Specific features of the excitation spectrum of helium II in a plasma initiated by an electron beam

The emission of a low-pressure helium plasma (P≤2 Torr) initiated by a monochromatic electron beam is investigated. It is found that an increase in the current leads to a drastic increase in the rate of charge exchange of doubly charged helium ions. The assumption is made that inelastic collisions of He⁺⁺ ions with metastable helium atoms provide the main channel of charge exchange of these ions due to the reaction He⁺⁺+Hem→ He⁺*+He ₀ ⁺ .     

Pentaquark decay is suppressed by chirality conservation

It is shown that, if the pentaquark \(\Theta ^ + = uudd\bar s\) baryon can be represented by the local quark current η_Θ, its decay Θ⁺→nK⁺(pK⁰) is forbidden in the limit of chirality conservation. The Θ⁺ decay width Γ is proportional to \(\alpha _s^2 \left\langle {0\left| {\bar qq} \right|0} \right\rangle ^2\), where \(\left\langle {0\left| {\bar qq} \right|0} \right\rangle ,q = u,d,s\), is quark condensate, and, therefore, is strongly suppressed. The polarization operator of the pentaquark current is calculated using the operator product expansion. The Θ⁺ mass found by the QCD sum rules method is in reasonable agreement with experiment.     

Das magnetische Moment des 2,083 MeV-Zwei-Protonen-Niveaus des gerade-gerade-Kerns Ce140

The nuclearg-factor of the 2·083 MeV-state of Ce¹⁴⁰ has been determined as:g=1·11±0·04 This value suggests the interpretation of the level as the (g7/2,d5/2)₄ two proton shell model configuration. The investigation implies an integral measurement as well as a time dependent differential measurement (spin rotation method) of the rotation of the 329 keV-487 keVγγ-angular correlation in strong external magnetic fields. Liquid sources of lanthanum nitrate solved in 3n HNO₃ were used in these experiments. Some cerium (IV)nitrate was added to make sure that the 4f;-electronic shell remained empty after theβ ^?-decay. This prevented paramagnetic effects. Additional runs were performed without adding cerium (IV)nitrate and finally by using liquid sources of lanthanum chloride solved in 2n HCl with some iron (II)-chloride added. It was expected that the Fe⁺⁺ ions would reduce the primarily formed Ce⁺⁺⁺⁺ ions into the Ce⁺⁺⁺ state. The Ce⁺⁺⁺ shell is paramagnetic and enlarges the effective magnetic field at the position of the nucleus by about 36%. As no definitely faster rotation could be observed, one has to conclude that the ion reaction Ce⁺⁺⁺⁺+Fe⁺⁺?Ce⁺⁺⁺+Fe⁺⁺⁺ takes more than about 10^?8s. The half life of the 2·083 MeV state has been redeterminded asT _1/2=(3·41±0·04)·10^?9s. Differential measurements of the angular correlation of the 329 keV-487 keV cascade as a function of the time delay showed that perturbations by internal fields were very small. The coefficientsA ₂ andA ₄ of the angular correlation and the attenuation parameterλ ₂ were determined from measurements with sources of the first type as:A ₂=?0·105±0·003A ₄=?0·001±0·002 andλ ₂=(0·0065±0·0040)·10⁹S^?1=(0·032±0·020)·λ A comparison with the theoretical coefficients of a (3-4-2)-cascade shows that the multipolarity of the 329 keV radiation is a mixture of 99·83%M1 and (0·17±0·03) %E2.     

Dominant decays of scalar leptoquarks and scalar gluons in the minimal four-color symmetry model

Fermionic and weak decays of the scalar leptoquarks S = S ₁ ⁽⁺⁾ , S ₁ ^(?) , and S _m and the scalar gluons F = F ₁ and F ₂ predicted by the minimal model involving four-color symmetry and the Higgs mechanism of quark-and lepton-mass splitting are considered. The widths and the branching ratios are calculated for these decays, and the results are analyzed versus the couplings and masses of decaying particles. It is shown that, at relatively small mass splittings Δm within scalar doublets (Δm < m _W), the fermionic decays S ₁ ⁽⁺⁾ → tl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → t \(\tilde \nu \) _j, F ₁ → t \(\tilde b\), and F ₂ → t \(\tilde t\), which are characterized by few-GeV widths for m _S, m _F < 1 TeV and decay branching ratios close to unity, are dominant, but that, for Δm > m _W, the weak decays S → S′W and F → F’W compete with the above fermionic decays. In the case of m _S < m _t, the processes S ₁ ⁽⁺⁾ → cl _j ⁺ , S ₁ ^(?) → v _i \(\tilde b\), S _m → bl _j ⁺ , and S _m → c \(\tilde \nu \) _j, whose total branching ratios are Br(S ₁ ⁽⁺⁾ → cl ⁺) ≈ Br(S ₁ ^(?) → v \(\tilde b\)) ≈ 1, Br(S _m → bl ⁺) ≈ 0.9, and Br(S _m → c \(\tilde \nu \)) ≈ 0.1, appear to be dominant decays of scalar leptoquarks. Searches for these decays at LHC and the Tevatron are of interest.     

