Reactions with 9Be at subbarrier energies

The ⁹Be+⁹Be, ⁹Be+¹⁰B, ⁹Be+¹¹B and ⁹Be+¹³C reactions have been studied at subbarrier energies measuring the cross sections for the characteristic γ-rays emitted by the residual nuclei and comparing them with the statistical evaporation prediction. A substantial enhancement in the αn channel, which contains the the α-transfer reaction from ⁹Be, has been observed in all the systems studied. Evidence suggesting that the α-transfer reaction is not exclusively a direct transfer process is being presented.     

Total reaction and transfer cross sections for 11B + 9Be and 13C + 9Be reactions at low energies

The total reaction cross sections for ¹¹B + ⁹Be and ¹³C + ⁹Be have been measured by the total γ-ray yield method over the energy intervals E_c.m. = 1.4–4.4 MeV and E_c.m. = 2.0–5.2 MeV, respectively. The cross sections for the neutron transfer reactions ¹¹B(⁹Be, ⁸Be)¹²B, leading to the ¹²B 0.953 and 1.674 MeV states, and ¹³C(⁹Be, ⁸Be)¹⁴C, leading to the ¹⁴C 6.094, 6.728 and 6.902 MeV states, have been obtained from the yields of the characteristic γ-rays. The α-transfer reaction ¹¹B(⁹Be, ⁵He)¹⁵N, leading to many unresolved ¹⁵N states, has been observed with large cross section. There is, however, no evidence for the ¹³C(⁹Be, ⁵He)¹⁷O transfer process in the ¹⁷O + nα channels. This different behaviour of the ¹¹B + ⁹Be and ¹³C + ⁹Be systems seems to indicate that the α-transfer reaction at sub-barrier energies is not a direct transfer process, and that it probably occurs via molecular state formation.     

Three particle reactions observed from 10Ne + 12C at 160 MeV

Coincidences between light particles (Z ? 4) and heavy ions (A ? 9) have been measured for the ²⁰Ne + ¹²C reaction at $\text{E}{}_{\mathrm{<mtext>lab</mtext>}}\text{(}{}^{20}\text{Ne}\text{) = 160}\text{MeV}$. α, ¹⁶O events from the ¹²C(²⁰Ne, α¹⁶O)¹²C reaction and α, ²⁰Ne events from ¹²C(²⁰Ne, α²⁰Ne)⁸Be have been found. Energy distributions and angular correlations of these events are consistent with α-decay from the intermediate nuclei ²⁰Ne and ²⁴Mg formed by inelastic scattering and α-transfer in a first reaction step.     

Alpha-transfer processes in heavy-ion scattering

In the differential cross sections for the elastic scattering between an α-conjugate target and projectile, a rising oscillatory structure is often observed in the backward-angle region. An α-transfer mechanism is proposed to explain this anomalous phenomenon. A nuclear molecularorbit approximation theory for both 1α- and 2α-transfer processes has been formulated and applied to ¹⁶O + ²⁰Ne and ¹²C + ²⁰Ne scattering systems with different projectile energies. The experimental rising structures shown in these scatterings are well reproduced with parameters fairly consistent with spectroscopic data. An independent-α-particle model wave function has been used for the evaluation of the exchange potential, which gives better agreement with experiment than the Buttle-Goldfarb approximation can usually provide.     

α-Transfer and a tetrahedral shape for 16O

The addition of a tetrahedral perturbation to the shell model in ¹⁶O produces α-particle clustering and has a strong influence on α-transfer processes. The cross-section enhancements for the reaction ¹²C(⁶Li, d)¹⁶O are studied as a function of the strength of perturbation and reasonable agreement with experiment is found for the three final states 0⁺, 3^? and 4⁺ in ¹⁶O which are described as members of the tetrahedral rotational band.     

A study of the α-transfer reaction in the 16O + 16O system at near-barrier energies

Excitation functions and angular distributions have been measured at energies near the Coulomb barrier for the elastic scattering of ¹⁶O from ¹⁶O and for the (¹⁶O, ¹²C) α-transfer reaction to the ground state and first excited state of ²⁰Ne. No evidence for (quasi-molecular) resonances was found in the transfer excitation functions. Exact-finite-range DWBA calculations were performed employing double-folded real and Woods-Saxon optical potentials for the distorted waves. The α-transfer reaction was found to be sensitive to the choice of the optical potential and generally better fits were obtained with the folded potentials.     

