Proton-hole states in Bi From the Po (t, α) reaction

The ²¹⁰Po(t, α)²⁰⁹Bi reaction has been studied at 20 MeV triton energy with an overall resolution of 20 keV FWHM. Absolute cross sections were established by a comparison of the (t, α) intensities to elastic triton scattering. The three lowest single-proton states in ²⁰⁹Bi were observed and spectroscopic factors were extracted from the measured cross sections by DWBA analysis. Starting at 2.43 MeV, six levels were strongly excited. These states have large 2p-1h proton components. The spectroscopic factors were extracted by a comparison of ²¹⁰Po(t, α) cross sections to ²⁰⁸Pb(t, α)²⁰⁷T1 single-proton-hole cross sections measured previously at the same bombarding energy. The observed states and their properties were analyzed within the framework of the particle- (or hole) vibration coupling model. Surface vibrational states in ²⁰⁸Pb coupled to single protons as well as the proton pair addition modes (states in ²¹⁰Po) coupled to a proton-hole were included in the analysis.     

Global optical model potential describing 12C-nucleus elastic scattering

We construct a new global optical model potential to describe the elastic scattering of ¹²C. The experimental data of elastic-scattering angular distributions and total reaction cross sections for targets from ²⁴Mg to ²⁰⁹Bi are considered below 200 MeV within the framework of the optical model. The results calculated using the derived global optical potential are then compared with the existing experimental data. The reliability of the global optical potential is further tested by predicting the elastic scattering data out of the mass and energy ranges, within which the global potential parameters are determined, and reasonable results are also obtained.     

Proton-nucleus elastic scattering at 156 MeV

Cross sections for the elastic scattering of 156 MeV protons on eleven targets ranging from ¹²C to ²⁰⁹Bi were measured and an optical model analysis has been performed. The effect of different optical potentials in DWIA inelastic scattering calculations is shown by some examples.     

Elastic scattering of 11B from 209Bi in the energy range 49.8 ⩽ E ⩽ 84.1 MeV

The elastic scattering of ¹¹B from ²⁰⁹Bi has been measured at laboratory energies of 49.8, 51.3, 52.2, 52.8, 54.3, 55.8, 59.8, 64.8, 69.8, 74.8 and 84.1 MeV. These data have been analyzed using a microscopic optical model and the energy dependence of the real and the imaginary parts of the optical potential at near barrier energies has been determined. The “threshold anomaly” observed in the real part of the potential is found to be consistent with the dispersion relation which connects the real and the imaginary parts of the potential. Inelastic scattering and transfer reactions have also been measured at energies of 51.3, 55.8, 59.8 and 74.8 MeV. DWBA calculations for the 3⁻ state in ²⁰⁹Bi are made. From the measured transfer probabilities, using a semiclassical approach the strength of the form factors have been obtained. The fusion cross sections have been derived at these energies from the corresponding quasi-elastic scattering angular distribution data. The fusion cross sections calculated using the energy dependent barriers extracted from the energy dependent real parts of the potential compare well with, that determined from quasi-elastic scattering data and are also in good agreement with simplified coupled channels calculation for fusion incorporating important inelastic and transfer channels.     

Spectroscopy of low-lying positive parity states in 30P from the study of the reaction (3He,d) at 14.0 MeV

The reaction ²⁹Si(³He, d)³⁰P was studied at an incident energy of 14.0 MeV. Spectroscopic strengths for 14 positive parity states up to an excitation of 4.50 MeV have been obtained using DWBA analysis. The incident channel optical-model parameters for the DWBA calculations were extracted from elastic scattering cross sections measured also at 14.0 MeV.     

光学模型与ADS靶的反应截面

利用核反应中光学模型理论,对质子入射能量从阈能到450MeV,加速器驱动的洁净核能系统的靶材209Bi、208Pb、202Hg、197Au、184W、181Ta与质子的反应进行了研究.给出了两套与实验数据符合很好的光学势参量;预言了质子与Bi、Pb、Hg、Au、W、Ta的反应截面;对现有的实验数据进行了理论验证.     

Neutron scattering from Bismuth,Strontium and Sodium at 14.8 MeV

Differential cross sections for the elastic and inelastic scattering of 14.8 MeV neutrons from Bi, Sr and Na have been measured with four neutron detectors participating in a time-of-flight system which had an energy resolution of 900 keV for the incident neutrons. The whole procedure was checked by scattering from carbon. For the elastic scattering of Bi, Sr and Na satisfactory optical-model fits were obtained. The absolute cross sections for excitation of collective states are compared to the distorted-wave theory for direct reactions, and a reasonable agreement has been found. The nuclear deformation parameters are extracted and compared to the values from other experiments.     

