Broken N=2 super Yang-Mills theories with a finite vacuum energy

It is shown that an explicit symmetry breaking of the N=2 ultra-violet finite super Yang-Mills theories through the addition of soft mass terms does not affect the finiteness of the vacuum energy above one loop. One-loop vacuum energy is finite provided the mass terms satisfy the sum rules Σ_J(2J+1)(−1)^2Jm_J^2K = 0 (K = 0, 1, 2).     

Loss calculations in weakly-guiding optical dielectric waveguides

The application of perturbation theory to a three-layer weakly-guiding slab waveguide composed of lossy dielectric media yields a simple formula for the attenuation coefficient α of a guided mode: α = (Σ³_i=₁a_iP_i)/ (Σ³_i= ₁P_i, where α_i, P_i are respectively the loss coefficient and model power in region i (i = 1, 2, 3). It is shown that this result can also be obtained from arguments based purely on geometric optics. The result is easily extended to apply to circularly-symmetric optical fibres where it yields confirmation of an earlier approximation for the power ratios P_i/(Σ²_i= ₁P_i).     

The pure rotational spectrum of ZnO in the XΣ and aΠi states

The pure rotational spectrum of ZnO has been measured in its ground X¹Σ⁺ and excited a³Π_i states using direct-absorption methods in the frequency range 239-514 GHz. This molecule was synthesized by reacting zinc vapor, generated in a Broida-type oven, with N₂O under DC discharge conditions. In the X¹Σ⁺ state, five to eight rotational transitions were recorded for each of the five isotopologues of this species (⁶⁴ZnO, ⁶⁶ZnO, ⁶⁷ZnO, ⁶⁸ZnO, and ⁷⁰ZnO) in the ground and several vibrational states (v = 1-4). Transitions for three isotopologues (⁶⁴ZnO, ⁶⁶ZnO, and ⁶⁸ZnO) were measured in the a³Π_i state for the v = 0 level, as well as from the v = 1 state of the main isotopologue. All three spin-orbit components were observed in the a³Π_i state, each exhibiting splittings due to lambda-doubling. Rotational constants were determined for the X¹Σ⁺ state of zinc oxide. The a³Π_i state data were fit with a Hund’s case (a) Hamiltonian, and rotational, spin-orbit, spin-spin, and lambda-doubling constants were established. Equilibrium parameters were also determined for both states. The equilibrium bond length determined for ZnO in the X¹Σ⁺ state is 1.7047 Å, and it increases to 1.8436 Å for the a excited state, consistent with a change from a π⁴ to a π³σ¹ configuration. The estimated vibrational constants of ω_e ∼ 738 and 562 cm⁻¹ for the ground and a state agreed well with prior theoretical and experimental investigations; however, the estimated dissociation energy of 2.02 eV for the a³Π_i state is significantly higher than previous predictions. The lambda-doubling constants suggest a low-lying ³Σ state.     

An exact result for the 1D random Ising model in a transverse field

It is shown exactly that for an N-site cyclic chain with hamiltonian H = ?Σ^N_i=1(γ_iS^x_i + J_iS^z_iS^z_iS^z_i+1), the gap in the excitation spectrum goes to zero when N → ∞ at the “critical point” given by the relation Π^N_i=1Γ_i = Π^N_i=1J_i.     

Rotational and vibrational temperatures of electronically excited BiN radicals in a chemiluminescent flame

Rotational and vibrational temperatures of electronically excited BiN radicals in a low-pressure Bi_x+N/N₂*/N₂+Ar chemiluminescent flame have been deduced from high-resolution Fourier-transform emission spectra. Bands of three electronic transitions, a³Σ⁺(a₁1)→X¹Σ⁺(X0⁺), b⁵Σ⁺(b₁0⁺)→X¹Σ⁺(X0⁺), and b⁵Σ⁺(b₁0⁺)→a ³Σ⁺(a₁1), were analysed to determine the optical temperatures in the a³Σ⁺(a₁1) and b⁵Σ⁺(b₁0⁺) states. The rotational temperatures characterising the rotational populations in the a₁1, v=0 and 1 states were determined from the a₁→X, 0-2, 0-3, 0-4, 1-1, and 1-2 bands. The b₁→X, 0-8 and 0-11 bands, and the b₁→a₁, 0-0 bands served to determine the rotational temperature of the radicals in the b₁0⁺, v=0 state. The temperatures derived from the various bands and transitions were well consistent and the mean rotational temperature was determined to be 353±18 K, which is close to the translational temperature of the gas.Vibrational temperatures of the radicals in the a₁1 and b₁0⁺ states were derived from band intensities of the a₁→X and from the b₁→X as well as b₁→a₁ systems, respectively. The Franck-Condon factors needed were calculated with RKR potentials deduced from literature values of the rotational and vibrational constants in the three states involved. The a₁1 vibrational temperature (336±21 K) was close to the rotational temperature, while the b₁0⁺ vibrational temperature (438±36 K) differed, likely due to the previously observed perturbation of the b₁0⁺ state.     

