Structure studies of neutron-rich beryllium and carbon isotopes

The structure of neutron-rich beryllium isotopes has been investigated using different heavy-ion induced transfer reactions. A strong sensitivity to the chosen core nucleus is found for the cores of ⁹Be and ¹⁰Be, respectively. With a ⁹Be core, molecular rotational bands up to high excitation energies are observed due to the pronounced 2α-cluster structure, whereas only few states at low excitation energies are populated with a ¹⁰Be core. For ¹¹Be a detailed investigation has been performed for the three states at 3.41 MeV, 3.89 MeV and 3.96 MeV, which resulted in the most probable spin-parity assignments 3/2⁺, 5/2^? and 3/2^?, respectively. Furthermore we have studied particlehole states of ¹⁶C using the ¹³C(¹²C,⁹C)¹⁶C reaction and found 14 previously unknown states.     

Structure studies of 11Be and 12Be: Observation of molecular rotational bands

Excited states of ¹¹Be have been studied with several transfer reactions. Nine states between 3.96 and 25.0 MeV excitation energy show the characteristic energy dependence of a rotational band. The deduced large moment of inertia is consistent with a 2α structure with large deformation. In ¹²Be four high-lying states observed at 7.3, 10.7, 14.6, and 21.7 MeV in the reaction ⁹Be(¹⁵N,¹²N)¹²Be, also form a rotational band with almost the same moment of inertia; tentative spin assignments of 2⁺–8⁺ are used.     

Dimers based on the α + α potential and chain states of carbon isotopes

Using the well established binding energies of one and two valence neutrons in the two-center α+α system (forming the states in ⁹Be and ¹⁰Be*) the structure of these nuclear dimers and their rotational bands including those with more than 2 nucleons are discussed using published transfer reaction data for Be and Boron isotopes. Based on the 0 ₂ ⁺ state in ¹²C which is supposed to be an 3α particle chain at an excitation energy of 7.65 MeV and using the binding energy of these valence neutrons in ⁹Be and ¹⁰Be*, chain states in the system ¹²C* + x neutrons are constructed. The energy position of the lowest chain states are estimated and ways for their population in reactions on ⁹Be and using radioactive beams are proposed. It is expected that these states are metastable and could have appreciable branches for γ-decay. Further extrapolations to longer chain states (polymers) in neutron rich light isotopes are made.     

Neutron polarizations from the9Be(d,n)10B and11B(d,n)12C reactions

Neutron polarization angular distributions were measured for the⁹Be(d,n)¹⁰B and¹¹B(d,n)¹²C reactions for deuteron energies of 5.47 and 5.34 MeV, respectively. Using neutron time-of-flight techniques, polarizations to eight states in¹⁰B and to six states in¹²C have been measured. Neutron polarization energy excitation functions for both reactions were measured for deuteron energies from 3.0 to 5.5 MeV in 0.25 MeV steps at 30° (lab). Distorted wave method calculations carried out to compare theoretical calculations against experimental results were not in good agreement with the data.     

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.     

12C(12C, 8Be)16O angular distributions and excitation functions between 35 and 69 MeV bombarding energy

An array of eight detectors has been developed for identifying the particle unstable ⁸Be nucleus from nuclear reactions with high detection efficiency. Absolute cross sections have been measured for the reaction ¹²C(¹²C, ⁸Be_g.s.)¹⁶O to the ground state and to several excited states in ¹⁶O. Excitation functions at seven angles from 15° to 45° (lab) in 5° steps have been measured for bombarding energies between E¹²_C(lab) = 35 and 69 MeV. Excitation functions were obtained for the following states in the residual nucleus ¹⁶O which were found to be strongly populated: g.s.(0⁺); 6.1 MeV (0⁺, 3^?); 6.9 MeV (2⁺); 10.4 MeV (4⁺); 11.1 MeV (4⁺); 14.7 MeV (6⁺,…) and 16.3 MeV (6⁺,…). The energy range is covered in 250 keV (c.m.) steps; at certain energy ranges in ¹²⁵ keV or 50keV steps. All excitation functions exhibit a strong energy dependence of the cross section; pronounced gross structures with superimposed fine structures, similar to those observed for ¹²C+¹²C elastic and inelastic scattering at these energies, are observed. At 19.3 MeV, where resonant structures were observed in the reactions ¹²C(¹²C, p)²³Na, ¹²C(¹²C, n)²³Mg and ¹²C(¹²C, d)²²Na, no resonance is found for the reaction studied here. At 60, 61 and 63 MeV angular distributions have been measured in 1° and 2.5°(lab) angular steps. The excitation functions have been analyzed in terms of Ericson fluctuations and cross-correlation functions.     

