Elastic and inelastic scattering of 185 MeV protons from 12C

The polarization of 185 MeV protons in elastic scattering and in the excitation of the 2⁺ state at 4.44 MeV and the 0⁺ state at 7.65 MeV in ¹²C has been measured in the angular region 2°–60°. Optical model calculations are performed for the elastic scattering. Angular distributions for the inelastic scattering from the 2⁺ state at 4.44 MeV and the 3^? state at 9.64 MeV are calculated in the distorted-wave impulse approximation (DWIA) as well as in the distorted-wave Born approximation (DWBA).     

Observation of the nuclear rainbow scattering for12C+12C atE Lab =300 MeV

The elastic and inelastic scattering of¹²C on¹²C has been measured in the angular range between 2.8° and 70.4° in the c.m. system atE _Lab =300 MeV. Optical model calculations have been performed with Woods-Saxon and folded potentials, the ground state and the first 2⁺-state were coupled in the calculations. The large cross sections of the elastic scattering at large angles is related to the nuclear rainbow scattering, which is centered at about 56°. This requires a potential depth of 100 MeV at a distance of 3 fm, the fit to the data is sensitive down to this region. The calculations with the folded potential show a better agreement with the data than those with the Woods-Saxon shape. The total reaction cross section of 1,420 mb, obtained from the optical model analysis, corresponds to the geometrical value; no transparency is observed.     

α + 12C scattering at 110 MeV: Has exotic 7.65 MeV Hoyle’s state signatures “alpha-condensate” structure?

We present new measurements of the α + ¹²C elastic and inelastic (to the states 4.44, 7.65, and 9.64 MeV) scattering at E _lab = 110 MeV in the wide angular range from ～10° to 175°, which enable us to examine the condensate and cluster properties of the low-lying excited states in ¹²C. We present the diffraction-radius analysis of our data together with a considerable amount of the existing data. The magnitudes of the diffraction radii for the ground and the first excited (4.44 MeV) states are found to be equal, whereas they appear to be enhanced by ～0.6 fm both for 7.65 and 9.64 MeV states. This result shows that the radius of the Hoyle’s 0 ₂ ⁺ , 7.65 MeV state in ¹²C is by a factor of ～1.2–1.3 larger than that of the ground state. It is demonstrated that the direct transfer mechanism of ⁸Be dominates at the largest angles in all four reactions reported here. The configuration corresponding to the transfer of ⁸Be in its ground state (I ^π = 0⁺) with L = 0 turns out to be the most important for the 7.65 MeV state of ¹²C. Evidence of existence of some features of α-condensed structure of the Hoyle’s 0 ₂ ⁺ state in ¹²C was obtained: its enhanced radius and large contribution of α-particle configuration with L = 0.     

Untersuchung von 0+−0+-Übergängen in12C,24Mg,28Si,32S und40Ca durch unelastische Elektronenstreuung

Transitions from the 0⁺ ground states to 0⁺ excited states at 7.65 (¹²C), 6.44 (²⁴Mg), 4.98 and 6.69 (²⁸Si), 3.78 (³²S) and 3.35 (⁴⁰Ca) MeV have been studied with 28 to 60 MeV electrons at scattering angles from 105 to 165°. Matrix elements and transition radii have been deduced, using DWBA-calculations. The monopole excitations can be uniquely distinguished from electric quadrupole excitations by the angular dependence of the cross sections. Some results forE2- andE3-transitions in¹²C,²⁸Si,³²S and⁴⁰Ca are given, too.     

Elastic and inelastic scattering of 178 MeV protons from 58Ni and 60Ni

The elastic and inelastic scattering of 178 MeV protons from ⁵⁸Ni and ⁶⁰Ni has been studied. Angular distributions were measured for the differential cross sections for elastic scattering as well as inelastic scattering from excited states below about 5 MeV, all with natural parity. For the elastic and for the inelastic scattering from the first excited state (2⁺ in both nuclei, the angular distributions for the polarization were also measured. The measurements extend out to c.m. angles of about 60°, corresponding to a momentum transfer of about 600 MeV/c.The elastic and inelastic scattering data were compared to the results of coupled-channel calculations in the vibrational model using a deformed spin-orbit interaction of the full Thomas form. Good agreement was found in general showing that the main features of the experimental results are well described in this model.     

Investigation of the inelastic deuteron scattering mechanism for 24Mg at E d = 15.3 MeV

Results from measuring the angular dependence of differential cross sections of elastic and inelastic deuteron scattering by the ²⁴Mg nucleus with the formation of the ground and first excited states 2⁺, 1.369 MeV at E _d = 15.3 MeV for deuteron angles interval from 21.5° to 161.5° (lab) are presented. Experimental results are compared with calculations in various approximations of the coupled channels model. The influence of heavy particle stripping mechanisms and consecutive particle transfer is also discussed.     