Ds+ → π+ π+ π− decay: The $$1^3 P_0 s\bar s$$ component in scalar-isoscalar mesons

We calculate the processes \(D_s^ + \to \pi ^ + s\bar s\) and D _s ⁺ → π⁺resonance, respectively, in the spectator and W-annihilation mechanisms. The data on the reaction D _s ⁺ → π⁺ρ⁰, which is due to the W-annihilation mechanism only, point to a negligibly small contribution of the W annihilation to the production of scalar-isoscalar resonances D _s ⁺ ?π⁺f₀. As to spectator mechanism, we evaluate the \(1^3 P_0 s\bar s\) component in the resonances f₀(980), f₀(1300), and f₀(1500) and broad state f₀(1200–1600) on the basis of data on the decay ratios D _s ⁺ ?π⁺f₀/(D _s ⁺ ?π⁺_θ). The data point to a large \(s\bar s\) component in the \(f_0 (980):40 \lesssim s\bar s \lesssim 70\% \). Nearly 30% of the \(1^3 P_0 s\bar s\) component flows to the mass region 1300–1500 MeV, being shared by f₀(1300), f₀(1500), and broad state f₀(1200–1600): the interference of these states results in a peak near 1400 MeV with the width around 200 MeV. Our calculations show that the yield of the radial-excitation state\(2^3 P_0 s\bar s\)is relatively suppressed, \({{\Gamma (D_s^ + \to \pi ^ + (2^3 P_0 s\bar s))} \mathord{\left/ {\vphantom {{\Gamma (D_s^ + \to \pi ^ + (2^3 P_0 s\bar s))} {\Gamma (D_s^ + \to \pi ^ + (1^3 P_0 s\bar s))}}} \right. \kern-\nulldelimiterspace} {\Gamma (D_s^ + \to \pi ^ + (1^3 P_0 s\bar s))}} \lesssim 0.05\).     

Secondary ion emission from a GaAs single crystal upon bombardment with Bi<Stack> <Subscript> <Emphasis Type="Italic">m</Emphasis> </Subscript> <Superscript>+</Superscript> </Stack> cluster ions

Secondary-ion mass spectra and energy distributions upon bombarding a gallium arsenide single crystal using Bi_m⁺(m = 1–5) cluster ions with energies of 2–12 keV are investigated. The gallium cluster ion yield grew nonadditively with the number of atoms in the cluster projectiles. A quasi-thermal component found in the energy spectra of secondary Ga⁺ and Ga₂⁺ ions is indicative of the occurrence of the thermal spike mode upon cluster ion bombardment. The quasi-thermal component in the yield of atomic Ga⁺ ions upon bombardment with Bi₂⁺–Bi₅⁺–ions is 35–75%.     

Umladung und Ionisation beim Durchgang von leichten und schweren Wasserstoffionen durch leichten und schweren Wasserstoff

Charge exchange and ionisation cross-sections were measured for the interaction of H⁺, H ₂ ⁺ , D⁺ and D ₂ ⁺ ions with H₂ and D₂ in the energy range 1.5–30 keV. In contrary to earlier measurements showing no isotope effect for a given ion velocity the results were as follows:

1. a)
   The charge exchange cross-sections depend on the proportion of the ion massm ₁ and the mass of the target moleculem ₂. The cross-sections increase with increasingm ₂/m ₁.     
   
