Three-body structure of <Emphasis Type="Italic">A</Emphasis> = 9 isobars (Be,Li, and C) and elastic proton scattering

Density profiles and static features (radii, magnetic moments, and quadrupole moments) are calculated with the wave functions found for A = 9 isobars on the basis of the α + α + n three-body model for the ⁹Be nucleus, the ⁷Li + n + n three-body model for the ⁹Li nucleus, and the ⁷Be + p + p three-body model for the ⁹C nucleus. The differential cross sections and analyzing powers for elastic proton scattering on ⁹Be at E = 220 MeV and 1.0 GeV and on ⁹Li and ⁹C at E = 700 and 60 MeV/nucleon (in inverse kinematics) are calculated within Glauber diffraction theory. All of the results are compared with available experimental data and with the results of the calculations performed by other authors.     

Subthreshold and near threshold K+ meson photoproduction\newline on nuclei

The inclusive K⁺ meson production in photon–induced reactions in the near threshold and subthreshold energy regimes is analyzed with respect to the one–step (γN→K ⁺ Y, Y=Λ,Σ) incoherent production processes on the basis of an appropriate new folding model, which takes properly into account the struck target nucleon removal energy and internal momentum distribution (nucleon spectral function), extracted from recent quasielastic electron scattering experiments and from many–body calculations with realistic models of the NN interaction. Simple parametrizations for the total and differential cross sections of the K⁺ production in photon–nucleon collisions are presented. Comparison of the model calculations of the K⁺ differential cross sections for the reaction γ+C¹² in the threshold region with the existing experimental data is given, that displays the contributions to the K⁺ production at considered incident energies coming from the use of the single–particle part as well as high momentum and high removal energy part of the nucleon spectral function. Detailed predictions for the K⁺ total and differential cross sections from γH², γC¹² and γPb²⁰⁸ reactions at subthreshold and near threshold energies are provided. The influence of the uncertainties in the elementary K⁺ production cross sections on the K⁺ yield is explored. Received: 12 April 1999 / Revised version: 11 September 1999     

Calculation of Be in an α-α-Λ Three-Body Model Using the Faddeev Equations

 The hypernucleus Be is investigated in an α-α-Λ three-body model using the Faddeev formalism. We use an α-α interaction in which the Pauli-forbidden states are correctly taken into account and we employ some phenomenological potentials between the α and Λ particles. We obtained two bound states for and , and three resonance states of . We studied the properties of these states by calculating the components and the expectation values of the potential for each partial wave. It is found that a few channels dominate in the α (α, Λ) and states, so that the alpha-clusters or the ⁸Be core are still alive in the nucleus. In a case where the two alpha particles are fixed on an axis the contour plots of the distribution of the Λ particle are shown. With the assistance of these plots one can visually understand that some of them are shell-model-like states while others are well developed cluster-model-like states. For the structure of Be, it is concluded that the Λ particle is loosely coupled in S- and P-wave orbits about the ⁸Be(0⁺) and ⁸Be(2⁺) core states. Finally, we discuss a redundant state in the Faddeev amplitude which could arise from the treatment of symmetrization. Received June 25, 1998; revised April 13, 1999; accepted for publication December 29, 1999     

Does break-up affect 9Be +209Bi fusion at the barrier?

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the 36.0 MeV ≤ E_lab≤ 50.0 MeV range, down to 0.6 mb, with high accuracy via in-beam detection of the ground state α-decay of the evaporation residues produced. The elastic scattering cross sections around 150° and 135° were also obtained with moderate angular resolution. The cross sections below the barrier are reproduced by coupled channel calculations which include only one break-up channel with a moderate strength and a phenomenological renormalization of the potential depth. These simple calculations overestimate the cross sections above the barrier most likely due to the fact that the ⁹Be break-up process becomes much stronger. The barrier distributions extracted do not have evident break-up signature since they show one-barrier structure. Received: 22 February 1999 / Revised version: 26 March 1999     

Positron scattering from alkaline-earth elements

The total (elastic + inelastic) cross sections fore ⁺ impact on alkaline-earth elements from Be to Ra are calculated by employing a complex spherical optical potential. This potential has static, polarization and absorption components. The positron energy range is from a few eV to several thousand eV. We have compared our elastic cross sections for Mg and Ca with the other available results and the agreement is good for energies above 100eV. We have also compared our absorption cross sections withe ⁻ ionization cross sections at high energies where our absorption cross sections are in good accord. We have made Bethe plots fore ⁺ scattering on these elements.     