A New Study of the Perturbations in theA1Π State of PN

TheA¹Π–X¹Σ⁺system of the PN molecule has been reexamined via high resolution conventional spectroscopy, at higher rotationalJ-values than those in previous studies. It is shown that perturbations occurring in theA¹Π (v= 0 to 3) levels give access to information concerning the (e³Σ⁻,a³Σ⁺,d³Δ,C¹Σ⁻,D¹Δ) valence states. Of particular interest are (1) the strong spin–orbit interaction between thee³Σ⁻andA¹Π (v_A= 2) levels, yielding 17 rotational energy levels of thee³Σ⁻state, and (2) the triple crossing occurring between theA¹Π (v_A= 3),d³Δ, andC¹Σ⁻levels.     

New observations and analyses of the laser excited fluorescence of the A1Σu+-X1Σg+ bands of the Na2 molecule

A medium power (～50 mW, 6328 Å) HeNe laser is used to excite the A¹Σ_u⁺-X¹Σ_g⁺ fluorescence of the Na₂ molecule in a crossed heat pipe oven. The spectrum in the region 5800–8500 Å is recorded both photographically (3.4 M Ebert) and photoelectrically (GaAs detector) with an emphasis on accurate relative intensities and on the observation of higher vibrational levels in the ground state close to the dissociation limit. P and R doublets in four series originating from (v′ = 14, J′ = 45), (v′ = 16, J′ = 17), (v′ = 22, J′ = 86), and (v′ = 25, J′ = 87) levels are observed and identified. The first two series, known from earlier work, are extended further to longer wavelengths to include 13 to 17 additional ground-state vibrational levels. The latter two series are observed for the first time. They originate from higher J′ levels and span a wide range of v″ levels (0 ≤ v″ ≤ 48). Effective RKR potentials for specific J″ (= 17, 45, 86, and 87) quantum numbers of the ground state are constructed and from them the true (rotationless) potential energy curve (for X¹Σ_g⁺) is derived which (a) reproduces the RKR curve previously given by Kusch and Hessel and (b) extends the curve from 5.77 to 7.26 Å (outer turning point). The dissociation energy D_e is estimated from these data to be 6022 ± 21 cm^?1.     

Magnetic rotation observation of the C2b3Σg− ← a3Πu transition using a color center laser

The magnetic rotation observation of the C₂b³Σ_g^? ← a³Π_u Ballik-Ramsay system using a color center laser is reported. This is the first detection of this system in absorption. Three bands, 0 ← 1, 1 ← 2, and 2 ← 3, were identified in the spectral range 3650–4030 cm^?1. The last two bands were observed for the first time. In magnetic rotation many satellite lines (ΔN ≠ ΔJ) which would be very weak in normal absorption have been observed with intensity comparable to the main branch lines. This permits a slight improvement in the accuracy of some of the fine structure constants. A variety of lineshapes are observed for the various branches by magnetic rotation. Because the b³Σ_g^? fine structure is small, giving a partial overlap, the peak frequency of a magnetic rotation signal usually does not correspond to the center frequency of the normal absorption signal of that transition. A computer program has been written to predict magnetic rotation lineshapes and obtain the peak frequency displacements. Various observed and calculated lineshapes are displayed and compared.     

Experimental determination of the radiative lifetime of the 0, 1, 2, 3 vibrational levels of the B2Σ+ state in CO+

By observing the decay of intensity of vibrational bands of the B²Σ⁺ - X²Σ⁺ and B²Σ⁺ - A²Π_i systems, the lifetimes of the 0, 1, 2, 3 vibrational levels of the B²Σ⁺ state of CO⁺ has been measured. The values are respectively τ=(56.8±1.3), (61.6±0.9), (66.9±2.2) and (70.5±2.9) ns. The variation of the function R_e(r?) cannot be obtained from the lifetime values of the B²Σ⁺ state.     

Line-shape of the vibrational bands of the CN- UV emission spectra in alkali halide-cyanide mixed crystals

Measurements of the line-width of the vi$\text{b}$rational bands associated to the a³Π→X¹Σ⁺ electronic transition of the CN ion in alkali halide-cyanide mixed crystals at 2K–250K have been performed. It is obtained that the a³Π→X¹Σ⁺ electronic transition is coupled to a dominant mode of 110 cm^-1 with strength 1.2 in KCN_0.01C?_0.99. From the line-shape of the vibrational bands in all crystals at 4.2K it is suggested that this mode can be ident$\text{i}$fied with a breathing mode of the neighbouring alkali ions.     

