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.     

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.     

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 The previously unpublished rotational levels of Dieke and Heath for the $\text{A}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, B³Π_g and C³Π_u states are referenced to the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 anharmonic force field of phosphorus trifluoride from the millimeter wave spectra of vibrationally excited states

The millimeter rotational spectra of PF₃ have been recorded for all four excited fundamental vibrational states. A coriolis resonance between ν₁ and ν₃ results in anomalous distortion constants for these states and can be analyzed to yield $\text{|ζ}{}_{13}{}^{\mathrm{y}}\text{| = 0.392}$. The value of $\text{ζ}{}_{33}{}^{\mathrm{c}}$ is found to be 0.4194 which does not fit the coriolis sum rule due to anharmonic resonance. Equilibrium values for the centrifugal distortion constants are determined and have been used to find the harmonic force field. All available data is used to determine some of the anharmonic force constants.     

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.     

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.     

Excitation intensity dependence of shallow donor bound exciton luminescence in n-GaAs

Luminescence measurements were performed on high purity epitaxial n-GaAs $\text{(}\text{1 × 10}{}^{14}\text{cm}{}^3\text{< n <}\text{3 × 10}{}^{15}\text{cm}{}^3\text{)}$ for various excitation intensities I₀ in the range $\text{8 mW}\text{cm}{}^2\text{< I}{}_0\text{<}\text{4 W}\text{cm}{}^2$. The luminescence line corresponding to the radiative decay of the shallow donor bound exciton, (D⁰, X), broadens with increasing I₀ and appears as a doublet for $\text{I}{}_0\text{? 1}\text{W}\text{cm}{}^2$, while the two-electron replica of the (D⁰, X) remains a single narrow line. The doublet structure of the (D⁰, X) at elevated excitation levels is due to missing luminescence intensity in the center of the line as a consequence of low (D⁰, X) concentration in a layer extending 1–2 μm from the sample surface into the bulk. The low concentration of (D⁰, X) is attributed to capture of (D⁰, X) quanta into surface states, extending to lower energies from the Fermi level fixed by the shallow donors. Comparison of the present results with luminescence spectra obtained by various authors reveals, that unexplained spectral features in the (D⁰, X) region of n-GaAs reported in the literature are a consequence of high excitation intensity and correspond to the effect reported here. In partly compensated p-GaAs with donor concentrations as given above, the (D⁰, X) did not transform into a doublet structure even at $\text{W}\text{cm}{}^2$ excitation intensity.     

The effect of a non-minimally coupled scalar field upon classical thermodynamics

It is known that a scalar field that is non-minimally coupled to the geometry implies a varying gravitational “constant” G_eff, and hence a violation of the continuity equations, $\text{T}\text{?}{}^{\mathrm{ik}}{}_{\mathrm{;k}}\text{≠ 0}$, where $\text{T}\text{?}{}_{\mathrm{ij}}$ is the uncorrected energy-momentum tensor. This in turn upsets classical thermodynamics. 3he simplest resolution of this difficulty is to multiply all energetic quantities by $\text{G}{}_{\mathrm{<mtext>eff</mtext>}}\text{G}{}_{\mathrm{<mtext>N</mtext>}}$, where G_N is the newtonian gravitational constant. This modified thermodynamics is applied to the scalar-field version of the cosmological model of Zee, for which it is shown to cause restoration of the symmetry above some critical temperature T_c close to the Planck temperature. We also illustrate how the second law of thermodynamics is always obeyed, correcting a recent discussion by Davies.     

