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).     

Investigation of the ν5 band of methylacetylene by infrared laser Stark and microwave spectroscopy

Microwave spectra have been studied in the ground and v₅ = 1 (CC stretching mode) states of methylacetylene. From these data, dipole moments and rotational and centrifugal distortion constants have been determined, as follows: μ_D⁽⁰⁾ = 0.7839 ± 0.0010 D, μ_D⁽⁵⁾ = 0.7954 ± 0.0010 D, B₅ = 8508.119 ± 0.003 MHz, D_J⁽⁵⁾ = 1.8 ± 0.2 kHz, and D_JK⁽⁵⁾ = 169 ± 1 kHz. Laser Stark spectra have been obtained for the ν₅ band of this molecule and from these spectra the following vibration-rotation parameters have been determined: ν₅⁰ = 93.27540 ± 0.00007 cm^?1, A₅ - A₀ = ?227.0 ± 2.3 MHz and D_K⁽⁵⁾ - D_K⁽⁰⁾ = ?0.05 ± 0.50 MHz. The higher-J and -K states of the v₅ = 1 state appear to be purturbed.     

The Stark and Zeeman effects in methyl silane

The Stark and Zeeman effects in methyl silane in the ground vibronic state have been studied in detail using the molecular-beam electric-resonance method. For a symmetric rotor without internal rotation, the rotational dependence of the effective dipole moment for matrix elements diagonal in J has been shown by Watson, Takami, and Oka to have the form μ_Q = μ₀ + μ_JJ(J + 1) + μ_KK². It is shown here that, to this order, a complete characterization of the Stark effect requires only one more parameter, namely, the effective anisotropy (α_| - α_⊥)_eff in the polarizability. From Stark measurements alone, the true anisotropy cannot be separated from the additional dipole distortion constant shown by Aliev and Mikhaylov to enter dipole matrix elements off-diagonal in J. By studying nine different transitions (J, K, m_J) → (J, K, m_J ± 1) in CH₃²⁸SiH₃, values were obtained for the four Stark parameters: μ₀ = 0.7345600(33) D, μ_J = 8.83(35) μD, μ_K = ?32.82(37) μD, and (α_| - α_⊥)_eff = 1.99(16) × 10^?24 cm³. These errors reflect only the internal consistency in the data; the absolute error in μ₀ is 32 μD. The modification of the Stark effect by internal rotation is discussed; it is shown that the only significant effect here is to modify the interpretation of μ₀. The change in μ₀ upon isotopic substitution of ³⁰Si for ²⁸Si was determined: $\text{μ}{}_0\text{(}{}^{30}\text{Si) - μ}{}_0\text{(}{}^{28}\text{Si) = 67.0(2.0) μD}$. A study of molecular magnetic effects in CH₃²⁸SiH₃ has yielded the two molecular g factors, g_⊥ = ?0.036391(21) nm and g_| = ?0.10667(13) nm, as well as the anisotropy in the susceptibility $\text{(χ}{}_{\mathrm{|}}\text{- χ}{}_{\mathrm{\perp }}\text{) = ?44.9(2.3) × 10}{}^{\mathrm{?30}}\text{J}\text{T}{}^2$. The molecular quadrupole moment has been calculated.     

Amino wagging and inversion in hydrazine: K′ = 1 levels in the first excited state of the antisymmetric wagging vibration

The infrared absorption spectrum of NH₂NH₂ vapor has been observed in the region 899–1077 cm^?1, where the antisymmetric wagging band (v_a = 1 ← 0) appears, by the use of a Fourier transform spectrometer with a practical resolution of 0.003 cm^?1. In the region 925.0–925.6 cm^?1, the spectrum was also observed with a tunable diode laser, and a component, β, of the ^pQ₂ cluster has been further resolved. Most of the absorption lines assignable to β-^pP₂(J″), γ-^pP₂(J″), β-^pQ₂(J″), γ-^rQ₀(J″), β-^rR₀(J″), and γ-^rR₀(J″), where J″ = 2 ～ 15, have been identified. From these observed transition frequencies, in combination with the ground state energy levels given by microwave spectroscopy, the energy level structure of the K′ = 1 rotational states was determined. From this, the following molecular parameters for the v_a = 1 state were determined: molecular asymmetry, B′-C″ = 0.00017 cm^?1; a parameter q₅ describing an umbrella motion Coriolis interaction (q₅K) about the a axis, q₅ = ?0.0030 cm^?1; its J(J + 1) variation, q_5j = 0.00014 cm^?1; and a parameter describing an umbrella-motion K-type doubling g₅J(J + 1), g₅ = 0.000021 cm^?1.     

