Microscopic and macroscopic aspects of 135 MeV proton scattering from 16O

Differential cross sections have been measured for the scattering of 135 MeV protons from ¹⁶O and data from the transitions to 13 states (up to 19.5 MeV excitation) have been analysed using microscopic and macroscopic nuclear reaction models. Extensive collective model calculations have been made of the transitions to all natural-parity states. The deformation parameters for the 4p4h rotational band are in good agreement with theoretical models. The inelastic scattering data from the excitation of the negative-parity states have also been analysed in the distorted-wave approximation using microscopic (shell and RPA) models of nuclear structure and with density-dependent two-nucleon t-matrices. For positive-parity states, we report the first shell-model calculation using the complete 2?ω basis space and find that the triplet of 2p2h states (4⁺, 2⁺, 0⁺) around 11 MeV excitation is quite well described by this model, as may be a 1⁺ state which is observed for the first time by proton scattering from ¹⁶O.     

The reaction 14C(3He,n)16O and the coexistence model of 16O

The reaction ¹⁴C(³He, n)¹⁶O has been measured at a ³He bombarding energy of 25.4 MeV. The zero-degree differential cross section for the excitation of the three low lying 0⁺T = 0 states, at energies 0.0, 6.05 and 12.05 MeV are, respectively, 1.33 ± 0.10, 0.49 ± 0.10, and 0.50 ± 0.10 mb/sr These measured cross sections are in rough agreement with single-step zero-range DWBA calculations using an empirically determined ¹⁴C ground state wave function and in which the Brown and Green coexistence-model wave functions are used to describe the ¹⁶O 0⁺ states. The angular distribution of the transition to the ground state is measured between 0° and 32°.     

High-spin states of 26Mg populated in the 12C(18O, α) reaction

The structure of ²⁶Mg has been investigated by means of the ¹²C(¹⁸O, α) reaction. Several previously unknown states were populated between excitation energies of 0 to 16 MeV. Excitation functions were measured for 126 states for bombarding energies between 43.2 and 45.9 MeV in 300 keV steps at a lab angle of 7°. The experimental energy averaged differential cross sections were compared with statistical model calculations and good agreement was obtained for the states whose spins and parities were previously established. The statistical model calculations were used to suggest the spins and parities for the rest of the states. In particular, candidates for 6⁺ and 8⁺ states were interpreted as members of three rotational bands in ²⁶Mg: the ground-state band, the K = 2⁺ band based on the 2.938 MeV 2⁺ state, and a K = 0⁺ band based on the 3.588 MeV 0⁺ state. Back bending of the yrast band is observed and it is suggested that it may be due to band crossing of the ground-state and first excited K = 0⁺ bands.     

Coupled-channels study of projectile and target excitation in the scattering of 6Li from 12C and 16O

Coupled-channels calculations are presented tor elastic and inelastic ⁶Li + ¹²C scattering at E_c.m. = 16 MeV and 20 MeV, and for ⁶Li + ¹⁶O at 18.7 MeV. Excitation of states within ⁶Li, ¹²C and ¹⁶O are treated with rotational, rotation-vibration and vibrational models only. The 3⁺⁶Li and 2⁺¹²C states are strongly coupled to the elastic scattering and reduce the strengths of both the real and imaginary potentials. The 3^?16O state reduces only the strength of the imaginary potential. All other states are weakly coupled and have little effect on each other or the potential. The data are reasonably well described, with there being some preference for the 3^? state in ¹²C to be K = 0. Excitation of the 0₂⁺ state in ¹²C requires a combination of β-vibration and monopole breathing-mode form factors. The deformation lengths found are in poor agreement with those deduced from electron or proton scattering.     

