V. Paar

Coupling of a three-particle (hole) valence-shell cluster to quadrupole vibrations (Alaga model): The Z = 50 region: odd Ag and I isotopes; and the Z = 28 region: odd Mn and Ga isotopes

Abstract The present approach includes two important physical correlations: the interaction between single-particle degrees of freedom and the vibrational field and the Pauli principle for three particles or holes in the valence shell. No new parameters have been introduced. In this way, both the explicit appearance of broken and promoted pairs and the anharmonicities from the neighbouring doubly even nuclei are accounted for. The model is generally characterized b y the coexistence of quasivibrational and quasirotational features. Typical quasirotational elements are the quasiband pattern and the I = j − 1 anomaly, while a typical quasivibrational element is the multiplet structure. Both features are naturally introduced by the mechanism of the cluster field coupling. Nuclei with Z = 50 ± 3 and Z = 28 ± 3 are qualitatively discussed within the framework of the present approach. A detailed qualitative and quantitative description of the properties of low-lying states (energy spectra, electromagnetic properties, transfer reactions) as well as a comparison with experiment are given for 107, 109Ag, 127I, 55Mn, and 69Ga, which are typical and well-known representatives of odd Ag, I, Mn, and Ga nuclei, respectively.

A parabolic rule for the energy dependence on x = I(I + 1) for proton-neutron multiplets in odd-odd nuclei

An analytic expression for the energies of the states of the proton-neutron multiplet (jpjn)I = |jp-jn&,…,jp + jn is derived as a quadratic function x = I(I + 1) owing to the exchange of the quadrupole and the spin-vibrational phonon. A discussion of this parabola, its consequences and illustrative applications are presented. The parabolic rule is suggested to serve as a guideline on the classification and investigation of states in odd-odd nuclei.

SU(6) quadrupole phonon model for even and odd nuclei and the SU(3) limit

Abstract Analogous to the equivalence between the SU(6) quadrupole-phonon model (TQM) and the interacting boson model (IBM), the equivalence is pointed out for odd systems between the SU(6) particle quadrupole-phonon coupling model (PTQM) and the interacting boson-fermion model (IBFM). PTQM is formulated starting from the Dyson representation for the odd system. Different aspects of the SU(3) limit of TQM and PTQM are studied; the quadrupole-phonon block structure of rotational bands in even and odd nuclei and analytic expressions based on the coherent state; signature effects generated in PTQM; electromagnetic properties and correction factors for PTQM; overlaps of the PTQM analogs of Nilsson states with Coriolis-coupled Nilsson states and the relation to the rotational model representation.

“Decoupled” and “strongly coupled” band patterns in the particle-vibration coupling model

Abstract “Decoupled” or “strongly coupled” band patterns are generated in leading order bu coupling a particle (hole) to anharmonic phonons. The type of the pattern depends on the sign and magnitude of Q ( j ) Q vib .

An experimental and theoretical investigation of the structure of 210Pb

Abstract The 208 Pb(t, p) 210 Pb reaction has been performed at a bombarding energy of 20 MeV. Angular distributions using solid-state counters and a magnetic spectrograph were obtained for levels up to 5 MeV of excitation. The different transitions are interpreted in terms of multipole pair addition modes, and support for the existence of multipole pairing fields is obtained from the analysis. The data are also compared with calculations using realistic force wave functions. No new correlations from the latter calculations not already present in the multipole pairing description were found. Special attention is paid to the transition to the 3 − state at 1.869 MeV which has a large component of the two-phonon state ¦3 − ( 208 Pb) ⊗ g.s. ( 210 Pb)〉. It is shown that both ground state correlations and indirect transfer processes have to be invoked to explain the data. The two-step processes are treated in the coupled-channel Born approximation.

A study of 75Se by neutron capture and the SU(3)-SU(5) transition in the quadrupole-phonon representation

Abstract The γ and e − spectra following thermal neutron capture in 74 Se were studied with curved-crystal, β, and pair spectrometers. Precise energies have been obtained for the transitions and levels at low energies. Two primary E2 transitions were found. The neutron separation energy for 75 Se was determined as 8027.6 keV. Precise γ-energies following the electron capture decay of 75 Se were also measured, resulting in precise level energies in 75 As. The calculation of the energy levels in 75 Se has been performed in the SU(6) particle-vibrational model (PTQM) and 27 theoretical states have been tentatively assigned to the experimental levels. The spectrum of the core nucleus 74 Se has been calculated in the SU(6) quadrupolephonon model (TQM). The structure of theoretical states, the relation to SU(3) and SU(5) limits, and potential energy surface are discussed. The E2, M1 and E1 transitions have been calculated in PTQM and compared to the experiment. Also, an overview is presented of theoretical explanations of the I = j , j −1, j −2 anomalous triplet emphasizing the rule with shell-model classification corrected for quadrupole phonons.

A simple explanation of the sign and magnitude of quadrupole moments in even-A Fe, Zn, Cd, Te and Hg isotopes

Abstract Coupling valence-shell protons (cluster) to the vibrational field gives the sign and magnitude of quadrupole moments in Fe, Zn, Cd, Te and Hg as a consequence of the shell structure. Competition of contributions of the available valence proton configurations determines the sign and magnitude of the quadrupole moment of two-proton clusters. The field-induced polarization effect always leads to an enhancement of the cluster quadrupole moment.

Diagramatic perturbation treatment of the effective interaction between two-photon states in closed shell nuclei: The Jπ = 0+ states in 208Pb

We present in this the following letter a unified picture for describing the closed shell nuclear spectrum, in particular, those states that are strongly excited in the (t,p), (p,t) reactions and/or inelastic scattering processes. In the shell-model language these are the 2p, 2h and 1p - 1h states (pairing and surface vibrational states), and those generated by coupling these states among themselves (two-phonon states). In the collective model the 2p, 2h and 1p - 1h states are usually referred as the elementary excitations of the closed shell systems. The coupling between the elementary excitations is treated microscopically in perturbation theory (anharmonicities of the phonon nuclear spectrum) and an effective interaction among the phonons is obtained. In particular, we calculate the interaction among the Jπ = 0π states ∣ gs(206Pb) ⊗gs(210Pb); 0〉 and ∣ 3−(208Pb) ⊗3−(208Pb); 0〉 and compare the results with the 206Pb(t,p) and 210Pb(p,t) reaction data.

Asymptotic cancellation for the tensor M1 operator versus particle-vibration coupling away from doubly closed shell nuclei

Abstract For M1 transitions which are l -forbidden in zeroth order, asymptotic cancellation appears among second- and higher-order contributions to the matrix element of the tensor M1 operator. This leads to approximate reestablishment of the zeroth-order value, although the wave functions of the initial and final state are rather mixed.

Properties of 63Cu negative parity states in the semimicroscopic model

Abstract The semimicroscopic model assuming a proton coupled to a quadrupole vibrator, with states up to three phonons included, is applied to 63Cu. Parametrization different from that by Bouten and Van Leuven is used. Blairs spectroscopic factors are well reproduced, and the experimentally known properties of B(E2) values are obtained. The influence of particle-hole excitations in the internal phonon structure within this parametrization appears to be small. The configuration ¦(f 7 2 −1P 3 2 )2〉 is a dominant proton excitation in the one-phonon state.