Precision line parameter measurements for selected K = J inversion lines of ammonia

Using a computer controlled microwave spectrometer, the self-broadened linewidth and -shift parameters have been simultaneously measured for the K = J inversion lines of ammonia. It is shown that the ΔF = ±1 quadrupole hyperfine components make appreciable contributions to the observed widths. With the exception of the J, K = 5, 5 line, the observed linewidths are in agreement with those calculated from both the Anderson and Murphy-Boggs theories. However, the line-shift parameters are not in agreement with the Anderson theory predictions.     

Measurement of the nuclear magnetic dipole moment of Au197 and hyperfine structure measurements in the ground states of Au197, Ag107, Ag109 and K39

Using an atomic beam magnetic resonance apparatus the nuclear magnetic dipole momentμ _I of the stable isotope Au¹⁹⁷ was measured directly with the doublet method. The result isμ _I(Au¹⁹⁷)=0.143491 (9)μ _n, uncorrected for atomic diamagnetism. Further hyperfine structure measurements were performed in the ground states of K³⁹, Ag¹⁰⁷, Ag¹⁰⁹ and Au¹⁹⁷ with the following results:Δv(K³⁹)=461.719723 (38) MHzΔv(Ag¹⁰⁷)=1712.512111 (18) MHzΔv(Ag¹⁰⁹)=1976.932075 (17) MHzΔv(Au¹⁹⁷)=6099.320184 (13) MHzg _J(Ag¹⁰⁷)/g _J(K39)=1.0000260 (20)g _J(Au¹⁹⁷)/g _J(K39)=1.0005076 (20).     

A survey ofΔK=0 dipole transitions from low lyingJ=1 states in rare earth nuclei

High resolution photon scattering experiments on various Nd-, Gd-, Dy-, Er- and Yb-isotopes yielded new information about the energy and absolute ΔK=0 groundstate transition strengths ofJ=1 levels with excitation energies between 1.5 and 4 MeV. The lowest of theseJ ^π=1^? states are suggested to be the bandheads of aK ^π=0 ^? octupole vibrational band, whereas the origin of the higher lying states is unknown.     

The pure inversion spectrum of 15ND3 in the v2 = 1 state

The inversion spectrum of ¹⁵ND₃ in the v₂ = 1 state was investigated in the millimeter wave region between 70 and 125 GHz. The inversion splitting (J = 0, K = 0) was calculated to be 97 279.998(35) MHz. The K = 3 splitting constants and the electric dipole moment have also been determined.     

Millimeter wave spectrum of acetonitrile oxide,CH3CNO,in the ν10 vibrational manifold: The ground state and the state v10 = 1

The pure rotational spectrum of CH₃CNO was measured in the frequency range 75 to 230 GHz. For the ground state, transitions were measured for J between 9 and 28 and for K from 0 to 12. In the v₁₀ = 1 state the measurements range from J = 0 to 19 and from K = 0 to 11. Numerous perturbations are observed, apparently due to accidental resonances with levels in other vibrational states. The contributions due to ΔK = 2, Δl = 2 matrix elements (l-type resonance and l-type doubling) are accounted for by matrix diagonalization, and the effects due to accidental resonances are presented graphically.     

Infrared-microwave double resonance in CH3OH using a Zeeman-tuned 3.5-μm HeXe laser

Infrared microwave double resonance signals have been observed for CH₃OH using the 3.5-μm HeXe laser line. When microwave transitions in the ground vibrational state are pumped, the double resonance signals are obtained on two infrared transitions v = 1 ← 0 of ν^CH(a′); v = 1, J, K, μ = 4, 2, 1 ← v = 0, J, K, μ = 3, 2, 1, and 4, 3, 1 ← 3, 3, 1. Three weak double resonance signals are due to the collision-induced transitions. Their relative intensities have been explained successfully by using the rate constants of collision-induced transitions which are proportional to the dipole matrix elements between the states involved in the transitions.     

