Neutral mesons with heavy quarks and mixing angles in the six-quark model

In the framework of the six-quark model, based on the gauge group SU(2)_L × U(1) we have obtained expressions for the amplitudes of $\text{K}{}^0\text{?}\text{K}{}^0\text{,}\text{D}{}^0\text{?}\text{D}{}^0\text{,}\text{B}{}^0\text{?}\text{B}\text{B}{}_{\mathrm{S}}{}^0\text{?}\text{B}{}_{\mathrm{S}}{}^0\text{,}\text{T}{}^0\text{?}\text{T}{}^0\text{and}\text{T}{}_{\mathrm{c}}{}^0\text{?}\text{T}{}_{\mathrm{C}}{}^0$ transitions at final 4-momenta of external lines Feynman box diagrams. We have estimated the correctness of using the approximation of extremely small 4-,omenta of valence quarks, composing K⁰-like mesons. The constraints for the parameters of the unitary matrix of weak charged currents have been found at arbitrary value of the t-quark mass. Estimates of numerical values for the mixing parameters and for the parameters of CP violation for neutral systems similar to $\text{K}{}^0\text{?}\text{K}{}^0$ are given.     

Observation of compensation effects during the thermal dissolution of aluminum oxide layers on tungsten and molybdenum 〈111〉 and on tungsten {110} in the presence of electric fields

Aluminum oxide layer dissolution was studied between 700 and 1200 K in the substrate areas of W〈111〉, Mo〈111〉, and on W{110} by means of FEM. Varying the electric field strength, F, between +45 and $\text{+105}\text{MV}\text{cm}$, two types of dissolution could be observed: dissolution by surface diffusion (low F's) and dissolution by ion desorption (high F's). It is assumed that aluminum suboxides — preferentially AlO — are involved in the dissolution processes. The preexponential factors, A_F, of an Arrhenius-Frenkel type equation were measured as a function of F. The field dependence of A_F is determined by the dissolution mechanism: (a) dissolution by diffusion: $\text{log}\text{A}{}^0{}_{\mathrm{F}}\text{=}\text{log}\text{A}{}^0{}_0\text{?}\text{ΔμF}\text{2.3k}{}^1\text{T}$ (μ  molecular dipole moment, ¹T ≡ isokinetic for W〈111〉, log A⁰₀ = ? 6.0 and ${}^1\text{T = 940}\text{K}$; for Mo〈111〉, log A⁰₀ = ? 3.1 and ${}^1\text{T = 860}\text{K}$; and (b) dissolution by ion desorption: $\text{log}\text{A}{}^{\mathrm{+}}{}_{\mathrm{F}}\text{=}\text{log}\text{A}{}^{\mathrm{+}}{}_0\text{+}\text{n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{F}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{2.3k}{}^1\text{T}$; for A⁺₀ = ? 22 and ${}^1\text{T = 1200}\text{K}$; for W〈111〉, log A⁺₀ = ? 21 and ${}^1\text{T = 1200}\text{K}$. Using earlier proposed safeguards, isokinetic relationships (compensation effects) could be established for each of the two dissolution processes. The coordinates of the isokinetic points have the following average values: $\text{log}{}^1\text{A}{}^0{}_0\text{= 2.5}$ and ${}^1\text{T = 920}\text{K}$ for diffusion; $\text{log}{}^1\text{A}{}^{\mathrm{+}}{}_0\text{= ? 1}$ and ${}^1\text{T = 1240}\text{K}$ for ion desorption. The entropy changes (at $\text{T =}{}^1\text{T}$, zero field strength, and unit pressure) for the phase changes: solid layer → diffusion layer and solid layer → ion gas, are of the order of $\text{30}\text{cal}\text{K}$ · mol and $\text{90}\text{cal}\text{K}$ · mol, respectively. The two dissolution mechanisms can be described by the following Arrhenius-Frenkel type equations:

$\text{τ}{}^0{}_{\mathrm{F}}\text{=}{}^1\text{A}{}^0{}_0\text{exp}\text{[}\text{? (E}{}^0{}_0\text{+ ΔμF)}\text{k}{}^1\text{T}\text{]}\text{exp}\text{[(}\text{E}{}^0{}_0\text{+ ΔμF)}\text{kT}\text{]}$

for diffusion and

$\text{τ}{}^{\mathrm{+}}{}_{\mathrm{F}}\text{=}{}^1\text{A}{}^{\mathrm{+}}{}_0\text{exp}\text{[}\text{? (E}{}^{\mathrm{+}}{}_0\text{? n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{F}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}\text{k}{}^1\text{T}\text{]}\text{exp}\text{[(}\text{E}{}^{\mathrm{+}}{}_0\text{? n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{F}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}\text{kT}\text{]}$

for ion desorption.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Uniqueness of the standard electroweak gauge model