A study of 3He capture in light nuclei

Excitation functions at θ = 90° have been measured for ${}^{16}\text{O}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0?2,\; 3?5,\; 6}}\text{)}{}^{19}\text{Ne}$, ${}^{15}\text{N}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0,\; 1?4}}\text{)}{}^{18}\text{F}\text{,}{}^{14}\text{N}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0,\; 1,2,3}}\text{)}{}^{17}\text{F}$, and ${}^{20}\text{Ne}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0\; +\; 1}}\text{)}{}^{23}\text{Mg}$, in the range E_{3He = 3–19 MeV}. The first reaction has also been studied at θ = 40°. Excitation functions at 90° have also been measured for and ${}^4\text{He}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0\; +\; 1}}\text{)}{}^7\text{Be}$ for E_3He = 19–26 MeV. Angular distributions have been measured for the first four reactions.For the most excitation functions, a broad peak is observed, several MeV wide, centred at about E_x≈ 20 MeV. Superimposed on this, in some cases, are narrower peaks, with width ≈ 1 MeV. Energies and widths have been extracted for all resonances.Cluster-model calculations have been carried out, using methods similar to those which have proved successful for low-lying states in A= 18–19 nuclei. No satisfactory correspondence with the present results was found. The shell model has been used to calculate Γ_3He and Γ_γ for 1?ω excitations in the final nuclei. These generally show good agreement with the trends of the experimental data. The results are consistent with the excitation of the giant dipole resonance in ³He capture, but much more weakly than in proton capture.     

Medium-spin levels and the character of the 20.4 ns 132+ isomer in 145Gd

Levels of the N = 81 nucleus ¹⁴⁵Gd have been investigated by in-beam γ-ray and conversion electron spectroscopy with the ¹⁴⁴Sm(³He, 2n) reaction. Fourteen new low- and medium-spin states between 1.0 and 2.4 MeV excitation, the known yrast levels up to spin $\text{21}\text{2}{}^{\mathrm{+}}$, five other high-spin non-yrast states and a new 20.4 ns $\text{13}\text{2}$ isomer at 2200.2 keV in ¹⁴⁵Gd have been observed. The isomer decays via a fast 927.3 keV E3 transition with B(E3) = 48 ± 7 W.u. Another weaker decay branch is a mixed, strongly hindered E1 + M2 + E3 transition to the $\text{v}\text{h}{}^{\mathrm{?1}}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ state. We propose an octupole $\text{v}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{j}{}^{\mathrm{?2}}\text{× 3}{}^{\mathrm{?}}$ main configuration for the isomer, analogous to the 997 keV $\text{13}\text{2}{}^{\mathrm{+}}$ isomer in ¹⁴⁷Gd. The levels of ¹⁴⁵Gd are discussed on the basis of the spherical shell model.     

Lorentz contracted geometrical model

The model assumes that when two high energy particles collide each behaves as a geometrical object which has a Gaussian density and is spherically symmetric except for the Lorentz-contraction in the incident direction. Folding the two spatial distribution together we obtain the slope (b) of the elastic diffraction peak in terms of the c.m. velocities (β_i and β_j) and the sizes (A_i and A_j) of the two incident particles. These sizes are assumed to have the experimental s-dependence of σ_tot ∝ πA² for each reaction. The combined s-dependence of the σ_tot's and the β's gives the s-dependence of the elastic slope $\text{b}{}_{\mathrm{ij}}\text{(s) =}\text{1}\text{2}\text{(A}{}_{\mathrm{i}}{}^2\text{β}{}_{\mathrm{i}}{}^2\text{+ A}{}_{\mathrm{j}}{}^2\text{β}{}_{\mathrm{j}}{}^2\text{)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(s)}\text{σ}{}^{\mathrm{ij}}{}_{\mathrm{<mtext>tot</mtext>}}\text{(∞)}$. This formula agrees with the experimental slope for p-p, $\text{p}$-p, K⁺-p, K^?-p and π^±-p elastic scattering from 3 to 1500 GeV/c, with only 3 parameters: A_π² = 6.1, A_K² = 3.3 and A_p² = 10.5 (GeV/c)^?2.     

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.     

