An experimental investigation of the radiative structure decay K+ → e+υγ

The decay K⁺ → e⁺υγ has been investigated. For the structure-dependent part with positive γ-helicity (SD₊) the branching ratio $\text{Γ(}\text{SD}{}_{\mathrm{+}}\text{)}\text{Γ(}\text{K}{}_{\mathrm{\mu 2}}\text{) = (2.33 ± 0.42) × 10}{}^{\mathrm{?5}}$ is obtained from 51 ± 3 events observed in the kinematical region E_e ? 235 MeV, E_γ > 48 MeV and θ_eγ > 140°. For the corresponding part with negative γ-helicity we obtain an upper limit Γ(SD_?)/Γ(SD₊) < 11 (90% CL) from the sample of electrons with energies 220 MeV ? E_e < 230 MeV and with no γ in the backward direction. This upper limit implies that the ratio of structure-dependent axial vector amplitudes lies outside the region $\text{?1.8 < a}{}_{\mathrm{<mtext>K</mtext>}}\text{υ}{}_{\mathrm{<mtext>K</mtext>}}\text{< ?0.54}$.For the decay $\text{K}{}^{\mathrm{+}}\text{→}\text{e}{}^{\mathrm{+}}\text{νν}\text{ν}$ the limit $\text{Γ(}\text{K}{}^{\mathrm{+}}\text{→}\text{e}{}^{\mathrm{+}}\text{νν}\text{ν}\text{)/Γ(}\text{K}{}_{\mathrm{e2}}\text{) < 3.8}$ 90% confidence level) was found.     

An upper limit to the cross section for the reaction νμe−→νμe− at SPS energies

Candidates for the purely leptonic process $\text{ν}{}_{\mathrm{\mu }}\text{e}{}^{\mathrm{?}}\text{→}\text{ν}{}_{\mathrm{\mu }}\text{e}{}^{\mathrm{?}}$ have been searched for in the bubble chamber Gargamelle exposed to the CERN-SPS antineutrino wide-band beam. No single e^?, of energy greater than 1 GeV, was found in a total of 230 000 pictures, corresponding to 7400 charged current events. This leads to an upper limit for the observed cross section of $\text{σ}{}_{\mathrm{<mtext>obs</mtext>}}\text{< 1.6 × 10}{}^{\mathrm{?42}}\text{(}\text{E}{}_{\mathrm{\nu }}{}^{\mathrm{?}}\text{GeV}\text{)}$ cm² (90% C.L.). Interpretation of this value in terms of the standard W Weinberg-Salam model yields an upper limit to the mixing parameter sin²θ_W < 0.39 at 90% C.L.     

Optical detection of cyclotron resonance of electron and holes in CdTe

Cyclotron resonance of electron and holes have been optically detected at 70 GHz and at 1.8 K in n-type CdTe. The bare effective masses, in unit of the free electron mass, are found to be: $\text{m}{}^1\text{= 0.088 ± 0.004}$, $\text{m}{}^1{}_{\mathrm{lh}}\text{= 0.12 ± 0.01}$, $\text{m}{}^1\text{= 0.60 ± for H // <100>}$, and $\text{m}{}^1{}_{\mathrm{e}}\text{= 0.089 0.004}$, $\text{m}{}^1{}_{\mathrm{lh}}\text{= 0.11 ± 0.01}$, $\text{m}{}^1{}_{\mathrm{hh}}\text{= 0.69 ± 0.02}$ for H // <111>. The Luttinger valence band parameters deduced from these measurements are: γ₁ = 5.3 ± 0.5, γ₂ = 1.7 ± 0.3 and γ₃ = 2.0 ± 0.3, in fair agreement with the calculations of Lawaetz.     

Analysis of the I = 0 s-wave for ππ and KK̄ scattering

We show that if one uses a coupled channel parametrisation for the I = 0 S-wave in processes $\text{ππ → ππ, ππ →}\text{K}\text{K}\text{?}$ and KK? → KK? (the last deduced from a $\text{p}\text{?}\text{p → ππ + K}{}_1{}^0\text{K}{}_1{}^0\text{experiment}$) taking properly into account the analytic structure of these waves, then it is possible to fit simultaneously all cross-sections for the above processes, in the ranges $\text{700 < s s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1900}\text{MeV}$ for the first fit, $\text{2M}{}_{\mathrm{<mtext>K</mtext>}}\text{< s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1500}\text{MeV}$ for the second, $\text{2M}{}_{\mathrm{<mtext>K</mtext>}}\text{< s}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{< 1170}\text{Mev}$ for the last. None of the three usually claimed resonances ?, S¹, ?′ show up in the corresponding eigenphase analysis.     