The 19.7 MeV resonance in the system 16O + 12C

The 19.7 MeV structure in the system ¹²C + ¹⁶O is investigated by measuring angular distributions and excitation functions for elastic and inelastic scattering with very high resolution. From a quasi phase shift analysis, it is deduced that the structure is a true resonance with J^π = 14⁺. The deduced small elastic partial width indicates that the structure of this state is intermediate between a molecular and a compound state.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Scattering of antiprotons from carbon at 46.8 MeV

Antiproton-carbon elastic and inelastic scattering cross sections have been measured at 46.8 MeV over an angular range 6° ? θ ? 59° with a magnetic spectrometer. Fits to the elastic and inelastic 4.44 MeV excited state cross sections put realistic limits on the strengths of the real and imaginary parts of the antiproton-carbon optical potential. The continuum cross section due to carbon break-up appears to be smaller than it is for corresponding proton data.     

Elasticp+12C scattering between 0.3 and 2 MeV

Absolute differential cross-sections ofp+¹²C elastic scattering have been measured atθ _cm=89.1°, 118.7°, 146.9° for bombarding energies between 0.3 and 2.0 MeV. Revised level parameters of the first three excited states in¹³N have been extracted with aR-matrix analysis. It is shown that the influence of the bound ground-state of¹³N has an appreciable effect on low-energy scattering. Recent predictions concerning Mott-Schwinger polarization are also discussed.     

Elastic and inelastic scattering of 12C by 12C in the energy range between 10 and 37.6 MeV

The elastic and inelastic scattering of ¹²C by ¹²C has been measured over a wide angular range employing a kinematical analysis with the help of position-sensitive detectors. The bombarding energy was varied in 200 keV steps between 10 and 37.6 MeV. The cross sections are analysed in the framework of compound fluctuations and the direct reaction model.     

Elastic and inelastic scattering of nucleons from 16O

Measurements of differential elastic and inelastic cross sections for neutron scattering from ¹⁶O at incident energies 18 to 26 MeV are presented. In addition to cross sections for neutron scattering differential cross sections for proton scattering up to 66 MeV are described in terms of phenomenological optical model potentials. At 24.5 MeV incident energy inelastic scattering up to 11.5 MeV excitation was measured. The elastic and inelastic compound nucleus contributions were examined. Direct inelastic scattering from the normal parity states was calculated using the DWBA and coupled-channel formalisms. The inelastic scattering cross section from non-normal parity state 2⁻ was calculated using the coupled-channel formalism via multi-step processes. Cross sections due to inelastic scattering from some of the states, which are thought to be members of an excited state rotational band were calculated using both vibrational and rotational approaches and were compared.     

A second-order vibrational model applied to the scattering of electrons and α-particles from 12C

Transition densities for monopole excitations and for virtual excitations are derived in the second-order vibrational model. Form factors for electron scattering calculated in the Born approximation and angular distributions for α-particle scattering, obtained in coupled channel calculations, are compared with experimental results for the elastic scattering and the inelastic scattering from the 2⁺ level at 4.44 MeV, the 0⁺ level at 7.65 MeV and the 3^? level at 9.64 MeV in ¹²C.     

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.     

Refractive scattering and the nuclear rainbow in the interaction of12, 13C with12C at 20MeV/N

The elastic and inelastic scattering and the neutron transfer have been measured for the systems¹²C +¹²C and¹³C +¹²C at 20MeV/N up to θ_cm= 60° with theQ3D -spectrometer. The angular distributions of the elastic scattering show an enhanced cross section at angles larger than 40°. It can be identified as refractive scattering with the clear signature of a nuclear rainbow.L-cut-off calculations show that these contributions come fromL-values which are significantly lower than the grazingL-value. The deflection function has a broad minimum in thisL-range which is typical for rainbow scattering. TheS-matrix is decomposed by a phenomenological parametrization into a refractive and a diffractive part. The interference of these amplitudes plays an important role in the rainbow enhancement. The spatial localization of the refractive scattering is deduced from the turning points of the corresponding trajectories; a localization between 2.5 fm and 4 fm is found. Semi-classical calculations with complex trajectories in the single-turning-point approximation show good agreement with the quantummechanical calculations. Refractive contributions are not observed in the inelastic scattering. This can be explained by reducing the strength of the conventional collective form factor in the internal region. In contrast to this the enhancement at large angles is seen in the one-neutron transfer channels where the refractive scattering is dominant. This is the first observation of such contributions to heavy-ion transfer reactions.     

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.     

Isobaric analog resonances in the 82se+p system investigated by (p,p'γ) angular correlations and low-lying states in 83Se

Low-lying states in ⁸³Se have been studied through proton-induced isobaric analog resonance (IAR) reactions. Excitation functions for elastic and inelastic proton scattering were measured in the bombarding energy range 4.5– to 7.7 MeV. Angular distributions of proton inelastic scattering cross sections for the reaction ⁸²Se(p, p')⁸²Se(0.655 MeV 2⁺) and angular correlations of the inelastic protons and the associated 2⁺-0⁺ de-excitation γ-rays were measured on observed resonance peaks. In the analysis for the inelastic scattering, direct reaction contributions to the IAR were taken into account. Correlations between the low-lying states in ⁸³Se and the excited 2⁺ core state are discussed.