Resonance Raman effect in thiourea

Raman spectra of thiourea have been observed in H₂O and D₂O solutions with the exciting laser beams of 514.5, 488.0, 457.9, 363.8, 325.0, and 257.3 nm. The resonance Raman excitation profile of the 729-cm^?1 line has been examined in the region of the 237-nm absorption band ($\text{π}{}_{\mathrm{<mtext>CS</mtext>}}{}^1\text{← π}{}_{\mathrm{<mtext>CS</mtext>}}$) by use of a solvent shift of the absorption band instead of by changing the wavelength of the exciting beam. The depolarization degree of this line was measured and its overtone Raman line was also observed. On the basis of the results of these experiments, it has been concluded that the 729-cm^?1 Raman line, assignable to the CS stretching vibration, derives its intensity solely from the 237-nm band when it is excited at 257.3 or 325.0 nm. On exciting in the region 363.8–514.5 nm, however, contributions of the higher-frequency bands are predominant rather than the contribution from the 237-nm band. The Raman line at 1520 cm^?1 of thiourea-d₄ is assignable to the NCN antisymmetric stretching vibration. From its excitation profile, its intensity has been considered to come from a vibronic coupling between the excited electronic states of the 220-nm ($\text{π}{}_{\mathrm{<mtext>CS</mtext>}}{}^1\text{← π}{}_{\mathrm{<mtext>N</mtext>}}\text{? π}{}_{\mathrm{<mtext>N</mtext>}}$) and the 197-nm ($\text{π}{}_{\mathrm{<mtext>CS</mtext>}}{}^1\text{← π}{}_{\mathrm{<mtext>N</mtext>}}\text{+ π}{}_{\mathrm{<mtext>N</mtext>}}$) bands.     

Coupling supersymmetric Yang-Mills theories to supergravity

We extend the technique of Cremmer et al. to couple arbitrary chiral multiplets with supersymmetric Yang-Mills interactions to N = 1 supergravity. We present the general form of the lagrangian and the detailed form of the scalar potential is spelled out. In the case of N chiral multiplets, “minimally” coupled to supergravity, we derive, in the absence of gauge interactions, a model-independent mass formula Supertrace $\text{M}{}^2\text{= Σ}{}_{\mathrm{J}}\text{(?)}{}^{\mathrm{2J}}\text{(2J + 1)m}{}_{\mathrm{J}}{}^2\text{= 2(N ? 1)m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}^2$, where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the gravitino mass. A concrete example of the super Higgs effect involving N chiral multiplets is exhibited.     

Core polarization for M2 transitions in odd-A tin isotopes

The reduced M2 transition probabilities $\text{11}\text{2}{}^{\mathrm{?}}{}_1\text{→}\text{7}\text{2}{}^{\mathrm{+}}{}_1$ in the odd-A isotopes ^109–121Sn are found to reveal a specific behaviour. B(M2) values are calculated in the framework of the quasiparticlephonon model. The coupling of a quasineutron with the 2⁺, 3^? and 2^? one-phonon core excitation is taken into account. Inclusion of all one-phonon 2^? states up to 24 MeV in the wave functions of the excited states $\text{11}\text{2}{}^{\mathrm{?}}{}_1\text{and}\text{7}\text{2}{}^{\mathrm{+}}{}_1$ reduces the theoretical B(M2) values by 3–4 times as compared to the single-particle values. The specific B(M2) dependence on the mass number appears to be due to the pairing effect.     

Subject index for volume 88

The emission and excitation spectra of the aromatic thioketone xanthione have been measured in Shpolskii matrices at 15 K. Under these conditions a sharp and rich vibrational structure is observed in the lowest triplet and the first and second excited singlet states. The phosphorescence excitation spectrum places the origin of the T₁ ← S₀ transition at 15 143 cm^?1, while that of the $\text{S}{}_1\text{(n, π}{}^1\text{) ← S}{}_0$ absorption is tentatively assigned to the band at 16 093 cm^?1. The phosphorescence spectrum, which shows only a weak CS stretch vibrational band, is dominated by ring vibrations. In accordance with the previous analysis of ODMR measurements, it is suggested that T₁ and T₂ states are energetically very close, thereby resulting in a lowest triplet state of heavily mixed n, $\text{π}{}^1\text{-π}$, $\text{π}{}^1$ character. No mirror-image relationship is found between the relatively strong S₂ → S₀ fluorescence and the excitation spectrum of the $\text{S}{}_2\text{(π, π}{}^1\text{) ← S}{}_0$ transition. The latter is dominated by a long, pronounced 336-cm^?1 progression.     

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.     

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.     

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 $\text{(σ2p)}{}^2\text{(π2p)}{}^3\text{(π}{}^1\text{2p)}{}^2$.