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.     

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.     

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.     

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     

Effect of quadrupole and octopole vibrations of206Pb on the 1j 15/2 neutron particle state of207Pb

The quadrupole as well as the octopole vibrational states of²⁰⁶Pb are coupled to the 2g _9/2, 1i _11/2 and 1j _15/2 neutron states to explain the fragmentation of 1j _15/2 state in²⁰⁷Pb as observed in the²⁰⁶Pb(d,p) reaction. The structures of weak fragmented 1j _15/2 states are deduced through the particle-core coupling scheme.     

Excitation of inner hole states in heavy nuclei with the (τ, α) reaction at 205 MeV

Energy spectra have been measured for the (τ, α) reaction at 205 MeV on⁹⁰Zr, ^118,124Sn and ²⁰⁸Pb. Results on the valence neutron shells and on the inner 1f_7/2 shell in ⁹⁰Zr, 1g_9/2 subshell in ^118,124Sn (T_< and T_> components) and 1h_11/2 subshell in ²⁰⁸Pb are presented.     

γ Spectroscopy of 209Pb with deep inelastic reactions

High spin states in nuclei around ²⁰⁸Pb were populated in deep inelastic collisions of ⁷⁶Ge, ¹³⁶Xe, and ²⁰⁸Pb projectiles with ²⁰⁸Pb targets at beam energies about 12% above the Coulomb barrier. New states in ²⁰⁹Pb were found by measuring γ-γ-coincidences. They are interpreted as the yrast states that originate from the coupling of one neutron to the lowest excitations of the ²⁰⁸Pb core. The results are discussed in the frame of the shell model. Received: 22 November 1997     

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.     

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.     

Observation of the 2<Superscript>-</Superscript> state in <Superscript>208</Superscript>Pb with a major s<Subscript>1/2</Subscript>p<Subscript>3/2</Subscript> structure and structure of ten more 2<Superscript>-</Superscript> states

From ²⁰⁸Pb (p, p’) via isobaric analog resonances in ²⁰⁹Bi , at E _x = 6420 keV in the doubly magic nucleus ²⁰⁸Pb , a new state with spin 2^- with half the s _1/2 p _3/2 strength and major g _7/2 f _5/2 , d _3/2 f _5/2 fractions is identified. Ten more 2^- states up to E _x = 7.0 MeV are identified and their structure discussed, among them six states with new spin assignments. The known 6314 1^- state is shown to contain almost the entire s _1/2 p _3/2 strength.     

MO X-ray angular distributions from 1 GeV208Pb+208Pb and209Bi+209Bi collisions

The Doppler shift and the anisotropy of the MO X-rays above the separated-atomK-lines have been measured in²⁰⁸Pb+²⁰⁸Pb and²⁰⁹Bi+²⁰⁹Bi collisions at beam energies between 4.2 and 4.8 MeV/u. The Doppler shift is found to be consistent with a source moving with 90% of the center of mass velocity of the colliding system. One peak is observed in the anisotropy spectrum. This peak might be attributed to transitions from the continuum into the minimum of the 2p _1/2 σ MO or from the 3p _1/2 σ and 2p _3/2 σ MO's into the 2 _sσ MO near the united atom limit. Radiative electron capture and secondary electron bremsstrahlung could be excluded as major sources of the observed radiation. Contrary to lighter systems no anisotropy corresponding to transitions into the 1 _sσ orbital could be observed.     

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.     

Shell model and octupole states in148Gd from in-beam experiments

Through (α, 4n) and (τ, 3n) reactions the high-spin states in the two-neutron nucleus¹⁴⁸Gd were populated up toI ^π=21? at 7.2 MeV, including numerous states above the yrast line. The¹⁴⁸Gd energy spectrum is interpreted in terms of the spherical shell model. Identification of the (νf _7/2 i _{1 3/2})_10? state gives the νi _13/2 single particle energy free of octupole admixtures as 2.1(1) MeV. Eight high-spin states between 1.2 and 3.7 MeV were identified as the couplings of the two valence-particles to the¹⁴⁶Gd octupole phonon, and three above-lying levels are assigned as double-octupole excitations including a 12⁺ state which decays by anE3-E3 stretched cascade. All these octupole levels can be quantitatively predicted from the one-particle x phonon spectrum of¹⁴⁷Gd. The high-spin states above 3 MeV are four-quasiparticle excitations ofπ ⁺¹ π ^?1 ν ² andπ ² ν ² type and their energies are in good accord with shell model estimates.     

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 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.     

A study of high spin states in the transitional nucleus90Mo

The reaction⁵⁸Ni(³⁶Ar, 4p)⁹⁰Mo has been studied at a beam energy of 149 MeV. A detector array consisting of the OSIRIS spectrometer (12 Compton-suppressed Ge detectors), four charged-particleδE detectors and seven NE-213 neutron detectors at the VICKSI accelerator in Berlin has been used to measure the gamma radiation inγγ- and particle-γγ-coincidence mode. An additional Ge detector was placed at 162? to the beam direction to provide information on DCO ratios. The level scheme of⁹⁰Mo has been extended up to an excitation energy of about 12 MeV and probable spin 23?. Some 70 transitions and 40 levels have been newly identified. Spin assignments have been proposed on the basis of measured DCO ratios. Shell model calculations in a model space consisting of the proton 1f _5/2, 2p _3/2, 2p _1/2, and 1g _9/2 orbits and the neutron 2p _1/2, 1g _9/2, 1g _7/2, 2d _5/2, 2d _3/2, and 3s _1/2 orbits with some truncation were made for states above 9? and the predicted structure of these states is discussed.     

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.     

Quasiparticle-phonon model calculations on doubly even Zn and Ge nuclei

The doubly even isotopes of Zn and Ge have been investigated in a model in which two quasiparticle excitations, constructed in a (0f _7/2), 1p _3/2, 0f _5/2, 1P _1/2, 0g _9/2 configuration space, are coupled with quadrupole vibrations of the core, viz.⁴⁰Ca or⁵⁶Ni. The 0f _7/2 orbit is excluded in case of a⁵⁶Ni core. The spectra, except for low-lying excited 0⁺ states, could be reproduced reasonably well. The calculatedE2 strengths and quadrupole moments are in fair agreement with experiment.