Breakup of 8B and the 7Be(p, γ)8B reaction

The calculated rate of events in some of the existing solar neutrino detectors is directly proportional to the rate of the ⁷Be(p, γ)⁸B reaction measured in the laboratory at low energies. However, the low-energy cross sections of this reaction are quite uncertain as various measurements differ from each other by 30–40%. The Coulomb dissociation process which reverses the radiative capture by the dissociation of ⁸B in the Coulomb field of a target, provides an alternate way of accessing this reaction. While this method has several advantages (like large breakup cross sections and flexibility in the kinematics), the difficulties arise from the possible interference by the nuclear interactions, uncertainties in the contributions of the various multipoles and the higher order effects, which should be considered carefully. We review the progress made so far in the experimental measurements and theoretical analysis of the breakup of ⁸B and discuss the current status of the low-energy cross sections (or the astrophysical S-factor) of the ⁷Be(p, γ)⁸B reaction extracted therefrom. The future directions of the experimental and theoretical investigations are also suggested. Work supported by EPSRC, UK, grant nos J/95867 and L/94574.     

Study of the 3He(4He,γ)7Be and 3H(4He,γ)7Li Reactions in an Extended Two-Cluster Model

 The ³He(⁴He, γ)⁷Be and ³H(⁴He, γ)⁷Li reactions are studied in an extended two-cluster model which contains α + h/t and ⁶Li + p/n clusterizations. We show that the inclusion of the ⁶Li + p/n channels can significantly change the zero-energy reaction cross sections, S(0), and other properties of the ⁷Be and ⁷Li nuclei, like the quadrupole moments Q. However, the results agree with the known correlation trend between S(0) and Q. Moreover, we demonstrate that the value of the zero-energy derivatives of the astrophysical S-factors are more uncertain than currently believed. Received June 17, 1999; revised February 22, 2000; accepted for publication April 17, 2000     

Low–energy photodisintegration of 9Be and α+α+n→9Be +γ reactions at astrophysical conditions

A semi–microscopic model for the low–energy photodisintegration of the ⁹Be nucleus is constructed, and the experimental data are analyzed with its help. The older radioactive isotope data are supported by this analysis. The theoretical photodisintegration cross section is derived. The astrophysical rates for the reaction α+α+n→⁹Be+γ and the reverse photodisintegration of ⁹Be are calculated. The new reaction rate for α+α+n→⁹Be+γ is compared with previous estimations. Received: 19 January 1998     

Measurements of elastic scattering for 7Be, 7Li + 9Be systems and fusion cross sections for 7Li + 9Be system

Elastic scattering angular distributions have been measured for ⁷Be + ⁹Be system at E_lab = 17, 19 and 21 MeV in the angular range θ_cm=26^○–58°, and for ⁷Li + ⁹Be system at E_lab= 15.75, 24 and 30 MeV. An optical model (OM) analysis of these data have been carried out. For the ⁷Li + ⁹Be system fusion cross sections were obtained at E_lab = 15.75, 24 and 30 MeV by measuring the α-evaporation spectra from the compound nucleus at backward angles. The measured α-evaporation spectra were reproduced by the statistical model calculations and fusion cross sections were extracted therefrom. The ratios of the experimental fusion cross sections to the total reaction cross sections (obtained form OM analysis) were found to be rather small. This result suggests that break-up process has a strong influence on fusion process leading to a reduction in fusion cross section.     

Role of <Superscript>8</Superscript>Be heavy stripping mechanism in the <Emphasis Type="Italic">α</Emphasis> + <Superscript>12</Superscript>C inelastic scattering to the near-3<Emphasis Type="Italic">α</Emphasis>-threshold states in <Superscript>12</Superscript>C

The angular distributions of α + ¹²C elastic and inelastic (to the 4.44 MeV, 2⁺; 7.65MeV, 0⁺; and 9.64MeV, 3⁻ states) scattering at 110 MeV are characterized by pronounced enhancement and strong oscillations at large angles. We performed calculations of the differential cross sections of these reactions assuming a potential scattering in the forward hemisphere and the direct transfer of ⁸Be cluster θ _c.m. > 90°. We showed that the α + ⁸Be cluster configuration with relative angular momentum L = 0 dominates in the Hoyle state being 4.4 times larger than that in the ground state. This result also contributes to the verification of αBEC hypothesis and is consistent with the conjecture of a dilute 3α structure of the Hoyle state. In the 9.64 MeV, 3⁻ state, a positive interference of all allowed α + ⁸Be configurations with a dominance of the p-orbital (49%) α-⁸Be relative motion is found. This finding manifests the exotic 3α, but hardly condensed structure of the 9.64-MeV 3⁻ state in ¹²C.     

