Measurement of the cross section for the reaction <Superscript>20</Superscript>Ne(<Emphasis Type="Italic">n,α</Emphasis>)<Superscript>17</Superscript>O in the neutron-energy between 4 and 7 MeV

The cross section for the reaction ²⁰Ne(n, α)¹⁷O was measured in the neutron-energy range 4–7 MeV. An ionization chamber equipped with a Frisch grid combined with a pulse-shape digitizer was used as a detector. Gaseous neon that served as a target on which the reaction being studied proceeded was added to the gas filling the ionization chamber. The partial cross sections for the α ₀, α ₁, α ₂, and α ₃ channels of the reaction ²⁰Ne(n, α)¹⁷O were obtained for the first time.     

α-particle spectrum in the reaction p + 11B → α + 8Be* → 3α

Using a simple phenomenological parametrization of the reaction amplitude we calculated α-particle spectrumin the reaction p + ¹¹B → α + ⁸Be* → 3α at the resonance proton energy of 675 keV. The parametrization includes Breit-Wigner factor with an energy-dependent width for intermediate ⁸Be* state and the Coulomb and the centrifugal factors in α-particle-emission vertices. The shape of the spectrum consists of a well-defined peak corresponding to emission of the primary α and a flat shoulder going down to very low energy. We found that below 1.5MeV there are 17.5% of α’s and below 1MeV there are 11% of them. The text was submitted by the author in English.     

Direct and sequential radiative three-body reaction rates at low temperatures

We investigate the low-temperature reaction rates for radiative capture processes of three particles. We compare direct and sequential capture mechanisms and rates using realistic phenomenological parametrizations of the corresponding photodissociation cross-sections. Energy conservation prohibits sequential capture for energies smaller than that of the intermediate two-body structure. A finite width or a finite temperature allows this capture mechanism. We study generic effects of positions and widths of two- and three-body resonances for very low temperatures. We focus on nuclear reactions relevant for astrophysics, and we illustrate with realistic estimates for the α-α-α and α-α-n radiative capture processes. The direct capture mechanism leads to reaction rates which for temperatures smaller than 0.1 GK can be several orders of magnitude larger than those of the NACRE compilation.     

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     

Investigation of <Emphasis Type="Italic">γ</Emphasis>-ray fold distributions in N ≤ 82 Gd,Eu and Sm nuclei: Observation of a double-humped fold distribution

Cross-sections and γ-ray fold distributions have been measured for the ⁹⁷Mo+⁵¹V, ¹⁰⁰Mo+⁴⁸Ti and ¹¹⁴Cd+³⁶S reactions at energies of 238, 215 and 182 MeV of the ⁵¹V, ⁴⁸Ti and ³⁶S projectiles, respectively. For the ⁹⁷Mo(⁵¹V, α2n ¹⁴²Eu reaction channel a double-humped fold distribution has been observed. This fold distribution can only be understand if an incomplete-fusion reaction mechanism associated with the α-particle emission is assumed. The ⁹⁷Mo(⁵¹V, α n ¹⁴³Eu reaction channel represents an incomplete-fusion reaction channel as well and its single-humped fold distribution can be described on the same footing as that of the α2n channel. The fold distributions associated with xn and pxn channels can be explained assuming complete-fusion reactions. For the calculations in terms of an incomplete-fusion reaction mechanism a narrow angular momentum window, ranging from ≈ 68 to 82ℏ has been assumed for the ⁹⁷Mo(⁵¹V, αn and α2n reaction channels. The complete-fusion reaction mechanism is considered to be negligible in this angular-momentum range.     

Combined dynamical and statistical approach to describing induced fission of heavy nuclei

A combined dynamical and statistical approach to describing induced fission of heavy nuclei is proposed. This approach takes into account the nuclear-dissipation phenomenon and the double-humped structure of the fission barrier. A method that is intended for calculating the angular distribution of fission fragments and which is applicable over a broad range of excitation energies is discussed. The potential of the approach is demonstrated by addressing the problems of self-consistently describing experimental data on fission probabilities for plutonium and americium isotopes, the yields of shape isomers in the α+²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV and the d+^242,240Pu reactions at deuteron energies in the range E _d = 20–30 MeV, fission times in the α + ²³⁸U reaction at alpha-particle energies in the range E _α = 20–32 MeV, and angular distributions of fission fragments in the α + ²³⁸U, ²³⁷Np reactions at alpha-particle energies in the range E _α = 20–100 MeV.     

