High spin states in205Pb and a precision test of the nuclear shell model for three nucleons

Using the²⁰⁴Hg(α, 3n) reaction withα-particles of about 40 MeV, we have proved by applying nowadays conventionalγ-ray spectroscopy in-beam technique, that there are two isomeric states in²⁰⁵Pb at the excitation energies 5,161.3 and 3,195.5 keV having the half-lives 71±3 and 217±5 ns, respectively. These isomeric states have spins and parities 33/2⁺ and 25/2^? and are mainly due to thei ₁₃ ^2/?3 andi ₁₃ ^2/?2 p ₁ ^2/?1 configurations, respectively. This conclusion is supported by the experimentalg-factors of these states being ?0.159±0.008 and ?0.0676±0.0011, respectively. It is furthermore shown that theE2 effective neutron charge is the same forE2 transitions from the 33/2⁺ state in²⁰⁵Pb and from the 12⁺ state in²⁰⁶Pb as required by the assumption that the²⁰⁸Pb core is responsible for the totalE2 strength of the neutron holes, and that these states are due to thei ₁₃ ^2/?3 andi ₁₃ ^2/?2 configurations. The calculatedB(E3) values ofE3 transitions from isomeric states in²⁰⁵Pb and²⁰⁶Pb agree reasonably well with the experimental values as expected from the assumption that theE3-strength should come from particle coupling to the octupole states of the²⁰⁸Pb core. The energies of the six most well established excited states in²⁰⁵Pb with angular momenta in the region 19/2–33/2 were calculated using empirical single-particle energies, empirical two-particle interactions and angular momentum algebra. The average deviation between experimental and calculated energies is ?3 keV and the root mean square deviation 6 keV as compared to the uncertainty ± 5 keV in the nuclear masses used in the calculation. For the orbits concerned the shell model is thus valid with an extremely high precision. The contribution of effective three-particle interaction in these orbits must consequently be less than about 5 keV.     

The proton optical-model potential near the Coulomb barrier

Proton elastic scattering data from ¹⁹⁷Au, ²⁰⁸Pb and ²⁰⁹Bi at energies near the Coulomb barrier are analyzed. The energy dependences of the real volume and imaginary surface-derivative potential depths V_R and W_SF of a local optical-model potential with fixed geometric parameters are found to be much more rapid than at higher energies. The strong energy dependence of V_Rnear the Coulomb barrier is explained in terms of the non-locality of the nucleon-nucleus interaction.     

Total reaction cross section for 12C + 16O below the Coulomb barrier

The energy dependence of the total reaction cross section, σ(E), for ¹²C + ¹⁶O has been measured over the range E_c.m. = 4–12 MeV, by detecting γ-rays from the various possible residual nuclei with two large NaI(Tl) detectors placed close to the target. This technique for measuring total reaction cross sections was explored in some detail and shown to yield reliable values for σ(E). Although the principal emphasis of this work was placed on obtaining reliable cross sections, a preliminary study has been made of the suitability of various methods for extrapolating the cross section to still lower energies. The statistical model provides a good fit with a reasonable value for the strength function, 〈γ²〉/〈D〉 = 6.8 × 10^?2, over the range E_c.m. = 6.5–12 MeV, but predicts cross sections which are much too large for E_c.m. < 6.5 MeV. Optical model fits at low energies are especially sensitive to the radius and diffuseness of the imaginary component of the potential and, since these are still poorly known at present, such extrapolations may be wrong by orders of magnitude. A simple barrier penetration model gives a moderately good fit to the data and seems to provide the safest extrapolation to lower energies at the present time. It is clear, however, that our knowledge of the heavy-ion reaction mechanism at low energies is incomplete, and that cross-section measurements at still lower energies are needed to establish the correct procedure for extrapolating heavy-ion reaction cross sections to low energies.     

The effect of density dependent Av18 effective interaction on the ground state properties of heavy closed shell nuclei

The channel-dependent Argonne Av₁₈ effective two-body interactions (CDEI) which are generated through the lowest order constrained variational (LOCV) calculation for asymmetric nuclear matter with the charge-dependent Av₁₈ bare nucleon–nucleon potential are used to calculate the ground state properties of heavy closed shell nuclei such as ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb. The harmonic oscillator basis, and the local density approximation (LDA) are applied to create the relative and the center of mass dependent effective two-body potential. We get more binding with respect to the similar calculation with the Reid types potentials. It is tried to omit the LDA and perform full calculation with the Av₁₈CDEI for light nuclei. The results indicate that the LDA works quite well. It is also shown that in case of heavy closed shell nuclei and unlike our previous report with Reid68Day   interaction, the contributions of higher partial waves (J>2$J>2$) are very important for the calculations with Av₁₈ potential and we get reasonable agreement between our calculated binding energies and RMS radii, with those predicated by the others methods, and the experimental data. Finally, the various aspects of channel and density dependent two-body effective interactions are discussed.     