Analysis of pp → K+K− π+π− around 1 GeV/c

Approximately 100 000 four-prong antiproton annihilations in hydrogen were measured. A clean, unbiased sample of 842 K⁺K^?π⁺π^? events was obtained. This reaction is dominated by $\text{K}{}^1\text{(～45\%)}$ and ?⁰(～20%) production, with smaller amounts of A₂⁰(～15%) and ?(～5%) production. 25% of the reactions involved double resonance production. No significant three-body resonance production is observed.     

Tunable laser Stark-difference spectra of CD3OH

We present Doppler resolution limited spectra of the P(J) and R(J) multiplets for J ≦ 10 of the 10-μm CO stretch band of ¹²CD₃¹⁶OH using a tunable diode laser. Relative frequencies within the multiplets accurate to ±0.0002–0.0005 cm^?1 are obtained, but no absolute frequencies are given. We are able to assign most of the hindered rotation and K substructure in these multiplets. The assignments are based on analyses of Stark-difference spectra combined with the ground-state microwave data and the intensity variations which are expected theoretically. The ground and excited state A, K = 1 asymmetry splitting parameters are measured to be δ₁″ = (8.5450 ± 0.0080) × 10^?3cm^?1 and δ₁′ = (9.7706 ± 0.0080) × 10^?3cm^?1, respectively. The ground-state value agrees well with the microwave results. A rapid-scan system for recording data and a computer-aided technique for calibrating and plotting the spectra are described.     

Microwave measurements and calculations of quadrupole coupling effects in CH3I and CD3I

The transitions J = 1 ← 0, K = 0; J = 2 ← 1, K = 0; and J = 2 ← 1, K = 1 of CH₃I and CD₃I were measured using a Stark-modulated microwave spectrometer. Iodine quadrupole coupling strengths were analyzed to determine variations with deuterium substitution on the methyl group and variations with centrifugal distortion. Quadrupole coupling strengths were described by the expression $\text{eQq}{}_0\text{+ aJ(J + 1) + bK}{}^2\text{+}\text{cK}{}^4\text{J(J + 1)}$. Explicit expressions are given for a, b, and c for a symmetric top in terms of molecular parameters. For CH₃I eQq₀ = ?1934.11 ± 0.02 MHz and for CD₃I eQq₀ = ?1928.95 ± 0.04 MHz. Rotational constants obtained are B(CH₃I) = 7501.274 ± 0.002 MHz and B(CD₃I) = 6040.298 ± 0.007 MHz. The observed fractional change in halogen quadrupole coupling of 0.0027 is related to previous results for methyl chloride and methyl bromide.     

The electric dipole moment of methyl fluoride

The Stark effect of CH₃F is extensively used as a calibration standard in laser Stark spectroscopy. The accepted value for the dipole moment of the ground vibrational state of CH₃F is less accurate than the precision of laser Stark measurements, and questions have also been raised about the literature value. New molecular beam spectroscopy measurements have been made of the ratio of the Stark effect in the J = 1, K = 1 and J = 2, K = 2 CH₃F states to that of the 01¹0 vibrational state of OCS. The results were $\text{μ}{}_{1.1}\text{(}\text{CH}{}_3\text{F}\text{)}\text{μ}{}_{010}\text{(}\text{OCS}\text{)}\text{= 2.638905(23)}$ and $\text{μ}{}_{2.2}\text{(}\text{CH}{}_3\text{F}\text{)}\text{μ}{}_{010}\text{(}\text{OCS}\text{)}\text{= 2.63894(10)}$. This produces a dipole moment of 1.85840 D with precision relative to OCS of 10 ppm and absolute accuracy of 43 ppm.     

Assignment of submillimeter laser lines in CH3I

We propose explanations for three laser lines observed in CH₃I by Dyubko, Svich and Fesenko. Two lines are respectively assigned to (J = 16, K = 6) → (J = 15, K = 6) and (J = 45, K = 6) → (J = 44, K = 6) in the ν₆ = 1 state. Th e third one might be explained as (ν₃ = 2, J = 54, K) → (ν₃ = 2, J = 53, K).     