Two-pion decay of the P 11(1440) resonance excited in αp Scattering at 1 GeV/nucleon

Semiexclusive measurements of the two-pion production reaction p(α, α′)pππ have been carried out at an energy of E _α = 4.2 GeV at the Saturne-II (Saclay) accelerator with the SPES4-π installation. The two-pion production reaction was investigated by simultaneous registration of the scattered α particle and the secondary proton. The obtained results show that the two-pion decay of the P ₁₁(1440) resonance excited in the target proton in this reaction proceeds predominantly with emission of two pions in the isospin I = 0, S-wave state. The text was submitted by the authors in English. the SPES4-π Collaboration     

Analysis of the excitation functions of (α, xnyp) reactions on natural copper

Excitation functions of the reactions⁶³Cu[(α, n), (α, 2n)+(α, pn)] and⁶⁵Cu[(α, n), (α, 2n), (α, 3n), (α, 4n)+(α, p3n)] were investigated up to 50 MeV using stacked foil activation technique and Ge(Li) gamma ray spectroscopy method. Since natural copper used as the target has two odd-mass stable isotopes of abundance,⁶³Cu(69.17%) and⁶⁵Cu(30.83%), their activation in some cases, gives the same residual nucleus through different reaction channels but with very different threshold energies. In such cases, the individual reaction cross sections are separated with the ratio of theoretical cross sections. The experimental results were compared with the predictions of preequilibrium hybrid model of Blann. A general agreement was found in all reactions using initial exciton numbern ₀=4(4p0h) and also preequilibrium fraction depends on the incident particle energy.     

Investigation of alpha particle induced reactions on thulium

Alpha particle induced reactions on the target element thulium were investigated up to 75 MeV, using foil-stack activation technique and Ge(Li) gamma ray spectroscopy method. Excitation functions for eight reactions of the type¹⁶⁹Tm(α, xn),x=1 − 4;¹⁶⁹Tm(α, pxn),x=3; and¹⁶⁹Tm(α, αxn),x=1, 2, 4 were investigated. Of these, four reactions¹⁶⁹Tm(α, p3n),¹⁶⁹Tm(α, αn),¹⁶⁹Tm(α, α2n)¹⁶⁹Tm(α, α4n), were studied for the first time and in the remaining four reactions, some 19 new energy-point cross-sections were measured for the first time. The experimental cross-sections were compared with the predictions of pre-equilibrium hybrid model, as well as the more recent index model, using the initial excition number,n ₀=4 (4p0h). Both the models show better agreement in respect of (α, xnyp) type of reactions. However they are equally bad for (α, αxn) type of reactions which involve theα-particle in the exit channels, and for which some direct reaction contributions are indicated.     

Measurement and analysis of alpha particle induced reactions on gold

Stacked foil activation technique and Ge(Li) gamma ray spectroscopy have been used for the measurement of excitation functions of¹⁹⁷Au(α,xn) (x=1−3),¹⁹⁷Au(α,2pn) and¹⁹⁷Au(α,αn) reactions up to 50 MeV. The experimental cross-sections were compared with the predictions of pre-equilibrium hybrid model, as well as with the more recent index model. A general agreement was found in all reactions using initial exciton numbern ₀=4(4p0h) except for¹⁹⁷Au(α,n) reaction, where index model gives fairly good agreement withn ₀=5(5p0h).     

