Widths of the isobaric analog state of 208Pb

Both escape and spreading widths are evaluated microscopically in a consistent framework for the isobaric analog of the ²⁰⁸Pb ground state. A TDA Green function is obtained within the space of discretized J = 0⁺ proton-particle neutron-hole configurations using the Skyrme interaction. Couplings of these configurations with continuum and more complicated configurations are included into TDA matrix elements with a form of energy dependent terms. The energy and the widths of the isobaric analog resonance are obtained as a result of the matrix diagonalization. Comparison is made of the results with the former theoretical calculations as well as experimental data.     

Excitation energies of particle-hole states in 208Pb and the surface delta interaction

The schematic shell model without residual interaction (SSM) assumes the same excitation energy for all spins in each particle-hole configuration multiplet. In ²⁰⁸Pb, more than forty states are known to contain almost the full strength of a single particle-hole configuration. The experimental excitation energy for a state with a certain spin differs from the energy predicted by the SSM by ?0.2 to +0.6 MeV. The multiplet splitting is calculated with the surface delta interaction; it corresponds to the diagonal matrix element of the residual interaction in the SSM. For states containing more than 90% strength of a certain configuration and for the centroid of several completely observed configurations, the calculated multiplet splitting often approximates the experimental excitation energy within 30 keV. The strong mixing within some pairs of states containing the full strengths of two configurations is explained.     

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.     

Shell model interaction between proton holes and between proton holes and neutron particles around 208Pb

An effective residual interaction between particles and holes for shell model calculations around ²⁰⁸Pb, derived from the interaction between free nucleons, is compared with the measured properties of proton-hole neutron states in ²⁰⁸Tl and the interaction between proton holes is adjusted to newly measured level energies in ²⁰⁶Hg. These interaction elements are particularly relevant for neutron-rich nuclei. The adjustment of two mixing elements reproduces the known γ-decay data in ²⁰⁸Tl. Received: 2 April 2002 / Accepted: 2 May 2002     

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.     

The role of the tensor force for high-spin states of unnatural parity in 208Pb

The influence of the residual particle-hole tensor force on the wavefunctions of the high-spin states of unnatural parity in ²⁰⁸Pb is investigated. The form factors for the electroexcitation of such states have been calculated within the formalism of the random-phase approximation with and without the consideration of the meson exchange currents in the nuclear electromagnetic current. Special attention is devoted to the 12⁻ states which appear to be very good places to look for the effects of interest.     

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.     

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.     

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.     

RPA description of the electric polarizability of the nucleon

Excited states of the nucleon are described as RPA configurations on a mean-field ground state taken from the MIT bag model. A residual interaction of a structure as in the Nambu-Jona-Lasinio model is used. The particlehole states are coupled to good total angular momentum and isospin. Valence excitations of particle-hole type and quark-antiquark (q $\bar q$ ) states from the Dirac-sea are included. The dependence of the baryon spectrum and multipole response functions on the coupling constantG is studied. At critical values ofG the 3q-ground state becomes degenerate with strongly collectiveq99-2 modes. The model is used to calculate the averaged electric polarizability of the neutron and the protonα. Without residual interactionα=7·10^?4 fm ³ is found. With residual interaction the value increases toα=(?11)·10^?4 fm ³. The measured value ofα is reproduced within experimental error bars.     

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.     

Discovery of deeply bound π− states in the208Pb(d,3He) reaction

Narrow lines were observed around 133 MeV excitation energy in the²⁰⁸Pb(d,³He) reaction atT _d=300 MeV/u using the Fragment Separator System at GSI. They are assigned to the deeply boundπ ^??²⁰⁷Pb states with configurations of $\left( {2p} \right)_{\pi ^ - } $ (3p_1/2, 3p_3/2) _n ^?1 .     

Excitation of high-spin unnatural parity states in 208Pb from the (p,p′) reaction at 135 MeV

Differential cross sections for the excitation of states at 6.42, 6.73 and 7.04 MeV in ²⁰⁸Pb by 135 MeV protons are reported. Both the excitation energies and the backward peaked angular distributions observed in this experiment and in a recent (e, e′) experiment strongly suggest that these states are predominantly one-particle-one-hole excitations with J^π = 12^?, 14^? and 12^?, respectively. The present (p, p′) data are interpreted using a distorted wave impluse approximation and the effect of configuration mixing between the two 12^? states is investigated.     