It is proved that the standard SU(2) × U(1) electroweak gauge model is unique against any extension if the effective low-energy neutral-current interaction is to be precisely of the form $\text{(4G}{}_{\mathrm{F}}\text{/}\text{2}\text{) (j}{}_{\mathrm{\mu }}{}^{\mathrm{(3)}}\text{?}\text{sin}{}^2\text{θ}{}_{\mathrm{<mtext>W</mtext>}}\text{j}{}_{\mathrm{\mu }}{}^{\mathrm{<mtext>em</mtext>}}\text{)}{}^2$naturally.     

Study of the three-proton three-neutron-hole nucleus 208At

Levels in ²⁰⁸At were populated in the ²⁰⁹Bi(α, 5n) reaction, and the subsequent radiation was studied using γ-spectroscopic methods including γ-ray excitation function and angular distribution, γγ(t) coincidence and γt measurements, as well as measurements of conversion electrons. The excited spectrum of ²⁰⁸At is found to consist of two almost disconnected parts which are proposed to originate from seniority-three proton and neutron cascades. Two isometric states are observed. A $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 45 ± 2}\text{ns}$ state at 1090 keV is proposed to have the main configuration and J^π = 10^?. A high-spin isomer with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.5 ± 0.2 μs at 2276}\text{keV}$ is assigned to be the state. Shell-model arguments are used to assign configurations to most of the observed levels. Transition rates are discussed.     

Non-analyticity of the entropy and Nernst's law in random spin systems

It is shown explicitly for a soluble model that a random spin system can have an entropy which is non-analytic at (H = 0, T = 0), with $\text{(}\text{?S}\text{?H}\text{)}{}_{\mathrm{H=0}}$ and/or $\text{(}\text{?}{}^2\text{S}\text{?H}{}^2\text{)}{}_{\mathrm{H=0}}$non-vanishing in the T → 0 limit, while nevertheless Nernst's law is satisfied.     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

The measurement of the rotational relaxation times of OCS from the nutation signals

The time dependence of microwave absorption was measured for the J = 2-1 and J = 3-2 transitions of OCS under on- and off-resonant conditions utilizing Stark and source modulation, respectively. The two effective pressure parameters obtained under the two conditions, which correspond to $\text{(T}{}_2{}^{\mathrm{?1}}\text{+ T}{}_1{}^{\mathrm{?1}}\text{)}\text{4πP}$ and $\text{(2πT}{}_2\text{P)}{}^{\mathrm{?1}}$, respectively, according to the Bloch equation, are different beyond experimental error; the difference $\text{(T}{}_2{}^{\mathrm{?1}}\text{? T}{}_1{}^{\mathrm{?1}}\text{)}\text{2πP}$ is 0.94 ± 0.38 (2.5σ) MHz/Torr for J = 2?1. This difference was also determined to be 1.19 ± 0.30 MHz/Torr from the dependence of the nutation frequency on the microwave power.     

On the theory of localized spin and phonon excitations in amorphous ferromagnets

Within the framework of a perturbation theory and a quasicrystalline approximation we have solved the linearized equation of motion for the circular spin component S⁺_j = S^x_j + iS^y_j in a one-dimensional amorphous ferromagnet with periodic external excitation of the spin S⁺₀ at site j = 0. It is shown that localized spin modes of the simple form $\text{«S}{}^{\mathrm{+}}{}_{\mathrm{j}}\text{a}\text{?}\text{= S}{}^{\mathrm{+}}\text{(q0) exp[iq}{}_0\text{· R}{}_{\mathrm{j}}\text{- iω(q0) t] exp (-gk?R}{}_{\mathrm{j}}\text{?)}$ with fall-off-length κ^-1 are solutions of the ensemble-averaged equation of motion. On the other hand, we have a damping of extended spin waves according to exp(-Γt). A simple relation is derived between the fall-off-length κ^-1 of localized spin modes and the damping factor Γ of extended spin waves. Analogous results hold for phonons in amorphous materials.     