Transfer, sequential decay, and quasi-free reactions induced by 18-MeV 6He beam on 6Li, 7Li, and 12C

The ⁶He + ^6,7Li and ⁶He + ¹²C scattering and reactions have been studied using an 18-MeV ⁶He beam. Experimental results for the elastic scattering on all three targets are in fair agreement with optical model predictions, using the potentials found in the analysis of the ⁶Li scattering on the same targets and at close beam energies. Several two-body exit channels show clear signatures of a direct reaction mechanism allowing extraction of spectroscopic information. The measured angular distribution for the ⁶He + ⁶Li → α + ⁸Li reaction indicated close similarity between the α + 2n configuration in ⁶He and the α + d configuration in ⁶Li. The obtained results for α-particle pickup from both ⁶Li and ⁷Li give large values of α spectroscopic factors for some ¹⁰Be states, indicating their well-developed α + ⁶He cluster structure. The exotic two-proton pickup reaction (⁶He, ⁸Be) was studied, as well as two-neutron and triton transfer reactions. Quasi-free scattering of ⁶He on deuteron and α particle in ⁶Li was also observed. The sequential decay reactions ⁶He + ⁶Li → ⁶He + α + d, ⁶He + ⁶Li → 2α + t + n, ⁶He + ⁷Li → ⁶He + α + t, and ⁶He + ¹²C → ¹⁰Be + 2α were clearly seen, and α clustering of some states in ^6,7Li, ^8–10Be, and ¹⁴C was thus studied. Several new spectroscopic results obtained for some ¹⁰Be states support the existence of a molecule-like rotational band in ¹⁰Be with a very large moment of inertia. The text was submitted by the authors in English.     

Doppler shapes of the γ line in the <Superscript>9</Superscript>Be(α, nγ)<Superscript>12</Superscript>C reaction in plasma at temperatures <Emphasis Type="Italic">T</Emphasis><Subscript>α</Subscript> < 0.6 MeV

A parametrization of the partial cross section of the ⁹Be(α, nγ)¹²C reaction in the α-particle energy range of 0.3–7.9 MeV is presented, along with the count rates of γ quanta. The need to consider subbarrier (Eα < 1.9 MeV) α-particles in plasma for temperatures T _α < 0.2 MeV is substantiated. The shapes of the Doppler-broadened 4.44 MeV γ line and the count rates of γ quanta in the plasma of the JET tokamak are measured for the first time and compared to the calculated values. An estimated T _α ≲ 160 keV is obtained.     

Recent Result of Muon Catalyzed t–t Fusion at RIKEN-RAL

We have measured X-rays and neutrons associated with the muon catalyzed t–t fusion process at the RIKEN-RAL Muon facility. In the X-ray measurement, we observed K_α and K_β X-rays originating from the muon sticking process in muon catalyzed t–t fusion, and obtained the K_α X-ray yield and the K_β/K_α intensity ratio. An average recoil energy of the (μ⁻α) atoms in a solid T₂ medium was determined from the observed Doppler broadening width of the K_α X-ray line. The obtained t–t fusion neutron has shown an exponential time spectrum with a single component and a continuous energy spectrum with a maximum energy of 9 MeV. We have determined the t–t fusion neutron yield, the t–t fusion cycling rate and the muon sticking probability from the neutron data. The obtained maximum neutron energy is a very peculiar value from the view point of the reaction Q value (11.33 MeV) with the three-particle decay mode at the exit channel: t + t → α + n + n + Q. The obtained neutron energy distribution was analyzed by a simple model with two neutron energy components; reasonable agreement has been obtained, suggesting a strong (n–α) correlation in the exit channel of the t–t muon catalyzed fusion reaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nuclear spins, magnetic moments and α-decay spectroscopy of long-lived isomeric states in 185Pb

Alpha-decay properties of the neutron-deficient isotope ¹⁸⁵Pb were studied at the PSB-ISOLDE (CERN) on-line mass separator using the resonance ionisation laser ion source (RILIS). The nuclei of interest were produced in a 1.4 GeV proton-induced spallation reaction of a uranium graphite target. In contrast to previous studies, two α-decaying isomeric states were identified in ¹⁸⁵Pb. The relative production of the isomers, monitored by their α-counting rates, could be significantly changed when a narrow-bandwidth laser at the RILIS setup was used to scan through the atomic hyperfine structure. Based on the atomic hyperfine structure measurements, along with the systematics for heavier odd-mass lead isotopes, the spin and the parity of these states were interpreted as 3/2^- and 13/2⁺ and their nuclear magnetic moments were deduced. The α-decay energy and half-life value for the I ^π = 13/2⁺ isomer are E _α = 6408(5) keV, T _1/2 = 4.3(2) s, respectively; while for the I ^π = 3/2^- isomer ( T _1/2 = 6.3(4) s) two α-decays with E _α1 = 6288(5) keV, I _α1 = 56(2)% and E _α2 = 6486(5) keV, I _α2 = 44(2)% were observed. By observing prompt α-γ coincidences new information on the low-lying states in the daughter isotope ¹⁸¹Hg was obtained. Received: 7 February 2002 / Accepted: 19 February 2002     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