Spin distributions in the vibrational excitations of closed-shell nuclei

Self-consistent Hartree-Fock and RPA calculations with the Skyrme-type interaction SGII are used for a systematic investigation of the 1⁺ and the triplet 0^?, 1^?, 2^? states in ⁴⁰Ca and ²⁰⁸Pb. Response functions to spin-dependent multipole operators are calculated and the particle-hole structure of the spin-dependent collective states is studied. Collective spin-dependent 0^? and 1^? states above the giant dipole resonance as well as a collective spin-independent 2^? state (twist mode) are identified. Transition spin and current densities are calculated for the collective excitations and found to be useful for the study of these excitation modes.     

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.     

An ensemble of random particle-hole matrices with collective eigenstates

An ensemble of random particle-hole matrices is studied as a function of the signs of the matrix elements. When all matrix elements have the same sign, a theorem due to Perron ensures the existence of a coherent state: the collective particle-hole state. The example of Gamow-Teller transitions between²⁰⁸Bi(1+) and²⁰⁸Pb(0+) is considered and the strength of the Gamow-Teller giant resonance as well as the fluctuations in the ensemble are studied. When a fractionp of matrix elements are of opposite sign, we find that a giant resonance may still exist providedp is small enough. Its magnitude and position in the spectrum are studied. The method proposed is valid for any particle hole excitation. The two body matrix elements of several interactions are analysed and are shown to fit into a unique valuep=0.2 for the 1 + states.     

以一组统一的高斯函数为基函数的双原子分子的Hartree-Fock-Roothaan波函数(Ⅰ)——第一,二列元素的双原子氢化物AH,AH±和AH*

我们采用一组统一的基函数,从头计算第一、二列元素的双原子氢化物以及第一列元素的同核和异核双原子体系的波函数。本文是三篇一组文章的第一篇,得到了双原子氢化物的电子波函数以及轨道能量和总能量等物理量,原子核间距取实验值和(或)理论值。这些波函数是狭义Hartree-Fock方程的以Double Zeta收缩高斯型函数为基函数的展开式。这些态包括体系的基态AH、一些低激发态AH^*和正负离子态AH^±,A表示周期表中Li到F和Na到Cl的各种元素。计算限于闭壳层电子组态或只带一个没有填满的开壳层电子组态。作为例子,三种基态AH的电子波函数表报道于文中。 关键词：     

Exciton level densities with spin and parity based on random matrix model

Level densities for fixedJ ^π and the exciton number are evaluated for closed shell nuclei⁴⁰Ca and²⁰⁸Pb. The single particle spectra and wave functions are generated by Woods-Saxon potentials. The effects of the residual interaction are taken into account statistically by the method of generating function and Grassmann integral. The matrix elements for the residual interaction are assumed to be random variables with Gaussian distributions whose second moments are calculated by using a zero range interaction. The second moments are evaluated for fixedJ ^π by ignoring the Pauli principle between active nucleons and the spectator. This approximation is shown numerically to be very good. The partial level densities are calculated using the second moments as well as independent particle model spectra. The resulting level densities spread over wider energy ranges, have a smoother energy dependence and are enhanced at low energies compared with the independent particle model densities, although the total level densities do not differ by much.     

High-spin states in 208Pb

High-spin states in ²⁰⁸Pb have been studied by γ-ray-spectroscopy methods in deep inelastic reactions induced by beams of ²⁰⁸Pb, ¹³⁶Xe and ⁷⁶Ge beams on a thick ²⁰⁸Pb target. The 11⁺ ₂ state and new γ-transitions between the one-particle one-hole states of highest spin have been found and electromagnetic matrix elements verified. High-spin states of two-particle two-hole structure have been detected for the first time. The results are compared to shell model calculations with realistic interactions in the complete Kuo-Herling space. Received: 31 October 2000 / Accepted: 26 March 2001     

Onset of deformation in polonium nuclei

The systematics of the positive-parity states in ^194–208Po are studied within the framework of the Particle-Core Model. The wavefunctions of the 2 ₂ ¹ states have been extracted using the Quasiparticle Random Phase Approximation. The increase in the collective motion comes from the increased proton-neutron interaction when both particles occupy high-j orbitals