   

Krein formula with compensated singularities for the ND-mapping and the generalized Kirchhoff condition at the Neumann Schrödinger junction

The Neumann Schrödinger operator \(\mathcal{L}\) is considered on a thin 2D star-shaped junction, composed of a vertex domain Ω_int and a few semi-infinite straight leads ω _m , m = 1, 2, ..., M, of width δ, δ ? diam Ω_int, attached to Ω_int at Γ ? ?Ω_int. The potential of the Schrödinger operator l ^ω on the leads vanishes, hence there are only a finite number of eigenvalues of the Neumann Schrödinger operator L _int on Ω_int embedded into the open spectral branches of l ^ω with oscillating solutions χ _±(x, p) = \(e^{ \pm iK_ + x} e_m \) of l ^ω χ _± = p ² χ _±. The exponent of the open channels in the wires is

$K_ + (\lambda ) = p\sum\limits_{m = 1}^M {e^m } \rangle \langle e^m = \sqrt \lambda P_ + $

, with constant e _m , on a relatively small essential spectral interval Δ ? [0, π ² δ ^?2). The scattering matrix of the junction is represented on Δ in terms of the ND mapping

$\mathcal{N} = \frac{{\partial P_ + \Psi }}{{\partial x}}(0,\lambda )\left| {_\Gamma \to P_ + \Psi _ + (0,\lambda )} \right|_\Gamma $

as

$S(\lambda ) = (ip\mathcal{N} + I_ + )^{ - 1} (ip\mathcal{N} - I_ + ), I_ + = \sum\limits_{m = 1}^M {e^m } \rangle \langle e^m = P_ + $

. We derive an approximate formula for \(\mathcal{N}\) in terms of the Neumann-to-Dirichlet mapping \(\mathcal{N}_{\operatorname{int} } \) of L _int and the exponent K _? of the closed channels of l ^ω . If there is only one simple eigenvalue λ ₀ ∈ Δ, L _intφ0 = λ _0φ0 then, for a thin junction, \(\mathcal{N} \approx |\vec \phi _0 |^2 P_0 (\lambda _0 - \lambda )^{ - 1} \) with

$\vec \phi _0 = P_ + \phi _0 = (\delta ^{ - 1} \int_{\Gamma _1 } {\phi _0 (\gamma )} d\gamma ,\delta ^{ - 1} \int_{\Gamma _2 } {\phi _0 (\gamma )} d\gamma , \ldots \delta ^{ - 1} \int_{\Gamma _M } {\phi _0 (\gamma )} d\gamma )$

and \(P_0 = \vec \phi _0 \rangle |\vec \phi _0 |^{ - 2} \langle \vec \phi _0 \),

$S(\lambda ) \approx \frac{{ip|\vec \phi _0 |^2 P_0 (\lambda _0 - \lambda )^{ - 1} - I_ + }}{{ip|\vec \phi _0 |^2 P_0 (\lambda _0 - \lambda )^{ - 1} + I_ + }} = :S_{appr} (\lambda )$

. The related boundary condition for the components P ₊Ψ(0) and P ₊Ψ′(0) of the scattering Ansatz in the open channel \(P_ + \Psi (0) = (\bar \Psi _1 ,\bar \Psi _2 , \ldots ,\bar \Psi _M ), P_ + \Psi '(0) = (\bar \Psi '_1 , \bar \Psi '_2 , \ldots , \bar \Psi '_M )\) includes the weighted continuity (1) of the scattering Ansatz Ψ at the vertex and the weighted balance of the currents (2), where

$\frac{{\bar \Psi _m }}{{\bar \phi _0^m }} = \frac{{\delta \sum\nolimits_{t = 1}^M { \bar \Psi _t \bar \phi _0^t } }}{{|\vec \phi _0 |^2 }} = \frac{{\bar \Psi _r }}{{\bar \phi _0^r }} = :\bar \Psi (0)/\bar \phi (0), 1 \leqslant m,r \leqslant M$

(1)

,

$\sum\limits_{m = 1}^M {\bar \Psi '_m } \bar \phi _0^m + \delta ^{ - 1} (\lambda - \lambda _0 )\bar \Psi /\bar \phi (0) = 0$

(1)

. Conditions (1) and (2) constitute the generalized Kirchhoff boundary condition at the vertex for the Schrödinger operator on a thin junction and remain valid for the corresponding 1D model. We compare this with the previous result by Kuchment and Zeng obtained by the variational technique for the Neumann Laplacian on a shrinking quantum network.

     

On the binding of atoms with antiatoms

The stability of X⁺Y⁺X^?Y^? Coulomb molecules consisting of X⁺Y^? atoms and X^?Y⁺ antiatoms to dissociation is studied. On the basis of multiparameter variational calculations, it is found that such molecules are stable to dissociation into X⁺X^? atoms and Y⁺Y^? antiatoms if the mass ratio of particles X and Y lies in the range 0.4710<m _X /m _Y <2.1231. The e⁺e⁺e^?e^?, π⁺μ⁺π^?μ^?, t⁺d⁺t^?d^?, p⁺K⁺p^?K^?, and d⁺p⁺d^?p^? molecules satisfy this condition.     