Special features of the <Emphasis Type="Italic">K</Emphasis> = 0 channel in nuclear fission

The opinion that the K = 0 fission channel is completely closed if the spin J and the parity π of the nucleus undergoing fission do not satisfy the condition (?1) ^J = π is widespread. On the basis of a detailed analysis of quantum numbers characterizing the rotational states of deformed nuclei, it is shown that this opinion is erroneous. In fact, the K = 0 channel may be partly open. Its suppression is caused by special features of fission barriers in the state being considered. It is also shown that factors that suppress the K = 0channel may exist even in states characterized by J and π values such that they satisfy the condition (?1) ^J = π. More precise information about the contribution of the K = 0 channel may be obtained by measuring the hexadecapole component of the angular distribution of fragments originating from the slow-neutron-induced fission of aligned nuclei.     

Moments of the spectra for rotational transitions induced by collisions or by external perturbations

Considered first is the cross sectiond σ(J′←J)/dω for the rotational transitionJ′←J of a linear rotator in collisions. The set of cross sections for a givenJ and for allJ′ defines a discrete spectral distribution as a function of the transition energy ΔE=E(J′)?E(J). In both the classical and the quantum mechanical sudden approximations the moments \(S(\mu ;J) = \sum\limits_{J'} {(\Delta {\rm E}} )^\mu d\sigma (J' \leftarrow J)/d\omega \) of ordersμ=2n andμ=2n+1 (n=0,1,...) are polynomials of degreen in the rotational energyE(J). The special cases forn=0 indicate thatS(0;J) andS(1;J) are independent ofJ. This is a theorem proved elsewhere. Explicit expressions forS(μ; J) of low orders are presented. They are derived on the assumption of equal relative velocitiesv andv′ before and after the collision. Correction onS(μ;J) for the difference betweenv andv′ is made to the lowest order in terms ofS(μ+1;J) forv=v′. The quantum mechanical results for linear rotators are extended to spherical-top and symmetric-top rotators. These results apply not only to the collision cross section but also to a physical quantity expressible in the form ¦〈Γ′¦F¦Γ〉¦² of a transition probability withany F that is independent of the initial and final rotational states ¦Γ〉 and ¦Γ′〉.     

Beam maser measurements of hyperfine structure in chloroacetylene-d

The J = 1-0 transitions in ³⁵ClCCD were measured using a beam maser spectrometer giving a molecular resonance linewidth of 3 kHz (FWHM). Analysis of the data yielded quadrupole coupling strengths eqQ(D) = 208.5 ± 1.5, eqQ(³⁵Cl)= 79 739.5 ± 1 kHz and the ³⁵Cl spinrotation interaction strength C(Cl) 1.3 ± 0.1 kHz. The rotational constant obtained is B = 5 186 973.9 ± 1.0 kHz. The accuracy of measured molecular parameters is improved by a factor of 20 or better.     

The pure inversion spectrum of 14ND3 in the v2 = 1 state

The inversion spectrum of ¹⁴ND₃ in the v₂ = 1 state was investigated in the millimeter wave region 89–127 GHz. The inversion splitting (J = 0, K = 0) was calculated to be 106 354.355(32) MHz. The nitrogen quadrupole coupling constant, the K = 3 splitting constant, and the electric dipole moment were also determined.     

Analysis of the 2ν3 band of 12CD3F at 5.06 μm recorded under high resolution

The 2ν₃(A₁) band of ¹²CD₃F near 5.06 μm has been recorded with a resolution of 20–24 × 10^?3 cm^?1. The value of the parameter (α^B ? α^A) for this band was found to be very small and, therefore, the K structure of the R(J) and P(J) manifolds was unresolved for J < 15 and only partially resolved for larger J values. The band was analyzed using standard techniques and values for the following constants determined: ν₀ = 1977.178(3) cm^?1, B″ = 0.68216(9) cm^?1, D″_J = 1.10(30) × 10^?6 cm^?1, α^B = (B″ ? B′) = 3.086(7) × 10^?3 cm^?1, and β^J = (D″_J ? D′_J) = ?3.24(11) × 10^?7 cm^?1. A value of α^A = (A″ ? A′) = 2.90(5) × 10^?3 cm^?1 has been obtained through band contour simulations of the R(J) and P(J) multiplets.