Determination of molecular constants of nitric oxide from (1-0), (2-0), (3-0) bands of the 15N16O and 15N18O isotopic species

The (1-0), (2-0), and (3-0) transitions of ¹⁵N¹⁶O and ¹⁵N¹⁸O are investigated. The wavenumbers of the rotation-vibration lines are reported for the overtone bands and the ${}^2\text{Π}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{-}{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ (1-0) subband. It is shown that in the data reduction it is advantageous to calculate first merged spectroscopic constants ignoring the Λ-type doubling. The vibrational constants ω_e, ω_ex_e, ω_ey_e and the vibrational dependence of the rotational constants are determined. The study of ¹⁵N¹⁸O allows the determination of the equilibrium values of the centrifugal distortion correction A_De to the spin-orbit constant and of the spin-rotation constant γ_e from the isotopic invariance of the ratios $\text{A}{}_{\mathrm{<mtext>De</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}$ and $\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}$. It is found that $\text{A}{}_{\mathrm{<mtext>De</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}\text{= (?3.9 ± 1.3) × 10}{}^{\mathrm{?6}}$ and $\text{γ}{}_{\mathrm{<mtext>e</mtext>}}\text{B}{}_{\mathrm{<mtext>e</mtext>}}\text{= (?4.00 ± 0.05) × 10}{}^{\mathrm{?3}}$.     

Oblate ground-state shapes of 11 h 189Pt and 2.8 d 191Pt

With nuclear orientation on $\text{11}\text{h}\text{3}\text{2}{}^{\mathrm{?189}}\text{Pt}\text{, 2.8}\text{d}\text{3}\text{2}{}^{\mathrm{?191}}\text{Pt}$ and $\text{4.0}\text{d}\text{13}\text{2}{}^{\mathrm{<mtext>+\; 195\; </mtext><mtext>m</mtext>}}\text{Pt}$ in Os and NMR on oriented ¹⁸⁹Pt and ¹⁹¹Pt in Fe electric and magnetic hyperfine splitting frequencies were measured. The nuclear moments are deduced to be: ¹⁸⁹Pt: |μ| = 0.434(9) μ_N, Q = ?0.65(26) b; ¹⁹¹Pt: |μ| = 0.500(10) μ_N, Q = ?0.64(26) b; ^195mPt: Q = +1.42(60)b. The negative spectroscopic ground-state quadrupole moments of ¹⁸⁹Pt and ¹⁹¹Pt must be due to oblate ground-state deformations, thus indicating that the prolate-oblate phase transition in Pt is located at A < 189.     

The emission spectra of H35Cl+, H37Cl+, D35Cl+, and D37Cl+ in the region 2700–4100 Å

The $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}\text{-X}{}^2\text{Π}$ emission spectrum of HCl⁺ has been measured and analyzed for four isotopic combinations. These analyses extend previous work and provide rotational constants for the v = 0–2 levels of the ground state and for the v = 0–9 levels of the excited state. RKR potentials have been determined for both states, although the upper state could not be fitted precisely to such a model. Calculated relative intensities based on these potentials demonstrated that the electronic transition moment must change rapidly with lower state vibrational quantum number. Although considerable caution should be exercised in applying the concept of equilibrium constants to the $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}$ state, the following are the best estimates of these constants (in cm^?1) for the $\text{X}{}^2\text{Π}$ state of H³⁵Cl⁺: B_e = 9.9406, ω_e = 2673.7, A_e = ? 643.7, and $\text{r}{}_{\mathrm{e}}\text{= 1.315}\text{A}\text{?}$. For the $\text{A}{}^2\text{Σ}{}^{\mathrm{+}}$ state of H³⁵Cl: T_e = 28 628.08, B_e ～ 7.505, ω_e ～ 1606.5, and $\text{r}{}_{\mathrm{e}}\text{= 1.514}\text{A}\text{?}$.     

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

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

QED distributions for hard photon emission in e+e− → μ+μ−γ

The hard photon emission in e⁺e^? → μ⁺μ^?γ is investigated to order α³. Formulas for a number of distributions are obtained, when neglecting terms of order (m_e/?)² and (m_μ/?)². Both charge-even and charge-odd contributions are calculated. The total contribution to the charge asymmetry parameter

$\text{? =}\text{[}\text{d}\text{σ(θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{?}\text{d}\text{Oσ(π?θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{]}\text{[}\text{d}\text{σ(θ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{+}\text{d}\text{σ(π ? σ)}\text{d}\text{O}{}_{\mathrm{\mu }}{}^{\mathrm{+}}\text{]}$

does not exceed 5% for the c.m.s. energy 2? = 3 GeV.     

