Collision-induced dissociation of H 2 + ions into the fragmentations H+H(2p) and H++H(2p)

Using a photon-particle delayed coincidence method the energy distributions of H +H(2p) and H⁺+H(2p) fragment pairs have been measured arising from collisional dissociation of 10 keV H ₂ ⁺ ions incident on various target gases. H fragments in their 2p state are identified by the Lymanα radiation emitted. The distribution of H+H(2p) fragment pairs arising from dissociative charge exchange reveals a sharp increase below 0.2 eV in the center-of-mass frame of the H ₂ ⁺ ion. This is ascribed to predissociation of vibrational levels of higher H₂ Rydberg states close above then=2 dissociation limit by those H₂ Rydberg states which separate into H+H(2p) fragments. Only direct transitions into the continuum of theGK ¹ ∑ _g ⁺ state may compete. Some structure at 0.3–0.5 eV is attributed to the three statesI ¹ П _g,i ³ П _g, andh ³ bE _g ⁺ having potential barriers of this height. The distributions for H⁺+H(2p) have maxima at 3.4, 3.8, and 4.2 eV for a H₂, Ar, and He target, respectively, indicating that the 2pπ _u state as well as the 3dσ _g state ofH ₂ ⁺ is excited. The H+H(2p) process has a greater probability than the H⁺+H(2p) process for Ar and H₂ targets, though all electronic H₂ states under consideration are bound.     

The dual (p,q)-Alexander-Conway Hopf algebras and the associated universal ℐ-matrix

The dually conjugate Hopf algebrasFun _p,q (R) andU _p,q (R) associated with the two-parametric (p,q)-Alexander-Conway solution (R) of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebraU _p,q (R) is extracted. The universal ?-matrix forsFun _p,q (R) is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ?-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ?-matrix and the FRT matrix generators,L ^(±), forU _p,q (R) are derived from the ?-matrix.     

Low-energy γp scattering and determination of proton polarizabilities

For the first time, an analysis of all experimental data on the differential cross section for elastic γp scattering at photon energies below 150 MeV is performed in order to determine the electric (α _p) and magnetic (β _p) polarizabilities of the proton. A fit to these data with two free parameters α p and β _p embedded into the theoretical cross section obtained on the basis of finite-energy s-channel dispersion relations gives the following world-average values of the proton polarizabilities: α _p=11.7±0.8 (stat.+syst.)±0.7 (model), β _p=2.3±0.9 (stat.+syst.)±0.7 (model) in units of 10^?4 fm³. The first error is combined—it takes into account the statistical and systematic errors in the experimental cross sections—while the second error comes from the theoretical uncertainties in the dispersion-theory cross sections.     

K-Ionization probability across the 460-keV12C(p,p 0) resonance

We have remeasured theK-shell vacancy production probabilityP _K across the 460-keV¹²C(p, p ₀) resonance, previously investigated by Duinker et al. We are unable to confirm the large (～70 %) variation ofP _K across the resonance, found by Duinker et al. for protons elastically scattered at 125°. Our values for the ratioP _K (142°)/P _K (16°) are independent (within±20%) of the proton bombarding energy over the resonance region, in agreement with theoretical predictions by Blair and Anholt, Feagin and Kocbach, McVoy and Weidenmüller. Our average value for this ratio, equal to 0.88 ±0.06, agrees with the value 0.88 calculated by Amundsen and Aashamar.     

Inclusive prompt photon production inpp and\bar p p interactions

High transverse momentum (p _T ) production of pions and photons in proton-proton and proton-antiproton interactions are studied within the QCD framework and compared with the presently available experimental data. Scaling violation effects are included, and shown to be important at largep _T . Predictions are made for the γ/π⁰ ratio at collider energies. The possibility of extricating the gluon distribution function from the invariant cross section data for the process \(\bar p\) +p→γ+X is suggested.     

Diffraction dissociation in the reaction p+p→Λ°+K++p at the CERN ISR

The exclusive reaction pp→Λ°K⁺p has been studied at 0.1<?t_pp<0.6 GeV² and energies √s=45 GeV and 53 GeV at the CERN ISR. Diffractive excitation p→Λ°K⁺ occurs predominantly in the mass range M(Λ°K⁺)≈2.1 GeV and peaks at 1.7 GeV. The cross section for pp→Λ°K⁺p is 10±3μb for M(Λ°K⁺)<2.5 GeV, and the t_pp dependence is exp (bt) with b=7.0±0.5 GeV^?2.     