A pair approximation of the spin fluctuation theory of itinerant-electron ferromagnets

We discuss a pair approximation of the spin fluctuation theory, which is an extension of the single-site theory proposed by the present author and can include the effect of the short-range magnetic order (SRMO). Numerical calculations of b.c.c. iron show that SRMO for neighbouring sites j and l, $\text{Γ≡}\text{〈m}{}_{\mathrm{j}}\text{m}{}_{\mathrm{l}}\text{〉}\text{〈m}{}^2{}_{\mathrm{j}}\text{〉}$, is about 0.21–0.14 at $\text{T}\text{T}{}_{\mathrm{c}}\text{=1.0?2.0}$. This is considerably smaller than the value (Γ～0.8) proposed by Korenman, Murray and Prange for an analysis of sloppy spin waves of iron, while it coincides with the value (Γ≌0.12–0.18) given by Shastry, Edwards and Young with the use of the spherical Heisenberg model with exchange interactions extending to far nearest neighbours.     

A simplified Fokker-Planck operator for unlike-particle collisions

The linearized Fokker-Planck operator reads $\text{C}{}^1{}_{\mathrm{jk}}\text{= C(f}{}_{\mathrm{1j}}\text{, f}{}_{\mathrm{0k}}\text{)}$. The first term is rather simple, but the second one is very complicated. A much simpler - though exact - form of C(f_0j, f_1k) is proposed, for a special class of f_1k occuring in diffusion theory.     

Influence of self-fields on the Vlasov equilibrium and stability properties of relativistic electron beam-plasma systems

The influence of self-fields on the equilibrium and stability properties of relativistic beam-plasma systems is studied within the framework of the Vlasov-Maxwell equations. The analysis is carried out in linear geometry, where the relativistic electron beam propagates through a background plasma (assumed nonrelativistic) along a uniform guide field $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, It is assumed that $\text{ν}\text{γ}{}_0\text{? 1}$ for the beam electrons (ν is Budker's parameter, and γ₀mc² is the electron energy), but no a priori assumption is made that the beam density is small (or large) in comparison with the plasma density, or that conditions of charge neutrality or current neutrality prevail in equilibrium. It is shown that the equilibrium self-electric and self-magnetic fields, $\text{E}{}_{\mathrm{r}}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{r}}$ and $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$, can have a large effect on equilibrium and stability behavior. Equilibrium properties are calculated for beam (j = b) and plasma (j = e, i) distribution functions of the form f_b⁰(H, P_θ, P_z) = F(H ? ω_rbP_θ) × δ(P_z ? P₀)(j = b), and $\text{f}{}_{\mathrm{j}}{}^0\text{(H, P}{}_{\mathrm{\theta }}\text{, P}{}_{\mathrm{z}}\text{) = f}{}_{\mathrm{j}}{}^0\text{(H ? ω}{}_{\mathrm{rj}}\text{P}{}_{\mathrm{\theta }}\text{? V}{}_{\mathrm{j}}\text{P}{}_{\mathrm{z}}\text{?}\text{m}{}_{\mathrm{i}}\text{V}{}_{\mathrm{j}}{}^2\text{2}\text{)}$ (j = e, i), where H is the energy, P_θ is the canonical angular momentum, P_z is the axial canonical momentum, and ω_rj (the angular velocity of mean rotation for j = b, e, i), V_j (the mean axial velocity for j = e, i), and P₀ are constants. The linearized Vlasov-Maxwell equations are then used to investigate stability properties in circumstances where the equilibrium densities of the various components (j = b, e, i) are approximately constant. The corresponding electrostatic dispersion relation and ordinary-mode electromagnetic dispersion relation are derived (including self-field effects) for body-wave perturbations localized to the beam interior (r <R_b). These dispersion relations are analyzed in the limit of a cold beam and cold plasma background, to illustrate the basic effect that lack of charge neutrality and/or current neutrality can have on the two-stream and filamentation instabilities. It is shown that relative rotation (induced by self-fields) between the various components (j = b, e, i) can (a) result in modified two-stream instability for propagation nearly perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$, and (b) significantly extend the band of unstable k_z-values for axial two-stream instability. Moreover, in circumstances where the beam-plasma system is charge-neutralized but not current-neutralized, it is shown that the azimuthal self-magnetic field $\text{B}{}_{\mathrm{\theta }}{}^{\mathrm{s}}\text{(r)}\text{e}\text{?}{}_{\mathrm{\theta }}$ has a stabilizing influence on the filamentation instability for ordinary-mode propagation perpendicular to $\text{B}{}_0\text{e}\text{?}{}_{\mathrm{z}}$.     