Possible mechanisms of fragmentation of 16O nuclei with a momentum of 4.5 GeV/c per nucleon in track emulsions

The angular distributions of doubly charged fragments of ¹⁶O nuclei having a momentum of 4.5 GeV/c per nucleon and interacting with track-emulsion nuclei were studied. The experimental angular distributions of doubly charged fragments of a ¹⁶O nucleus are not described by the statistical model of the fragmentation of nuclei. The possible channels of fragmentation of ¹⁶O nuclei may include ¹⁶O → 2⁸Be → 4α, ¹⁶O → ⁸Be +⁸ Be* → 4α, ¹⁶O → 2⁸Be* → 4α, ¹⁶O → α+¹²C, ¹⁶O → α +¹²C* → α + 3α, ¹⁶O → α +¹²C* → α + pα ⁷Li, ¹⁶O → α +¹²C* → α + 2⁶Li, ¹⁶O → α +¹²C* → α + pt2α, ¹⁶O → Li + B, and ¹⁶O → Li* + B*.     

16O, 24, 26Mg, 28Si, 32S, 40Ca(α, 12C) and multi-α-cluster transfer reactions

The (α, ¹²C) reaction has been studied on a variety of nuclei, A = 16 to 40, at E_α = 90.3 MeV. The data indicate a rapid fall-off of cross sections with increasing target mass, approximately as A_t^{?5 ± 1}. This and other systematics are used to estimate cross sections for multi-α-cluster transfer reactions in heavy nuclei and suggest σ_T < 10^?34 cm² consistent with present experimental limits. The data for ²⁴Mg(α, ¹²C)¹⁶O has been studied in more detail and indicates a selective population of final states including ¹⁶O g.s., with oscillatory angular distributions in some instances. Finite-range distorted-wave Born approximation calculations for direct ⁸Be pickup have been performed utilizing cluster overlap amplitudes obtained with zero-order SU(3) wave functions. The calculations are in qualitative, and often quantitative, agreement with shapes and absolute magnitudes of the measured angular distributions although the cross sections for certain α-cluster states (2⁺, E_x ≈ 7 MeV; 4⁺, E_x ≈ 10.3 MeV) are greatly overestimated with this model. Other more complicated mechanisms, such as successive α-transfer, cannot be excluded. The systematics of the calculated ⁸Be cluster overlaps and the calculated and measured (α, ¹²C) cross sections are investigated, and implications for multi-α-cluster transfer reactions are discussed.     

Semiclassical analysis of α-transfer reactions

Semiclassical concepts are used to gain insight into α-transfer reactions. These reactions, interpreted as one-step direct reactions on the basis of DWBA analyses, are treated in analogy with single nucleon transfer reactions for which it is known that semiclassical methods are successful. In this case however the probability of transfer appears to be greatest at a distance of closest approach which is larger than the grazing distance by the order of the α-particle radius. This increase in the effective “grazing” distance is interpreted as a manifestation of the α-particle size at the time of transfer. Angular distributions are calculated semiclassically for the reactions ²⁰⁸Pb(¹⁶O, ¹²C)²¹²Po at 93 MeV and ⁴⁰Ca(¹²C, ⁸Be)⁴⁴Ti at 45 MeV lab energy. They are seen to give a reasonable fit to experiment. Partial wave amplitudes for transfer are also studied.     

Alpha cluster states in 16O

A very successful cluster-core model for the rotational bands of light nuclei has been extended to treat excited core states. The resulting coupled-channels problem has been solved for the ${}^{16}\text{O }{}^{12}\text{C + α}$ system. As well as the known + ve and ? ve parity bands many new levels are predicted and compared with experiment. The agreement between theory and experiment is very good both for the excitation energies and the decay properties. We predict the positions of two low-spin non-natural parity levels with E_x < 20 MeV and the positions of many high-spin states. In particular, we explain why the 8⁺ level seen in α-transfer at 22.5 MeV could not be found in the α-scattering cross sections and predict a second 8⁺ at 24.4 MeV. We discuss how the levels may be regarded as members of rotational bands and determine the terminating J-values for these bands. Finally we show that the usual rotational model would be a poor approximation for the cluster bands of ¹⁶O.     

Cross section measurements for the 9Be+9Be System at subbarrier energies

The total reaction cross section and the characteristic y-ray cross sections have been measured for the ⁹Be+ ⁹Be reaction in the energy range E_cm = 1.4–3.4 MeV, detecting the prompt γ-rays emitted by the various residual nuclei with two Nal detectors in nearly 4π geometry and with a germanium detector, respectively. The differential elastic cross sections for the same system have also been measured at e_c.m.= 2.2, 2.7 and 3.2 MeV. The cross sections calculated with the “standard” and the proximity optical model potentials, which describe well the total reaction cross sections of the light nuclei, agree with the ⁹Be + ⁹Be elastic-scattering data, but underpredict the total reaction cross section by a factor of 2 to 3. The characteristic γ-ray measurements show that all two-particle emission channels, nα ¹³C, nn¹⁶O, np¹⁶N and αα¹⁰Be are enhanced by about that factor, while the single-particle emission channel, p¹⁷N, is not enhanced.     

