Low energy π-π resonances in the Veneziano model

We attempt to impose elastic unitarity on the forward π-π scattering using the Veneziano Amplitude together with a crossing symmetric subtraction term as an input. TheN/D method is used and thep, ? mesons are interpreted as CDD poles. The self consistency requirement led to the evalutation of the low energy parameters and theS andP-wave phase shifts. The values of the scattering lengths obtained area ₀ ⁰ =0.084m _π ^?1 ,a ₂ ⁰ =?0.024m _π ^?1 ,a ₁ ¹ =0.047m _π ^?3 .     

Two-particle production inK + p interactions at 32 GeV/c

Results are presented on two-particle inclusive production inK ⁺ p interactions at 32 GeV/c. We study thex _1,2=x ₁+x ₂ dependence of invariant structure functions of (ππ)-pairs and compare them to single particle inclusive distributions in the fragmentation regions. Distributions of particles observed at Feynmanx ₂ in association with various “trigger” particles or systems atx ₁ in the same hemisphere are dicussed in terms of the reduced variable \(\tilde x_2 = x_2 /(1 - |x_1 |)\) . We further present absolute production rates and production ratios of π⁺'s and π^?'s associated with π^±,K _s ⁰ , Λ, \(\bar \Lambda \) ,K ^*+ (890), (K _s ⁰ π⁺), and (π⁺ π^?)-triggers, and compare them with qualitative predictions of the quark recombination model. Forwardbackward correlations between (K _s ⁰ π^±), (K _s ⁰ ,p), (Λ, π^?), \((\bar \Lambda \pi ^ \pm )\) , and (p, π^?) pairs are also discussed.     

The decay of the Bethe-Salpeter kernel inP(ϕ)2 quantum field models

We extend methods of high temperature expansions to show that for even weakly coupledP(?)₂ quantum field models the Bethe-Salpeter kernel has 4 particle decay. More precisely ifK denotes the Euclidean Bethe-Salpeter kernel $$|K(x_1 ,x_2 ,x_3 ,x_4 )| \leqq Oe^{ - m_0 (1 - \varepsilon )d_2 } ,$$ wherex=(x ⁰,x ¹),d ₂=2|x ₁ ⁰ +x ₂ ⁰ ?x ₃ ⁰ ?x ₄ ⁰ |+|x ₁ ⁰ ?x ₂ ⁰ |+|x ₃ ⁰ ?x ₄ ⁰ | and ε(λ)→0 as λ→0. Our methods apply to otherr particle irreducible kernels.     

On the signatures of the canonical and the metrical energy densities of vector fields

The energy-density components Θ ₀ ⁰ andT ₀ ⁰ of the canonical and of the metrical energy-momentum tensors Θ _k ⁱ andT _k ⁱ for a statical field of vector mesons have opposite signatures: Θ ₀ ⁰ =H=?T ₀ ⁰ =?L. From this property some relativistic and field-theoretical theorems can be deduced in an elementary way.     

Inclusive ϱ0,K *±(892) andf production in\bar p p Interactions at 12 GeV/c

Inclusive production of ?⁰,K ^*±(892), andf is studied in \(\bar p\) p interactions at 12 GeV/c. The inclusive cross sections for ?⁰,K ^*±(892), andf are found to be 6.7±0.3 mb, 1.0±0.2 mb, and 1.4±0.3 mb, respectively. The differential cross sections are presented as a function of c.m. rapidity, Feynmanx and square of the transverse momentump _T ² . Comparison with the correspondingpp data shows some interesting differences which can be attributed to the \(\bar p\) p annihilation. The results are compared with the predictions of the quark fusion model.     

Inclusive resonance production in 7.3 GeV/c\bar pp interactions

We present results on inclusive baryon and meson resonance production in \(\bar pp\) interactions at 7.3 GeV/c. Total inclusive and semi-inclusive cross sections are given for Δ(1232),∑ ^*(1385), ?⁰,f andK ^*±(892) production. For the meson resonances separation into annihilation and non-annihilation components has been made, the annihilation component being dominant at this energy. We find that the energy dependence of inclusive cross sections for ?⁰ production inpp interactions and \(\bar pp\) non-annihilations shows a type of scaling behaviour previously reported for ?, ψ, ψ′ and ? production inpp interactions.Δ ⁺⁺, ?⁰ andK ^*± production are studied in terms of Feynmanx,y ^* andp _T ² . For the vector mesons we compare they ^* andx dependences with the predictions of simple quark models.     