Complexified Pöschl–Teller II potential model

With the help of complexifying a five-parameter exponential-type potential model, we obtain a general complex version of the Pöschl–Teller II potential, , where q_c=q₀e^2iαε, real V₁>0, q₀>0 and $\text{0<λε<}\text{π}\text{2}$. It has been shown that this complex potential is P-pseudo-Hermitian and PT-symmetric, where the parity operator P acts on the position operator as $\text{PxP}{}^{\mathrm{-1}}\text{=}\text{ln}\text{q}{}_0\text{λ}\text{−x}$. The discrete energy eigenvalues are shown to be real when $\text{V}{}_2\text{⩾−}\text{q}{}_0\text{λ}{}^2\text{4}$ while they are complex conjugate pairs if $\text{V}{}_2\text{<−}\text{q}{}_0\text{λ}{}^2\text{4}$.     

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

Neutral pion production by weak neutral currents in neutrino and antineutrino reactions

A study is presented of single π^o production in neutrino and antineutrino interactions in Gargamelle filled with freon CF₃Br. Limits on the neutral to charged current cross-section ratios $\text{R}{}_{\mathrm{v}}\text{=σ(v}\text{N}\text{→v}\text{N}\text{′π}{}^{\mathrm{o}}\text{)/2 σ(v}\text{N}\text{→ μ}{}^{\mathrm{-}}\text{N}\text{′π}{}^{\mathrm{o}}\text{)}$ and $\text{R}{}_{\mathrm{<mtext>\nu </mtext>}}\text{= σ(}\text{ν}\text{N}\text{→}\text{ν}\text{N}\text{′π}{}^{\mathrm{o}}\text{)/2 σ(}\text{ν}\text{N}\text{→ ω}{}^{\mathrm{+}}\text{N}\text{′π}{}^{\mathrm{o}}\text{)}$ are found to be $\text{0.10 < R}{}_{\mathrm{\nu }}\text{< 0.20}\text{and}\text{0.26 < R}{}_{\mathrm{<mtext>\nu </mtext>}}\text{< 0.44}$ at 68% confidence level.     

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.     

Molecular three-body approach to Λ9Be and Σ9Be hypernuclei

The dependence of the low-lying spectra of ${}_{\mathrm{\Lambda ,\; \Sigma }}{}^9\text{Be}$ hypernuclei on hyperon-α interaction in the molecular α + α + Λ(Σ) scheme has been studied. A suggestion is made for obtaining the strengths of both p-wave and spin-orbit Λ-α interactions from the experimental ${}_{\mathrm{\Lambda }}{}^9\text{Be}$ spectrum. A relation between the Σ⁰-binding energies $\text{B}{}_{\mathrm{\Sigma }}\text{(}{}_{\mathrm{\Sigma }}{}^9\text{Be}\text{)}$ and $\text{B}{}_{\mathrm{\Sigma }}\text{(}{}_{\mathrm{\Sigma }}{}^9\text{He}\text{)}$ has been established and on its basis a prediction is made about a possible binding energy of ${}_{\mathrm{\Sigma }}{}^5\text{He}$.     

Study of the photon spectrum in the decay KS0→π+π−γ

The branching ratio $\text{Λ(}\text{K}{}_{\mathrm{<mtext>S</mtext>}}{}^0\text{→π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{γ)}\text{Λ(}\text{K}{}_{\mathrm{<mtext>S</mtext>}}{}^0\text{→π}{}^{\mathrm{+}}\text{π}{}^{\mathrm{?}}\text{)}$ has been determined to be (2.68±0.15)×10^?3 for photon energies $\text{E}{}_{\mathrm{\gamma }}{}^1$ greater than 50 MeV in the K_S⁰ rest frame. The decay K_S⁰→π⁺π^?γ is found to be dominated by the internal bremsstrahlung transition. The branching rato of a possible direct transition is found to be less than 0.06 × 10^?3 at 90% confidence level for $\text{E}{}_{\mathrm{\gamma }}{}^1\text{> 50}\text{MeV}$.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

