The need for long range components in the effective nuclear interaction

It is shown that if one uses single particle energies from experiment and a delta residual interaction it is not possible to obtain the energy of the giant dipole and spurious states of ²⁰⁸Pb, and at the same time obtain reasonable results for the low lying two-particle spectra of ²¹⁰Pb or ²¹⁰Po. Related to the above problem, the isobaric analog state of ²⁰⁸Pb (in ²⁰⁸Bi) comes much too low in calculations using realistic interactions. It is noted here that the above difficulties can be overcome, phenomenologically at least, by adding to the effective interaction some long range repulsive components. The Bansal-French and the Schiffer interactions are examples of these. However, the dipole-dipole component of the Schiffer interaction gives much too large a splitting between the dipole state and spurious state.     

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.     

Sub-Coulomb transfer reactions on 208Pb with carbon and oxygen projectiles

Single-neutron transfers induced by ^{12, 13}C and ^{16, 17, 18}O projectiles on ²⁰⁸Pb and the ¹²C(¹⁷O, ¹⁶O)¹³C reaction have been studied at energies close to the Coulomb barrier. These processes are well described by the distorted-wave Born approximation. Coupled-channels effects are found to be small. Normalization factors have been determined for all projectile and target transitions, and also for the triton-deuteron overlap by comparison with previous measurements of the ²⁰⁸Pb(d, t)²⁰⁷Pb reaction. The root-mean-square (rms) radii of single-particle neutron wave functions in ²⁰⁸Pb and ²⁰⁹Pb were calculated using known spectroscopic factors. The distribution of the point neutron excess density in the surface region of ²⁰⁸Pb has been derived and its rms radius determined to be 5.93 ± 0.13 fm with a local potential model. This is in good agreement with theoretical predictions, but is considerably larger than estimates based on Coulomb energy differences. The phenomena of core polarisation by the odd particle or hole outside ²⁰⁸Pb is discussed using the single-particle orbitals determined in this work.     

Core polarisation effect on the 3p 1/2, 3p 3/2, 2f 5/2, 2f 7/2 and 1i 13/2 proton states of209Bi

The weak fragments of the 3p_1/2, 3p_3/2, 2f_5/2, 2f_7/2 and 1i_13/2 proton states of²⁰⁹Bi as seen in the²⁰⁸Pb (³He,d) reaction can be explained with the coupling of the renormalised proton states and the vibrational states of²⁰⁸Pb. The energies of the zerothorder proton shell-model states as well as the collective admixtures of the weak fragmented proton states of²⁰⁹Bi have been deduced from the core-particle coupling model.     

Spin determination of isobaric analogue resonances in209Bi and207Bi by proton polarization measurements

The polarization of elastically scattered protons from²⁰⁸Pb and²⁰⁶Pb was measured. The spins of some isobaric analogue resonances in²⁰⁹Bi and²⁰⁷Bi in the energy region from 16.2 to 17.8 MeV were determined.     

Molecular-orbital X-rays from 1 GeV 208Pb + 208Pb and 209Bi + 209Bi collisions

We have measured the spectra of continuum X-rays above the characteristic K lines for 4.5 to 4.8 MeV/N ²⁰⁸₈₂Pb → ²⁰⁸₈₂Pb, Pb → Bi, Bi → Pb and Bi → Bi collisions. Above ≈400 keV X-ray energy the spectral shape and intensity agree roughly with calculations of Kirsch et al. for the 1sσ molecular-orbital (MO) X-ray spectrum from Pb-Pb. Deviations from the theory below ≈400 keV suggest transitions to other MO's.     

Damping of single-particle states and giant resonances in208Pb

The damping width of single-particle states and of giant resonances is estimated in ²⁰⁸Pb, based on the excitation of surface modes and T = 1 pairs. The damping is dominated by the collectivity of the surface modes, with the pairing modes playing a weaker role. For both the single-particle states and giant resonances, the predicted damping is somewhat small. This could be due to the neglect of T = 0 particle-particle correlations or to the neglect of the volume modes. The damping for the giant resonances is reduced by the coherence between particle and hole.     