Mößbauereffekt in157Gd und155Gd

Using the Mössbauer technique electric hyperfine interactions of the first excited non-rotational states at 64 keV in¹⁵⁷Gd and at 86.5 keV in¹⁵⁵Gd have been determined in GdF₃ and GdCl₃· 6H₂O. For the ratio of quadrupolmoments the ratiosQ ₆₄ ¹⁵⁷ /Q _g ¹⁵⁷ =1.74±0.04,Q _86.5 ¹⁵⁵ /Q _g ¹⁵⁷ =?0.07 ± 0.21 andQ _g ¹⁵⁵ /Q _g ¹⁵⁷ =0.78 ± 0.06 were found. In addition isomer shifts were observed from which a ratio δ〈r²〉 ₆₄ ¹⁵⁷ /δ〈r²〉 _86.5 ¹⁵⁵ =?2.6±0.15 can be inferred.     

EPR studies on the di-nitrogen centers with nonequivalent atoms in a reddish-brown plastically deformed diamond

Two new di-nitrogen centers, which were labeled M2 and M3, were found together with known W7 and N4 centers in an unusual reddish-brown natural diamond. The following magnetic hyperfine interaction parameters (expressed in MHz) were determined for the two nitrogen atoms:A ₁ ⁽¹⁾ =117.95(5),A ₁ ⁽²⁾ =A ₁ ⁽³⁾ =84.48(5),A ₂ ⁽¹⁾ =7.1(1),A ₂ ⁽²⁾ =A ₂ ⁽³⁾ =6.6(1) for M2 andA ₁ ⁽¹⁾ =121.55(5),A ₁ ⁽²⁾ =A ₁ ⁽³⁾ =85.90(5),A ₂ ⁽¹⁾ =6.0(1),A ₂ ⁽²⁾ =5.4(1),A ₂ ⁽³⁾ =5.1(1) for M3. Hyperfine interaction tensors for the nitrogen atom N₁ with a larger interaction have axial symmetry about the <111> direction, but those for the other nitrogen atom, N₂, appear to be small, almost isotropic. Probable models of the M2 and M3 centers are suggested and discussed.     

Perpendicularev mass fromW decay

We point out properties of the “perpendicularev mass”, defined in terms of transverse momentap _t byM _T ² (ev)=2|p _eT | |p _vT |?2p _eT ·p _vT , that make it particularly well suited toW mass and width determinations. We give an analytic expression for its distribution inW production and subsequentW→ev decay a \(\bar pp\) colliders, accurate to order 〈p _WT ² /M _W ² 〉≈1%. A maximum likelihood fit of this formula to the five UA1 events givesM _W=80.3 _?3 ⁺⁶ GeV.     

Inclusive Λ(1,520) production in 100 GeVp Be interactions

The reactionpBe→Λ(1,520)X has been measured at 100 GeV incident momentum in the kinematic range 0.15<x<0.35 \((x = 2p_\parallel ^{c.m} /\sqrt s )\) andP _T <1 GeV. The invariant cross section is compatible with that measured forpp interactions at the CERN-ISR. The differential cross sectiondσ/dp _T ² is fitted to an exponentiale ^?αp _T ² with α=2.7 GeV^?2.     

Hölder’s inequality for matrices

We prove that for arbitraryn×n matricesA ₁,A ₂,…,A _m and for positive real numbersp ₁,p ₂,…,p _m withp ₁ ^?1 +p ₂ ^?1 +…+p _m ^/?1 =1, the inequality 1 $$|Tr(A_1 A_2 ...A_m )^2 |< \mathop {II}\limits_{k = 1}^m [Tr(A_k^\dag A_k )^{p_k } ]P_k^{ - 1} $$ holds.     

Hyperfeinstrukturaufspaltung und Lebensdauer des 72 P 3/2-Terms von Rb85 und Rb87

The hyperfine structure splitting of the 7² P _3/2 state of Rb⁸⁵ and Rb⁸⁷ has been measured with optical double resonance. The following hfs interaction constants have been obtained: Rb⁸⁵:A _7p ⁸⁵ =3.71(1) MHz;B _7p ⁸⁵ =3.68 (8)MHz. Rb⁸⁷:A _7p ⁸⁷ =12.57(1) MHz;B _7p ⁸⁷ =1.71 (3)MHz. These values yield quadrupole moments ofQ _7p,hfs ⁸⁵ =+0.316(7) barn andQ _7p,hfs ⁸⁷ =+0.147(2)barn which are reduced by application of the Sternheimer correction toQ _7p ⁸⁵ =+0.267(6) barn andQ _7p ⁸⁷ =+0.124(2) barn. The averaged ratio of the uncorrected values of Q_hfs in the 5p and 7p ² P _3/2 stake isQ _5p,hfs/Q _7p,hfs=1.07(3). This has to be compared with the correction factors for polarization of the core of electrons by the nuclear quadrupole moment (1?R)_5p/(1?R)_7p=1.07. The agreement between the measured and calculated ratio indicates a net antishielding of the nuclear quadrupole moments of rubidium by the core of electrons as has been predicted bySternheimer. The lifetime of the 7² P _3/2 state of the RbI-spectrum is:τ(7² P _3/2, Rb)=2.4(2)·10^?7 sec.     