The description of hypernuclei in the continuum shell-model

The advantage of the continuum shell-model in describing nuclear reactions producing hypernuclei is discussed. Numerical results obtained within this model for the (K ^?,π ^?) reaction on⁹Be,¹²C,¹⁶O and⁴⁰Ca are presented.     

Strangeness exchange reaction on nuclei

Population of hypernuclear states has been observed in recoiless Λ production of the strangeness exchange reaction (K^?, π^?) on ⁹Be, ¹²C, ¹⁶O, ³²S and ⁴⁰Ca.     

Investigation of the reaction mechanism for the four-particle photodisintegration of a carbon nucleus

The four-particle photodisintegration of a carbon nucleus in the reactions ¹²C(γ, p)³H2α and ¹²C(γ, n)³H2α is investigated by a method that employs a diffusion chamber in a magnetic field. It is shown that these reactions proceed according a sequential-type scheme: excited states of ¹¹B and ¹¹C nuclei decay to weakly excited states of ⁸Be, ⁷Li, and ⁷Be nuclei. It is concluded that nucleons are knocked out from the s shell. In the excitation curve for the 2α system in the reaction ¹²C(γ, p)³H2α, a resonance is found between the maxima corresponding to the ground and the first excited state of the ⁸Be nucleus, and this resonance is identified as a ghost anomaly. The branching fractions of the decay modes are determined. The angular distributions of nucleons in the reaction c.m. frame are measured. The energy dependence of the asymmetry coefficient for the angular distributions is obtained. A fast increase in this coefficient is observed in the energy range 38–40 MeV. It is concluded that the asymmetry coefficient depends on the excitation energy of the final nucleus in the region of intermediate photon energies.     

Selective excitation in kaon-nucleus inelastic scattering

The K⁺ meson (kaon) inelastic excitation of low-lying (E_x = 0–15 MeV) T = 0 collective states in ¹⁶O is theoretically studied as a function of energy and momentum transfer. The distorted wave impulse approximation is used to calculate angular distributions and total inelastic cross sections for exciting the first J^π = 2⁺, 3^?, 4⁺ and 5^? states at lab energies from threshold to 400 MeV. The distortions are represented in a Kisslinger-type optical potential constructed from elementary K⁺-nucleon amplitudes. Total nuclear elastic and reaction K⁺-nucleus cross sections are computed to demonstrate sensitivity to choice in K⁺-nucleon amplitudes. Fermi motion effects are also assessed using a simple averaging procedure. The weak absorption character of the kaon is reflected in the inelastic calculations which predict selective excitation of low spin states at low momentum transfer and high spin states at high momentum transfer.     

Search for cluster structure of excited states in 14 C

We have studied three different 2n-transfer reactions on a ¹²C target, the 2p pick-up reaction on ¹⁶O and the ⁵He transfer in the reaction ⁹Be(⁷Li,d)¹⁴C. Combined with a systematic search through experimental results for transfer reactions, inelastic excitations and other data, we have established an almost complete spectroscopy for ¹⁴C up to 18 MeV excitation. We identify states with single-particle structure that have oblate shapes and states corresponding to proton excitations that are connected to oblate (triangular) cluster states. Further we list states of prolate shape which have no simple structure related to the low-lying oblate states of ¹²C. These are proposed to have strong -clustering and to form rotational bands as a parity inversion doublet, with high moment of inertia. With these results it is possible for the first time to identify chain states expected in the isotope ¹⁴C.Received: 3 November 2003, Revised: 23 December 2003, Published online: 24 August 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.60.Gx Cluster models     

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.     

