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.     

The continuum shell-model neutron states of209Pb

The neutron strength distributions of the three high-spin 1k _17/2, 2h _11/2 and 1j_13/2 states of²⁰⁹Pb have been obtained within the formalism of the core-polarisation effect where the effect of interaction of the neutron shell-model states of²⁰⁹Pb with the collective vibrational states (originating also from the giant resonances) have been taken into consideration. The theoretical results have been discussed in the light of works on 1k _17/2, 2h1_11/2 and 1j_13/2 neutron orbitals of²⁰⁹Pb. The shell-model energies of the neutron states have been obtained by Skyrme-Hartree-Fock method     

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.     

One- and two-step processes in natural- and unnatural-parity 208Pb(p,t)206Pb reaction at Ep = 22 MeV

Reaction mechanism and nuclear-structure dependence of the natural- and unnatural-parity ²⁰⁸Pb(p, t)²⁰⁶Pb(2⁺, 3⁺, 4⁺, 5⁻ and 7⁻) reaction are studied by using a 22 MeV polarized proton beam. Angular distribution of the analyzing power for the second 3⁺(3₂⁺) transition has an opposite sign to that for the 3₁⁺ one and the difference is explained in terms of the j-dependence in the sequential two-step (p, d)(d, t) process. The observed analyzing powers and cross sections for the two 3⁺ transitions are reproduced by the finite-range first- and second-order DWBA calculation. Two-step analysis is necessary to explain the variety of angular distributions of the analyzing powers for the natural-parity transitions. Microscopic analysis in terms of the one- and two-step (p, t) calculation is made for the transitions to the 2_1–5⁺, 4_1–3⁺, 5_{1, 2}⁻ and 7₁⁻ states in ²⁰⁶Pb. The calculation reproduces the absolute values of the observed cross sections within a factor of 2.     

Spectrum of the high spin neutron hole states of205Pb

The high resolution (³He,α) reaction on²⁰⁶Pb shows the distribution of the 2f _7/2, 1h _9/2 and 1i _{1 3/2} neutron states of²⁰⁵Pb within the 6 MeV excitation energy of²⁰⁵Pb. The spectrum of these three-hole states is obtained within the hole-core vibrational coupling scheme. The shell model energies of the neutron hole states arising from the core-polarization effect are compared with the Bansal-French energy weighted sum rule. The possible implication of the present neutron hole energies has been discussed in the light of the deduced shell model wave functions of the collective states of²⁰⁶Pb.     

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.     

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.     

Gross structure in excitation functions for207Pb(p,p′)207Pb in the region of overlapping isobaric analogue resonances

Prominent resonances in the reaction²⁰⁷Pb(p, p′)²⁰⁷Pb leading to the low-lying states in²⁰⁷Pb(1/2^? g.s., 5/2^? 0.57 MeV, 3/2^? 0.89 MeV, 7/2^? 2.33 MeV) are observed betweenE _p =16 and 18 MeV. The structures in the excitation functions are interpreted as being due to analogues of states in²⁰⁸Pb which are mixtures of neutron particle-hole configurations.     

Particle-hole excitations in the208Pb mass region

Spectra, magnetic dipole moments and spectroscopic factors of a number ofA=205–209 nuclei as well asM1 transitions in²⁰⁸Pb are investigated in terms of large-scale shell-model calculations which include 1p ?1h excitations and for some nuclei 2p ?2h excitations. The calculated spectra agree well with the data. The calculatedg-factors are in fair agreement with the data in most cases. The predicted strength forM1 transitions to low-lying states in²⁰⁸Pb is less than that obtained from previous calculations. Spectroscopic factors forl=0 proton pick-up from²⁰⁸Pb and²⁰⁶Pb agree very well with recent experimental data from (e, e′p) reactions.     

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.     

Nucleon transfer reactions to rotational states induced by206, 208Pb projectiles

In a systematic study of nucleon transfer reactions accompanied by Coulomb excitation we have bombarded¹⁵²Sm,¹⁶⁰Gd and²³²Th with^{206, 208}pb beams at incident energies close to the Coulomb barrier. Particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and in nucleon transfer reactions. One-neutron stripping and pick-up reactions on¹⁵²Sm were observed leading to known states of the rotation alignedi _13/2-bands in¹⁵³Sm and¹⁵¹Sm. In the¹⁶⁰Gd+^{206, 208}Pb systems no significant population of low lying states of product nuclei was found in the nucleon-transfer channels. Large cross sections were observed for one- and two-neutron pick-up from²³²Th at an incident energy of 6.4 MeV/u. Around the grazing angle they are of the same order of magnitude as the cross section measured for inelastic scattering. The results are analyzed in the framework of semiclassical models.     

