Alignment and resonances in 12C+12C inelastic scattering

Using the out-of-plane γ-ray particle coincidence method we have measured the spin alignment P_zz of excited ¹²C(2⁺) nuclei from ¹²C+¹²C inelastic scattering in the energy range 16 MeV ? E_cm ? 33 MeV.P_zz varies strongly as a function of energy and angle. The correlation of resonant structures in the cross section with maxima of the alignment is particularly clear in mutual inelastic scattering and in θ_cm = 90° single inelastic scattering.     

Intermediate resonance of inelastic 12C + 12C scattering

The intermediate resonances observed in the inelastic ¹²C + ¹²C cross sections to the single and mutual 2₁⁺(4.43 MeV) excitations and the single 3₁^? (9.64 MeV) excitation are studied by the coupled-channel method with the use of the coupling interaction derived by the folding procedure between ¹²C and ¹²C. It is shown that the model is successful in reproducing the gross structures of the inelastic cross sections and especially the correlated resonance energies of the inelastic channels. The inelastic resonances are shown to be due to the molecular resonances in an adiabatic potential between two ¹²C, which reproduces correctly the coupled channel resonances.     

Scattering and reactions of 14C + 14C and 14C + 14C

We have studied elastic scattering, inelastic scattering and several transfer channels of the systems ¹⁴C + ¹⁴C and ¹⁴C + ¹²C over a wide range of energies up to E_c.m. = 35 eMeV and 32 MeV, respectively. The reaction channels were identified by means of kinematic coincidences between solid-state detectors, γγ coincidences were measured to determine cross sections for mutual inelastic scattering of ¹⁴C + ¹⁴C.Pronounced regular gross structures, similar to those found for ¹⁶O + ¹⁶O, are observed in the elastic excitation function of ¹⁴C + ¹⁴C at θ_c.m. = 90°, The angular distributions measured at the energies of the maxima and an optical-model analysis suggest that one or a few surface partial waves dominate the scattering behaviour. Correlated structure of narrower width is found in the inelastic channels and, to a lesser degree, in the transfer channels which appear with rather small cross sections.In ¹⁴C + ¹²C elastic scattering the gross structures are strongly fragmented, in contrast to ¹⁴C + ¹⁴C but similar to ¹²C + ¹²C. While the ¹²C(2⁺) excitation is very weak, the observed strengths of the ¹⁴C(3^?) excitation and of neutron transfer point to a substantial role of these channels as coupling partners to the elastic configuration and to their influence on the elastic scattering behaviour. A correlated intermediate structure is observed near 23.5 MeV, where a dominance of l = 18 is suggested by the elastic scattering angular distribution. This unexpectedly high l-value exceeds l_graz at this energy by at least two units of ?.     

Generator-coordinate study of inelastic α + 12C scattering

A multi-channel calculation performed with the generator coordinate method is presented for α + ¹²C scattering. The inelastic channel α + ¹²C(2⁺) is included. Bound-state and resonance energies are determined for J^π = 0⁺ up to 6⁺. For the negative parity levels, the results are very similar to those obtained with a single-channel calculation. The positive parity resonances are more numerous and in better qualitative agreement with experiment in the multi-channel calculation. However, an incorrect value for the threshold energy α + ¹²C(2⁺) channel prevents one from obtaining a quantitative agreement with experiment.     

Microscopic investigation of the 12C + 12C interaction

The ¹²C + ¹²C system is studied in the framework of the generator coordinate method. Each ¹²C nucleus is described by a closed $\text{p}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ subshell. Phase shifts and resonances are determined for several effective two-body interactions involving a spin-orbit term. The existence and properties of simple local equivalent potentials for the ¹²C + ¹²C collision are discussed. The ¹²C + ¹²C system is too light to be well described by potentials independent of the angular momentum or weakly dependent on it.     

Time-dependent Hartree-Fock calculations for 14N + 12C reactions

We present Time-Dependent Hartree-Fock calculations for the massasymmetric system ¹⁴N + ¹²C in the range 20 ? E_cm ? 114. A simplified effective interaction of the Skyrme form has been used and the orbital angular motion of the ions has been treated in the rotating frame approximation. The overall magnitude of the calculated fusion cross-section is in agreement with experiment. The calculated differential cross section for direct inelastic reaction products is proportional to ${}^1\text{sin θ}$. This is in contrast to the exponential decrease observed experimentally.     

46.8MeV的p+12C非弹性散射

在Glauber多重散射理论框架下，使用跃迁密度方法和三种N湮没势，计算了46.8MeV的反质子在¹²C上的非弹性散射微分截面. 理论曲线与实验数据符合得较好. 关键词： Glauber理论 反质子 非弹性散射 湮没势 跃迁密度     

Alpha-heavy-ion angular correlations from 28Si + 12C

Alpha particles have been measured in coincidence with heavy recoil nuclei from the ²⁸Si + ¹²C reaction. At E_lab = 87 MeV angular correlations for alphas between 15° and 55° and heavy ions at angles ?9°, ?12° and ?15° have been taken. An excitation function of coincidence events with θ_α = 30° and θ_HI = ?12° has been measured for 84 MeV < E_lab < 91.5 MeV. The results are well described by a statistical-model calculation for compound nucleus decay. No evidence is found for additional processes.     