Mass and magnetic moment of Σ− by the exotic atom method

The energies and lineshapes of five circular transitions (n = 15 → n = 14 through n = 11 → = 10) of the Σ^?Pb atom were measured wit of the transitions 15 → 14 through 12 → 11 were determined; these energies were compared with energies calculated from quantum electrodynamics, and the mass of Σ^? was adjusted to achieve a best fit. The result was m_Σ^? = 1197.24 ±0.15 MeV. The lineshape of the 12→11 transition, which is broadened by the fine structure, has been analyzed to extract the magnetic moment of Σ^?. The result was μ_Σ^? = ?1.40_?0.28^+0.41or 0.651_?0.40^+0.28 nuclear magnetons. Comparisons with SU (3) predictions are made.     

On the character of three 8+ states in 192Pb

Three low-lying 8⁺ states have been identified in ¹⁹²Pb . A newly observed cascade of $ \gamma$ -rays built directly on the 8⁺ ₁ state is compared to the previously identified, weakly rotational band above the 11^- $ \pi$ i _13/2 , h _9/2 isomer in the same nucleus, and to analogous structures in ¹⁹⁴Pb . The similarity of all four structures lends support to the suggestion that the 8⁺ ₁ configurations are of a similar oblate deformation to the 11^- isomers. The excitation energies of all three 8⁺ states in ¹⁹²Pb and ¹⁹⁰Pb are compared to systematics. The possibility that one of the 8⁺ states in ¹⁹²Pb is associated with a prolate shape is discounted.     

Measurement of the elliptic flux of Z ⩾ 2 charged particles in collisions of relativistic nuclei with photoemulsion nuclei

The azimuthal asymmetry is measured for the emission of Z ≥ 2 particles from the interaction of ²²Ne, ²⁴Mg, ³²S, ⁵⁶Fe, ¹⁹⁷Au, and ²⁰⁷Pb nuclei with photoemulsion nuclei that is induced by semicentral collisions characterized by projectile energies in the range E _pr = 1.88–200 GeV per nucleon and by impact-parameter (b) values in the range 0.12 ≤ b/b _max ≤ 0.70. The results of these measurements are compared with the results of similar measurements for protons. It is found that, at a low energy of E _pr ≈ 2 GeV per nucleon, the ratio of the azimuthal-anisotropy coefficients v ₂ for Z ≥ 2 particles and protons is 6 ± 2, but that, for energies in the region E _pr ≥ 4 GeV per nucleon, the coefficients in question agree with each other. This may suggest that, at low energies, Z ≥ 2 particles are predominantly formed at an early stage of the development of a collective flow. For E _pr ≥ 4 GeV per nucleon, these particles are presumably formed at the stage of nuclear-matter expansion. Other possible explanations for the results of the observation of an elliptic flux of Z ≥ 2 particles are discussed.     

E2 component in subcoulomb breakup of 8B

We calculate the angular distribution and total cross section of the ⁷Be fragment emitted in the break up reaction of ⁸B on ⁵⁸Ni and ²⁰⁸Pb targets at the subcoulomb beam energy of 25.8 MeV, within the non-relativistic theory of Coulomb excitation with proper three-body kinematics. The relative contributions of the E1, E2 and M1 multipolarities to the cross sections are determined. The E2 component makes up about 65% and 40% of the ⁷Be total cross section for the ⁵⁸Ni and ²⁰⁸Pb targets respectively. We find that the extraction of the astrophysical S-factor, S₁₇(0), for the ⁷Be(p,γ)⁸B reaction at solar energies from the measurements of the cross sections of the ⁷Be fragment in the Coulomb dissociation of ⁸B at sub-Coulomb energies is still not free from the uncertainties of the E2 component.     

Energy dependence of the 16O208Pb effective interaction

The Coulomb-nuclear interference in the excitation probability of the 2.615 MeV (3⁻) state of ²⁰⁸Pb by ¹⁶O at θ_CM=172° for bombarding energies 57 MeV ⩽E_lab⩽79 MeV has been studied. The data are described by an effective interaction which has a behaviour similar to that expected from the dispersion relation connecting the real and imaginary parts of the generalized optical potential.     