The external field problem for QCD

In lattice gauge theory, many computations such as the strong coupling expansions, mean field theory, or the few plaquette models require the evaluation of the one-link integral in the presence of an arbitrary N × N complex matrix source (J). For SU(N) gauge theories, we express our general solution to the external field problem as an integral over the maximal abelian subgroup [U(1)]^N?1

where S₀ = 2Σ_kz_k cos(φ_k ? θ), z_j are eigenvalues of √JJ⁺, e^2iNθ=detJ/detJ⁺, and G is an appropriate jacobian determinant. Our explicit solution follows from differential Schwinger-Dyson equations cast in a separable form by using fermionic variables, and the special cases of N = 2, 3 and ∞ agree with earlier derivations.     

On (πμ) atoms produced in K0L decay

The branching ratio for producing (πμ) atoms in K⁰_L decay is calculated. Using the approximate solution of the Bethe-Salpeter equation for the (πμ) atom, the S-matrix element of this process is written in a more precise form than that obtained intuitively. Furthermore, all corrections of $\text{O}\text{(α) (α =}\text{e}{}^2\text{4π}\text{)}$ are considered. As a result, the branching ratio may be used to determine the form factor ζ = f_?(0)/f₊(0) of K⁰_L.     

A determination of the spin of the hypernucleus 12ΛB: (II). A complete analysis

The probability distribution calculated for the decay sequence ${}^{12}{}_{\mathrm{\Lambda }}\text{B(g.s.) →}{}^{12}\text{C}{}^1\text{π}{}^{\mathrm{?}}\text{→ αααπ}{}^{\mathrm{?}}$ passing through the (J^P_N) = (2⁺, 1) intermediate state ¹²C¹ (16.11 MeV) is cast in a symmetrical form and used to calculate the likelihood for $\text{J = 1}\text{relative to}\text{J = 2}\text{for}{}^{12}{}_{\mathrm{\Lambda }}\text{B(g.s.}\text{)}$ on the basis of the 85 examples available for this decay process. This procedure has optimum sensitivity, is free from the uncertainties of the comparisons previously made using only projected angular distributions, and strongly indicates that J^P = 1^? holds for ¹²_ΛB(g.s.). An appendix points out that all the data for the decay sequence passing through the (J^P_N, T) = (1⁺, 0) level of ¹²C¹ is well fitted for J = 1 if the J = 1 → J_n = 1 transition amplitude a_s1 takes a value in the range a_s1/s = 0.08 to 0.09.     

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.     

High resolution Fourier spectroscopy of P2 infrared emission spectrum: Analysis of two new systems b3Πg → w3Δu and A1Πg → W1Δu

The investigation of the emission infrared spectrum of P₂ was performed with a high resolution Fourier spectrometer. Two new electronic systems were attributed to b³Π_g → w³Δ_u and A¹Π_g → W¹Δ_u transitions. The molecular parameters are obtained by a complete fitting procedure. The main equilibrium constants of the new states are (in cm^?1):

$\text{ω}{}^3\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 243228.07 ω}{}_{\mathrm{e}}\text{= 591.3 ω}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.5}$

$\text{B}{}_{\mathrm{e}}\text{= 0.256040 δ}{}_{\mathrm{e}}\text{= 0.001409 D}{}_{\mathrm{e}}\text{= 19.0 X 10}{}^{\mathrm{?8}}$

$\text{W}{}^1\text{Δ}{}_{\mathrm{u}}\text{T}{}_{\mathrm{e}}\text{= 31096.64 W}{}_{\mathrm{e}}\text{= 627.206 W}{}_{\mathrm{e}}\text{X}{}_{\mathrm{e}}\text{= 2.331}$

$\text{B}{}_{\mathrm{e}}\text{= 0.2628 δ}{}_{\mathrm{e}}\text{= 0.0014 D}{}_{\mathrm{e}}\text{= 23 X 10}{}^{\mathrm{?8}}$

     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

The A′(3Π2) state of ICl

Although $\text{A′(}{}^3\text{Π}{}_2\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$ is forbidden in near case c molecules the A′ ← X transition can be efficiently accomplished by the three-step sequence $\text{A′(}{}^3\text{Π}{}_2\text{) ← D′(2) ← A(}{}^3\text{Π}{}_1\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$. Transitions to a range of levels of A′, v_A′ = 2–38, have been recorded by this means, using J-selective polarization-labeling spectroscopy. Principal constants of the A′ state of I³⁵Cl are T_e = 12682.05, ω_e = 224.57, ω_eχ_e = 1.882, ω_ey_e = ?0.0107, B_e = 0.08653, and α_e = 0.000675 cm^?1. The A′ state is therefore similar in its physical characteristics to two other (relatively) deep states, $\text{A(}{}^3\text{Π}{}_1\text{)}$ and $\text{B(}{}^3\text{Π}{}_0\text{+)}$, of the 2431 configuration.     