9Be + 12C, 9Be + 16O,9Be + 19F reactions at energies below the barrier

The ¹⁶O + ⁹Be reactions have been studied from E_c.m. = 2.0 MeV to 5.1 MeV, an energy near the top of the Coulomb barrier. The cross section for the neutron transfer reaction ⁹Be(¹⁶O,¹⁷O¹ (0.87 MeV))⁸Be has been measured over this range by detecting the prompt 0.87 MeV γ-rays. The total fusion cross section has been determined from E_c.m. = 2.8 to 5.1 MeV by observing individual γ-ray transitions in the evaporation residues with a Ge(Li) detector, and then summing the separate yields. Direct processes are found to dominate the reaction yield below E_c.m. = 4 MeV. A comparison of the energy dependence of the fusion cross section for this reaction and the ¹²C + ¹³C reaction, which proceeds via the formation of the same compound nucleus, ²⁵Mg, reveals differences at sub-barrier energies. Optical model and incoming-wave boundary condition calculations are presented. Data have also been obtained for the near optimum Q-value neutron-transfer reactions ⁹Be(¹²C, ¹³C¹)⁸Be and ⁹Be(¹⁹F, ²⁰F)⁸Be, and these are discussed in terms of a simple model of sub-barrier direct reactions.     

The (12C, 8Be) reaction on 12C, 16O, 24,26Mg, 40,48Ca, 54Fe AND 58Ni between 50 and 65 MeV bombarding energy

Absolute cross sections have been measured for the (¹²C, ⁸Be_g.s.) reaction from the target nuclei ¹²C, ¹⁶O, ²⁴Mg, ²⁶Mg, ⁴⁰Ca, ⁴⁸Ca, ⁵⁴Fe and ⁵⁸Ni at various energies between 50 and 65 MeV bombarding energy (lab) using a highly efficient detection system for ⁸Be. The results are presented in form of particle spectra and angular distributions. Except for the lightest target nuclei ¹²C and ¹⁶O, the cross sections decrease rapidly with angle and a one-step direct reaction mechanism is indicated. Satisfactory agreement of the data is obtained with DWBA calculations, using the finite range computer code LOLA of DeVries which treats recoil effects exactly. The spectroscopic factors extracted for the (¹²C, ⁸Be) reaction are close to those obtained from (⁶Li, d), (⁷Li, t) and (¹⁶O, ¹²C) reactions. The selective excitation of the same final states in all of these reactions, as far as data are available, and the close agreement of the spectroscopic factors are interpreted as evidence for a rather simple α-transfer in these reactions in contrast to a more complicated transfer of four nucleons.     

Alpha strength factors in medium nuclei

Alpha strength factors are calculated for use in heavy-ion induced α-transfer reactions and in (α, p) reactions on medium nuclei. Detailed calculations are performed in a weak coupling shell model to study the distribution of α-strength over the nuclear states and to explore the α-clustering amplitudes of j-j coupled basis states. Alpha clustering in a model space with states of good isospin as well as states described in neutron-proton formalism is discussed. It is found that the α-cluster strength contained in the configurations (pf)⁴, (sd)⁴, (pf)³(sd)¹ and (pf)¹(sd)³ fragments among several or many states. For the (pf)²(sd)² configuration, conversely, most of the α-strength exists in the lowest state of the configuration, and such states form a band of positive parity states which exhibits rotational properties. A brief comparison with (α, p) and ⁵⁴Fe (¹⁶O, ¹²C)⁵⁸Ni experiments is made. The α-transfer probability was calculated in a semiclassical model. The effects of correlations which produce enhancements of factors of ten are essential to explain observed enhancements in the α-strengths. Alpha strength factors for the (sd)⁴ configurations for nuclei in the Zr region are also given.     

Statistical giant resonance effects in heavy-ion radiative capture

Heavy-ion radiative capture has been observed in the two reactions ⁹Be(¹²C, γ)²¹Ne and ¹⁶O(⁷Li, γ)²³Na for c.m. energies between 3 and 9 MeV. High-energy γ-rays populating levels up to 4.7 MeV in the final nuclei were detected with a large volume, anticoincidence-shielded NaI spectrometer. Peak cross sections for individual transitions in both reactions were found near 60 nb/sr. For ⁹Be + ¹²C all excitation functions were rather smooth with a broad bump around E_c.m = 5–6 MeV. Statistical model calculations were in good agreement with the data suggesting that perhaps as much as half of the GDR strength in ²¹Ne is statistical. More structure was found in ¹⁶O + ⁷Li superimposed on still sizeable statistical yield. Previous measurements of the same reaction were found to be partially in error.     