Microscopic study of the 12C + 16O system

An angular momentum projected microscopic calculation is performed for the ¹²C + ¹⁶O system with an effective nuclear force and the exact Coulomb interaction. The ¹²C wave function is projected on a 0⁺ state. Parametrizations of the Coulomb interaction between the nuclei are fitted. The L-projected energy curves present a quite complicated structure especially for the negative parity states. The role played by critical angular momenta is put into evidence. A generator coordinate calculation gives several bands of bound, quasibound and virtual states. Excellent agreement in energy and angular momentum is obtained with the 13.7 MeV (J = 9), 19.7 MeV (J = 14), 22.7 MeV (J = 15) and other resonances.     

Surface and volume contributions to real and imaginary parts of the heavy-ion optical potential

Starting from the Feshbach expression for the optical potential, explicit formulae for the real and the imaginary parts of the optical potential between two heavy ions (HI's) are obtained. They are each composed of a volume and a surface term. The contributions to the volume term are calculated in two nuclear Fermi liquids which flow through each other starting from the realistic Reid soft core nucleon-nucleon (NN) interaction. Since the Fermi surface is formed by two spheres one obtains a complex Brueckner reaction matrix which is approximated by a complex, effective local interaction. It is used in a fully antisymmetrized double folding procedure to obtain the volume terms of the optical potential between the two HI's. The surface contributions are directly calculated in the collision of the two finite HI's. The collective surface vibrations (3^? octupole state and 2⁺, 4⁺ (T = 0) giant resonances for the ¹⁶O?¹⁶O collision) are included as intermediate states. This yields especially an imaginary contribution at the surface which reduces the transparency found with the volume terms alone. The method is applied to ¹⁶O?¹⁶O scattering at 83 and 332 MeV laboratory energy. The local approximations to the real and imaginary parts obtained in this way agree well with phenomenological fits. The surface terms improve the agreement of the differential cross section at 80 MeV where experimental data are available.     

Indication of Δ-hole configurations in 12C(15.11 MeV)

A strong energy dependent enhancement is seen in inelastic pion scattering from ¹²C to the 1⁺, T = 1 state at 15.11 MeV, but not to the 1⁺, T = 0 state at 12.71 MeV. This enhancement may be interpreted as evidence for the direct excitation of delta-hole (Δ-h) components in the wave function of the T = 1 state. The required Δ-h amplitude is estimated and found to be in agreement with calculations of Bohr and Mottelson.     

The (18O, 20Ne) reaction on the even Ni isotopes and the mass of 62Fe

The (¹⁸O, ²⁰Ne) reaction on the even Ni isotopes has been studied at 63.0 MeV with ΔE-E time-of-flight telescopes. From the measured ground-state Q-value for the ⁶⁴Ni(¹⁸O, ²⁰Ne)⁶²Fe reaction, ?1.97±0.20 MeV, a mass excess ?58.87±0.20 MeV is obtained for the ⁶²Fe nucleus. This result is in good agreement with a recent measurement of the β-endpoint energy. Angular distributions for the transitions to the Fe ground states, leaving ²⁰Ne in its ground and 1.63 MeV 2⁺ excited state, yield relative spectroscopic strengths in fair agreement with DWBA calculations based on simple shell-model estimates.     

Do analogs of the Hoyle state exist in <Superscript>16</Superscript>O?

The root-mean-square radii of short-lived 0⁺-states in ¹⁶O were obtained for the first time from an analysis of α+¹⁶O diffraction scattering. Data on elastic and inelastic α+¹⁶O scattering were analyzed on the basis of the modified diffraction model in the range of projectile energies between a few tens of MeV units to 400 MeV. No case of a significant enhancement of the radius with respect to its ground-state value was observed. In particular, this concerns the 15.1-MeV 0 ₆ ⁺ state, which lies near the threshold for breakup to four alpha particles and for which we did not confirm a giant radius predicted by the alpha-particle-condensate model. This result disproves the hypothesis that the ¹⁶O nucleus in the 0 ₆ ⁺ state has a rarefied structure and appears to be an analog of the known Hoyle state at 7.65 MeV (0 ₂ ⁺ ) in ¹²C.     