High-resolution optogalvanic study of the c4(0)1Πu, c′5(0)1Σu+, and a″(0)1Σg+ Rydberg states of N2

A new optogalvanic technique with an rf discharge was applied to a high-resolution study of the Rydberg states of N₂. The Ledbetter band, c₄(0)¹Π_u ← a″(0)¹Σ_g⁺, and a new visible band, c′₅(0)¹Σ_u⁺ ← a″(0)¹Σ_g⁺, were studied at a Doppler-limited resolution of 0.05 cm^?1. A Doppler-free method was also applied to resolve overlapped lines. Precise wavenumbers were determined for the rotational transitions of the two Rydberg bands. The rotational and the centrifugal constants for the lowest Rydberg state, a″(0)¹Σ_g⁺, were determined to be B₀ = 1.913748(42) cm^?1 and D₀ = 6.088(99) × 10^?6 cm^?1, where the numbers in parentheses are the standard deviation and apply to the last digits.     

Description of negative parity yrast states in156Er

Positive and negative parity yrast states are studied in ₆₈ ¹⁵⁶ Er₈₈ with a particle number projected Hartree-Fock-Bogoliubov method constrained on an average angular momentum. The theory predicts a second anomaly of the positive parity yrast states due to the alignment of ah _11/2 proton pair. The double backbending in the negative yrast band is understood: AtJ ^π=9^? to 11^? it is due to the intersection of the (πg _7/27/2⁺)×(πh _11/27/2^?) and the (πi _13/21/2⁺)×(πh _9/23/2^?) 2q.p. bands. The second backbending found experimentally fromJ ^π=21^? to 23^? is connected with an alignment of ai _13/2 neutron pair of the core in the proton 2q.p. band.     

Spectroscopy of AlO: Combined analysis of the AΠi → XΣ and BΣ → XΣ transitions

A combined analysis of the A²Π_i → X²Σ⁺ and B²Σ⁺ → X²Σ⁺ band systems of AlO, involving 21,500 line assignments, has been performed. The analysis indicates that the previously reported γ values of the B²Σ⁺ state are questionable. The present analysis shows that γ(B²Σ⁺) ≈ 0.014 cm⁻¹, essentially independent of the vibrational level. The positive sign is consistent with second order interaction with the higher-lying C²Π_r and lower-lying A²Π_i states. It also appears that many of the previously reported γ and γ_D values of X²Σ⁺ (v > 0) are doubtful. In fact, γ(X²Σ⁺) is observed to become increasingly negative for v″ > 1, due to second order interaction with the low-lying A²Π_i state. The present results are based on models where the hyperfine structure of the ²Σ⁺ states has been taken into account explicitly. Intensity patterns of the branches of the B²Σ⁺ → X²Σ⁺ system have been shown to be influenced by the case bβ_S coupling in the ground state v = 0,1 levels. This gives rise to intensity differences of around 10 percent in the R₁/R₂ and P₁/P₂ doublet components. The synthesized intensity patterns are fully in accord with the F₁/F₂ assignments of the present work.     

An investigation of radiative transition probabilities for the A1Σu+-X1Σg+ bands of Na2

The absolute radiative transition probabilities are calculated for previously observed spontaneous emission from A¹Σ_u⁺ (v′,J′) → X¹Σ_g⁺ (v″, J″ = J′ ± 1) reported in the preceding paper and by Woerdman (Chem. Phys. Lett.53, 219 (1978)). The calculations employ accurate hybrid potential energy curves, based on Rydberg-Klein-Rees (RKR), ab initio and long-range results, and a hybrid transition moment function, based on ab initio calculations. These calculated probabilities are compared with the various experimental results; while overall agreement is reasonable, detailed differences do occur.     

Perturbation Facilitated Optical-Optical Double Resonance spectroscopy of the 6Li233Σg+, 23Πg, 13Δg,b3Πu,and a3Σu+ states

The technique, Perturbation Facilitated Optical-Optical Double Resonance, has provided spectroscopic access to and molecular constants for the 3³Σ_g⁺ (v = 1–9), 2³Π_g (v = 0–24), 1³Δ_g (v = 3–14), b³Π_u (v = 0–17), and a³Σ_u⁺ (v = 0–6) states of the ⁶Li₂ molecule. Perturbation Facilitated Optical-Optical Double Resonance takes advantage of two weak spin-orbit perturbations, A¹Σ_u⁺ (v = 2, J = 33) ∼ b³Π_u (v = 9, F₁, N = 32) and A¹Σ_u⁺ (v = 9, J = 20) ∼ b³Π_u (v = 15, F₁, N = 19), to excite from X¹Σ_g⁺ (v = 0 or 1) into single rotation-vibration levels of ³Λ_u (F₁ fine structure component only) via the spin-mixed intermediate levels. The ³Λ_u (F₁ only) states are sampled in resolved fluorescence spectra from Perturbation Facilitated Optical-Optical Double Resonance-populated ³Λ_g levels.     