Alpha-particle condensation in nuclei: Experimental problems

Recently, it was supposed the nα light nuclei may have structures resembling the diluted gas of α particles which could be considered as Bose-Einstein condensate (αBEC) in nuclear systems. At the present time, the only more or less definite candidate for an αBEC state predicted by theory is the second 0⁺ state of ¹²C (E = 7.65 MeV) located near the threshold ¹²C → 3α. We discuss several possible experimental approaches to study the properties of interest of the 7.65-MeV level of ¹²C. Among them are shift of the positions of the rainbow minima in the inelastic scattering to this level, extraction of the empirical inelastic form factor from the α and ³He scattering and its comparison with theoretical predictions, and getting information on the ⁸Be transfer reaction form factor. The conclusion was drawn that new measurements of ¹²C(α, α′) ¹²C(7.65) inelastic scattering at ∼120 MeV in the full angular range would be most adequate to solving the problem. The possibility of observation of αBEC effects in heavier nα nuclei is also discussed. In particular, ¹¹²Ba is of great interest owing to possible existence of an α-particle “halo” outside the Z = N = 50 core. The text was submitted by the authors in English.     

Muon catalyzed fusion and muon to 3He transfer in solid T2 studied by X-ray and neutron detection

X-ray and neutron measurements were carried out for muon catalyzed fusion and related phenomena in solid T₂. The X-ray originated from the μ^- to α sticking in muon catalyzed fusion; t + t + μ ^- → (μ ^- α) + 2n was measured for the first time, yielding K _α X-ray intensity of (μα) atom and the intensity ratio of K _β to K _α . Utilizing the phenomena of ³He accumulation in solid T₂, the X-ray in the μ^- transfer process from (tμ) to ³He was detected, providing a formation rate and radiative decay branching-ratio of (t ³Heμ) molecule. From fusion neutron measurements, estimated values were obtained for (ttμ) molecular formation rate as well as sticking probability ω_t in ttμ fusion. A possible new insight in t + t fusion reaction process at a low energy limit is also obtained. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the Uniqueness of Gravitational Centre

The dual volume of order α of a convex body A in R ⁿ is a function which assigns to every a ∈ A the mean value of α-power of distances of a from the boundary of A with respect to all directions. We prove that this function is strictly convex for α > n or α < 0 and strictly concave for 0 < α < n (for α = 0 and for α = n the function is constant). It implies that the dual volume of a convex body has the unique minimizer for α > n or α < 0 and has the unique maximizer for 0 < α < n. The gravitational centre of a convex body in R³ coincides with the maximizer of dual volume of order 2, thus it is unique.      

Energy calibration of a Δ<Emphasis Type="Italic">E</Emphasis>-<Emphasis Type="Italic">E</Emphasis> scintillation telescope in (α, p) reaction

A procedure for and the results from the energy calibration of a ΔE-E scintillation telescope used in experiments performed at the INR to study the nd-breakup reaction are described. The telescope was calibrated using a beam of α particles with an energy of 30 MeV of the U-120 cyclotron (INP). Secondary protons from the ^10,11B(α, p) reaction were recorded by the ΔE-E telescope at several recording angles and with the application of different absorbing foils. The calibration results from the ΔE-E telescope were obtained over the interval E _p = 10–30 MeV, allowing us to measure the energies of secondary protons in the ndbreakup reaction when the energy of primary neutrons is 20–60 MeV.     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000