Investigation of the 6p 2(3 P 0)n p Rydberg series of bismuth by multiphoton excitation

Rydberg states of the odd-parity series 6p ²(³ p ₀)n p of BiI are excited by a three-photon process. A two-photon dissociation of Bi₂ into excited atomic states followed by a one-photon absorption leads to highly excited atomic Rydberg states up ton = 32. States of the even-parity Rydberg series 6p ²(³ p ₀)nsJ=1/2,ndJ=3/2 andndJ=5/2 are also observed. In order to avoid the background caused by ionization of the bismuth molecules we performed a two-color excitation with pulsed dye lasers. With this experiment the 6p ²(³ p ₀)npJ=3/2 Rydberg series could be resolved up ton=75. The increasing quantum defect of this series is due to a perturbing state close to the first ionization limit. By a MQDT analysis we obtain the energy of the perturbing state and a value of 58,761.68±0.1 cm^?1 for the first ionization limit of atomic bismuth.     

A spectroscopic study of 18F: (I). The 17O(p,p)17O and 17O(p, α0)14N reactions

The ¹⁷O(p, p)¹⁷O and ¹⁷O(p, α₀)¹⁴N reactions have been studied in the energy range E_p = 0.5–1.33 MeV. Excitation functions for elastic scattering measured at several angles give l_p values for six resonances and J^π; T values of 3⁺; 1 and 2⁺; 1 for the states at 6.16 and 6.28 MeV, respectively. From both reactions, J^π limitations were found for six resonant levels. The ¹⁷O(p, α₀)¹⁴N reaction also yields information on T-assignments and level formation parameters. Experimental results are discussed in terms of shell-model configurations.     

Messungen der Winkelverteilung der 440 keV-γ-Strahlung aus der Reaktion23Na (p,p′ γ)23Na in den ResonanzenE p =1281 keV undE p =1456 keV

The angular distribution of the 440 keV-γ-radiation following the reaction²³Na(p, p′)²³Na has been measured. The experimental results areW(Θ)=1-(0,147±0,05)P ₂(cosΘ) in the resonanceE _p =1281 keV andW(Θ)=1-(0,099 ± 0,06)P ₂(cosΘ) in the resonanceE _p =1456 keV.     

Polarization effects in ionizing thermal energy collisions of laser-excited Ne(3p 3 D 3) atoms with Ar atoms

Using transverse and longitudinal excitation of a collimated metastable Ne(3s ³ P _2.0) beam with average velocities of 500, 800, and 1,200 m/s by means of a single mode dye laser on the²⁰Ne(3s ³ P ₂→3p ³ D ₃) transition, we have investigated ionizing collisions of polarized Ne(3s ³ P ₂) and Ne(3p ³ D ₃) atoms with Ar atoms. The product electrons were energy analyzed with high resolution (9–25 meV). The resulting Ne(3p ³ D ₃) electron spectra exhibit a strong dependence on the three types of laser polarization (π _∥,π_⊥, σ_?), chosen to prepare the excited atoms. In contrast, the Ne(3s ³ P ₂) spectra are only weakly dependent on polarization. Detailed model calculations have been carried out for the Ne(3p)+Ar cross sections, using computed excited-state potential curves, semi-empirical ionic potentials, and local autoionization width functions. A semiclassical closecoupling method is applied to describe the evolution of the polarized collision system in the coupled entrance channels. It is found that a single autoionization widthΓ(R) is not sufficient to describe the measured polarization effects properly. The dependence ofΓ on the initial and final state is expressed in terms of few reduced electronic transition matrix elements, which are determined by comparison of measured and calculated total cross sections and Ar⁺(² P _3/2)/Ar⁺(² P _1/2) branching ratios for ionizing collisions of the various Ne(3pJ=1,2,3) multiplet states with Ar. The matrix elements corresponding to Ar(3pσ)→Ne(2pσ) electron transfer during autoionization are found to dominate, but Ar(3pπ)→Ne(2pπ) transfer has also to be included. The resulting calculated electron spectra reproduce the measured polarization effects in a semi-quantitative way.     

Gamma-rays from the24Mg(p,γ)25Al reaction for proton energiesE p=800 keV toE p=1,830 keV

The yield curve and resonance strengths of resonances in the²⁴Mg(p, γ)²⁵Al reaction for the proton energy rangeE _p=800 keV toE _p=1,830 keV, have been determined and the existence of a resonance atE _p=1.184 MeV confirmed. Single energy spectra as well as decay schemes and branching ratios are given for these resonances. An upper level of 2.0×10^?15 sec for the lifetime of the 3.079 MeV level in²⁵Al results from a Doppler shift attenuation measurement carried out on the 2.624 MeV gamma line originating in the 3.070 MeV→0.455 MeV transition in²⁵Al.     

Pole approximation in the quasi-free t + p scattering and the t(p,d)d reaction via the t + d interaction

The t(p,p)t and t(p,d)d channels have been investigated in an indirect way through the ²H(t,tp)n and ²H(t,dd)n three-body reactions performed at E _t = 35.5?MeV in quasi-free kinematics. The agreement with direct data supports the pole approximation at energies above the Coulomb barrier.     