Energy dependence of the 24Mg(16O, 12C)28Si reaction

Excitation functions for the reaction ²⁴Mg(¹⁶O, ¹²C)²⁸Si(g.s., 2⁺₁) were measured at 5°(lab) in the energy range 32 < E_c.m. < 49 MeV. Although the resonant structure, previously observed at lower energies, becomes progressively weaker, three new correlated maxima have been observed near E_c.m. = 37.5, 40.2 and 43.5 MeV. Angular distribution measurements at these energies yield spin assignments, from P²_j(cos θ) comparisons, of 27, 29 and 31, respectively. Attempts to find a consistent optical-model fit to the elastic scattering in the entrance channel and an exact finite-range DWBA fit to the four-nucleon transfer reaction in this energy range were unsuccessful. Such a failure is to be expected if strong couplings between the elastic channel and inelastic channels of either the initial or final system are important. The features of the resonance phenomena in the transfer reaction are discussed within a band crossing model framework.     

Axially symmetric time-dependent Hartree-Fock study of the 208Pb + 208Pb reaction

A time-dependent Hartree-Fock calculation assuming axial and reflection symmetry constraints is performed for the head-on collision of ²⁰⁸Pb + ²⁰⁸Pb systems at E_lab≈1600 MeV. The calculation suggests the excitation of surface modes in the reaction and the energy loss characteristic of a deep inelastic process. An estimate of neck-radius and neck-formation time is given.     

Structure of 13C from an R-matrix analysis of 12C + n scattering and reaction cross sections

Differential cross sections for ¹²C + n elastic and inelastic scattering and for the ²C(n, α) ⁹Be reaction, together with high resolution total cross-section data were analyzed by means of a multilevel multichannel R-matrix program to determineJ, π, and γ_λc for states in ¹³C up to E_x = 13.5MeV. Good overall fits to the data were obtained throughout this large energy range. Spin and parity assignments for thirteen states above E_x = 9.5MeV for which there had been either no previous J^π assignments or only tentative assignments have been made in this study. The present results are in good agreement with previous analyses and model calculations.     

Electron scattering and α-cluster description of 12C and 20Ne

The elastic and inelastic electron scattering form factors in the ground-state band of ¹²C and ²⁰Ne have been calculated using the Brink α-cluster model projected wave functions. From a systematic comparison with experiment it is concluded that usual central forces like the Brink-Boeker B1 force give an unrealistically large clustering while that obtained using density dependent interactions like the Skyrme S1 force is too low. For intermediate values of the clustering it is possible in ¹²C to reproduce simultaneously the elastic as well as the inelastic form factors to the 2₁⁺(4.44 MeV), 3₁^?(9.64 MeV) and 4₁⁺(14.08 MeV) states for not too large transfers. Noticeable discrepancies between calculated and experimental 2₁⁺ and 3₁^? inelastic form factors at transfers higher than 1.5 fm^?1 reveal inherent weaknesses of the α-cluster wave functions which are not corrected after inclusion of the θ-vibrations.     

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.     

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.     

Inelastic scattering of 12C and 13C on 63Cu leading to core-excited states

The inelastic scattering of ¹²C and ¹³C projectiles has been studied on ⁶³Cu at 45 MeV incident energy. The core-excited states (based on 2⁺ in ⁶²Ni) show individual differences in the angular distributions which are due to second-order couplings (transfer and inelastic transitions). However, the sum of the core-excited states yields the same cross section as observed in the inelastic scattering of ¹²C at 48 MeV on ⁶²Ni (2⁺).     

Nuclear charge radii of the carbon isotopes 12C, 13C and 14C

Muonic X-ray energies of the K-series of the carbon isotopes ¹³C and ¹⁴C have been determined relative to ¹²C. For the first time, muonic atom measurements using radioactive ¹⁴C have been performed. Model-independent equivalent nuclear charge radii R_k,α and their differences have been deduced. The R_k,α radii increase by 10(14) and 32(11) am respectively with the filling of the $\text{1}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron Subshell. The results are compared with recent elastic electron scattering data. The former natural carbon data have been reanalysed using a new value for the nuclear polarization. In terms of the rms charge radius, we then obtain $\text{〈r}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 2.472(16)}\text{fm}$ for the ¹²C isotope.     

Spins of resonances in the 12C + 12C system

By measuring angular distributions we have assigned J^π = 6⁺ to a resonance at E_c.m. = 7.50 ±0.05 MeV in the ¹²C + ¹²C system.     

194Pt(12C, 12C′) reaction and the triaxial-rotor model

Elastic and inelastic scattering differential cross sections for the ¹⁹⁴Pt(¹²C, ¹²C′) reaction at a bombarding energy of 78 MeV have been measured. Data have been obtained for 0⁺, 2⁺, 4⁺, and 2^+′, states in ¹⁹⁴Pt. The data have been analyzed using a rigid asymmetric-rotor model in coupled-channels reaction calculations. It is found that satisfactory fits to all data can be obtained but only if the hexadecapole deformation is included in the asymmetric-rotor model.     

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.     

Three-nucleon transfer on 12C: The 12C(α, p)15N reaction at 96.8 MeV

Angular distributions of protons from the ¹²C(α, p)¹⁵N reaction have been measured over the angular range from 10–70° at an α-particle bombarding energy of 96.8 MeV. Well defined particle groups are observed up to an excitation energy of 18 MeV in ¹⁵N. The relatively small number of states excited implies a selectivity both in the reaction mechanism and in structure effects. DWBA calculations using a semi-microscopic three-nucleon form factor have been performed using several different sets of wave functions. Good agreement in the ratio σ_exp/σ_th is obtained for most states using the ¹⁵N wave functions of de Meijer. The strongest state in the (α, p) spectrum is observed at 15.397 MeV in ¹⁵N and DWBA calculations give good agreement for a $\text{13}\text{2}{}^{\mathrm{+}}$ assignment. This state has been observed only in other three-nucleon transfer reactions involving heavy ions. The recent discovery of a $\text{9}\text{2}{}^{\mathrm{+}}$ state at 10.693 MeV in a p+¹⁴C resonance measurement is supported by our analysis.