Study of neutron-rich nuclei with an m -scheme cluster-orbital shell model approach

We propose an m -scheme approach of the cluster-orbital shell model (COSM) formalism. In order to take into account the contribution of the unbound states, the radial wave function is treated as the super position of the Gaussian functions with different width parameters. We apply the m -scheme COSM to oxygen isotopes. Energies and r.m.s. radii of oxygen isotopes are studied.     

Cluster-Orbital Shell Model Approach with a Treatment of Partially Pauli-Forbidden States

We study the origin of a sudden change of the radius of oxygen isotopes at ²³O in terms of a coupled-channel model approach. We use the cluster-orbital shell model approach for describing the system. Qualitatively, the sudden change of the radius can be understood as the competition of occupation of the valence neutrons and the component of the core configuration. For the ²³O case, the effect of the partially Pauli-forbidden states of the 1s _1/2-orbit is small in the excited-core configuration.     

Elastische Elektronenstreuung an14N,15N,16O und18O bei kleiner Impulsübertragung

Elastic electron scattering cross sections of¹⁴N and¹⁶O have been measured relative to the proton and of¹⁵N and¹⁸O relative to the lighter isotope (¹⁴N,¹⁶O resp.) using gas targets. The momentum transfer ranged from 0.22 to 0.48 fm^?1. The data were analyzed by phase shift calculations assuming harmonic oscillator shell model charge distributions. The following rms charge radii have been deduced: R_m(¹⁴N)=2.540±0.020 fm R_m(¹⁵N)=2.580±0.026 fm R_m(¹⁶O)=2.718±0.021 fm R_m(¹⁸O)=2.789±0.027 fm. The errors include statistical and systematic uncertainties and an estimate of effects due to the choice of the model. The radius differences of the isotopes are smaller than the values predicted by anA ^1/3 relation     

Pigmy and giant dipole states in stable and unstable oxygen isotopes

We have studied dipole states of oxygen isotopes in large scale shell model calculations. The calculated photoreaction cross sections in ¹⁶O, ¹⁷O and ¹⁸O give reasonable agreement with experimental observations both in the low energy region below ?ω=15 MeV and in the high energy giant resonance region (15 MeV < ?ω ≤ 30 MeV). We found that the transition strength below dipole giant resonance (?ω ≤ 15 MeV) exhausts about 10% of the classical Thomas-Reiche-Kuhn sum rule and more than 40% of the cluster sum rule in heavier oxygen isotopes than ¹⁷O. The predicted Pigmy strengths in ²⁰O and ²²O are also confirmed by recent Coulomb excitation experiment at GSI.     

The (18O,16O) reaction on even tin isotopes

The two-neutron transfer reaction^ASn(¹⁸O,¹⁶O)^A+2Sn has been measured for the isotopes A=112, 116, 118, 120, 122 and 124 at bombarding energies of 57 and 60 MeV together with the elastic scattering. Angular distributions have been analysed for the transitions to the ground state and to the first excited 2⁺ state. The observed ground state transition is strongly enhanced. The theoretical DWBA analysis is performed with a finite range 2n-transfer form factor including recoil correction. The calculated cross section reproduces the observed systematic change over all isotopes. The absolute cross sections are normalized by a factor of 4.7 and 7.5, depending on the two different sets of 2n-wave functions used in the analysis. The results confirm the prediction of the pairing model that the transition strengths of a neutron pair between the ground states of even tin isotopes are the same.     

14O核中子闭壳效应的探讨

在引入了BCS理论的相对论平均场模型框架内,通过系统研究氧同位素偶偶核的单粒子能级间隔、单粒子能级占有概率比、对作用效应和粒子数涨落,比较了¹⁴O,²²O和²⁴O三个核的中子闭壳效应,最后从理论上预言丰质子核¹⁴O有着比丰中子核²²O和²⁴O更强的中子闭壳效应. 关键词： 相对论平均场模型 能级间隔 占有概率 粒子数涨落     

Heterodyne measurements of 12C18O, 13C16O,and 13C18 O laser frequencies; mass dependence of Dunham coefficients

Difference frequencies between rare isotope CO lasers and a ¹²C¹⁶O laser have been measured by optical heterodyne techniques. These data for ¹²C¹⁸O, ¹³C¹⁶O, and ¹³C¹⁸O have been used together with the 15 previously reported Dunham coefficients Y_kl for ¹²C¹⁶O to determine a set of mass independent parameters Δ_kl and U_kl defined by Y_kl = μ^-(k/2+l)[1+m_e(Δ^C_kl/M_C + Δ^O_kl/M_O)] U_kl. The 01, 1 0, and 20 correction terms were found to be statistically significant. Line frequencies calculated from the resulting 15 Dunham coefficients for the rare isotopes are accurate to a few MHz in the measured laser bands.     

