Levels of 209Po and 211Po populated in one-neutron stripping and pickup from 210Po

Energy levels of ²⁰⁹Po have been populated with the ²¹⁰Po(d, t)²⁰⁹Po and ²¹⁰Po(p, d)²⁰⁹Po reactions at bombarding energies of 17.0 and 17.8 MeV respectively. Fifteen levels were observed below 2.7 MeV of excitation. Energy levels of ²¹¹Po were populated with the ²¹⁰Po(d, p)²¹¹Po reaction, also at 17.0 MeV. Thirty-five levels, almost all new, were observed below 3.9 MeV of excitation. Comparison of experimental angular distributions with DWBA calculations allowed l-value assignments and extraction of spectroscopic factors for many levels. In ²⁰⁹Po the observed level structure is well described in terms of a simple particle-vibration coupling model. In ²¹¹Po the level structure is more complex and the simple model is not adequate.     

Angular distribution analysis for quasi-elastic transfer reactions induced in209Bi targets with heavy ions

An analysis of angular distributions for quasi-elastic transfer reactions is proposed. The formalism used is derived from the general treatment of multinucleon transfer in the limits of DWBA approximation. It appears that for heavy ions, the use of real potentials with real trajectories remains a good approximation in the window ofl space concerned with quasi-elastic transfer reactions. This analysis has been tested by a series of experimental data obtained by bombardment of²⁰⁹Bi targets by¹⁴N,¹⁶O,¹⁹F,⁴⁰Ar and⁴⁰Ca. For incident energies near the Coulomb barrier, the deflection angle depends strongly on the excitation energy of the system so that a window ofQ values leads to very wide angular distributions. A slow decrease of the radius parameter with the increase of theZ ₁ Z ₂ product has been observed. This result can be correlated by an interaction distance (d=2.7–3fm) between half density radii of the two colliding nuclei.     

Experimental study of excitation functions and isomer ratios for 211, 212Po

Excitation functions have been measured for ground states and isomers populated in the ²⁰⁸Pb(α, n)²¹¹Po, ²⁰⁹Bi(α, np)²¹¹Po, ²⁰⁹Bi(α, p)²¹²Po and ²⁰⁹Bi(α, n)²¹²At reactions for α-beams ranging from 45 MeV to 172.5 MeV. The experimental results have been compared with theoretical calculations assuming direct and preequilibrium reaction mechanisms, respectively. It is found that the experimental excitation functions can be reproduced satisfactorily by calculations in the framework of the preequilibrium model. Isomer ratios have been extracted from the data as well. Their energy dependence can be reproduced by an optical-model calculation for beam energies larger than about 60 MeV.     

Reactions on 209Bi induced by intermediate energy protons and the effect of direct reactions

Excitation functions and ranges of recoil nuclei in the ²⁰⁹Bi(p, 3n)²⁰⁷Po, ²⁰⁹Bi(p, 4n) ²⁰⁶Po and ²⁰⁹Bi(p, p3n)²⁰⁶Bi reactions have been measured for incident energies from 18 MeV up to 52 MeV. It has been found that the recoil ranges in (p, p3n) reactions are rather shorter than those in (p, 4n), and that beyond E_p = 40 MeV the high energy tail of the excitation function for (p, p3n) is roughly flat, in contrast to the decreasing tail for (p, 4n). A theoretical analysis of the excitation functions and of the nuclear recoil ranges has been made. It has been found that in (p, p3n) reactions the direct process plays a very important part in the reaction mechanism. It is also found that the reaction mechanisms of (p, 3n) and (p, 4n) reactions should be interpreted by means of an admixture of the equilibrium compound process and the pre-equilibrium decay process at bombarding energies up to 40 MeV and 50 MeV, respectively, and that the direct process seems to appear at bombarding energies higher than these respective energies.     

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.     

The γ-Decays of 210Po-Levels from the (3He, d*γγ)-Reaction

An in-beam experiment with the subcoulomb reaction ²⁰⁹Bi(³He, d^*γγ)²¹⁰Po at 20.5 MeV was performed with two Euroball Cluster detectors in Cologne. It closed the gap between the low energy levels of the level-scheme and the high energy levels found in ²⁰⁹Bi(³He, d)²¹⁰Po and ²⁰⁸Pb(⁴He, t)²¹⁰Po particle experiments. New branchings have been found and the (³He, d^*γγ) reaction below the coulomb-barrier has been used successfully. Received: 17 December 1998 / Revised version: 27 January 1999     

Spectroscopy of excited states in212Po,210Pb,and213At employing18O induced few-nucleon transfer reactions