7 MeV dipole ground state transitions in 207Pb, 208Pb and 209Bi

The Doppler-broadened 7.117 MeV line from the ¹⁹F(p, αγ)¹⁶O reaction has been used to resonantly excite levels in ²⁰⁸Pb at 7071±2 and 7091±2 keV, in ²⁰⁷Pb at 7186±5 and 7206±5 keV and in ²⁰⁹Bi at 7179±5 and 7202±5 keV. On the basis of angular distribution measurements the 7071 and 7091 keV levels of ²⁰⁸Pb are assigned spins of 1 and assuming 100% ground state branching the widths are calculated to be 31±3 and 17±2 eV respectively. It is suggested that the states in ²⁰⁷Pb and ²⁰⁹Bi arise from the weak coupling of a $\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ neutron hole and an $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton respectively to one or the other of the ²⁰⁸Pb levels. The widths obtained in terms of _gΓ_o²/Γ are 15±4 and 25±5 eV for the 7186 and 7206 keV levels of ²⁰⁷Pb and 24±5 and 30±5 for the levels of ²⁰⁹Bi respectively. These values are consistent with the weak-coupling suggestion.     

Particle vibration coupling in207Pb

States in²⁰⁷Pb are observed in the proton decay of the lowest 5^? and 4^? analog resonances in²⁰⁸Bi. Evidence is given that one group of these states corresponds to the²⁰⁶Pb(2^ü, 0.8)?g _9/2 and²⁰⁸Pb(3^?, 2.6)?p ₃ ^2/?1 multiplets.     

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     

Partial fusion of a weakly bound projectile with heavy target at energies above the Coulomb barrier

Partial-fusion cross-sections for the systems ⁶Li + ²⁰⁸Pb, ⁹Be + ²⁰⁹Bi have been determined. The effect of breakup on fusion for weakly bound projectiles ⁶Li and ⁹Be incident on ²⁰⁸Pb or ²⁰⁹Bi targets has been discussed comparing experimental fusion cross-section excitation functions to those evaluated with a semi-classical approach. It is shown that complete fusion of a weakly bound projectile with heavy target is reduced, whereas the breakup process has very little influence on the total-fusion cross-section for some of the studied systems at energies above the Coulomb barrier.     

Shell model calculations of two to four identical-“particle” systems near 208Pb

The structure of the nuclei ^204–206Pb, ^210–212Pb, ²¹⁰Po, ²¹¹At, and ²¹²Rn is studied in terms of conventional nuclear shell models. An inert ²⁰⁸Pb core is assumed, and active particles (holes) are distuibuted in the low-lying single-particle (hole) orbits. Experimental single-particle energies are used for the one-body part of the effective residual interaction. Realistic interaction matrix elements developed for this mass region by Kuo and Herling are used for the matrix elements of the two-body part of the residual interactions. As much as possible, other effective one-body operators for electromagnetic observables are derived from experimental data on the single-particle (hole) nuclei ²⁰⁷Pb, ²⁰⁹Pb, and ²⁰⁹Bi. Observables treated are ground state binding energies, excitation energies, strengths for one- and two-particle transfers, and E2 and M1 observables. Generally, excellent agreement is found. The configuration mixing calculations do not remove anomalies in the magnetic moments of excited states in ²⁰⁶Pb and ²¹²Rn. Many states in these nuclei are predicted by the models which have not been observed as yet. It is found that a truncation scheme for doubly even nuclei treated here in which only seniority-0 and seniority-2 states are allowed is potentially very useful.     

