Orientation of199mHg by optical pumping detected by γ-radiation anisotropy

^199mHg was produced and mass separated at the ISOLDE facility (CERN). Nuclear orientation achieved by optical pumping via the resonance line 6s ^{2 1} S ₀→6s6p ³ P ₁,λ=2537Å was monitored by means of the anisotropy of theγ-radiation emitted in the cascade^199mHg(I=13/2⁺) $${}^{199m}Hg(I = 13/2^ + )\xrightarrow[{M4}]{}{}^{199*}Hg(I = 5/2^ - )\xrightarrow[{E2}]{}{}^{199}Hg(I = 1/2^ - ).$$ ^199*Hg(I=5/2^?)¹⁹⁹Hg(I=1/2^?). Maximum anisotropies of 35% (2,8%) were found in the M4 (E2) transition. A Zeeman scanning of the³ P ₁ state yielded the positions ofF=13/2 and theF=15/2 hfs components relative to the reference isotope²⁰⁴Hg at 15.13 (15) GHz and ?2.86 (15) GHz respectively. Isotopic shift and the quadrupole interaction constant were deduced from these values using the knownA factor.δv ^199m/2O4=v ^2O4?v ^199m=12.20 (16) GHzB=?0.86 (25) GHz. From theB factor the spectroscopic quadrupolment was calculated asQ _s =1.54 (44) barn.     

In-beam studies of203, 205Bi and shell-model features of odd-a bismuth isotopes

States in^{203, 205}Bi are populated using the reaction^{203, 205}Tl(³He,3n). Theπi _13/2 single-proton states and all the members of thev(2 ₁ ⁺ )?π h _9/2 quintuplet are identified in both nuclei. The half-lives of the isomericJ ^π=21/2⁺ states in both isotopes are measured and found to be 90±7 ns and 100±6 ns, and from these values suggestions for the half-lives of the previously reportedJ ^π=25/2⁺ isomers are made. The structures of the multiplets of the formv(Pb)?π h _9/2 are calculated in the framework of the shell model and it is shown that the main features can be derived from theπ?v ^?1 effective interaction. The wave functions of the 4 ₁ ⁺ and 4 ₀ ⁺ states in^{202, 204}pb are deduced indirectly from the calculation in^{203, 205}Bi.     

Atomic beam magnetic resonance investigations in the3 F 2 Ground State of177Hf,179Hf and180Hf

The 5d ²6s ^{2 3} F ₂ ground state of¹⁷⁷Hf,¹⁷⁹Hf and¹⁸⁰Hf has been studied using the atomic beam magnetic resonance method. The atomic beam was produced by an universal evaporation technique described in a previous paper. The results are¹⁸⁰Hfg _j (³ F ₂)=0.695812 (10)¹⁷⁷Hf Δv(³ F ₂;F=11/2?F=9/2)=991.7917 (10) MHz Δv(³ F ₂;F=9/2?F=7/2)=477.0081 (10) MHz Δv(³ F ₂;F=7/2?F=5/2)=162.8890 (10) MHz¹⁷⁹HfΔv(³ F ₂;F=13/2?F=11/2)=82.1320 (10) MHz Δv(³ F ₂;F=11/2?F=9/2)=392.8498 (10) MHz. The magnetic dipole and electric quadrupole moments of the¹⁷⁷Hf and¹⁷⁹Hf nuclear ground states as calculated from these hyperfine structure measurements are the following: μ(177)=0.75(8)μ _k , Q(177)=4.34 (65) barns μ(179)=?0.61 (6)μ _k , Q(179)=4.90 (75) barns.     