γ-ray spectroscopic techniques have been applied to measure properties of excited states (E ^*<2MeV) in²¹⁰Pb,²¹²Po, and²¹³At after populating these neutron rich (N=128) nuclei via¹⁸O induced few-nucleon transfer reactions on²⁰⁸Pb and²⁰⁹Bi targets. In²¹²Po an isomeric state is located atE ^*=1,477 keV with a halflife oft _1/2=14.7±0.3 ns. This state is interpreted to be the 8⁺ yrast level which decays to the ground state via the measured $$8^ + \left( {121.1 keV} \right)6^ + \left( {223.3 keV} \right)4^ + \left( {405.1 keV} \right)2^ + \left( {727.8 keV} \right)0^ + $$ γ-cascade.α-decay (E _α≈10.2 MeV) of the isomer is also observed. In²¹⁰Pb the time spectra for members of the 4⁺ (297.8keV) 2⁺ (799.4keV)0⁺ γ-cascade show a delayed component with a halflife oft _1/2=152±13 ns which is attributed to the known 8⁺ yrast state atE ^*=1.27 MeV. For²¹³At first results on theγ-decay of excited states are presented.     

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.     

Variation of total kinetic energy and mass distributions in the fusion-fission reaction of 16O,19F + 209Bi at near barrier energies

Fission fragment mass and energy distributions and their correlations have been measured for the ¹⁶O and ¹⁹F + ²⁰⁹Bi reactions over a wide range of excitation energies ( E ^* = 30-50 MeV). It is observed that in the case of ¹⁶O + ²⁰⁹Bi reaction, the average total fragment kinetic energy, <TKE> is nearly independent of the bombarding energy. However, in the case of ¹⁹F + ²⁰⁹Bi reaction, the average total kinetic energy of the fission fragments shows a peaking behaviour near the barrier. The variation in <TKE> at near barrier energies in the ¹⁹F + ²⁰⁹Bi system seems to be correlated with corresponding strong variation in the variance of the fragment mass distribution. The present results may imply certain dynamical effects leading to compact scission configurations in the fission of ¹⁹F + ²⁰⁹Bi system at near barrier bombarding energies. Received: 9 April 2001 / Accepted: 26 May 2001     

Decay of the 21/2− isomer in211Bi and structure of thevg 9 2/2 πh 9/2 levels

Gamma rays and conversion electrons have been measured in²¹¹Bi populated by the²⁰⁹Bi(t,p) reaction, and the near yrast levels were observed up to 21/2^?. The 21/2^? state is isomeric withT _1/2=70(5) ns. No alpha decaying isomer was found in²¹¹Bi. ObservedM1 transitions reveal mixing of the²¹⁰Pb parent states in the levels of²¹¹Bi. The levels and transitions are well reproduced by the shell model with experimental matrix elements and pure configurations.     

Two-proton multiplets in Po

The ²⁰⁹Bi(α,t)²¹⁰Po reaction at 45 MeV has been used to study ²¹⁰Po. Many new levels have been observed and proton configurations are suggested for the lowest three multiplets.     

Evidence of projectile polarisation effects on the reaction 208Pb(17O, 16O)209Pb

Coupled reaction channels calculations (CRC) of the reactions ²⁰⁸Pb(¹⁷O, ¹⁶O)²⁰⁹Pb leading to different states of ²⁰⁹Pb are compared with DWBA predictions at projectile energies of 78, 86 and 102 MeV. The calculations exhibit strong effects of multistep processes on Q-value and angular-momentum-mismatched transfer reactions. It is shown that the contribution to the transfer through the inelastic excitation of ¹⁷O contains a major part of the multistep effect. A simple three-channel model comprising the elastic, inelastic and transfer channels is constructed which simulates the CRC effects on the transfer cross sections. The polarization effects of the eliminated channels give rise to effective potentials which are mainly imaginary.     

The γ-decay of two-particle states in 210Bi

The γ-decay of excited states in ²¹⁰Bi up to 3330 keV excitation energy has been studied using the ²⁰⁹Bi(d, pγ)²¹⁰Bi reaction. From the observed decay scheme, tentative J^π values are made for 25 states. The excitation energies, (d, p) strengths and decay branching ratios of these states are compared with those calculated using the two-particle shell-model wave functions of Kim and Rasmussen and Kuo and Herling.     

Mechanism of reactions induced by 7 MeV deuterons on9Be [(d,p), (d,d), (d,t), (d,4He)]

Angular distributions of protons, deuterons, tritons and alpha-particles emitted from the reactions in thed+⁹Be-system atE _d =7 MeV as well as excitation functions at selected angles in the energy rangeE _d =6.5–7.5 MeV (LAB) were measured. The potential part of the elastic scattering is described by the phenomenological optical model. The compound nucleus contribution to all exit channels is determined using the Hauser-Feshbach model. The collective excitation of the 2.43 MeV excited state of⁹Be and transfer processes are analysed within the DWBA formalism. The analyses suggest a significant contribution of five-nucleon transfer to the (d,⁴He) channel.     