Messung des gR-Faktors des 2+-Rotationsniveaus von Dy160 nach der Spinrotationsmethode und Bestimmung der Multipolmischungen mehrerer γ-Übergänge im Zerfall des Tb160

A differential measurement of the spin rotation of Dy¹⁶⁰ in the 2+ rotational state was performed by using liquid sources of TbCl₃ solved in 3M HCl and applying an external magnetic field of 33 500 Gauss. No change of the Larmor precession frequency could be detected within the first 10·10^?9 s. It is concluded that the ground state of the electronic shell of Dy⁺⁺⁺ is reached in 6·10^?10 s after theβ-decay of Tb¹⁶⁰. The valueg _R=+0.364±0.011 was derived using 〈r^?3〉_eff=8.92 a. u. for the 4f-shell of Dy⁺⁺⁺. A comparison with the result ofCohen who studied the Mössbauer-effect in Fe₂Dy shows that the value of 〈r^?3〉_eff must be 10% larger in this compound. A measurement of the effective magnetic field at the position of the nucleus in a source of terbium metal was performed for different temperatures. It revealed a temperature dependence which is very similar to the paramagnetic susceptibility χ(T). We observed a strong attenuation ofγ γ-angular correlations in the 2+ rotational state. For liquid sources of TbCl₃ solved in 3M HCl the following attenuation parameters were measured:

$$\begin{gathered} \lambda _2 = (0.122 \pm 0.013) \cdot 10^9 {\text{s}}^{ - {\text{1}}} , \hfill \\ \lambda _4 = (0.235 \pm 0.024) \cdot 10^9 {\text{s}}^{ - {\text{1}}} . \hfill \\ \end{gathered}$$     

On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent propertiesin two-electron atoms/ions which include the negatively charged Ps^? (e^?e⁺e^?)and H^? ions, Heatom and positively charged, helium-like ions from Li⁺ to Ni²⁶⁺. All these ions areconsidered in their ground 1¹S-state(s). The slowly convergent properties selected inthis study include the electron-nulceus (r^2k_eN) and electron-electron (r^2k_ee) expectation values for k = 2, 3, 4 and 5.     

New Bounds on the Maximum Ionization of Atoms

We prove that the maximum number N _c of non-relativistic electrons that a nucleus of charge Z can bind is less than 1.22Z + 3Z ^1/3. This improves Lieb’s upper bound N _c  < 2Z + 1 Lieb (Phys Rev A 29:3018–3028, 1984) when Z ≥ 6. Our method also applies to non-relativistic atoms in magnetic field and to pseudo-relativistic atoms. We show that in these cases, under appropriate conditions, \({\limsup_{Z \to \infty}N_c/Z \le 1.22}\).     

Transverse polarization of the lepton in the decay process <Emphasis Type="Italic">B</Emphasis> → <Emphasis Type="Italic">Dlν</Emphasis><Subscript>l</Subscript> due to electromagnetic final-state interaction

The emergence of transverse polarization of the lepton in the decay processes B⁰ → D^?l⁺ν_l and \(B^ + \to \bar D^0 l + \nu _l \) for l = τ, μ is studied on the basis of the Standard Model in the leading approximation of heavy-quark effective theory. It is shown that a nonzero transverse polarization appears owing to electromagnetic final-state interactions at the one-loop level. Diagrams involving D and D* mesons in the intermediate state and making a nonzero contribution to the transverse polarization of the outgoing lepton are considered. If only these mesons are taken into account in evaluating the mean values of the τ-lepton polarization in the decays B⁰→D^?τ⁺ν_τ and \(B^ + \to \bar D^0 \tau ^ + \nu _\tau \), the results are 2.60×10^-3 and ?1.59×10^?3, respectively. The corresponding values of the transverse muon polarization averaged over the Dalitz plot are 2.97×10^?4 and-6.79×10^?4.     

Four-Leptonic Decays of Charged and Neutral <Emphasis Type="Italic">B</Emphasis> Mesons within the Standard Model

The branching ratios and differential distributions for the four-leptonic decays \({B^ - } \to {\mu ^ + }{\mu ^ - }{\bar v_e}{e^ - }\), \({B^ - } \to {e^ + }{e^ - }{\bar v_\mu }{\mu ^ - }\), and \({B^ - } \to {\mu ^ + }{\bar v_\mu }{\mu ^ - }{\mu ^ - }\) are calculated within the Standard Model. The branching ratios for the rare decays B_d,s → e⁺e^?μ⁺μ^? and B_d,s → μ⁺μ^?μ⁺μ^? are estimated. Methods for testing the lepton universality in rare multileptonic decays of charged and neutral B mesons are proposed.     