Evidence for a newK * \bar K state at a mass of 1,530 MeV withIJ PC=01++ observed inK − p interactions at 4.2 GeV/c

Evidence is presented for a newK ^* \(\bar K\) +c.c. resonance with a mass of (1,526±6) MeV, a width of (107±15) MeV and quantum numbersIJ ^PC=01⁺⁺. We call itD′ meson. Initially it is observed as aK ^* \(\bar K\) +c.c. enhancement in the reactionsK ^? p→(K _s ⁰ K ^±π^?)Λ at 4.2 GeV/c. The isospin assignmentI=0 comes from its further observation in the reactionsK ^? p→(K _s ⁰ K ^±π^?)Σ ⁰ andK ^? p→(K _s ⁰ K ^±π^?)Σ(1,385)⁰ but not inK ^? p→(K ⁺ K ^?π^?)Σ⁺ orK ^? p→(K _s ⁰ K ^±π^?)Σ(1,385)⁺. A maximum likelihood analysis of the (K \(\bar K\) π) decay Dalitz plots in the reactionsK ^? p→(K _s ⁰ K ^±π^?) determines theJ ^PC of theD′ meson to be 1⁺⁺. A satisfactorySU(3) fit is obtained to a 1⁺⁺ nonet composed of theI-1A ₁, theI=1/2Q _A with theD(1,285) and theD′(1,526) as theI=0 members having a mixing angle close to the magic one.     

Nuclear orientation and NMR/ON of205,207Po

^205,207Po have keen implanted with an isotope separator on-line into cold host matrices of Fe, Ni, Zn and Be. Nuclear magnetic resonance of oriented²⁰⁷Po has been observed in Fe and Ni, of²⁰⁵Po in Fe. The resonance frequencies for zero external field are $$\begin{gathered} v_L (^{207} Po\underline {Fe} ) = 575.08(20)MHz \hfill \\ v_L (^{207} Po\underline {Ni} ) = 160.1(8)MHz \hfill \\ v_L (^{205} Po\underline {Fe} ) = 551.7(8)MHz. \hfill \\ \end{gathered} $$ From the dependence of the resonance frequency on external magnetic field theg-factor of²⁰⁷Po was derived as $$g(^{207} Po) = + 0.31(22).$$ Using this value the magnetic hyperfine fields of Po in Fe and Ni were obtained as $$\begin{gathered} B_{hf} (Po\underline {Fe} ) = + 238(16)T \hfill \\ B_{hf} (Po\underline {Ni} ) = 66.3(4.6)T. \hfill \\ \end{gathered}$$ Theg-factor of²⁰⁵Po follows as $$g(^{205} Po) = + 0.304(22).$$ From the temperature dependence of the anisotropies ofγ-lines in the decay of^205,207Po the multipole mixing of several transitions was derived. The electric interaction frequenciesv _Q=eQV_zz/h in the hosts Zn and Be were measured as $$\begin{gathered} v_Q (^{207} Po\underline {Zn} ) = + 42(3)MHz \hfill \\ v_Q (^{207} Po\underline {Be} ) = - 70(20)MHz \hfill \\ v_Q (^{205} Po\underline {Be} ) = - 42(17)MHz. \hfill \\ \end{gathered}$$      

Dynamic stabilization of the helicalm=1 instability in a linear screw pinch

Dynamic stabilization of the helicalm=1 instability was studied in the linear high-β screw pinch ISAR III (T _i ≈50 to 500eV;n _e ≈5·10¹⁶ cm^?3; β≧0.5). The experimentally determined growth rates ω _i (0.5 to 3·10⁶ s^?1) and wavelengths (100 to 200 cm) of these modes are about the same as in a toroidal screw pinch and both agree well with theory. Two methods of dynamic stabilization were investigated. In both cases the stabilizing effects were better than expected from existing theory. In the first method an axially uniform oscillating field \(\tilde B_{zo} \) ·sin (ω _s t) was superposed on the quasi-steadyB _zo field (ω _s >ω _i ). Them=1 mode is stabilized and a stabilization condition \(\tilde B_{zo} /B_{zo} \gtrsim 2\omega _i /\omega _s \) holds. This stabilizing effect is very likely caused by inertial forces produced by enforcedm=0,k=0 oscillations of the plasma column. When working in resonance with the natural plasma oscillations, it is easier to satisfy the above condition. In the second method oscillating currents \(\tilde I_{zo} \) · sin (ω _s t) were added to the axial plasma currentI _zo to study the stabilization by dynamic shear (ω _s >ω _i ). Magnetic probe measurements showed that the \(\tilde I_z \) flows in the dilute plasma outside the dense plasma column. The measured skin depths and resistivities are larger than those expected from classical theory. Nevertheless, a reduction of the growth of them=1 mode occurred which was larger the more closely \(\tilde I_z \) flowed alongside the plasma column, giving a stabilization condition \(\tilde I_{zo} /I_{zo} > \omega _s /(5\omega _i )\) .     

