Optical potential analysis of proton elastic scattering from <Superscript>12</Superscript>C based on the <Emphasis Type="Italic">α</Emphasis>-particle model

Based on an α-particle model of ¹²C, an optical potential for intermediate-energy proton- ¹²C scattering is presented in the framework of the KMT theory. The parameterized proton- ⁴He amplitude, the required basic input for constructing the optical potential, is obtained by fitting the proton- ⁴He scattering data. The differential cross-sections and analyzing powers of the proton- ¹²C elastic scattering at incident energies ranging from 0.2 to 1.0GeV have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross-section and the analyzing power can be satisfactorily described. The proton- ¹²C total cross-sections have also been calculated, and the results are in good agreement with the experimental data at energies below 0.6GeV but underestimate the data about 6% at higher energies.     

Polarization phenomena in the intermediate energy elastic deuteron scattering from <Superscript>16</Superscript>C and <Superscript>16</Superscript>O nuclei

A model based on the multiple diffraction scattering theory and the α-cluster model with dispersion of target nuclei is proposed for describing the behavior of observables for the elastic deuteron scattering from ¹²C and ¹⁶O nuclei at intermediate energies. Differential cross-sections and analyzing powers calculated within this approach for incident-deuteron energies of 400 and 700 MeV are in a reasonable agreement with experimental data.     

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.     

Influence of projectile breakup on complete fusion

Complete fusion excitation functions for ^11,10B+¹⁵⁹Tb and ^6,7Li+¹⁵⁹Tb have been reported at energies around the respective Coulomb barriers. The measurements show significant suppression of complete fusion cross-sections at energies above the barrier for ¹⁰B+¹⁵⁹Tb and ^6,7Li+¹⁵⁹Tb reactions, when compared to those for ¹¹B+¹⁵⁹Tb. The comparison shows that the extent of suppression of complete fusion cross-sections is correlated with the α-separation energies of the projectiles. Also, the measured incomplete fusion cross-sections show that the α-particle emanating channel is the favoured incomplete fusion process. Inclusive measurement of the α-particles produced in ⁶Li+¹⁵⁹Tb reaction has been carried out. Preliminary CDCC calculations carried out to estimate the α-yield following ⁶Li breaking up into α+d fail to explain the measured α-yield. Transfer processes seem to be important contributors.     

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.     

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.     

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.     

Dynamics of α-clusters in N = Z nuclei

The systematics for binding energies per α-particle in N = Z nuclei, E _Bα/N _α, are studied up to ¹⁶⁴Pb. It is shown that, although a geometrical model can be used to explain the systematics for light nuclei, the binding energy per α-particle exhibits structures which are due to the well-known shells of the mean field of nucleons in nuclei. The overall dependence of E _Bα/N _α on N _α in N = Z nuclei (for the ground-state masses) can be described in a liquid-drop model of α-particles. Conditions for a phase change with the formation of an α-particle condensate, a dilute Bose gas in excited compound nuclei are discussed for E _Bα/N _α = 0, at the thresholds. This is achieved when the binding energy per nucleon in nuclei is equal to or smaller than in the α-cluster. At somewhat smaller excitation energies the appearance of a Bose gas with a closed-shell core (N = Z, e.g. of ⁴⁰Ca) is proposed within the same concept. The experimental observation of the decay of such condensed α-particle states is proposed with the coherent emission of several correlated α-particles not described by the Hauser-Feshbach approach for compound-nucleus decay. This decay will be observed by the emission of unbound resonances in the form of ⁸Be and ¹²C ^* (0⁺ ₂) clusters.     

Narrow α + <Superscript>28</Superscript>Si elastic-scattering states at high excitation in <Superscript>32</Superscript>S

The excitation function and angular distributions of elastic α-particle scattering on ²⁸Si have been measured in the laboratory energy range 6-28 MeV using a backscattering technique on a thick target, yielding a continuous energy distribution. More than 200 narrow states are observed, with widths in the range ∼ 30-100 keV at excitation energies E ^* = 13-32 MeV. Angular distributions at backward angles were measured, and angular momentum values of more than 83 states have been deduced. The analysis gives spin-parities J ^π, α-partial widths Γ_α and reduced widths of the narrow high-lying resonant states in ³²S. The experimentally observed states display both the negative- and the positive-parity rotational-like sequences with seemingly no parity splitting, a finding which is at variance with most potential-model predictions. The deduced effective moment of inertia indicates a more extended structure than the ground-state configuration. The observed strength of each ℓ-value is analyzed in terms of an underlying split doorway state of Lorentzian form, which yields an interpretation as fragmented rotational α + ²⁸Si states. Received: 26 June 2000 / Accepted: 16 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: kkallman@abo.fi RID="b" ID="b"Present address: Swedish Polytechnic, FIN-65200 Vasa, Finland. Communicated by D. Guerreau     

Investigation of the structure of lower excited states of the 28Si nucleus in α scattering at Eα = 30.3 MeV

The differential cross sections of the ²⁸Si(α, αγ)²⁸Si reaction at E _α = 30.3 MeV, calculated according to the coupled channel method (CCM) with the FRESCO program, are presented for a wide α-particle scattering region with the excitation of the lower ²⁸Si states (0⁺, ground; 2⁺, 1.78 MeV; 4⁺, 4.62 MeV; 0⁺, 4.96 MeV; 3⁻ + 4⁺, 6.88 MeV + 6.89 MeV). The coupling factors are calculated in the Nilsson model.     

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.     