A sum rule description of giant resonances at finite temperature

A generalization of the sum rule approach to collective motion at finite temperature is presented. The m₁ and m_?1 sum rules for the isovector dipole and the isoscalar monopole electric modes have been evaluated with the modified SkM force for the ²⁰⁸Pb nucleus. The variation of the resulting giant resonance energies with temperature is discussed.     

A study of deuteron quadrupole moment effects in sub-coulomb scattering of tensor polarized deuterons

Measurements of the tensor analyzing power T₂₀ are presented for deuteron elastic scattering from ²⁰⁸Pb at energies below the Coulomb barrier. It is found that, for energies below about 7 MeV, T₂₀ arises primarily from the interaction of the deuteron quadrupole moment with the nuclear electric field gradient. Contributions to T₂₀ from nuclear interactions with the target are shown to be very small for E_d ? 5 MeV. Measurements of T₂₀ at E_d = 4 MeV, accurate to ± 8 × 10^?5, are presented. After correcting for deuteron stretching and a number of additional small effects, the data are used to make a new determination of the quadrupole moment. The result, Q = 0.282 ± 0.019 fm², is in good agreement with the conventional value deduced from molecular hyperfine structure data.     

Fragmentation of the high spin discrete neutron and proton states of209Pb and209Bi

The distribution of the discrete 1h _9/2, 2f _7/2, 1i _13/2 and 2f _5/2 proton states of²⁰⁹Bi and 2g _9/2, 1i _11/2, 1j _15/2 and 2g_7/2 neutron states of²⁰⁹Pb have been obtained within the particle-vibration coupling model calculation and compared with the experimental datas baising on the most recent high resolution stripping reaction on²⁰⁸Pb using 480 MeV¹²C projectile. The optimised shell model energies arising from the core-polarisation effect have profound influence for both the study of the structures of the high spin continuum shell model states of²⁰⁸Pb and stability of superheavy nuclei.     

Self-consistent calculation of phonon gyromagnetic ratios in 208Pb

Within the Theory of Finite Fermi Systems the gyromagnetic ratios g _L ^ph of all low-lying phonons in ²⁰⁸Pb are calculated. The input data, i.e., single-particle energies, single-particle wavefunctions, and the ph interaction are derived from the Energy Density Functional by Fayans et al. For the 3 ₁ ^? phonon which is the most collective state, the g _L ^ph value is close to the prediction of the collective Bohr-Mottelson (BM) model. Gyromagnetic ratios of other phonons that are included in our calculations, two 5^? states and six positive parity phonons, differ significantly from the BM model prediction.     

The (p,t) reaction on 12C, 54Fe and 208Pb at 80 MeV

Angular distributions have been measured for the low-lying levels of the residual nuclei for the ¹²C, ⁵⁴Fe and ²⁰⁸Pb(p, t) reactions at E_p = 80 MeV. The shapes of these angular distributions are generally well reproduced by the zero-range distorted-wave Born approximation (DWBA). Enhancement factors extracted from the data show that the DWBA predicts relative strengths consistent with those observed at lower bombarding energies. However, the overall empirical DWBA normalization at E_p = 80 MeV is observed to be $\text{1}\text{12}$ ($\text{1}\text{4}$) of that required at 40 MeV for ²⁰⁸Pb (⁵⁴Fe).     

Radiationless transition probabilities in muonic208Pb,232Th,and238U

The probabilities for non-radiative (n.r.) excitationsP _n.r. in the muonic nuclides²⁰⁸Pb,²³²Th, and²³⁸U have been determined from (μ^?,γγ)-measurements by comparing the intensities of muonic X-ray transitions in single and coincidence spectra. The value ofP _n.r. (3p→1s), measured for the first time, is about 90% for the actinides²³²Th and²³⁸U, but only about 8% for²⁰⁸Pb. The value ofP _n.r. (3d→1s) is found to be 10 % for²³³Th, 13% for²³⁸U, and about 4% for²⁰⁸Pb. For²⁰⁸Pb a vanishing strength of the n.r. decay of the 2p-level is found, while for²³²Th and for²³⁸U n.r. strengths of about 20% and 26%, respectively, are observed. By regarding two subcomplexes of the 2p→1s transitions leading to different mean excitation energies the n.r. transition probabilities were found to be different for²³⁸U only, 21.6% and 31.1.%, respectively.     