Conserved-vector-current hypothesis and the\bar v_e e^ - \to \pi ^ - \pi ^0 process

Based on the conserved-vector-current (CVC) hypothesis and a four-ρ-resonance unitary and analytic VMD model of the pion electromagnetic form factor, theσ _tot(E _v ^lab ) and dσdE _π ^lab of the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) process are predicted theoretically for the first time. Their experimental approval could verify the CVC hypothesis for all energies above the two-pion threshold. Since, unlike the electromagnetic e⁺e^?→π⁺π^? process, there is no isoscalar vector-meson contribution to the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) reaction, accurate measurements of theσ _tot(E _v ^lab ) that moreover is strengthened with energyE _v ^lab linearly could solve now a widely discussed problem of the mass specification of the first excited state of theρ(770) meson. As a by-product, an equality \(\sigma _{tot} (\bar v_e e^ - \to \pi ^ - \pi ^0 ) = \sigma _{tot} (e^ + e^ - \to \pi ^ - \pi ^0 )\) is predicted for \(\sqrt s \approx 70 GeV\) .     

On the free energy of the hopfield model

The general theory of inhomogeneous mean-field systems of Raggio and Werner provides a variational expression for the (almost sure) limiting free energy density of the Hopfield model $$H_{N,p}^{\{ \xi \} } (S) = - \frac{1}{{2N}}\sum\limits_{i,j = 1}^N {\sum\limits_{\mu = 1}^N {\xi _i^\mu \xi _j^\mu S_i S_j } } $$ for Ising spinsS _i andp random patterns ξ^μ=(ξ ₁ ^μ ,ξ ₂ ^μ ,...,ξ _N ^μ ) under the assumption that $$\mathop {\lim }\limits_{N \to \gamma } N^{ - 1} \sum\limits_{i = 1}^N {\delta _{\xi _i } = \lambda ,} \xi _i = (\xi _i^1 ,\xi _i^2 ,...,\xi _i^p )$$ exists (almost surely) in the space of probability measures overp copies of {?1, 1}. Including an “external field” term ?ξ _μ ^p h^μμξ _i=1 ^N ξ _i ^μ S_i, we give a number of general properties of the free-energy density and compute it for (a)p=2 in general and (b)p arbitrary when λ is uniform and at most the two componentsh ^μ1 andh ^μ2 are nonzero, obtaining the (almost sure) formula $$f(\beta ,h) = \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } + h^{\mu _2 } ) + \tfrac{1}{2}f^{ew} (\beta ,h^{\mu _1 } - h^{\mu _2 } )$$ for the free energy, wheref ^cw denotes the limiting free energy density of the Curie-Weiss model with unit interaction constant. In both cases, we obtain explicit formulas for the limiting (almost sure) values of the so-called overlap parameters $$m_N^\mu (\beta ,h) = N^{ - 1} \sum\limits_{i = 1}^N {\xi _i^\mu \left\langle {S_i } \right\rangle } $$ in terms of the Curie-Weiss magnetizations. For the general i.i.d. case with Prob {ξ _i ^μ =±1}=(1/2)±?, we obtain the lower bound 1+4?²(p?1) for the temperatureT _c separating the trivial free regime where the overlap vector is zero from the nontrivial regime where it is nonzero. This lower bound is exact forp=2, or ε=0, or ε=±1/2. Forp=2 we identify an intermediate temperature region between T_*=1?4?² and T_c=1+4?² where the overlap vector is homogeneous (i.e., all its components are equal) and nonzero.T _* marks the transition to the nonhomogeneous regime where the components of the overlap vector are distinct. We conjecture that the homogeneous nonzero regime exists forp≥3 and that T_*=max{1?4?²(p?1),0}.     