High-spin states in206Bi populated in the205Tl(α, 3n) reaction

Using alpha-particles in the energy range 35–51MeV and in-beam gamma ray and conversion electron spectroscopy techniques the reaction²⁰⁵Tl(α, 3n)²⁰⁶Bi was studied. A 15±1ns isomeric 15⁺ state was found at an excitation energy of 3147keV in²⁰⁶Bi. The main configuration of the isomeric state is suggested to beπh _9/2 vp ₁ ^2/?1 i ₁₃ ^2/?2 . The isomeric state decays mainly through a stretched cascade of five gamma rays to the previously known 0.88ms 10^? state of theπh _9/2 vi ₁₃ ^2/?1 (j ^?2)₀₊ configuration at an excitation energy of 1045 keV. A shell model calculation of the yrast states has been performed and it is found that the calculation agrees fairly well with the experiments. The average deviation between experimental and calculated energies for the yrast states with angular momenta in the region 6–18 is +4keV and the root mean square deviation is 22 keV.     

Alpha-decay study of188Pb and180,182Hg

Theα decay of mass-separated¹⁸⁸Pb and^180,182Hg has been studied at the GSI on-line mass separator. Alpha singles spectra as well asα-X-t andα-e-t coincidence events were collected. Fine structure in theα decay of¹⁸⁸Pb was measured for the first time, feeding the 2₁ ⁺ and 0₂ ⁺ states in¹⁸⁴Hg. Theα decay of^180,182Hg feeds low-lying states in^176?178Pt. One of these states could be identified as a 0⁺ state. The deexcitation pattern could be established. As a by-product an alpha-decay scheme of¹⁸⁰Au towards levels in¹⁷⁶Ir is given.     

The impact parameter dependence of the K MO X-ray emission in208Pb +208Pb collisions

The emission probabilities for quasimolecular K-x-radiation (K-MOR) have been measured in²⁰⁸Pb +²⁰⁸Pb collisions at 4.3 MeV/u and 4.8 MeV/u as a function of the scattering angle using the particle-photon-coincidence technique. The probabilities exhibit a superposition of two exponential slopes with different fall-off constants. We identify the sharp fall off at very small impact parameters (<60 fm) with the K-MOR contribution from the decay of 1sσ-vacancies. The flatter slope for impact parameters larger than 60 fm is attributed to the radiative decay of holes in 2p _1/2 σ molecular states. In this way, experimental “1sσ-MOR-emission probabilities” could be extracted and compared with theory. For 4.3 MeV/u the1sσ- and 2p _1/2 σ-excitation probabilities could also be determined and have been compared to coupled-channel calculations and to a scaling law for 1sσ excitation.     

Inelastic scattering and nucleon transfer in the system232Th+206Pb near the Coulomb barrier

Nucleon transfer accompanied by Coulomb excitation was studied in the system²⁰⁶Pb+²³²Th atE _Lab=6.4 MeV/u. Particle-particle-gamma coincidence techniques were used to identify excited states of reaction products populated through inelastic scattering and nucleon transfer reactions. The mean excitation energy was measured by means of aγ-ray energy and multiplicity filter consisting of 6 NaI detectors. Large cross sections for one-neutron and two-neutron pick-up from²³²Th are observed. The impact-parameter dependence of the neutron transfer is analyzed in terms of semiclassical barrier penetration models. Using realistic neutron potentials with a diffuse surface, the experimental data are in accordance with the assumption of a “cold” transfer to states near the yrast line.     

208Pb(p, α)205Tl reaction at 16.475 MeV

The (p, α) reaction was studied on a²⁰⁸Pb target at 16.475 MeV. Nineteen states were observed in²⁰⁵Tl, up to 3.6 MeV in excitation. Angular distributions were obtained for five strong proton-hole transitions, and DWBA fits made to determinelj values. Results are compared with previous²⁰⁶Pb(t, α)²⁰⁵Tl,²⁰⁶Pb(d,³He)²⁰⁵Tl,²⁰⁵Tl(p, p′), and²⁰⁵Tl(n, n′) work.     

Interplay of valence-shell clusters and the vibrational field in205Pb and206Pb

The properties of²⁰⁵Pb and²⁰⁶pb are described in the cluster vibrational field coupling model. Excitation energies, strengths for one-particle transfers,E2 andM1 observables are compatible with the available experimental data. Other theoretical approaches for these nuclei are discussed and compared with the results of the present investigation.     

Damping of the high-spin neutron hole orbitals of the207Pb

The neutron strength functions of the high-spin 1g _7/2 and 1h _11/2 hole states of the²⁰⁷Pb have been deduced within the formalism of the hole-core vibrational coupling scheme. The attenuation of the shell-model strengths of these two high-spin hole states have been compared with the distribution of the neutron strength functions of the discrete 1h _9/2 and 1i _13/2 states. The theoretical results have been discussed in the light of the recent experimental findings on the neutron hole orbitals of the²⁰⁷Pb nucleus. Side by the side the implication of the present research works has been reviewed on the basis of the other existing theoretical calculations on the high-spin neutron hole states of the²⁰⁷Pb.     

Fragmented 2d 5/2, 1g 7/2 and 1g 9/2 deep proton-hole states of207TI

The three proton-hole states ?2d_5/2, 1g_7/2 and 1g_9/2 are found to be fragmented as a result of coupling of these states with the 3^?, 5^?, 2⁺, 4⁺ and 6⁺ collective states of²⁰⁸Pb. The excited states in²⁰⁸Pb (t,α) reaction can be quantitatively explained in terms of altered 2d_5/2, 1g_7/2 and 1g_9/2 states with the hole-core coupling model.