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 interacting boson model structure of 16O

The recently proposed interacting boson approximation (IBA) is applied to the structure of ¹⁶O. The T = 0, J = 0⁺, 2⁺, 4⁺, 1^?, 3^? states below 18 MeV are calculated and compared with the known experimental levels. The agreement obtained indicates the usefulness of the IBA. The limitations of the model are briefly discussed.     

Elastic and inelastic scattering of 120 MeV 18O from 208Pb and the spin alignment of the 2+ state of 18O

The elastic and inelastic scattering of ¹⁸O ions at 120 MeV from a target of ²⁰⁸Pb have been studied. Cross sections for excitation of the 2⁺ state at 1.982 MeV in ¹⁸O and of the 3^? state at 2.61 MeV in ²⁰⁸Pb were measured. In addition, the populations of the m-substates for the ¹⁸O excitation were deduced from the Doppler-broadened line shapes. The data were subjected to a coupled-channels analysis using either Woods-Saxon or folding-model potentials. In addition, the ¹⁸O excitation was found to be described very well by use of a semi-microscopic model. The analyses consistently indicated the presence of a positive static hexadecapole moment of several e · fm⁴ for the 2⁺ state of ¹⁸O. The m-substate population distributions were found to be better fitted if a vector spin-orbit coupling was introduced for the 2⁺ state of ¹⁸O with a sign opposite to that for the nucleon-nucleus case.     

Two-nucleon T = 0 transfer reactions in the 0p shell

The ¹⁶O(d, α)¹⁴N, ¹⁴N(d, α)¹²C and ¹²C(d, α)¹⁰B reactions at E_d = 40MeV and the ¹²C(α d)1¹⁴N at E_α = 55 MeV were investigated. A total of seventeen transitions are analysed in terms of one-step, zero-range DWBA calculations, using the two-particle coefficients of fractional parentage obtained from the Cohen-Kurath Op shell wave functions. For most transitions, fair agreement is obtained between experiment and calculation, possible exceptions being the transition to the E_x = 4.43 MeV, J^π = 2⁺ state in ¹²C and to the E_x = 2.15 MeV, J^π = 1⁺ state in ¹⁰B, for which the calculations predict too much L = 0 strength. Where possible, a comparison with previous (p, ³He) results is made. In ¹⁴N a state at E_x = 11.04 MeV was observed for which the values (J_π; T) = (3⁺; 0) are suggested. In ¹²C we found, in addition to the well known T = 0 states, two relatively sharp T = 0 states at E_x = 19.50 ± 0.10 and 20.55 ± 0.10 MeV. The shape and strength of the angular distribution for the transitions to these states can be approximately accounted for by the calculations, although no one-to-one correspondence between observed and predicted levels could be established.     

Excitation of ground and gamma bands in the 24Mg(α, α')24Mg reaction at 120 MeV

The cross sections for excitation of the members of the ground state (g.s.) band 0^?(g.s.), 2⁺ (1.37 MeV) and 4⁺ (4.12 MeV) and the γ-band 2⁺_γ (4.24 MeV), 3_γ⁺(5.24 MeV) and 4_γ⁺(6.01 MeV) in ²⁴Mg have been measured in inelastic α-scattering at E_α = 120 MeV. The excitation of these states are found to be well described by a coupled-channel calculation (CCBA) performed in the framework of the asymmetric rotational model. Two sets of parameters are found to give excellent fits to the data, but in both a direct coupling between the ground state and the 4⁺ state is found necessary.     