New aspect in transient magnetic fields using heavy ion beams

Transient field precessions have been measured with the first excited 2 ₁ ⁺ -state as probe for ions of²⁸Si traversing Fe at v_ion?1v₀ and 13v₀(v₀=c/137) and⁶²Ni being stopped in Fe. The degree of polarization deduced for the Si ions, p_1s=0.19(6), is consistent with low-velocity data. There is clear evidence that the field strength is attenuated by heavy ion beams. For the⁶²Ni(2 ₁ ⁺ ) state at 1.173 MeV a g-factor value of g=0.34(7) was obtained in good agreement with a previous result.     

Hadronisation effects in event-shape moments

We study the moments of hadronic event shapes in e ⁺ e ^? annihilation within the context of next-to-next-to-leading order (NNLO) perturbative QCD predictions combined with non-perturbative power corrections in the dispersive model. This model is extended to match the NNLO perturbative prediction. The resulting theoretical expression has been compared to experimental data from JADE and OPAL, and a new value for α _s (M _Z ) has been determined, as well as of the average coupling α ₀ in the non-perturbative region below μ _I =2 GeV within the dispersive model: $$\begin{array}{rcl}\alpha_s(M_Z)&=&0.1153\pm0.0017(\mathrm{exp})\pm0.0023(\mathrm{th}),\\[5pt]\alpha_0&=&0.5132\pm0.0115(\mathrm{exp})\pm0.0381(\mathrm{th}).\end{array}$$ The precision of the α _s (M _Z ) value has been improved in comparison to the previously available next-to-leading order analysis. We observe that the resulting power corrections are considerably larger than those estimated from hadronisation models in multi-purpose event generator programs.     

On the behavior of the πN partial wave amplitudes ats=0

The behavior of theπN partial wave amplitudes in the limitss→+0 ands→? 0 is related to backward scattering in thes- andt-channel, respectively. Assuming Mandelstam analyticity we prove with the aid of the Phragmen-Lindelöf theorem that the amplitudes for high energy backward scattering inπN→πN andππ→N¯N are equal and therefore dominated by the same exchange mechanism, namely Reggeized Fermion exchange. The dominating Regge trajectory is the Δ_δ-trajectory, and it is shown that theπN partial wave amplitudes diverge fors→±0 as \(s^{ - \alpha \Delta _\delta (0) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . — Reduced amplitudes are defined which are regular ats=0. — Using recent results ofπN backward scattering real and imaginary part of thes-wave amplitudef ₀₊ ^(?) are calculated in the interval 0≦s≦7.     

Inclusion relations for the spaces L(ℝ), \mathcal{H}\mathcal{K} (ℝ) ∩ \mathcal{B}\mathcal{V} (ℝ), and L 2(ℝ)

The inclusion relations for the spaces $ \mathcal{H}\mathcal{K} $ (I), L(I), $ \mathcal{H}\mathcal{K} $ (I) ∩ $ \mathcal{B}\mathcal{V} $ (I), and L ²(I) are found. On unbounded intervals, functions in $ \mathcal{H}\mathcal{K} $ (I) ∩ $ \mathcal{B}\mathcal{V} $ (I) need not be Lebesgue integrable.     

Determination of the isotopic shift of192Hg in the line λ=2537 Å by Zeeman scanning the Hanle signal

The Hanle signal in theλ=2 537 Å resonance line of an line mass separated¹⁹²Hg was Zeeman scanned from a spectral lamp containing isotopically pure²⁰⁴Hg. The isotopic shift was redetermined asδv ^192/204=v ²⁰⁴?v ¹⁹²=?27.7(3) GHz. The application of this method to even-even isotopes still further from stability is discussed.     