Study of the reaction238U (α, α′f) atE α=480 MeV

The excitation function of the fission probability P _E E _x) for²³⁸U has been measured in the reaction²³⁸U(α, α′ f) at 480 MeV bombarding energy. The reaction mechanism of this reaction is discussed for excitation energies belowB _nf , the threshold for second chance fission, and aboveB _nf up toE _x =37 MeV. In comparing with results from fission induced by photons and by particle transfer reactions the (α, α′f) reaction gives too low values for the fission probabilityP _f at excitation energies well aboveB _nE . The role of the quasi-elastic knock-out process in this reaction is discussed.     

Low- and medium-spin states in theN=124 isotones208Po and209At

Excited levels in²⁰⁸Po and²⁰⁹At were populated in the reactions (p, 2n) and (³He, 3n), and²⁰⁸Po also in the EC-decay of the²⁰⁸At ground state, which was produced in the²⁰⁹Bi(³He, 4n) reaction. The experimental procedures comprised gamma-ray excitation functions,γ- γ coincidences, as well as gamma-ray angular distribution and conversionelectron measurements, both on- and off-line. The properties of about twenty-five levels in each nuclide were studied. In²⁰⁸Po the energy of the 8⁺→6⁺ transition could be determined to be 4.0±0.2keV and the 8⁺ state thus has an excitation energy of 1,528 keV. The effective quadrupole charge of theh _9/2 proton can be derived ase _eff(τ h _9/2)=1.69(15)e. For the previously reported isomeric half-lives more accurate values are obtained, the systematics of electricL=1, 2 and 3 transition rates are discussed, and their microscopic structure is elucidated. Shell model considerations are used to support the configuration assignments, as are the logft values for the strongest²⁰⁸At(EC)²⁰⁸Po decay branches. The effect of core polarixation on the excitation energies of yrast states is studied in both²⁰⁸Po and²⁰⁹At. Many of the states populated in the²⁰⁸At EC decay are shown to be of core-excited character.     

The 1h92 proton orbit size in 209Bi

Angular distributions of α-particles from the reaction ²⁰⁹Bi(t, α)²⁰⁸Pb (ground state) have been measured at bombarding energies E_t = 8.5 MeV and E_t = 9.0 MeV. Zero-range (ZR) DWBA analyses of the data are used to determine the radial extent of the wave function of the $\text{lh}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ orbit in which the transferred proton is bound in ²⁰⁹Bi. The applicability of the sub-Coulomb ZR DWBA treatment is investigated by comparison of ZR and exact finite-range DWBA calculations. A value of the (t, α) normalization constant of (20.8 ± 3.1) × 10⁴ MeV² · fm³, based on forward dispersion relations, has been obtained from this comparison. The asymptotic amplitude of the wave function is measured directly and the rms radius is extracted via a Woods-Saxon model. A value of √〈r²〉 = 6.10_?0.08^+0.12 fm, corresponding to a point proton and to a local Woods-Saxon potential, is obtained. The rms radius and radial wave function of the $\text{1}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton are compared with the results of electron scattering and muonic atom data on targets of ²⁰⁹Bi and ²⁰⁸Pb and with the results of Hartree-Fock calculations.     

On the fission width of isobaric analogue states

The experimental cross sections of the reactions ²⁰⁹Bi(p, f) and ²⁰⁶Pb(α, f) are analyzed to estimate the ratio Γ_f/Γ_tot for the IAS. From the comparison of the values Γ_f for the nuclear states with different isospins it follows that strong isospin effects exist in the nuclear fission process involving ²¹⁰Po.     

A SEMI-CLASSICAL ANALYSIS ON THE REACTION 12C+209Bi AT BOMBARDING ENERGIES SLIGHTLY ABOVE THE COULOMB BARRIER

For reactions induced by light heavy ion such as ¹²C, at bombarding energy slightly above the coulomb barrier, using semi-classical theory, neglecting macroscopic frictional force, the reaction mechnisms are sorted by the orbital angular momentum of the entrance channel from the classical deflection functions fitting elastic scattering. Moreover, inserting a transfer probability factor representing the Q-Window effect into the semi-classical angular distribution formula of Kalinkin and Grabowski, we obtain a formula for the differential cross-section per unit energy interval. The calculated results, including the elastic scattering angular distributions, energy spectrum and angular distributions of emitted α-particles in quasi-elastic process, complete fusion cross-section, fusion-fission cross-sections and the exitation functions of evaporated neutron, agree with the experimental data on the reaction ¹²C+²⁰⁹Bi reported by our Institute.