Direct mass measurements of the neutron-rich light isotopes of lithium through fluorine

The direct mass measurements of the neutron-rich nuclei¹¹Li,¹⁴Be,¹⁷B,^19–20C,^20–22N,^23–24O, and^25–27F have been performed using the Time-of-Flight Isochronous (TOFI) spectrometer. We observe a notable drop in the two-neutron separation energies for the oxygen and fluorine isotopes afterN=15. This behavior is interpreted using the shell model.     

Nuclear reaction cross sections of 16O + 16O obtained by γ-ray detection

The partial production cross sections for reaction residues produced by the fusion of ¹⁶O with ¹⁶O have been measured at E_c.m = 9–30 MeV by detecting the characteristic γ-rays with a Ge(Li) detector. The dominant products are ²⁴Mg and ²⁷A1 corresponding to 2α and αp emission from the compound nucleus, respectively. The total γ-producing cross sections σ_R were also derived by summing the partial cross sections after correction for the observed (average) γ-ray angular distributions. The trend in the total cross sections is very similar to the trends derived from an optical model or a statistical-evaporation model calculation. The partial production cross sections were compared with other experimental results at 11.9 MeV and 30 MeV and with the results of the statistical-model calculation. It is concluded that the treatment of angular momentum in the calculation is inadequate for describing the partial cross sections. Structure in the partial and total cross section excitation functions is observed with minima occurring at E_c.m. = 27, 24, 20, 17.5, and possibly 15 MeV. Some of this structure is well established by the statistical accuracy of the data and most, but perhaps not all of it, is correlated in the various channels. This structure is compared with that observed in another experiment and some of its implications are discussed.     

Isotopic fractionation between gaseous and dissolved carbon dioxide

The isotopic fractionation between gaseous carbon dioxide and an equilibrated aqueous solution of the gas has been measured at temperatures between 0° and 60 °C for the carbon isotopes and close to 0 °C for the oxygen isotopes. ¹³C¹⁶O₂ is slightly less, and¹²C¹⁶O¹⁸O slightly more soluble than¹²C¹⁶O₂, the actual values for the fractionation,?, being ?(1.18?0.0041 ·t)‰ (temperature,t, in °C) for the carbon isotopes and about 0.8‰ at 0°C for the oxygen isotopes. A theoretical expression is derived for the vapour-solute equilibrium system by treating it in a similar manner as the pure vapour-liquid system. The calculated isotopic fractionation for carbon dioxide, using data on the pure vapour-liquid system, is in satisfactory agreement with the experimental results.     

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.     

Dependence on collision energy of the stereodynamical properties of the 18O + 32O2 exchange reaction

We report a quantum stereodynamical study of the ¹⁸O + ¹⁶O¹⁶O(v = 0, j = 1) → ¹⁸O¹⁶O(v′ = 0, j′) + ¹⁶O oxygen exchange reaction at four different collision energies. We calculated the polarisation moments and generated stereodynamical portraits related to the key vectors involved in this collision process. Ozone complex-forming approaches of reactants are then deduced. The results indicate that different approaches are possible but strongly depend on the collision energy and other parameters of the collision. We also conclude that the reaction globally tends to favour a perpendicular approach with increasing energy.     

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.     