Study of high energetic electrons emitted during heavy ion collisions

Double differential cross sectionsd ² σ/dΩdE were measured for high energetic electrons emitted in heavy ion collisions. Electrons were detected in the energy range of 60 keV-500 keV for various target projectile combinations 66≦Z _u =Z _t +Z _p ≦145 and projectile velocities between 7 % and 10 % of the speed of light. Clear evidence was found that these electrons stem from the united atom formed during the collision. Slope and height of the spectra are discussed with respect to the momentum distribution of strongly bound states (i.e. theL-shell) at momenta far above the mean value. In addition for the systems S, Ni, Br→Pb electrons were detected in coincidence withK x-rays of Pb. By this method the contribution of theK-shell of the combined system to the total spectrum could be separated. Binding energies of theK-shell were estimated by a slope comparison between the coincident and single spectrum. The resulting values are close to the united atom limit.     

The PbPb collision

The reaction ²⁰⁸Pb on ²⁰⁸Pb was studied at bombarding energies of 7.0 and 7.57 MeV/u. One-particle inclusive measurements using a large-area position-sensitive ionisation chamber delivered the kinetic energy, charge and scattering angle of the reaction products. A precise calibration of the stopping power for very heavy ions in the detector gas was performed. The measured Wilczynski diagrams show, for increasing loss of kinetic energy, an increase of the mean scattering angle. It is attributed to the dominance of the repulsive Coulomb forces with respect to the attractive nuclear forces. The element distribution for the ²⁰⁸Pb on ²³⁸U reaction at 7.5 MeV/u was also measured and compared to the PbPb and UU reactions. Fission probabilities are derived as a function of charge and total kinetic energy loss. The most striking result is seen in the σ_z² versus TKEL correlation: the average rate of energy loss per nucleon exchange is abnormally large. It is shown that this behaviour is associated with the double magic closed shell character of the colliding nuclei. Nuclear structure information is extracted through a simple parametrisation.     

A microscopic theory of giant electric isovector resonances

The electric multipole isovector (τ = 1) giant resonances for Δτ_z = 0, ± 1 are studied using the self-consistent HF-RPA theory.The distributions of strength, energies, the isospin compositions and other properties of the J = 0⁺, 1^?, 2⁺ resonances in the ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb regions are calculated. Sum rules for the charge-exchange Δτ_z = ±1 excitations are derived.     

The distribution of205Tl proton hole states and estimation of the root mean square radii of206Pb and208Pb from their charge distributions

The fragmentations of the 3s _1/2, 2d _3/2, 2d _5/2 and 1.h _11/2 proton states were deduced using the hole-core coupling model calculation and compared with recent²⁰⁶Pb ( \(\vec d\) ,³He) reaction data. The energies of the proton fragments carrying the main shell-model strengths were used to deduce the radial wave functions of²⁰⁵T1 and²⁰⁷Tl that give rise to charge distributions of these nuclei. From their respective charge distributions, root mean square radii of²⁰⁶Pb and²⁰⁸Pb were extracted.     

On the production of superheavy elements

Since the discovery of Deformed Superheavy Nuclei (1983–85) a bridge connects the island of SHE to known isotopes of lighter elements. What we know experimentally and theoretically on the nuclear structure of SHE is reported in a first section. The making of the elements, with an analysis of production cross sections, and the macroscopic limitation to Z=112+ε is presented in a second section. The break-down of fusion cross sections in the ‘Coulomb Falls’ within a range of about 10 elements is introduced as the universal limiting phenomenon. How the nuclear structure of the collision partners modifies the on-set of this limitation is presented in Section 3. Reactions induced by deformed nuclei are pushed by side collisions to higher excitation energies (4n- and 5n-channels), whereas reactions driven by the cluster-like, closed-shell nuclei, ²⁰⁸₁₂₆Pb and ¹³⁸₈₂Ba, are kept at low excitation energies (1n- and 2n-channels). The on-set of production limitation for deformed collision partners is moved to smaller effective fissilities x=0.68⩽0.72, whereas for spherical clusters the on-set is delayed x=0.76⩾0.72 and x=0.79⩾0.72 for ¹³⁸Ba and ²⁰⁸Pb, respectively. An outlook, what remains to be studied in the future, ends the article. To cite this article: P. Armbruster, C. R. Physique 4 (2003).