Synthesis of superheavy nuclei in the reactions of 244Pu and 248Cm with 48Ca

This paper presents results of the experiments aimed at producing long-lived superheavy elements located near the spherical-shell closures with Z ⩾ 114 and N ⩾ 172 in the ²⁴⁴Pu + ⁴⁸Ca and ²⁴⁸Cm + ⁴⁸Ca reactions. The large measured α-particle energies of the newly observed nuclei, together with the long decay times and spontaneous fission terminating the chains, offer evidence of the decay of nuclei with high atomic numbers. The decay properties of the synthesized nuclei are consistent with the consecutive α-decays originating from the parent nuclides ^{288, 289}114 and ²⁹²116, produced in the 3n and 4n evaporation channels with cross-sections of about a picobarn. The present observations can be considered as experimental evidence of the existence of the “island of stability” of superheavy elements. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: utyonkov@sungns.jinr.ru     

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     

Inclusion of Final-State-Interaction Effects at Higher Energies in the Photodisintegration of the α-Particle

Final-state-interaction (FSI) effects are included in the treatment of the photodisintegration of the α-particle via the K-matrix approximation. These are applied to the exact AGS-type integral equation for this process at photon energies 50–100 MeV. Direct comparison with the plane-wave (Born) approximation indicates that these effects are small, which explains the good fit to the data we found previously. The FSI in the integro-differential equation treatment of the problem in configuration space are included by means of effective nucleon-trinucleon potentials constructed via an exact inverse scattering method and by using the phase shifts obtained from the K-matrix approach to the 3 + 1 → 3 + 1 scattering. Comparison between this approach and the integral-equation approach confirms the validity of this model previously employed at low energies using experimental phase shifts. Finally we show that the photonuclear cross sections are sensitive to the details of the boundstate wave functions of the ³He and ⁴He as calculated exactly via the AGS equations and in the integro-differential-equation approach, which for the ⁴He neglects higher-order correlations. Received April 18, 1994; revised September 12, 1994; accepted for publication October 12, 1994     

Measurement and analysis of excitation functions for alpha induced reactions on iodine and cesium

The excitation functions for the reactions¹²⁷I(α, 2n)¹²⁹Cs,¹²⁷I(α, 4n)¹²⁷Cs,¹³³Cs(α, 2n)¹³⁵La and¹³³Cs(α, 4n)¹³³La have been measured up to ≈50 MeVα-particle energy using the stacked foil activation technique. Measured excitation functions are compared with pre-equilibrium geometry dependent hybrid model calculations. It has been found that theoretical calculations using an initial exciton numbern ₀=4 (2p+2n+0h) give good agreement with experimental excitation functions.     

Elastic scattering of electrons by helium atoms in high energy higher order Born approximation

The differential cross-sections forē-helium elastic scattering are calculated by using Yateshigh-energy higher order Born approximations, through 0 (K _i ^{Emphasis>−2} ) of the incident electron momentum, and comparisons have been made with the recent theoretical and experimental results.     

Cubic potential models for cluster radioactivity

Cluster radioactivity is a process by which nuclei equal and heavier than the α-particle is emitted spontaneously. The clusters usually emitted in this process are the α-particle, carbon, oxygen, neon, magnesium, silicon etc. When the mass of the cluster becomes comparable with the mass of the daughter, symmetric fission takes place. Thus the cluster radioactivity is an intermediate process between the well known α-decay and the spontaneous fission. In earlier years such cluster radioactivity was found mostly in actinide nuclei like radium, uranium etc. Very recently it has been predicted that such decays are possible in a new region around ¹¹¹Ba. There has been an exciting experimental detection of the emission of ¹²C from ¹¹¹Ba leading to ¹⁰²Sn, which is attracting a lot of attention recently. To study the phenomenon of cluster radioactivity there are various theoretical models in vogue. The existing models generally fall under two categories: the unified fission model (UFM) and the preformed cluster model (PCM). The physics of the UFM and the PCM are completely different. The UFM considers cluster radioactivity simply as a barrier penetration phenomenon in between the fission and the α-decay without worrying about the cluster being or not being preformed in the parent nucleus. In the PCM clusters are assumed to be preborn in a parent nucleus before they could penetrate the potential barrier with a given Q-value. The basic assumption of the UFM is that heavy clusters as well as the α-particle have equal probability of being preformed. In PCM, clusters of different sizes have different probabilities of their being preformed in the parent nucleus. We have developed three fission models during the last decade using the cubic potential for the pre-scission region. The use of these models in the study of cluster radioactivity in both the actinide and barium regions will be discussed in this talk in comparison with the other existing theories.     

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).     

Production of Δ<Superscript>0</Superscript>(1232)-resonances in p + <Superscript>12</Superscript>C collisions at a momentum of 4.2 GeV/c

The production of Δ ⁰(1232)-resonances in p + ¹²C collisions at 4.2 GeV/c was investigated with 4π acceptance. The masses and widths of the resonances were obtained from ananalysis of foreground and background invariant-mass distributions of pπ ⁻ pairs obtained using an angular criterion. The fraction of charged π ⁻-mesons coming from the Δ ⁰(1232) decay was estimated and compared to those obtained in earlier analyses. The momentum, transverse momentum, kinetic energy, rapidity, and emission angle distributions as well as the invariant cross-sections of Δ ⁰(1232)-resonances werere constructed in the laboratory frame. The freeze-out temperature of theΔ ⁰(1232)-resonances produced in p + ¹²C collisions was estimated and compared to the freeze-out temperatures obtained using different methods for Δ(1232)-resonances produced in other experiments with different sets of colliding nuclei at various incident energies.