Dynamical Localization for the Random Dimer Schrödinger Operator

We study the one-dimensional random dimer model, with Hamiltonian H _ω =Δ+V _ω , where for all x∈ $\mathbb{Z}$ , V _ω(2x)=V _ω(2x+1) and where the V _ω(2x) are i.i.d. Bernoulli random variables taking the values ±V, V>0. We show that, for all values of Vand with probability one in ω, the spectrum of His pure point. If V≤1 and V≠1/ $\sqrt 2$ , the Lyapunov exponent vanishes only at the two critical energies given by E=±V. For the particular value V=1/ $\sqrt 2$ , respectively, V= $\sqrt 2$ , we show the existence of new additional critical energies at E=±3/ $\sqrt 2$ , respectively, E=0. On any compact interval Inot containing the critical energies, the eigenfunctions are then shown to be semi-uniformly exponentially localized, and this implies dynamical localization: for all q>0 and for all ψ∈ $\ell$ ²( $\mathbb{Z}$ ) with sufficiently rapid decrease $${\mathop {\sup }\limits_t} r_{\psi ,I}^{\left( q \right)} {\kern 1pt} \left( t \right): = {\mathop {\sup }\limits_t} \left\langle {P_I \left( {H\omega } \right)\psi _t ,\left| X \right|^q P_I \left( {H\omega } \right)\psi _t } \right\rangle < \infty $$ Here $\psi _t = e^{- iH_{\omega ^t}} \psi$ , and P _I(H _ω) is the spectral projector of H _ωonto the interval I. In particular, if V>1 and V≠ $\sqrt 2$ , these results hold on the entire spectrum [so that one can take I=σ(H _ω)].     

Inclusive production ofK *(892) andΣ(1385) in\bar p p interactions at 3.6 GeV/c and a test of factorization hypothesis

We present a study of the inclusive production ofK ^*(892) and ∑^t+-(1385)+cc at 3.6 GeV/c from \(\bar p\) p interactions. The sensitivity of the exposure is 35.4 events/μb. Longitudinal and transverse momentum distributions are presented. The indirect production ofK _s ⁰ from parentK ^* and that of Λ's from parent Σ(1385) are studied. The shape of thex distribution of Λ's for \(p\xrightarrow{{\bar p}}\Lambda \) are calculated from \(p\xrightarrow{p}\Lambda \) and \(p\xrightarrow{{\pi ^ - }}\Lambda \) and compared with the experimental distributions. The difference of antiparticle production cross-section ofK _s ⁰ in the central region is compared with the expectation from Mueller-Regge formalism.     

Asymptotic inverse spectral problem for anharmonic oscillators

We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??²+x ²?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)～|x|^?α V(x) with a trigonometric even functionV(x)=Σa _mcosω _m x. The eigenvalues ofL are shown to be λ _k =k+μ _k with small μ _k =O(k ^?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ _k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ^?α|V(x) ofB from asymptotics of {µ _k }. ₁ ^∞      

K-conversion coefficient of the 53.3 keV transition and\frac{K}{{L + M}}-ratio of the 13.34 keV transition in73Ge

TheK-conversion coefficient of the 53.3 keV transition in⁷³Ge was measured by coincidence techniques to be αk ₁=7.1 ± 0.6 indicating very good agreement with heory forM2-radiation. The \(\frac{K}{{L + M}}\) -ratio of the 13.34 keV transition to the ground state was determined using the same techniques. The resulting value \(\left( {\frac{K}{{L + M}}} \right)_2 \) =0.36 ± 0.03 supports theE2-character of this radiation and therefore a spin assignment of \(\frac{5}{2}\) for the 13.34 keV level. The measured lifetime of this transition (T _1,2=(2.95 ± 0.05) μsec) corresponds to a factor of 15 greater than the Weisskopf estimation for a pureE2-transition. A short discussion of a possible transfer of the collectivity of the⁷²Ge-nucleus to the⁷³Ge-nucleus is given.