Spectroscopic study of the N = 27 nuclei by means of the (τ, α) reaction

The (τ, α) reaction on ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr and ⁵⁴Fe target nuclei has been studied at 25 MeV incident energy. Angular distributions have been measured from 5° to 40° with a split-pole spectrometer in a large range of excitation energy. A local zero-range DWBA analysis has been carried out, using an isospin-dependent potential for the calculation of the neutron form factor, in order to get a coherent set of spectroscopic factors for both T_> and T_< levels in different nuclei. Assignments of l-values have been done for a large number of levels, most of them previously unknown, and energy centroids of hole states have been determined. Spectroscopic factors in ³⁹Ca, ⁴⁷Ti, ^{49, 52, 53}Cr have also been obtained for strongly excited states. A sum rule analysis has been carried out for the N = 27 nuclei: the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{T}{}_{\mathrm{<}}$ hole strengths are generally fully exhausted by the observed levels, whereas only a fraction of the $\text{1}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ strength has been evidenced. The $\text{1}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{, 1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ analog states have been observed in all nuclei; in ⁵³Fe, the $\text{1}\text{d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{and}\text{2}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ analog states appear to be split in several components. In addition, a CRC analysis has been carried out for some levels with angular distributions not accounted for by a direct pick-up process. These levels are tentatively identified with states resulting from the coupling of one $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ neutron hole with excited states of the target nucleus. In particular, the $\text{5}\text{2}{}^{\mathrm{?}}\text{and}\text{9}\text{2}{}^{\mathrm{?}}$ members of the $\text{[2}{}^{\mathrm{+}}\text{?}\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{?1}}\text{]}$ configuration have been identified in each final nucleus. Unambiguous J^π assignments are made; and the two-step (τ, α) reaction therefo e appears as a useful spectroscopic tool, especially for investigating high spin states.     

The spectrum of HeNe+

Discharges through mixtures of helium and neon show two band groups near 4250 and 4100 Å as first observed by Druyvesteyn. These bands, assigned to the HeNe⁺ ion by Tanaka, Yoshino, and Freeman, have been studied under high resolution and have been fairly completely analyzed. The upper state of the transition is a very weakly bound state resulting from $\text{He}{}^{\mathrm{+}}\text{(}{}^2\text{S) +}\text{Ne}\text{(}{}^1\text{S}{}_0\text{)}$. There are two lower states resulting from the two components of $\text{Ne}{}^{\mathrm{+}}\text{(}{}^2\text{P) +}\text{He}\text{(}{}^1\text{S}{}_0\text{)}$. The upper of these two (${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) is also very weakly bound while the lower of the two, the ²Σ⁺ ground state, has a dissociation energy of 0.69 eV and an r_e value of 1.30 Å. All bands in both band groups show four branches designated R_ff, Q_ef, Q_fe, and P_ee. From their analysis the rotational constants in the various vibrational levels of the three electronic states have been determined. While no spin splitting in the B²Σ⁺ state has been found the ground state X²Σ shows a very large spin splitting and the $\text{A}{}_2{}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ state a very large $\text{Ω-type}$ doubling. The vibrational numberings in all these states were established by the study of the spectrum of ³HeNe⁺. At the same time the hyperfine structure observed in all lines of ³HeNe⁺ confirmed the nature of the upper state B²Σ⁺ as resulting from He⁺ + Ne, i.e., by charge exchange from the ground state. The ${}^2\text{Π}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ component of the ²Π state has not been observed, presumably because of low intensity.     

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

Methyl barrier to internal rotation and quadrupole coupling constants in S-methylchlorothioformate

Internal rotation A-E splittings have been observed in the ground state for both ³⁵Cl and ³⁷Cl isotopic species of S-methylchlorothioformate. The values $\text{V}{}_3\text{(}{}^{35}\text{Cl}\text{) = 893 ± 20}$ and $\text{V}{}_3\text{(}{}^{37}\text{Cl) = 890 ± 20 cal/mole}$ have been obtained. The anaalysis of the hyperfine structure gave $\text{χ}{}_{\mathrm{aa}}\text{(}{}^{35}\text{Cl}\text{) = ?49.2}$, $\text{χ}{}_{\mathrm{bb}}\text{(}{}^{35}\text{Cl}\text{) = 22.4}$ and $\text{χ}{}_{\mathrm{aa}}\text{(}{}^{37}\text{Cl}\text{) = ?39.0}$, $\text{χ}{}_{\mathrm{bb}}\text{(}{}^{37}\text{Cl) = 18.3 MHz}$. Only the syn-conformation of the methyl group with respect to the carbonyl group has been observed. A partial r₀ structure is given.     