Proton-Induced Deuteron Breakup Reaction at 65 MeV: Unspecific Configurations

 Cross sections and vector-analyzing powers for four unspecific configurations of the ²H(p,pp)n breakup reaction at E ^lab _p  = 65MeV were measured in a kinematically complete experiment. Measured observables are compared with rigorous Faddeev calculations using four realistic charge-dependent interaction models, the CD Bonn, Argonne v ₁₈, Nijmegen I, and Nijmegen II potentials with or without inclusion of the Tucson-Melbourne three-nucleon force. Coulomb effects are completely omitted. A satisfactory agreement between theory and experiment has been found. There exist, however, some discrepancies between measured and calculated analyzing-power distributions in certain kinematical regions. The effects of the Tucson-Melbourne three-body force are either negligible or slightly increasing the disagreement. Received May 12, 1999; revised March 3, 2000; accepted for publication April 26, 2000     

Structure of low-lying <Superscript>12</Superscript>C resonances

The hyperspherical adiabatic expansion is combined with complex scaling and used to calculate low-lying nuclear resonances of ¹²C in the 3α model. We use Ali-Bodmer potentials and compare results for other potentials α-α with similar ⁸Be properties. A three-body potential is used to adjust the ¹²C resonance positions to desired values extending the applicability of the method to many-body systems decaying into three α-particles. For natural choices of three-body potentials we find 14 resonances below the proton separation threshold, i.e. two 0⁺, three 2⁺, two 4⁺, one of each of 1^±, 2^-, 3^±, 4^-, and 6⁺. The partial-wave decomposition of each resonance is calculated as a function of the hyperradius. Strong variation is found from small to large distance. The connection to previous experimental and theoretical results is discussed and agreements as well as disagreements are emphasized.     

The α-<Superscript>12</Superscript>C scattering studied via the Trojan-Horse method

The Trojan-horse method has been suggested as a means to study a two-body reaction at astrophysical energies via a three-body breakup reaction. In order to test this method the ⁶Li(¹²C,α¹²C)²H reaction was studied in a kinematically complete experiment at an incident energy of 18 MeV. Coincidence spectra show the presence of the quasi-free α-¹²C scattering process. The excitation function of the three-body reaction is calculated in the plane wave impulse approximation assuming quasi-free scattering and is compared with the experimental data. Also, the excitation function of the virtual α-¹²C elastic scattering is extracted from the three-body reaction cross section at low deuteron momenta and compared with the behaviour of the free scattering cross section. Received: 4 June 1999 / Revised version: 15 November 1999     

Fusion around the barrier in 11,9Be +209Bi

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the range 37.5 MeV ≤ E _lab ≤ 45.0 MeV at the Munich Tandem via the observation of ground state α-decay of the evaporation residues. Fusion cross sections of ²⁰⁹Bi with the “halo”¹¹Be unstable projectile in the region around the Coulomb barrier were deduced from an experiment done with the same technique at the RIKEN Ring Cyclotron. Above the Coulomb barrier the ¹¹Be cross sections are larger than the ⁹Be ones in agreement with theoretical predictions based on the larger ¹¹Be halo radius. Also below the barrier these theories foresee the same behavior in disagreement with the experimental results, since the two cross sections are rather similar. Received: 2 April 1998     

Influence of the three-body coulomb effects on the values of asymptotic normalization coefficients (nuclear vertex constants) of astrophysical interest extracted from the modified DWBA approach for the peripheral proton-transfer reactions

From the exact three-body distorted wave amplitude obtained by other authors for the one-charged-particle-transfer reaction A(x, y)B within the strict three-body (x = y + a and B = A + a, where a is a transferred particle) model, its part is separated in which the three-body Coulomb dynamics of the transfer mechanism is taken into account correctly. The contribution of the three-body Coulomb dynamics of the transfer mechanism to the partial wave amplitudes at l ≫ 1 for the peripheral proton-transfer reactions ¹³C(³He, d)¹⁴N, ¹³C(¹⁴N, ¹³C)¹⁴N, and ⁹Be(¹⁰B, ⁹Be)¹⁰B is estimated within the three-body approach combining the dispersion method and the DWBA approach. For these reactions, the Coulomb renormalization factors, arising owing to correctly taking into account the three-body Coulomb dynamics of the proton-transfer mechanism in the DWBA cross sections, are calculated. A new estimate is obtained for the values of the asymptotic normalization factors for p + ¹³C → ¹⁴N, which also have astrophysical interest. The text was submitted by the authors in English.     