A simple Fourier photopolarimeter with rotating polarizer and analyzer for measuring Jones and Mueller matrices

The classic and simplest polarimetric scheme of examining a “sample” by placing it between a pair of linear polarizers and observing the intensity of the transmitted light can be transformed into a powerful photopolarimeter if the two polarizers are synchronously rotated at different speeds and the transmitted flux is linearly detected and its periodic waveform Fourier analyzed. In particular, if the angular speed of rotation of one polarizer is ω and that of the other is 3ω, the detected signal has the waveform, i=a₀ + Σ⁴_n=1a_n cos nω_ft + b_n sin nω_ft, where ω_f=2ω is the fundamental frequency. The nine Fourier amplitudes a₀ and (a_n, b_n), n=1,2,3,4, to be derived by performing a discrete Fourier transform (DFT) of the signal i, determine all nine elements of the 3×3 submatrix M_3×3 obtained by deleting the fourth row and fourth column of the Mueller matrix M. If the sample is nondepolarizing, the absolute values of all the four elements of the equivalent Jones matrix $\text{J}\text{=(J}{}_{\mathrm{ij}}\text{)}$, i,j=1,2 and their angle differences θ_ij?θ₂₂ (where θ_ij=argJ_ij) can be determined.     

Excitation transfer between excited electronic states of the H2 molecule due to interaction with a CO2 Laser beam

A spectroscopic study of the band systemsG ¹ Σ _g →B ¹ Σ _u andI ¹ Π _g →B ¹ Σ _u of H₂ emitted by a glow discharge in H₂ gas showed that the populations of theG ¹ Σ _g (v, J) states decrease for the benefit of theI ¹ Π _u (v′, J′) states when the discharge is irradiated by a powerful CO₂ Laser beam (power density 70 kW/cm²). The effect is interpreted as an absorption process in which two Laser photons intervene according to the transition scheme:G ¹ Σ _g →B″¹ Σ _u →I ¹ Π _g. A change of the populations of excited electronic states should lead to a change of the populations of excited atomic states as well.     

Transition Probabilities in the BΣ-XΣ and the BΣ-AΠ Electronic Systems of MgO

Transition probabilities for the B¹Σ⁺-X¹Σ⁺ and the B¹Σ⁺-A¹Π electronic systems are presented for v=0-4 and J=0-150 in each electronic state. The functional form of the electronic transition moment for the B-X transition is taken from published ab initio results. The B-A moment is assumed to have the same form and is scaled using empirical branching ratio data. The R_e(r) are used with Rydberg-Klein-Rees (RKR) wavefunctions to calculate transition probabilities for v=0-4 and J=0-150. The RKR potentials were calculated based on empirical spectroscopic constants.     

On distribution over the cathode surface of the current due to positive ions in discharge with oscillating electrons

The mechanisms of processes determining distribution of positive ions on the cathode surface in a discharge with oscillating electrons are studied. At low pressures P≤5×10⁻⁵ torr over the entire range of anode length variation l _a=0.5–11 cm, the ion current distribution over the cathode radius J _i(r) features a single maximum in the center and drops steeply with distance from the axis. At pressures P=1–4×10⁻⁴ torr, the distribution J _i(r) for short anodes (l _a<6 cm) is similar to the previous one but, for long anodes (l _a=6–10 cm), new maxima at higher J _i values have been detected. A physical explanation for the obtained results is proposed.     

Rotational analysis of the a3Π-X1Σ+ bands of GaD

A new method of producing strong and clean emission spectra of the gallium hydride/deuteride molecule has been developed. Five bands belonging to the gallium deuteride molecule (GaD) have been photographed under high resolution. The rotational analyses of the bands lying at 5669.14 Å (0-0) and 5675.10 Å (1-1) in the a³Π₁-X¹Σ⁺ transition, 5761.0 Å (0-0) and 5766.20 Å (1-1) in the a³Π_0⁺-X¹Σ⁺ transition, and 5760.85 Å (0-0) in the a³Π_0⁻-X¹Σ⁺ transition have been performed. Accurate rotational constants (B, D) have been determined for the X¹Σ⁺, a³Π_0^± and a³Π_1^± states. The Λ doubling in the a³Π₀ (v = 0) and a³Π₁ (v = 0 and 1) states are obtained.