Rotational bands in 195, 197Tl

High-spin states in ^{195, 197}Tl have been populated with (α, xn) reactions and studied by means of in-beam γ-ray and e^? spectroscopic methods. Complementary studies of the decay of ^{195, 197}Pb to ^{195, 197}Tl have been carried out. Several new features have been observed in these nuclei. The $\text{9}\text{2}{}^{\mathrm{?}}$ bands of ^{195, 197}T1. extended to $\text{27}\text{2}{}^{\mathrm{(?)}}$ and $\text{29}\text{2}{}^{\mathrm{(?)}}$, respectively, show a quenching of energy spacings between the $\text{23}\text{2}{}^{\mathrm{?}}$, $\text{25}\text{2}{}^{\mathrm{?}}$, $\text{27}\text{2}{}^{\mathrm{(?}}$ and $\text{29}\text{2}{}^{\mathrm{(?}}$ states. This has been interpreted as resulting from the coupling of a $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton to the ($\text{π}\text{h}{}^{\mathrm{?2}}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{)}{}_{\mathrm{8+,\; 10+}}$ configurations in the core nuclei ^{194, 196}Hg. Furthermore, positive-parity bands based on $\text{15}\text{2}{}^{\mathrm{+}}$ states were established up to the $\text{35}\text{2}{}^{\mathrm{(+)}}$ and $\text{29}\text{2}{}^{\mathrm{(+)}}$ states in ^{195, 197}Tl respectively. Probably these bands originate from the coupling of a h${}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton to a broken neutron pair. This pair consists of a rotation-aligned $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron and a low-j neutron in the $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, $\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ or $\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ shell. It is known to constitute the 5^? bands in ^{194, 196}Hg.     

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.     

A study of the excited electronic states of 9-fluorenone

Some spectroscopic properties of the low-energy electronic states of 9-fluorenone have been examined. The spectra in paraffin matrices at 4.2°K show detailed vibrational spectra. Two fluorescence spectra are observed; a diffuse emission arises from 9-fluorenone crystals in the paraffin matrix, and a sharp emission is characteristic of the molecule. The sharp fluorescence is analyzed in terms of known a₁ vibrational fundamentals. The sharp absorption is a near mirror-image to the fluorescence, so Herzberg-Teller vibrations are not prominent. The polarization in the crystal spectrum allows this low-energy transition near 23 000 cm^?1 to be assigned ${}^1\text{B}{}_2\text{←}{}^1\text{A}{}_1$. Because there is no vibronic perturbation in fluorescence, and certainly no out-of-plane modes, a $\text{π}{}^1\text{← n}$ transition seen at about 26 000 cm^?1 is tentatively assigned ${}^1\text{B}{}_1\text{←}{}^1\text{A}{}_1$. Another sharp absorption system is seen at 31 000 cm^?1 in the paraffin matrices at 4.2°K (linewidth 6 cm^?1) but no fluorescence was detected. The polarized crystal spectrum indicated the assignment of this system and another very strong system at 40 000 cm^?1 to be ${}^1\text{B}{}_2\text{←}{}^1\text{A}{}_1$, while other systems at about 34 000 cm^?1 and 44 000 cm^?1 are ${}^1\text{A}{}_1\text{←}{}^1\text{A}{}_1$.The phosphorescence spectrum of pyrene-d₁₀ held in a single crystal of 9-fluorenone at 4.2°K has been recorded. No delayed fluorescence from the host crystal is observed at 4.2°K but is intense at 77°K. The energy difference between host and guest triplet levels is estimated to be about 900 cm^?1 allowing the lowest triplet state of 9-fluorenone to be placed at 17 800 cm^?1.     

On the order of levels in charmonium

We prove a theorem concerning the energies of the 2S and 3D states in a potential $\text{V(r) =}\text{?g}{}^2\text{r}\text{+ V}{}_{\mathrm{<mtext>c</mtext>}}\text{(r)}$, where V_c is a non-singular confining potential. If $\text{(}\text{d}\text{d}\text{r)}{}^3\text{(r}{}^2\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ is positive, then the 3D state lies above the 2S state, provided

$\text{d}\text{d}\text{r}\text{1}\text{r}\text{d}\text{d}\text{r}\text{2V}{}_{\mathrm{<mtext>c</mtext>}}\text{+r}\text{d}\text{V}{}_{\mathrm{<mtext>c</mtext>}}\text{d}\text{r}\text{< 0, ?}{}_{\mathrm{r}}\text{>0.}$

For V_c = r^α, this corresponds to 0 < α < 2.     

An experimental study of the form factor in the decay K+ → πoe+ν

The q² variation of the factor $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)}$ in the decay K⁺→π⁰e⁺ν has been studied using a sample of even detected in the CERN 1.1 m³ heavy-liquid bubble chamber. The data are consistent with a linear development $\text{?}{}_{\mathrm{+}}\text{(q}{}^2\text{)=?}{}_{\mathrm{+}}\text{(0) (1+λ}{}_{\mathrm{+}}\text{q/m}{}^2{}_{\mathrm{\pi }}\text{)}$ with λ₊=0.027±0.008.