Adiabatic Hyperspherical Approach to the Problems of Muon Catalyzed Fusion

The adiabatic hyperspherical approach (AHSA) is applied for the numerical investigation of the scattering processes and resonances in Coulomb three-body mesic atomic systems. The results of the calculations of elastic and inelastic cross sections in low-energy collisions aμ + b (a, b = p, d, t), energies, lifetimes and local characteristics of resonant states of mesic molecular ions ⁿ Heaμ⁺ (n = 3, 4) are presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

Positron scattering from hydrocarbons

The total cross sections for positron impact on hydrocarbons have been calculated using the additivity rule in which the total cross section for a molecule is the sum of the total cross section for the constituent atoms. The energy range considered is from a few eV to several thousand eV. The total cross sections for positron impact on an atom are calculated by employing a complex spherical potential which comprises of a static, polarization and an absorption potential. We have good agreement with the experimental results for hydrocarbons for positron energy ⩾100 eV. Our results also agree with the available calculations for CH₄ and C₂H₂ which employed full molecular wavefunctions beyond 100 eV. Our absorption cross sections also agree with molecular wave-function calculations for C₂H₂ and CH₄ beyond 100 eV. We have shown the Bethe plots fore ⁺−C ande ⁺−H scattering systems and Bethe parameters have been extracted. We have fitted the cross section for positron impact on hydrocarbons in the formσ _t(C _n H _m )=naE ⁻ b+mcE ⁻ d in the energy range 300–5000 eV wherea=195.0543,b=0.7986,c=371.1757 andd=1.1379 withE in eV andσ _t in 10⁻¹⁶ cm².     

H<Superscript>+</Superscript><Emphasis Type="Bold">and He</Emphasis><Superscript>2+</Superscript> impact single and double ionization of lead

H⁺ and He²⁺ impact single and double ionization cross sections of ground state lead atoms have been calculated in the binary encounter approximation. Calculations of direct double ionization cross sections have been performed in the modified double binary encounter model. The accurate expressions of σ_ΔE (cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from Auger effect following ionization of inner shells have been considered in the present work. Our H⁺ impact single and double ionization cross sections are in good agreement with the experimental observations. In calculations of He²⁺ impact cross sections, the present theoretical approach shows limited success in the experimentally investigated region (50–350 keV amu^-1).     

Halo Structure of 19C via the (p,d) Reaction

 We have investigated the heaviest one-neutron halo candidate, the ¹⁹C nucleus. Few-body model calculations of cross-section angular distributions for the ¹⁹C(p,d)¹⁸C reaction together with test calculations carried out for the ¹⁷C(p,d)¹⁶C reaction at a low incident energy are presented for different possible halo-neutron configurations. We show that there is a clear distinction in particular between l _n  = 0 and l _n  = 2 halo transfers. The sensitivity of the cross sections to the assumed ¹⁹C single-neutron separation energy is discussed. Received October 13, 1999; revised November 25, 1999; accepted for publication April 29, 2000     

Subthreshold K + meson production in proton–nucleus reactions and nucleon spectral function

The inclusive K ⁺ meson production in proton–nucleus collisions in the near threshold and subthreshold energy regimes is analyzed with respect to the one–step (pN→K ⁺ YN, Y=Λ,Σ) and two–step (pN→NNπ, NN2π; πN→K ⁺ Y) incoherent production processes on the basis of an appropriate new folding model, which takes properly into account the struck target nucleon removal energy and momentum distribution (nucleon spectral function), extracted from recent quasielastic electron scattering experiments and from many–body calculations with realistic models of the NN interaction. Comparison of the model calculations of the K ⁺ total and double differential cross sections for the reaction p+C ¹² with the existing experimental data is given, illustrating both the relative role of the primary and secondary production channels at considered incident energies and those features of the cross sections which are sensitive to the high momentum and high removal energy part of the nucleon spectral function that is governed by nucleon–nucleon short–range and tensor correlations. It is found that the in–medium modifications of the available for pion and kaon production invariant energies squared due to the respective optical potentials are needed to account for considered experimental data. Received: 2 April 1997 / Revised version: 7 August 1997