Neutron emission spectra and angular distributions at 25.7 MeV neutron bombarding energies

Inelastic scattering of 25.7 MeV neutrons to unresolved final states with excitation energies up to ~13 MeV were measured for monoisotopic samples of ⁵¹V,⁵⁶Fe, ⁶⁵Cu, ⁹³Nb and ²⁰⁹Bi. Time-of-flight spectra were taken at several angles between 25° and 145° using the beam swinger spectrometer. Double differential cross sections, angle-integrated spectra and energy-binned angular distributions are compared with the predictions of pre-equilibrium theory.     

Photoexcitation of 209Bi and natHg using neutron-capture γ-rays from cobalt

Using neutron-capture γ-rays from cobalt, the ²⁰⁹Bi(γ,γ') and ^natHg(γ,γ') reactions were studied using a 53 cm³ Ge(Li) detector and the reactor facility at the Rhode Island Nuclear Science Center. Resonant scattering was observed at 4.924±0.005 MeV for ^natHg. Resonant scattering was observed at 5.609±0.005 MeV in ²⁰⁹Bi, with an effective cross section of 348±70 mb. The ratio of intensity scattered at 150° to that scattered at 100° was found to be 1.18±0.12 for ²⁰⁹Bi. This is consistent with a dipole transition to a $\text{9}\text{2}$ state but does not eliminate other transitions and spin assignments. No significant inelastic structure was found in the spectra from either sample. The improved energy specification in the present experiments has led to different energy assignments for the resonant states and hence, different incident intensities are producing the observed scattering. These differences lead to higher effective cross sections than those previously reported. Minimum ground state level widths for ²⁰⁹Bi and ^natHg were estimated to be 0.032 eV and 0.43 eV respectively. The need for high-resolution survey data to re-establish systematics is suggested.     

Does break-up affect 9Be +209Bi fusion at the barrier?

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the 36.0 MeV ≤ E_lab≤ 50.0 MeV range, down to 0.6 mb, with high accuracy via in-beam detection of the ground state α-decay of the evaporation residues produced. The elastic scattering cross sections around 150° and 135° were also obtained with moderate angular resolution. The cross sections below the barrier are reproduced by coupled channel calculations which include only one break-up channel with a moderate strength and a phenomenological renormalization of the potential depth. These simple calculations overestimate the cross sections above the barrier most likely due to the fact that the ⁹Be break-up process becomes much stronger. The barrier distributions extracted do not have evident break-up signature since they show one-barrier structure. Received: 22 February 1999 / Revised version: 26 March 1999     

Quadrupole moments and nucleon excitation strengths in even-A Sm isotopes

We present a coherent coupled-channel analysis of 7 MeV neutron and 16 MeV proton elastic and inelastic scattering from ^{148, 152, 154}Sm. The optical potential and nuclear deformation parameters are determined so as to fit not only these elastic and inelastic scattering data but also the low-energy neutron scattering properties and the total cross sections over a wide energy range. This analysis provides evidence of the same excitation strengths for both projectiles in the case of ^{152, 154}Sm, and of a smaller excitation strength for the proton than for the neutron in case of ¹⁴⁸Sm. Moreover the quadrupole moments of these deformed optical potentials are in good agreement with those extracted from Coulomb excitation measurements and from nuclear matter distribution calculations.     

Theoretical Calculations of Microscopic Nuclear Reaction Data for p+209Bi in Energy Region up to 300MeV

Based on nuclear reaction models, i.e., the optical model, evaporation model, exciton model and the direct reaction theory, cross sections of (p,xn) reactions and residual nuclei productions for p+²⁰⁹Bi reaction were calculated in energy region from threshold up to 300MeV and a set of proton optical potential parameters for ²⁰⁹Bi up to 500MeV were obtained. The direct inelastic cross sections were calculated with the distorted wave Born approximation theory. Theoretical results show that the direct inelastic cross sections of about 550mb are reasonable.     

Neutron elastic scattering from 116,118,120,122,124Sn

Accurate measurements of neutron differential elastic cross sections have been obtained from even isotopes of Sn. Data are presented for the elastic scattering of 11 MeV neutrons from ^{116, 118, 120, 122, 124}Sn, the elastic scattering for 24 MeV neutrons from ^{116, 118, 124}Sn and the neutron total cross section from ^{118, 120, 122, 124}Sn in the energy ranges 5.0–10.6 MeV and 20.0–26.0 MeV. The elastic scattering data are analyzed in terms of an empirical optical-model potential. The obtained optical-potential parameters are analyzed in terms of energy and isospin dependence and compared with those obtained from proton elastic scattering on even Sn isotopes.     