Note on conservation laws based upon traceless energy-momentum tensors in flat space-time

In this note we prove the following theorem. If in a flat space-time with metric g_ij(x) treferred to general coordinates xⁱ a vector ξⁱ(x) satisfies (Tⁱ_jξ^j)_;i=0 (semicolon denotes covariant differentiation) for all energy-momentum tensors of the set $\text{{}\text{T}{}^{\mathrm{ij}}\text{T}{}^{\mathrm{i}}{}_{\mathrm{j;i}}\text{=0;g}{}_{\mathrm{ij}}\text{T}{}^{\mathrm{ij}}\text{=0}$; T^ij = T^ji; T^iju_iu_j > 0 (where u_i is a time-like vector)}, then the vector ξⁱ defines a conformal motion. This theorem, which may be considered as a converse (in flat space-time) to a well-known result of Trautman, is a generalization of a result obtained by J. T. ?opuszański and J. Szczucka-Soko?owska [Reports on Mathematical Physics 11 (1977), 153] in which they assumed the vector ξⁱ was a polynomial in Minkowski coordinates.     

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.     

Phenomenological SU(1, 1) supergravity

We investigate the structure of phenomenological supergravity models which permit the hierarchy problem to be “solved” in the sense that $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and m_W are determined dynamically to be exp [-O(1)/α] × m_P. Such models must have a flat hidden sector potential, which is only possible if the theory has an underlying SU(1, 1) invariance. Flat SU(1, 1) theories necessarily have a zero cosmological constant and the hidden sector is an Einstein space with . The SU(1, 1) invariance is necessarily broken down to U(1) by the gravitino mass. If $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is the only source of SU(1, 1) breaking then the tree-level gaugino masses are small and $\text{A =}\text{3}\text{2}$, while values of A up to 3 and non-zero gaugino masses are possible if other sources of SU(1, 1) breaking are tolerated. Yukawa couplings may scale as some power of $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}$ in these models where $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ is generated dynamically, which may explain the hierarchy of Higgs-fermion Yukawa couplings: $\text{m}{}_{\mathrm{<mtext>f</mtext>}}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{=}\text{O}\text{(}\text{m}{}_{\mathrm{<mtext>W</mtext>}}\text{m}{}_{\mathrm{<mtext>P</mtext>}}\text{)}{}^{\mathrm{\lambda >0}}$? These models also permit the spontaneous violation of CP in the Yukawa coupling matrix. Numerical studies yield 20 GeV < m_t < 100 GeV in these phenomenological SU(1, 1) supergravity models. Speculations are presented about their relation to a fundamental theory based on extended supergravity.     

Decoupled bands and antialigned states: An illustrative example

We suggest that the properties of decoupled bands associated with high -j single-particle orbitals are similar to those of $\text{K}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}$ bands associated with $\text{j =}\text{1}\text{2}$ orbitals. Special attention is focussed on the so-called antialigned states. As an illustrative example we have studied the $\text{K}{}^{\mathrm{\pi }}\text{=}\text{1}\text{2}{}^{\mathrm{?}}$ bands in ¹⁹F and ²³Na, where the level energies and electromagnetic transition rates are evaluated in a simple weak-coupling model.     

Analysis of π N → K Λ and KN → π Λ using fixed-t dispersion relations,fesr and duality

A simultaneous analysis of low-energy (W ? 2 GeV) data for the reactions π^?p→ K^OΛ and K^?p → π^OΛ has been made using the hypothesis of two-component duality combined with fixed-t dispersion relations. Results are presented for the $\text{?}{}^1\text{Λπ}$ and $\text{N}{}^1\text{Λ}\text{K}$ couplings. The low-energy amplitudes are used to evaluate FESR integrals and lead to large EXD breaking for the $\text{K}{}_{\mathrm{<mtext>V</mtext>}}{}^1\text{?}\text{K}{}_{\mathrm{<mtext>T</mtext>}}{}^1$ helicity flip amplitudes.     

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 $\text{M}{}_8{}^0\text{:±iM}{}_5{}^0\text{:±iM}{}_6{}^0\text{:M}{}_9{}^0\text{≈ +2:?9:+10:+0.5}$.