the role of the energy gap. The singularities are smeared out by the spatial average. The effective normal core radius of a vortex diverges like $\text{(1 ?}\text{T}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ for T → T_c unlike the coherence length which diverges like $\text{(1 ?}\text{T}\text{T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$.     

Anomalous stoner enhancements in amorphous systems

An n-orbital model describing both elastic impurity scattering and exchange interaction is examined near its instability for itinerant ferromagnetism. At the critical point and at zero temperature, long range spin fluctuations cause anomalous enhancements of the density of states near the Fermi energy with $\text{?(E) - ?(E}{}_{\mathrm{F}}\text{) ∝ |E ? E}{}_{\mathrm{F}}\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ in three-dimensions (3D) and with ln²|E ? E_F| in 2D. An estimation of the conductivity $\text{σ(Ω)}$ in a continuum analog model reveals Ω^{$\text{1}\text{4}$} -and ln²$\text{|Ω}{}_{\mathrm{\tau }}\text{|}$-corrections in 3D and 2D respectively.     

The spectrum and structure of the He2 molecule: Characterization of the triplet states associated with the UAO's 4pσ, 5pσ, and 6pσ

The emission spectrum of the He₂ molecule has been rephotographed in the ～3200–4100 Å region and the $\text{4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, $\text{5pσ k′}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{6pσ n}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ transitions analyzed. The g, k′, and n states, which have not been reported previously, are characterized through v = 1, 2, and 1, respectively. Several small accidental perturbations have been observed in the rotational manifolds of the k′ and n states.     

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.     

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.     

Rotational bands in 195, 197Tl

High-spin states in ^{195, 197}Tl have been populated with (α, xn) reactions and studied by means of in-beam γ-ray and e^? spectroscopic methods. Complementary studies of the decay of ^{195, 197}Pb to ^{195, 197}Tl have been carried out. Several new features have been observed in these nuclei. The $\text{9}\text{2}{}^{\mathrm{?}}$ bands of ^{195, 197}T1. extended to $\text{27}\text{2}{}^{\mathrm{(?)}}$ and $\text{29}\text{2}{}^{\mathrm{(?)}}$, respectively, show a quenching of energy spacings between the $\text{23}\text{2}{}^{\mathrm{?}}$, $\text{25}\text{2}{}^{\mathrm{?}}$, $\text{27}\text{2}{}^{\mathrm{(?}}$ and $\text{29}\text{2}{}^{\mathrm{(?}}$ states. This has been interpreted as resulting from the coupling of a $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton to the ($\text{π}\text{h}{}^{\mathrm{?2}}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{8+,\; 10+}}$ configurations in the core nuclei ^{194, 196}Hg. Furthermore, positive-parity bands based on $\text{15}\text{2}{}^{\mathrm{+}}$ states were established up to the $\text{35}\text{2}{}^{\mathrm{(+)}}$ and $\text{29}\text{2}{}^{\mathrm{(+)}}$ states in ^{195, 197}Tl respectively. Probably these bands originate from the coupling of a h${}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton to a broken neutron pair. This pair consists of a rotation-aligned $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron and a low-j neutron in the $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ or $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ shell. It is known to constitute the 5^? bands in ^{194, 196}Hg.     

Structure of positive parity states in 29P and two-step processes in (p,t) reactions

From a study of (p,t) reactions on ³¹P and ³⁰Si it is suggested that in ²⁹P the states with $\text{J}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}_1{}^{\mathrm{+}}$ and $\text{1}\text{2}{}_2{}^{\mathrm{+}}$, the pair $\text{3}\text{2}{}_2{}^{\mathrm{+}}$, $\text{5}\text{2}{}_1{}^{\mathrm{+}}$, and the pair $\text{7}\text{2}{}_3{}^{\mathrm{+}}$, $\text{9}\text{2}{}_1{}^{\mathrm{+}}$ are related by weak coupling of a s${}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ proton with the states 0₁⁺, 0₂⁺, 2₁⁺ and 4₁⁺ respectively of ²⁸Si. Completely atypical L = 2 angular distributions have been obtained for the $\text{3}\text{2}{}_1{}^{\mathrm{+}}$ and $\text{5}\text{2}{}_2{}^{\mathrm{+}}$ states in ²⁹P and it is suggested that this is due to contribution by two-step processes.     

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.     

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.     

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.     

Laser excitation spectra of He2

Metastable $\text{a(2sσ)}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ He₂ molecules are produced by a dc discharge in a flowing He stream. Laser excitation downstream of the discharge produces excitation spectra for a number of He₂ states. LIF spectra are observed for the $\text{(npπ)}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ series for n = 4–9, excepting 5 and the $\text{(npπ)}{}^3\text{Π}{}_{\mathrm{g}}$ series for n = 5–15.     

Energy levels of bound polarons

A new variational wave function to describe the ground state and the excited states of a bound polaron is proposed. It is of the form

$\text{|Ψ〉 = c|O〉|ø}{}_{\mathrm{n}}\text{〉 +}\text{∑}\text{g}{}_{\mathrm{k}}{}^1\text{V}{}_{\mathrm{k}}{}^1\text{(e}{}^{\mathrm{<mtext>i</mtext><mtext>k·r</mtext>}}\text{? ρ}{}_{\mathrm{k}}{}^1\text{)a}{}_{\mathrm{k}}{}^{\mathrm{+}}\text{|O〉|ø}{}_{\mathrm{n}}$

. It is argued that this form is reasonable for all electron—phonon coupling α and all strengths β of the Coulomb potential. Numerical and analytical results are derived for the energy of the ground state and compared to existing results. Results for the energy of the lowest p-type excited state of the bound polaron are obtained.     