Determination of the spectroscopic quadrupole moments of 131Cs, 132Cs and 136Cs

Nuclear spectroscopic quadrupole moments of the radioactive isotopes ¹³¹Cs, ¹³²Cs, and ¹³⁶Cs have been determined from the hyperfine structure of the $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ state by the level crossing method. The results including a Sternheimer correction are: $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{131}\text{Cs}\text{) = ?0.625(6)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = +0.508(7)}\text{b}$, $\text{Q}{}_{\mathrm{<mtext>s</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = +0.225(10)}\text{b}$. The quadrupole moments of all the Cs isotopes from A = 131 to A = 137 are recalculated. It is shown, that nuclear quadrupole moments of a specific isotope obtained from different atomic P-states only agree within the limits of error after application of the Sternheimer correction. The increase of Q_s with decreasing neutron number conforms with other observations and theoretical calculations stating that for elements around Z = 55 nuclear deformation develops below N = 82. The staggering of the sign of Q_s may be interpreted as consequence of an oblate-prolate degeneracy of the nuclear energy surface. Some magnetic moments have been slightly improved: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{132}\text{Cs}\text{) = 2.219(7) μ}{}_{\mathrm{<mtext>N</mtext>}}$, $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{136}\text{Cs}\text{) = 3.705(15)μ}{}_{\mathrm{<mtext>N</mtext>}}$ (corrected for diamagnetism).     

A new proof of the invariance principle in scattering theory

For free and interacting Hamiltonians, H₀ and H = H₀ + V(r) acting in L²(R³, dx) with V(r) a radial potential satisfying certain technical conditions, and for ? a real function on R with ?′ > 0 except on a discrete set, we prove that the Moller wave operators

exist and are independent of ?. The scattering operator

$\text{S = (Ω}{}^{\mathrm{+}}\text{)1Ω}{}^{\mathrm{?}}$

is shown to be unitary. Our proof utilizes time independent methods (eigenfunction expansions) and is effective in cases not previously analyzed, e.g. $\text{V(r) =}\text{sin}\text{r}\text{r}$ and many others.     

First determination of the proton electromagnetic form factors at the threshold of the time-like region

From the measurement of $\text{B}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{=}\text{Γ(}\text{p}\text{p}\text{→}\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{)}\text{Γ}\text{p}\text{p}\text{→total}\text{= (3.2 ± 10}{}^{\mathrm{?7}}\text{)}$, obtained in an experiment at CERN with antiprotons at rest, a value of the proton electromagnetic form factors at the threshold of the time-like region is derived: |G_E| = |G_M| = 0.51 ± 0.08 at q² = -3.52 (GeV/c)².     

Transition magnetic moments of hadrons and sidewise dispersion relations

Systems of linear relations for the magnetic moments of the nucleon and transition moments μ_ωπγ, μ_?πγ and ${}^{\mathrm{\mu }}\text{N}{}^1{}_{1470}\text{N}\text{γ}$ are obtained on the basis of sidewise dispersion relations in the one-pion approximation. In such an approach the magnetic moments of the transition ω(?)→ πγ and $\text{N}{}^1{}_{1470}\text{→Nγ}$ are expressed in terms of the anomalous magnetic moments of the nucleon and the strong interaction coupling constants.     

Deviation from scaling in the triple-regge region of pp→ pX and fP universality

By generalizing $\text{f}\text{P}$ universality to Regge-particle “scattering” we obtain $\text{s}\text{d}\text{σ}\text{d}\text{t}\text{d}\text{M}{}^2\text{= F(}\text{s}\text{M}{}^2\text{,t)}$$\text{[1 +}\text{M}{}^{\mathrm{?1}}\text{b}{}_{\mathrm{<mtext>f</mtext>}}\text{(0)}\text{b}{}_{\mathrm{<mtext>P</mtext>}}\text{(0)}\text{]}$ for pp → pX, where b_f(t) and b_P(t) are the f and P Regge residues for, say, pp → pp. This agrees with the recent NAL data.