Eikonal approximation for magnetic electron scattering

The eikonal (high-energy) approximation of Yennie et al. for the scattering of electrons from nuclei has been extended to include the transverse interaction, and in particular the case of magnetic scattering. It is applied here to elastic magnetic scattering from ²⁰⁹Bi at 500 MeV as an example.     

Analysis of elastic and inelastic α + <Superscript>24</Superscript>Mg scattering within the <Emphasis Type="Italic">S</Emphasis> matrix model involving regge poles

A generalization of the phenomenological S-matrix model taking into account isolated Regge poles is proposed for simultaneously describing refractive effects in the cross sections for the elastic and inelastic scattering of light nuclei. The cross sections for elastic α + ²⁴Mg scattering are analyzed at energies of 50, 54, 65.7, 81, and 119 MeV. The analysis of the cross sections for elastic scattering is supplemented with an analysis of the inelastic scattering of alpha particles that is accompanied by the excitation of the first excited state (2⁺) of ²⁴Mg nuclei. It is shown that the proposed model makes it possible to describe satisfactorily all of the aforementioned cases of elastic and inelastic scattering, correctly reproducing the refraction Airy structures and anomalous large-angle scattering that are observed at large scattering angles.     

Analysis of proton transfer in polarized 7Li scattering by 208Pb at 33 MeV

Angular distributions of the differential cross section and the second-rank tensor analysing power T₂₀ have been measured for the one-proton transfer reaction induced by polarized ⁷Li on ²⁰⁸Pb at 33 MeV leading to several states in ²⁰⁹Bi. The experimental data were analysed simultaneously with data for elastic and inelastic scattering of ⁷Li by means of CCBA and CRC calculations. The spectroscopic factors for ²⁰⁹Bi states are obtained.     

Elastic and inelastic scattering of protons from Li between 25 and 45 MeV

The elastic and inelastic scattering of protons from ⁶Li has been studied at incident energies of 25.9, 29.9, 35.0, 40.1 and 45.4 MeV. The 2.18 MeV (3⁺, T = 0) first excited state of ⁶Li was found to be strongly excited, but the 3.56 MeV (0⁺, T = 1) second excited state was quite weakly excited. Angular distributions for excitation of the 2.18 MeV level were measured at all five energies, while angular distributions for excitation of the 3.56 MeV level were extracted only at 25.9 and 45.4 MeV. To test the applicability of the optical model for the scattering of protons from such a light nucleus the elastic scattering angular distributions have been analyzed using the eleven-parameter search code SEEK. Available polarization angular distributions were included in the analysis. Reasonable fits to the data have been obtained with an average geometry potential. Theoretical estimates of the real part of the optical potential and the inelastic scattering differential cross sections have been made using the microscopic model for proton-nucleus scattering. Both phenomenological and realistic forces have been considered and the necessary nuclear transition densities have been extracted from experimental elastic and inelastic electron scattering data. An estimate of a possible spin-spin term in the optical potential has also been made.     

Study of low-lying levels in 47Ca with the 48Ca(d, t)47Ca reaction

Angular distributions of cross sections [α(θ)] and vector analyzing powers [iT₁₁(γ)] have been measured for seven low-lying states or groups of states excited by the ⁴⁸Ca($\text{d}$, t)⁴⁷Ca reaction with 13.5 MeV deuterons and analyzed by the DWBA. On the basis of comparison of vector analyzing powers with DWBA calculations, spin-parity assignments have been made or confirmed for several states. Spectroscopic factors have been extracted. Angular distributions for weak states at 3.30 and 3.57 MeV excitation in ⁴⁷Ca could not be reproduced by DWBA calculations. Investigations of compound nucleus and multi-step contributions to the cross sections and analyzing powers for these states have been made by means of Hauser-Feshbach and CCBA calculations. Optical model parameters were obtained from analysis of 13.5 MeV deuteron elastic scattering cross sections and analyzing powers.     

Fusion around the barrier in 11,9Be +209Bi

The ⁹Be +²⁰⁹Bi fusion cross sections were measured in the range 37.5 MeV ≤ E _lab ≤ 45.0 MeV at the Munich Tandem via the observation of ground state α-decay of the evaporation residues. Fusion cross sections of ²⁰⁹Bi with the “halo”¹¹Be unstable projectile in the region around the Coulomb barrier were deduced from an experiment done with the same technique at the RIKEN Ring Cyclotron. Above the Coulomb barrier the ¹¹Be cross sections are larger than the ⁹Be ones in agreement with theoretical predictions based on the larger ¹¹Be halo radius. Also below the barrier these theories foresee the same behavior in disagreement with the experimental results, since the two cross sections are rather similar. Received: 2 April 1998