Projected quasiparticle calculations in large model spaces
Abstract
A general formalism is presented, by means of which number projected BCS quasiparticle calculations require only a little more computational effort than unprojected ones, even in large model spaces. It is a generalized and improved combination of known formalisms. Its advantages over those methods are discussed. The formalism is very well suited for applications where the BCS superfluidity parameters are different for initial and final states, such as particle transfer reactions and pairing vibrations. Extensive formulas are given.
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Projected linear response theory for charge-exchange excitations and double beta decay
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The broken pair model for nuclei and its recent applications
1988, Physics ReportsThe broken-pair model for nuclear structure is presented together with illustrative examples of its recent applications in various nuclear mass regions. The relationship with other models, in particular the shell model and the BCS model, is considered in some detail. The various ways in which the model has been presented in the literature are compared. The merits of several proposed extensions of the model are also discussed.
It is demonstrated that already the rather simple model with at most one broken pair can reproduce many properties of semic-magic nuclei. The rather complicated extension by breaking another pair is shown to be essential for the description of transitions between the excited states of the even semi-magic nuclei. The model, as presented here in a spherical shell model basis, is found to become less satisfactory for nuclei with several valence protons and neutrons. However, for such cases the broken-pair model provides considerable support for the use of the phenomenological boson models and may yield estimates for their parameters.
High-spin neutron excitations in neutron-deficient even-mass Pb isotopes
1986, Nuclear Physics, Section AHigh-spin states in 194, 196pb have been investigated using the 188Os(12C, χn)194, 196Pb and the 198Hg(α, 6n)196Pb reactions. The experiments included γ-ray excitation function, γ-γ coincidence, γ-∑γ coincidence, γ-ray angular distribution, lifetime and conversion electron measurements. The level schemes of 194Pb and 196Pb have been extended up to states with Jπ = 15− (E = 3955 keV) and Jπ = 20+ (E = 5444 keV), respectively. All levels except two new isomers which have most likely spin and parity and can be interpreted as neutron excitations. The excitation energies of levels with spin J ⩽ 12 are well accounted for by the one-broken-pair model including 1p1h excitations. The B(E2, 12+ −10+) values reflect the systematic trend for a pure configuration. Levels with spin 12 < J < 20 can be described as two-broken-pair model configurations. The excitation energies of these states can be reproduced quite well in a phenomenological approach in which two neutron holes are coupled to core excitations in the A + 2 nucleus and also by calculations performed within the two-broken-pair model. Within this framework the Jπ = 20+ state observed in 196Pb has a pure configuration.
The two new isomers have most likely a proton 2p2h structure. The excitation energy of the Jπ = 11− isomer in 196Pb agrees with that predicted for a deformed [404]−[514][606]11− state.
Microscopic approach to magnetic excitations in IBM-2
1985, Nuclear Physics, Section AStarting from the collective SD subspace of the shell model, we construct boson images of the hamiltonian and the M1 and M3 operators by using the OAI method. In the magnetic operators one-boson as well as two-boson terms are considered. Energy spectra and g-factors of 130,134Ba are well reproduced by this method. Relatively strong magnetic dipole and octupole transitions at Ex ∼ 2 MeV are predicted. The M1 and M3 electron scattering form factors are calculated. It turns out that the magnetic dipole operator is mainly a one-body operator in boson space, whereas the magnetic octupole operator contains important two-boson terms, which give sizeable contributions to the excitation strengths. These two-boson terms tend to diminish the F-spin selectivity of M3 excitations.
Spectroscopy of even Sn nuclei and generalized-seniority breaking
1985, Nuclear Physics, Section AProperties of even Sn nuclei are described in a broken-pair or generalized-seniority (νg) scheme. Special attention is paid to the degree of νg mixing in various types of low-lying states. A finite-range interaction as well as a surface-delta interaction (SDI) are employed and single-particle energies are deduced from spectra of odd Sn isotopes. It appears that up to 3 MeV no experimental indications for states with νg > 4 exist. The only low-lying states which are not included in the model are the members of the well-known two-proton-hole band.
With the SDI the νg mixing is in general a factor two less than with the finite-range force. For the latter an improvement of the description of energy spectra as well as electromagnetic decay is obtained due to about 20% νg = 4 admixtures in predominantly νg = 2 states. Only ground states, 21+ and 31− states have less than 10% of νg = 4 admixtures. We argue that the main origin of νg mixing is a particle-phonon coupling mechanism.
A strong fragmentation of two-phonon 0+, 2+, 4+ states by νg mixing emerges from the calculations. For the 0+ states the total two-phonon E2 transition strength is much less than predicted by phenomenological phonon or boson models.
Excitation strengths for unnatural-parity states are reduced by 30–40% by νg mixing. For natural-parity states this reduction is less; for 21+ and 31− enhancements by ground-state correlations overcompensate the reduction by fragmentation.
Do we understand IBM parameters?
1984, Nuclear Physics, Section AA microscopic calculation of interacting-boson model (IBM) parameters is performed for Xe isotopes within the framework of the broken-pair model. We employ a shell-model hamiltonian which reproduces the spectra of near-magic and semi-magic nuclei. As a first approximation we adopt the idea of Otsuka, Arima and Iachello, that IBM states represent fermion states built from collective S- and D-pairs — the SD space. We show that at least two effects are needed to explain the empirical values of IBM parameters. Firstly there is a reduction in collectivity of S- and D-pairs in states with several broken pairs, due to the Pauli-blocking effect of the latter. Secondly the shell-model hamiltonian mixes the SD space with other fermion states which are not explicitly represented in the IBM. Among the latter, states with a collective G-pair (J = 4) are the most important, but they contribute less than half of the total renormalization of the parameters. The calculated IBM parameters χ of the E2 transition operators exhibit similar trends to those which occur in the IBM hamiltonian.
We explain the IBM Majorana force as a renormalization effect on states with even J; not as a repulsion in states with odd J. The latter emerge as rather pure states which mix little with the non-collective fermion space. This indicates that they may be experimentally observable.
With our calculated parameters the IBM spectra and E2 transitions are of comparable quality to those obtained in IBM fits of the data.