Determination of quark-antiquark component of the photon wave function for <Emphasis Type="Italic">u,d, s</Emphasis> quarks

Based on the data for the transitions π⁰, η, η′ → γγ*(Q²) and reactions of the e⁺e^? annihilations e⁺e^? → ρ⁰, ω, ? and e⁺e^? → hadrons at 1<E _e+e? <3.7 GeV, we determine the light-quark components of the photon wave function \(\gamma * (Q^2 ) \to q\bar q(q = u,d,s)\) for the region 0 ? Q² ? 1 (GeV/c)².     

Untersuchung des Iridium-191m-Zerfalls

Theγ-radiation of the nuclear isomer Ir^191m (T _1/2=4.5 sec) has been investigated with the aid of a scintillation fast-slow coincidence-spectrometer. Theγ-rays of the 42 keV-transition have been measured for the first time. The conversion coefficient α of this transition was found to be α = 13500 ₊₂₁₁₀₀ ^?5200 in acceptable agreement with the value taken from the tables ofRose under the assumption of anE3-transition. Thus this assignment proposed earlier by other authors has been confirmed. TheK-conversion coefficient of the 129 keV-transition has been remeasured yielding α _K =2.32±0.06.     

Investigation of Rare Pion Decays with the PIBETA Spectrometer

Experimental results on pion decays obtained with the PIBETA spectrometer at the Paul Scherrer Institute (PSI) are reviewed. For pion beta decay π⁺ → π⁰е⁺ν (πβ), a precision measurement of relative probability yields Г(πβ) = [1.036 ± 0.004(stat) ± 0.004(syst) ± 0.003(π⁺→е⁺ν)] × 10^–8, which implies V_ud = 0.9728(30) for the corresponding element of the Cabibbo–Kobayashi–Maskawa mixing matrix. Using a sample of 65 × 10³ events, relative probability of the π⁺→е⁺νγ radiative pion decay (RPD) in the kinematic region of E_γ > 10 MeV and θ_eγ > 40° is measured as B^exp = 73.86(54) × 10^–8. A statistical analysis of measured E_e+ and E_γ distributions for this decay yield the values F_V = 0.0258(17) and F_A = 0.0117(17) for the pion weak formfactors. Assuming that F_V linearly depends on the е⁺ν invariant mass q² as F_V(q²) = F_V(0)(1 + aq²), the slope parameter is extracted as а = 0.10(6). The pion polarizability and neutral-pion lifetime are estimated as α_E = 2.78(10) × 10^–4 fm³ and τ(π⁰) = (8.5 ± 1.1) × 10^–17 s, respectively. The data for decays π⁺→ е⁺ ν and \({\mu ^ + } \to {e^ + }v\bar v\gamma \) have been collected and are being processed. The follow-up PEN experiment aims at reducing the uncertainty on the π⁺ → е⁺ ν relative probability by almost an order of magnitude (to 5 × 10^–4).     

Searching for signatures around 1920 MeV of a N<Superscript>*</Superscript> state of three hadron nature

We provide a series of arguments which support the idea that the peak seen in the \( \gamma\) p \( \rightarrow\) K ⁺ \( \Lambda\) reaction around 1920MeV should correspond to the recently predicted state of J ^P = 1/2⁺ as a bound state of K \( \bar{{K}}\) N with a mixture of a ₀(980)N and f ₀(980)N components. At the same time we propose polarization experiments in that reaction as a further test of the prediction, as well as a study of the total cross-section for \( \gamma\) p \( \rightarrow\) K ⁺ K ^- p at energies close to threshold and of dσ/dM _inv for invariant masses close to the two-kaon threshold.     

Stability of Coulomb systems

The stability of m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? Coulomb systems formed by particles of unit charge against dissociation is considered as a function of the particle mass. It is shown that, from the stability of the m ₁ ⁺ m ₂ ⁺ m ₃ ^? three-particle system, it follows that the m ₁ ⁺ m ₂ ⁺ m ₃ ^? m ₄ ^? four-particle system containing an additional particle of mass satisfying the condition m ₄ ^? ? m ₃ ^? is stable. The results of calculations of the stability domain for m ₁ ⁺ m ₂ ⁺ m ₃ ^? systems asymmetric in particle masses are reported. The stability of 39 asymmetric exotic four-particle molecules and mesic molecules against dissociation is established.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.