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.     

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.     

Asymptotic normalization coefficients and astrophysical direct capture rates

Peripheral transfer reactions can be used to determine asymptotic normalization coefficients (ANCs). These coefficients, which specify the normalization of the tail of the nuclear overlap function, determine S-factors for direct capture reactions at astrophysical energies. A variety of proton transfer reactions involving both stable and radioactive beams have been used to measure ANCs. Tests have demonstrated that ANCs determined from proton transfer reactions can be used to calculate astrophysical direct capture rates to within 9%. The ¹⁰B(⁷Be, ⁸B)⁹Be and ¹⁴N(⁷Be, ⁸B)¹³C reactions have been used to measure the ANC appropriate for determining the ⁷Be(p,γ)⁸B rate, and the ¹⁴N(¹¹C, ¹²N)¹³C reaction has been used to measure the ANC required to calculate the ¹¹C(p,γ)¹²N rate. Received: 1 May 2001 / Accepted: 4 December 2001     

Spectroscopy of 13Be

Six quasi-stationary states of ¹³Be populated in the ¹⁴C(¹¹B,¹²N) ¹³Be reaction at E_lab = 190 MeV are reported. A Q-value = −39.60(9) MeV and a mass excess, M.E.= 33.95(9) MeV, have been found for the lowest observed spectral line. The ground state is unstable with respect to one-neutron emission by 0.80(9) MeV. Excitation energies of 1.22(10), 2.10(16), 4.14(12), 5.09(14) and 7.0(2) MeV have been obtained for the observed spectral lines.     

Hyperchange exchange reactions on nuclei

In hypercharge exchange reactions (K^?, π^?) on light nuclei Λ particles with small recoil momentum have been produced. The observed hypernuclear states in _Λ⁹Be, _Λ¹²C and _Λ¹⁶O have simple neutron-hole Λ-particle configurations.     

The 12C(9Be,n)20Ne reaction

A study of the ¹²C(⁹Be, n)²⁰Ne reaction has been carried out at bombarding energies of 16 and 24 MeV. The spectra at both incident energies are dominated by a consistent set of levels between an excitation energy of 7.3 ± 0.4 and 15.7 ± 0.3 MeV. The rotational band based on the K^π = 0₃⁺ state appears to be strongly populated. Based on this selectivity, additional evidence is provided in favor of identification of the 8⁺ state at 15.9 MeV with this 0₃⁺ band. Angular distributions measured at the higher bombarding energy are compared with statistical compound-nuclear calculations. It appears that a non-statistical mechanism is responsible for the reaction's selective population of states with 8p-4h configuration. Such a mechanism, involving the preferential breakup of the ⁹Be into ⁸Be plus a neutron, is discussed.     

Spectroscopy of <Superscript>17</Superscript>C and (sd )<Superscript>3</Superscript> structures in heavy carbon isotopes

The structure of ¹⁷C has been investigated using the three-neutron transfer reaction (¹²C,⁹C) on a ¹⁴C target at 231MeV incident energy, the reaction Q-value is Q ₀ = - 46.930MeV. Eleven new states up to 16.3MeV excitation energy were identified. The same reaction has also been used on a ¹²C target ( Q ₀ = - 38.787MeV), and excited states in ¹⁵C up to 19MeV were observed. In ¹⁷C the three transferred neutrons populate (sd )³ configurations on the ¹⁴C core. The comparison of levels populated by the (¹²C,⁹C) reaction in ¹⁷C, ¹⁶C and ¹⁵C reveals a strong similarity of their properties. This concerns especially nine states in each of the three carbon isotopes, which show practically the same excitation energies except a constant mean shift of +5.82MeV for ¹⁶C and +6.65MeV for ¹⁵C with respect to ¹⁷C. The triples of states from the three isotopes, which correspond to each other, have also similar widths and cross-section ratios. It is concluded that the same (sd )³ structures are populated in the three carbon isotopes. The observed levels of ¹⁷C are also compared to the levels of ¹⁹O with known assignments and to shell model calculations, and their decay properties are discussed.     

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.