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.     

Rotation-vibration analysis of the Coriolis-coupled ν5g, ν6g, ν8g and ν9 bands of H2CCO

Medium resolution infrared grating spectra of gaseous ketene, H₂CCO were recorded between 1000 and 400 cm^?1, both at instrument temperature (40°C) and with cooling (?40°C). Interferometric Fourier spectra were also measured at ?70°C with resolution 0.22 cm^?1 between 450 and 330 cm^?1. The K structure of the fundamentals ν₅, ν₆, ν₈, and ν₉ was assigned. These fundamentals are coupled by a-axis Coriolis interactions. These couplings were analysed on the symmetric top basis for setting up the perturbation matrix and by utilizing the K-dependent Coriolis shifts of levels. A preliminary analysis of the Coriolis intensity anomalies was also undertaken.Band center values from combination differences are $\text{ν}{}_5{}^0\text{= 587.30 (27)}$ and $\text{ν}{}_6{}^0\text{= 528.36 (39)}\text{cm}{}^{\mathrm{?1}}$. Synthetic spectra indicate the band origins of ν₈ and ν₉ to be close to 977.8 and 439.0 cm^?1, respectively. Estimates of Coriolis coupling constants obtained from synthetic spectra are $\text{ζ}{}_{58}{}^{\mathrm{a}}\text{= + 0.33 (5)}$, $\text{ζ}{}_{68}{}^{\mathrm{a}}\text{= + 0.714 (20)}$, $\text{ζ}{}_{59}{}^{\mathrm{a}}\text{= ? 0.774 (20)}$, and $\text{ζ}{}_{69}{}^{\mathrm{a}}\text{= ? 0.30 (2)}$. Approximate ratios of unperturbed vibrational transition moments obtained from spectral simulations are $\text{M}{}_8{}^0\text{:±iM}{}_5{}^0\text{:±iM}{}_6{}^0\text{:M}{}_9{}^0\text{≈ +2:?9:+10:+0.5}$.     

A further contribution to the theory of the transient hot-wire technique for thermal conductivity measurements

We study the density of states of a one-dimensional tightbinding electron model with random hopping elements. The Hamiltonian is $\text{H = -∑}{}_{\mathrm{i}}\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i+1}}\text{+a}{}^{\mathrm{+}}{}_{\mathrm{i+1}}\text{a}{}_{\mathrm{i}}\text{)}$, where the $\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}$'s are independent identically distributed random variables. It is proved that the single particle density of states D(E) diverges near E = 0 as $\text{1}\text{|(E}\text{log}{}^3\text{|E|)|}$.     

(f72)7,0−2 configuration high-spin states in 60Co strongly excited in the 62Ni(d, α) reaction

The ${}^{62}\text{Ni}\text{(}\text{d}\text{, α)}{}^{60}\text{Co}$ reaction has been studied with 78 MeV vector polarized deuterons. Angular distributions of the differential cross section and vector analyzing power have been measured for strongly populated states in ⁶⁰Co up to an excitation energy of 5 MeV. The transferred orbital and total angular momenta L and J were determined from the characteristic shapes of the differential cross sections and vector analyzing powers yielding a number of new spin assignments. The J^π = 7⁺ stretched configuration was found to be distr least over nine states located at 1.51, 3.09, 3.46, 3.67, 3.78, 4.04, 4.55, 4.70 and 4.80 MeV.     

Observed and calculated interactions between valence states of the NO molecule

No perturbation between two valence states of NO has ever been identified, although many valence-Rydberg and several Rydberg-Rydberg perturbations have been extensively studied. The first valence-valence crossing to be experimentally documented for NO is reported here and occurs between the ¹⁵N¹⁸O B²Π (v = 18) and B′²Δ (v = 1) levels. No level shifts larger than the detection limit of 0.1 cm^?1 are observed at the crossings near $\text{J = 6.5 [B}{}^2\text{Π}\text{(F}{}_1\text{) ～ B′}{}^2\text{Δ}\text{(F}{}_2\text{)]}$ and $\text{J = 12.5 [B}{}^2\text{Π}\text{(F}{}_1\text{) ～ B′}{}^2\text{Δ}\text{(F}{}_1\text{)]}$; two crossings involving higher rotational levels could not be examined. Semi-empirical calculations of spin-orbit and Coriolis perturbation matrix elements indicate that although the electronic part of the $\text{B}{}^2\text{Π}\text{～ B′}{}^2\text{Δ}$ interaction is large, a small vibrational factor renders the ¹⁵N¹⁸O B (v = 18) ? B′ (v = 1) perturbation unobservable. Semi-empirical estimates are given for all perturbation matrix elements of the operators $\text{Σ}{}_{\mathrm{i}}\text{a}\text{?}{}_{\mathrm{i}}\text{l}{}_{\mathrm{i}}\text{·s}{}_{\mathrm{i}}$ and $\text{B(L}{}_{\mathrm{\pm }}\text{S}{}_{\mathrm{?}}\text{? J}{}_{\mathrm{\pm }}\text{L}{}_{\mathrm{?}}\text{)}$ which connect states belonging to the configurations $\text{(σ2p)}{}^2\text{(π2p)}{}^4\text{(π}{}^1\text{2p)}$, $\text{(σ2p)(π2p)}{}^4\text{(π}{}^1\text{2p)}{}^2$, and $\text{(σ2p)}{}^2\text{(π2p)}{}^3\text{(π}{}^1\text{2p)}{}^2$.