Off-shell effects in nucleon-deuteron polarization observables

A separable representation of theS-wave Paris potential and a phase-shift equivalent Yamaguchi-type potential significantly differing in their off-shell behaviours are used to calculate second-order polarization observables of elastic nucleon-deuteron scattering atE _D=10 and 20MeV. Off-shell effects are found that stem from differences in the nuclear interaction in the inner regionr?1.2 fm. Adding approximate Coulomb-distortion contributions to the purely nuclear Faddeev amplitudes proton-deuteron predictions are obtained. Coulomb effects are not found to be negligible. Comparison with experimental data, in particular, the spin-correlation parameterC _y,y of the reaction \({}^1\vec H(\vec d,d)^1 H\) forE _D=10MeV vector-polarized deuterons and the spin-transfer coefficientsK _y ^y′ ,K _x ^x′ andK _z ^x′ for \({}^2H(\vec p,\vec p)^2 H\) atE _p=10MeV, prefer the interaction model that contains an intermediate-range repulsion.     

Neutral strange particle production inK + p interactions at 32 GeV/c

The production properties ofK _s ⁰ , \(\bar \Lambda\) andK ⁺ p interactions at 32 GeV/c are investigated using the final statistics of the experiment. We present total and semi-inclusive cross sections and aver-age multiplicities. Estimates are given of the diffractive dissociation contributions to total and differential cross sections. Thex-,p _T ^?, and transverse mass dependence of inclusive and semi-inclusive distributions is discussed as well as properties of “prompt”K _s ⁰ 's. The ratio of “prompt”K ₈₉₀ ⁺ (K ₈₉₀ ⁰ ) to “prompt”K ⁰ cross sections is measured to be 1.03±0.12 (0.98±0.17). From a comparison of \(\bar \Lambda\) production inK ^± p interactions at 32 GeV/c, we estimate a strange sea-quark suppression of 0.26 ±0.02. The double differential cross sections ofK _s ⁰ 's is studied as a function of Feynman-x andp _T ² , and a Triple-Regge fit performed. The data are compared in detail to versions of the Lund-model for low-p _T hadronic collisions.     

Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Resonance strengths,branching ratios and mean lifetimes of nuclear energy levels in23Na

The gamma decay of the²²Ne(p, y)²³Na resonances in the proton energy rangeE _p=1.0→2.0 MeV has been investigated with a 20cm³ Ge(Li) detector. Implanted targets were used. The absolute strengths of the strongest resonances were determined and the branching ratios of twenty resonance levels and several bound states are reported. Mean lifetimes of the levels atE _x=2.078 MeV (18.7±3.5 fs), 2.393 MeV (580 _?190 ⁺³⁷⁰ fs), 2.641 MeV (88 _?14 ⁺²⁰ fs), 2.985 MeV (4.0 _?1.0 ^+1.3 fs), 3.679 MeV (24 _?4 ⁺⁵ fs), 3.915 MeV (7.4 _?2.0 ^+2.5 fs) and 4.775 MeV (<2.0 fs) were obtained from measurements of the gamma ray Doppler shifts.     

Charged particle and π0 multiplicity distributions and the annihilation properties of\bar p p interactions at 70 GeV/c

The elastic and inelastic \(\bar p\) p cross sections at 70 GeV/c have been determined in an experiment performed at CERN using BEBC equipped with a TST. The topological cross sections were measured and the moments of the inelastic multiplicity distribution are 〈n _c 〉=6.16±0.09, 〈n _c 〉/D=2.04±0.05 andf ₂ ^cc =2.97±0.03. The average number of Dalitz pairs per inelastic event is (3.12±0.09)×10^?2. Assuming that these all arise from π⁰ decay the average π⁰ multiplicity is \(\langle n_{\pi ^0 } \rangle = 2.71 \pm 0.14\) . The \(\bar p\) p?pp cross section differences lead to an annihilation cross section σ _A = 4.42±0.41 mb and the moments of the annihilation multiplicty distribution are 〈n _A 〉=8.0±0.3, 〈n _A 〉/D=2.5±0.2 andf ₂ ^A?? =?1.4±0.3. An independent check of σ _A was made by investigating fast forward charged and neutral secondary interactions in the TST and in the surrounding neon-hydrogen mixture, and gives a value σ _A = 5.0±1.6 mb. The ratio of fast \(\bar n\) to \(\bar p\) production in non-annihilation interactions at 70 GeV/c is found to be 0.45±0.11.