Nonstatistical structures in the excitation functions of20Ne(16O,12C)24Mg and20Ne(16O,20Ne)16O reactions

The data on the excitation functions of²⁰Ne(¹⁶O,¹²C)²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(1.37, 2⁺),²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(4.12, 4⁺+4.24, 2⁺) +²⁰Ne(¹⁶O,¹²C^*(4.44, 2⁺))²⁴Mg,²⁰Ne(¹⁶O,¹²C)²⁴Mg^*(6.01, 4⁺+6.43, 0⁺),²⁰Ne(¹⁶O,²⁰Ne)¹⁶O,²⁰Ne(¹⁶O,²⁰Ne^*(1.63, 2⁺))¹⁶O, and²⁰Ne(¹⁶O,²⁰Ne^*(4.25, 4⁺))¹⁶O reactions atθ _lab=13° fromE _c.m.=22.8 to 38.6 MeV have been subjected to a statistical analysis comprising of the calculations of the distribution of cross sections, deviation functions, cross-correlation functions, summed excitation functions, cross-channel correlation coefficients and coherence widths. The analysis confirms the existence of nonstatistical structures atE _c.m.=24.6, 27.8, 31.7 and 35.5 MeV, and identifies a new structure of the same nature atE _c.m. =25.6 MeV.     

Kernradien von12C,13C,14N und16O aus Elektronenstreuung zwischen 30 und 60 MeV

Elastic electron scattering cross sections of¹²C,¹⁴N and¹⁶O relative to the proton, and of¹³C relative to¹²C have been measured. Using harmonic oscillator wave functions the followingrms charge radiiR _m were deduced by phaseshift calculations: 2.395 (28) fm for¹²C, 2.384 (47) fm for¹³C, 2.492 (33) fm for¹⁵N, 2.666 (33) fm for¹⁶O. The ratioR _m (¹³C)/R _m (¹²C) is 0.995±0.008. The errors given do not include uncertainties from the model dependence of the evaluation which may be of the same magnitude.     

Delta-isobar configurations in 12C and 16O nuclei

The differential yield of the reaction ¹⁶O(γ, π ⁺ p) at the maximum photon energy of 450 MeV was measured in the region of high momentum transfers to the residual nuclear system. The experimental results obtained for the ¹⁶O nucleus and the cross section measured earlier for the reaction ¹²C(γ, π ⁺ p) were analyzed on the basis of a model that takes into account the admixture of isobar states in the nuclear wave function. The probabilities for the delta-isobar configurations in the ground states of the carbon and oxygen nuclei per nucleon were estimated empirically at 0.012 ± 0.003 ± 0.002 and 0.019 ± 0.003 ± 0.003, respectively.     

Nuclear rainbow in the elastic scattering of <Superscript>16</Superscript>O nuclei on carbon isotopes

An investigation of refractive effects in heavy-ion scattering is continued. For the elastic scattering of ¹⁶O nuclei on a ¹³C target at E(¹⁶O) = 132 MeV, the differential cross sections are measured for the first time in addition to previous measurements for targets from the carbon isotopes ¹²C and ¹⁴C. Airy structures that are similar for all isotopes and which have close cross sections are observed and are found to be consistent with the energy systematics of Airy minima that were obtained previously. The volume integrals of the real and imaginary parts of the optical potentials found in the present study are nearly identical for all of the isotopes considered here and are also in good agreement with the systematics obtained previously.     

Off-shell effects in O

We calculate the binding energy of ¹⁶O for a set of phase-shift-equivalent potentials previously studied in nuclear matter. Off-shell variations of up to 2.8 MeV per particle occur compared with about a 10 MeV per particle variation in nuclear matter. As in nuclear matter calculations a nearly linear relation exists between the variations in the binding-energy results and the wound integral k. We compare the ¹⁶O results with a nuclear matter calculation at the “equivalent” nuclear matter density of k_F = 1.13 fm⁻¹. This “equivalent” density reflects the fact that ¹⁶O has a surface and hence a lower average density than nuclear matter. The ¹⁶O and nuclear matter off-shell variations are comparable once one takes into account the lower average density of ¹⁶O and the suppression of the relative D-wave interaction — also a surface effect. We present a method of computing the correlated wave functions of finite nuclear systems and display such wave functions for ¹⁶O. The correlated wave functions of ¹⁶O and of nuclear matter are strikingly similar for all of the potentials studied.     

Study of optimum Q-value in 16O induced reactions on even Zr isotopes

Angular behaviour and optimum Q-value of ¹⁶O induced transfer reactions on the even Zr isotopes have been studied near the Coulomb barrier as a function of various parameters. The results are compared to semiclassical estimates including recoil effects and nuclear distortions of the Coulomb trajectories.