The 18O(18O, 16O)20O reaction at 52 MeV

The structure of the ²⁰O nucleus was studied by the ¹⁸O(¹⁸O, ¹⁶O)²⁰O reaction at E_1ab = 52 MeV. Angular distributions for the transitions to the lowest four states in ²⁰O were obtained and analyzed with finite-range DWBA calculations. Optical potential sets were used which fit the experimental elastic scattering differential cross sections over almost the whole angular range. The two L = 0 transitions to the ground state and the 4.45 MeV state of ²⁰O populated by the ¹⁸O(¹⁸O, ¹⁶O) reaction were analyzed with exact finite-range DWBA calculations using microscopic form factors. These calculations underestimate the absolute cross sections by a factor of 11. The relative strength of the two L = 0 transitions is well reproduced in the ¹⁸O(¹⁸O, ¹⁶O) reaction. However, DWBA calculations for the ¹⁸O(t, p)²⁰O reaction overestimated the relative cross sections for the excited 0⁺ state by a factor of 6. Several model wave functions were tested for the ground-state transition. It was found that the absolute cross sections of the (¹⁸O, ¹⁶O) reaction are very sensitive to the mixing of shell-model configurations. The angular distribution shapes are also slightly dependent on the mixing.     

Two-proton transfer reaction48Ca(18O,16C)50Ti at 102 MeV

Differential cross sections for¹⁸O elastic scattering and the (¹⁸O,¹⁶C) and (¹⁸O,¹⁷N) reactions on⁴⁸Ca were measured at 102 MeV using a Q3D magnetic spectrograph. The transitions to the 7/2^? ground state (g.s.) of⁴⁹Sc and the 0⁺ (g.s.), 2⁺ (1.554 MeV), 4⁺ (2.675 MeV), and 6⁺ (3.198 MeV) states of⁵⁰Ti were analyzed by DWBA calculations which include finite-range and recoil effects. Simple cluster-transfer calculations were done for all two-proton transfer transitions. For the 0⁺ (g.s.) transition a two-nucleon transfer code employing microscopic wave functions was also used. It was found that absolute cross sections for this kinematically well-matched transition were underrated by a factor of about 7 for a reasonable amount of configuration mixing in the nuclear states involved in this transition. This factor is very close to the value 5 derived for the similarly well-matched⁴⁸Ca(¹⁸O,¹⁶O)⁵⁰Ca reaction.     

The 12C(α, γ)16O reaction and stellar helium burning

The cross section for the reaction ¹²C(α, γ)¹⁶O has been measured for a range of c.m. energies extending from 1.41 MeV to 2.94 MeV, by using ¹²C targets of high isotopic purity, large NaI(T1) crystals, and the time-of-flight technique for the suppression of prompt neutron background and time-independent background. Gamma-ray angular distributions were measured at c.m. energies of 2.18, 2.42, 2.56 and 2.83 MeV. By means of theoretical fits, which include the coherent effects of the 1^? states of ¹⁶O at 7.12 MeV, 9.60 MeV, and those at higher energies, the electric-dipole portion of the cross section at astrophysically relevant energies has been determined. A three-level R-matrix parametrization of the data yields an S-factor at E_c.m. = 0.3 MeV, S(0.3 MeV) = 0.14^+0.14_?0.12 MeV · b. A “hybrid” R-matrix optical-m parameterization yields S(0.3 MeV) = 0.08^+0.05_?0.04 MeV · b. This S-factor is of crucial importance in determining the abundances of ¹²C and ¹⁶O at the end of helium burning in stars.     

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.     

Microscopic analysis of the 12C(α, γ)16O reaction

Electric transition probabilities in the ¹⁶O spectrum, and the ¹²C(α, γ_o,3¹⁶O capture cross sections are calculated with antisymmetric wave functions by the generator coordinate method. The influence of bound states on radiative capture is shown to be automatically included in the model. The reduced α-widths of the ¹⁶O bound states are discussed, and compared with previous theoretical and experimental estimates. The microscopic E2 capture cross sections to the O⁺₁ and 2₁⁺ states yield an astrophysical S-factor of 0.09 MeV · b at 0.3 MeV. An attempt to treat the El multipolarity by relaxing the long-wavelength approximation leads to a large underestimation of the γ-widths. Adopting the experimental γ- width and the theoretical reduced α-width of the 1₁^? state provides s_E1 = 0.30 MeV · b at 0.3 MeV.