Polarization in quasielastic (p,2p) scattering on a 4He nucleus at 1 GeV

The polarization of secondary protons from the (p, 2p) reaction induced by 1-GeV protons incident to a ⁴He nucleus was measured in a kinematically complete experiment. By using a two-arm magnetic spectrometer, two secondary protons from this reaction were recorded in coincidence at unequal scattering angles of Θ₁ = 18°?24.21° and Θ₂ = 53.22° over a broad range of the recoil-nucleus momentum K _B between 0 and 150 MeV/c. It was found that the measured polarization of either secondary proton is less than that observed in free elastic proton-proton scattering. The magnitude of this difference is determined by the mean binding energy of s-shell protons rather than by the effective nuclear density. The polarizations measured in inclusive quasielastic and elastic scattering of 1-GeV protons on ⁴He nuclei are presented for scattering angles in the range Θ₁ = 18° ? 24.21°.     

Measurement of π−p → π0n at large momentum transfer

New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/c, extending in momentum transfer up to ?t = 1.8 (GeV/c)², are reported and compared with an optical impact parameter model, together with previous data for the reaction π^?p → ηn at the same energy. The imaginary part of the pole trajectory b₀(s) is determined from the slope of the tangent to the maxima of $\text{(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{d}\text{σ}\text{d}\text{t}$. The linear increase of Im b₀(s) with log s, which has been observed at low energies, continues up to 40 GeV/c.     

The11B(p,p′)11B* reaction: An extended coupled-channels treatment

The predictions of a multi-configurational shell model continuum calculation for the¹¹B(p, p) and¹¹B(p,p′) reaction channels are discussed. In the calculated excitation function for the (p, p ₁) channel theT=1, 2^? resonances play a dominant role in the region of 22 MeV to 24 MeV excitation in¹²C. These model predictions are consistent with the known parent states in the¹²B system. Corroborative evidence is also obtained by comparing theory with the differential cross section data.     

Polarization of protons in C12(d,p)C13 reaction

The angular distributions of the polarization of protons from C¹²(d,p)C¹³(g.s) reaction were measured at 200 keV intervals for deuteron energies from 1.40 to 2.40 MeV. Elastic scattering on C¹² at 45 ° (lab) was used to analyze the polarization. Positive sign of the polarization corresponds to the vector productK _d ×K _p . The maximum polarization observed is about 30%. The results are not similar to those obtained from the mirror reaction C¹²(d,n)N¹³ in the same deuteron energy range.     

On the Lie-Trotter theorems inL p -spaces

In this paper we consider operatorsH ₀ andV possessing the following properties:

1. H ₀ is a positive self-adjoint operator acting inL ²(M, γ) with γ a probability measure, so that exp(?tH ₀) is a contraction onL ¹(M, γ) for eacht>0.
2. V is a semibounded multiplicative operator acting inL ²(M, γ) {fx379-1}

Under these assumptions theorems of Lie-Trotter type are derived for the operatorsH, H ₀, V, whereH is a self-adjoint extension of the algebraic sumH ₀+V, and is built by the form method. Under the additional assumption thatV(·)∈L ²(M, γ) we prove an essential self-adjointness ofH ₀+V. The results obtained are applicable to non-relativistic quantum mechanics.     

The15N(p,α 0)12C reaction at stellar energies

The¹⁵N(ρ, α₀)¹²C reaction has been investigated in the energy range ofE _p (lab)=78-810keV. The measurement of the excitation functions and α-particle angular distributions involved solid targets as well as a quasi-point supersonic jet gas target. The determination of absolute cross sections has been carried out with the gas target. The observed energy dependence of the total cross sections can be described in terms of two-level Breit-Wigner shapes including the resonances atE _p (J ^π)=335(1^?) and 1,028(1^?)keV. The data lead to a zero-energy intercept of the astrophysicalS(E) factor ofS(0)= 65±4MeV-b. The angular distributions are asymmetric around 90° and require an additional amplitude in the reaction mechanism, which interferes predominantly with the 335 keV resonance. The origin of this background amplitude is discussed.     

A study of the reaction p + p → p + p + X at ISR energies

We have performed an experiment to investigate the reaction p + p → p₁ + p₂ + X at the CERN Intersecting Storage Rings (ISR). The dependence of the cross-section on the mass and rapidity of the system X, and on the momentum transfer squared t₁, t₂ to the outgoing protons is studied. We observe signals for the production of ?, ω, f, and A₂ mesons in the missing-mass spectra, and conclusions are made about the contribution of double-Pomeron exchange.     

Impact parameter dependence of the probability for removal of the 2s and 2p atomic electrons by nuclei

The probability W(x) of inner shell ionization by nuclei as a function of the impact parameter x is expressed through the ionization matrix element M_if. Values of W(x) for removal of the 2s and 2p electrons are calculated with the first Born M_if and compared with the SCA result.