Measurement of spin-alignment of excited12C2+ nuclei in interactions of16O with12C usingγ-decay in flight

Measuring energy spectra of nuclei afterγ-decay of excited states in flight the spin alignment of¹²C₂₊ states has been measured. Inelastic scattering,¹⁶O(¹⁶C,¹²C₂₊)¹⁶O and the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O leading to¹²C₂₊ (4.43 MeV) state have been studied. Characteristic line shapes of the¹²C₂₊ peak were observed using a Q3D magnetic spectrometer. The magnetic substate (m-states) population has been deduced from the spectra as function of reaction angle. A comparison of the measuredm-state population with reaction models shows that the first reaction is consistent with inelastic scattering although discrepancies remain. Discrepancies are also obtained if the reaction¹²C(¹⁶O,¹²C₂₊)¹⁶O is interpreted using a FRDWBA transfer calculation. At least 1/3 of the cross section can be attributed toα-transfer. A calculation which couples transfer and inelastic scattering channels seems to be necessary.     

12C1 and 8Be production in 12C + 208Pb collisions

The mechanisms involved in the production of fast α-particles in ¹²C-induced reactions have been studied for the ¹²C + ²⁰⁸Pb system at the bombarding energies of E_12c = 132, 187 and 230 MeV. Absolute cross sections for the reactions ²⁰⁸Pb(¹²C. ¹²C¹→α + ⁸Be), ²⁰⁸Pb(¹²C, ⁸Be(g.s.)) and ²⁰⁸Pb(¹²C, ⁸Be(2.94 MeV)) have been determined by coincidence measurement of two or three correlated α-particles. Inclusive α-particle production cross sections were also measured at E_12c = 187 MeV. It is found that the inelastic process (¹²C, ¹²C¹→α + ⁸Be) does not contribute significantly to fast α-particle production but that the production of ⁸Be by projectile fragmentation is an important source of α-particles. At the highest bombarding energy (230 MeV) it appears that the ¹²C → 3α fragmentation reaction becomes more prominent at the expense of the ¹²C→α + ⁸Be fragmentation channel.     

Polarization of α-clusters in light nuclei?

The α-particle model of Brink is extended to allow for non-spherical clusters. This is done by admixingp-functions to thes-single particle states which represent, in the usual version of the model, the nucleons in a cluster. The results in the nuclei⁸Be,¹²C,¹⁶O, and²⁰Ne indicate that the spherical clusters represent the stable configurations.     

Search for highly deformed shape isomers in 28Si, 24Mg and 20Ne linked by successive alpha decays

Measurements of the ¹²C(¹⁶O,²⁰Neα)α, ¹²C(¹⁶O,αα)²⁰Ne, ¹²C(¹⁶O,⁸Be)²⁰Ne and ¹²C(¹⁶O,¹⁶Oα)⁸Be reactions have been performed at E_c.m. = 27.0 MeV. For decays proceeding through resonant states in the intermediate ²⁴Mg nucleus, angular correlation measurements have enabled spin assignments to be made and the dominant entrance channel angular momentum to be determined. The results are inconsistent with recent similar experiments which were interpreted as arising from successive α-decays from deformed shape isomeric states in ²⁸Si and ²⁴Mg.     

The breakup of24Mg into16O and8Be

The breakup of²⁴Mg into¹⁶O and⁸Be fragments has been studied using the reactions¹²C(²⁴Mg,¹⁶O⁸Be)¹²C and¹²C(²⁰Ne,¹⁶O⁸Be)⁸Be. In the latter case, discrete states are observed near 24–28 MeV of excitation in²⁴Mg and the yield from this reaction is an order of magnitude greater than that of the former. This implies the excited configuration populated in²⁴Mg is favoured by the transfer of an alpha-particle and would therefore suggest an association with a 4-particle 4-hole configuration. This suggests a link with the octupole stabilised deformed minimum which appears in Nilsson-Strutinsky calculations of the potential energy surface in²⁴Mg, and also with theα —¹⁶O —α structure predicted in cranked cluster model calculations. In the excitation spectrum no states appear above 31 MeV indicating a possible band termination in disagreement with recent results using the¹⁶O+¹²C reaction. These results are discussed in terms of the Harvey model.