Dose assessment of bremsstrahlung induced by beta-emitting radioisotopes of uranium-238 series and lead in human tissues

In the natural uranium-238 decay series, pure beta isotopes such as ²³⁴Th, ²³⁴Pa, ²¹⁴Pb, ²¹⁴Bi, ²¹⁰Pb and ²¹⁰Bi are released. The few lead isotopes such as ²¹¹Pb, ²¹²Pb, ²¹³Pb and ²¹⁵Pb are good beta emitters. In certain nuclear reactions of reactor these isotopes are released. These beta isotopes have maximum beta energies, which induce the bremsstrahlung radiation. The bremsstrahlung component of these beta isotopes has been traditionally ignored in dosimetry calculations. The shapes of bremsstrahlung spectra are a basic ingredient in the understanding and quantification of beta-ray dosimetry. The bremsstrahlung spectra produced by these high-energy isotopes such as ²³⁴Th, ²³⁴Pa, ²¹⁴Pb, ²¹⁴Bi, ²¹⁰Pb, ²¹⁰Bi, ²¹¹Pb, ²¹²Pb, ²¹³Pb and ²¹⁵Pb in bone, muscle and teeth are studied, and the computed spectral distributions are presented. The spectral shapes are primarily responsible for variations in the shapes of depth–dose distributions. They are intended to provide a quick and convenient reference for spectral shapes and to give an indication of the wide variation in these shapes. The evaluated beta bremsstrahlung dose as a function distance for the studied nuclides is also presented. The efficiency, intensity and dose rate of bremsstrahlung induced by beta isotopes of natural uranium-238 decay series and beta-emitting lead isotopes in human tissues such as brain, breast, heart, kidney, liver, muscle, pancreas and bone have also been studied in the present investigation. The values of bremsstrahlung dosimetric parameters are low for pancreas, but they are high for bone. For all studied tissues these parameters are high for ²³⁴Pa, but low for ²¹⁰Pb.     

High energy structures in heavy ion collisions: A multi-phonon description

Energy spectra of fragments from the³⁶Ar+²⁰⁸Pb reaction at 11 MeV/n exhibit structures at high excitation energies. These structures are interpreted in terms of target multi-phonon excitations built from giant resonances. The importance of such processes for the kinetic energy dissipation in heavy ion collisions is emphasized.     

Response functions of 58Ni, 116Sn AND 208Pb to the excitation of intermediate-energy α-particles

Inelastic scattering of 340 MeV and 480 MeV α-particles has been measured on ⁵⁸Ni, ¹¹⁶Sn and ²⁰⁸Pb up to 60 MeV excitation energy. Consistent background subtraction and multipole analysis has provided the repartition of multipole strength for all three nuclei. The so-obtained response functions show the already known low-energy giant resonances in a detailed way, as well as new giant resonances at high energy.     

What can be learnt about nuclear polarization from a consistency analysis ofe − cross sections and muonic X-rays for208Pb and the isotone pair209Bi/208Pb?

A joint analysis of recent electron scattering cross sections and muonic atom X-ray energies is performed for²⁰⁸Pb and the isotone pair²⁰⁹Bi/²⁰⁸Pb. From the compatibility of the experimental data one can learn about the nuclear polarisation correction. However, we find this information not to be as accurate as other authors claimed when we take into consideration the ambiguities in the treatment of the corrections of the higher levels.     

大气颗粒物滞留时间的确定方法及初步实验验证

通过研究大气颗粒物中222Rn子体活度比与颗粒物平均寿命之间的关系,建立了基于活度比估算大气颗粒物滞留时间(residence time of atmospheric aerosol,RTAA)的方法,并在相对理想条件下进行了实验验证.当氡室浓度稳定为1.816kBq/m3时,由214Bi/214Pb活度比计算出的RTAA为112.17min,与氡室的平均换气时间(104.17min)相当,表明大气颗粒物中同一衰变链上的放射性核素活度比(如214Bi/214Pb,210Bi/210Pb或210Po/210Pb)可以用于估算RTAA.     

High spin states in 210Pb

High spin states in nuclei in the ²⁰⁸Pb region were populated in deep inelastic collisions of ¹³⁶Xe and ²⁰⁸Pb projectiles with thick ²⁰⁸Pb targets at about 50 MeV above the Coulomb barrier. Prompt and prompt-delayed γ-ray coincidences were measured. Four new states above the 8⁺ isomer in ²¹⁰Pb were found and spins and parities assigned from theoretical expectations. The results are discussed in the frame of shell model theory.     

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.