K. Allaart

Neutron excitations in even mass Sn nuclei

Abstract High-spin neutron quasi-particle excitations in the even-mass 110–118 Sn nuclei have been investigated using Cd(α, 2nγ)Sn reactions. The experiments included γ-ray excitation function, γ-γ coincidence, lifetime, γ-ray angular distribution, γ-ray linear polarization and conversion electron measurements. Four new isomeric states were identified, i.e. the J π = 6 + state at 2480 keV in 110 Sn(T 1 2 = 8.3±0.4 ns ) , the J π = 8 − state at 3440 keV in 112 Sn(T 1 2 = 0.58±0.06 ns ) , the J π = 8 − state at 3190 keV in 114 Sn (T 1 2 = 0.35±0.20 ns ) and the J π = 7 − state at 2909 keV in 116 Sn (T 1 2 = 0.5±0.3 ns ) . These isomers and in addition several new levels observed in 110–114 Sn can be related to neutron quasi-particle excitations. Spin and parity assignments to known levels are firmly established. The data are interpreted within the framework of the broken-pair model, including proton 1p-1h excitations. Excitation energies and static moments are well accounted for by this model. Experimental transitions rates however, are not always well reproduced by the calculations, especially for E λ decays between excited states of the type J → J - λ . It is argued that in such cases collective two-broken-pair admixtures dominate the transitions.

High-spin neutron excitations in neutron-deficient even-mass Pb isotopes

Abstract High-spin states in 194, 196 pb have been investigated using the 188 Os( 12 C, χn) 194, 196 Pb and the 198 Hg(α, 6n) 196 Pb 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 194 Pb and 196 Pb have been extended up to states with J π = 15 − ( E = 3955 keV) and J π = 20 + ( E = 5444 keV), respectively. All levels except two new isomers which have most likely spin and parity J π = 10 − ( 194 Pb ) and J π = 11 − ( 196 Pb ) 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 ( i 13 2 ) 2 configuration. Levels with spin 12 J i 13 2 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 J π = 20 + state observed in 196 Pb has a pure ( i 13 2 ) 4 configuration. The two new isomers have most likely a proton 2p2h structure. The excitation energy of the J π = 11 − isomer in 196 Pb agrees with that predicted for a deformed 1 2 + [404] − 29 2 − [514] 13 2 + [606] 11 − state.

The broken pair model for nuclei and its recent applications

Abstract The 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.

FBCS for odd nuclei and the inverse gap equations: Application to N = 50 isotones

Abstract The single-quasiparticle descriptions of odd superfluid nuclei by BCS theory and by particle number projection methods are compared with the exact lowest-seniority shell model. The purpose is to trace systematic inadequacies of the inverse-gap-equations (IGE) method to extract single-particle energies from spectroscopic data on odd nuclei and to improve that method by using number projection techniques. The IGE method yields too large a spacing of single-particle energies especially near closed subshells and also the force strengths are not correctly given in general. A similar method based on particle number projection leads to correct results. A conventional two-quasiparticle BCS calculation of the spectra of even nuclei with parameters obtained by the IGE method leads to other results than when for both the odd and the even nuclei a number-conserving description is used. In the former approximation particle-hole like states are relatively too high and particle-particle or hole-hole like states too low in energy, which may strongly influence the configuration mixing. As a practical application the spectra and a few other spectroscopic properties of the even single-closed-shell nuclei with 50 neutrons are calculated.

The FBCS model and the inverse gap equations applied to the tin isotopes

The FBCS model for odd nuclei and the inverse gap equations are applied to a whole sequence of tin isotopes,viz.111–125Sn. From spectroscopic data on the odd isotopes, the single-particle energies and interaction strengths are obtained. With these parameters the lowest states of the even isotopes are calculated by a number-projected two-quasiparticle diagonalization and by the usual BCS one. This is done with two Gaussian interactions and the SDI. In the case of the Gaussian forces the experimental energies are well reproduced by the number-projected treatment. Effective charges for Eλ transitions, which are required to reproduce the experimental transition rates, are rather constant for the whole series of isotopes, in case of the number-projected treatment. In addition a number of spectroscopic factors for one-nucleon transfer reactions are calculated and good agreement with experiments is observed.

Spectroscopy of even Sn nuclei and generalized-seniority breaking

Abstract Properties of even Sn nuclei are described in a broken-pair or generalized-seniority ( ν g ) scheme. Special attention is paid to the degree of ν g 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 ν g > 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 ν g 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% ν g = 4 admixtures in predominantly ν g = 2 states. Only ground states, 2 1 + and 3 1 − states have less than 10% of ν g = 4 admixtures. We argue that the main origin of ν g mixing is a particle-phonon coupling mechanism. A strong fragmentation of two-phonon 0 + , 2 + , 4 + states by ν g 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 ν g mixing. For natural-parity states this reduction is less; for 2 1 + and 3 1 − enhancements by ground-state correlations overcompensate the reduction by fragmentation.

Comparison between the bcs and the FBCS formalisms as approximations to the low-seniority shell model

Abstract A discussion is given of the discrepancies between the wave functions of single-closed-shell nuclei as obtained from the BCS formalism and those from the FBCS formalism. Sources of these discrepancies for the ground states are made clear and demonstrated by simple examples. The difference between the BCS and FBCS two-quasiparticle spectra may especially become large when the number of particles corresponds to a closed subshell structure and if subshells of low degeneracy occur near the Fermi level. As an illustration the states of the even N = 50 nuclei are calculated in both approximations and compared to those of the exact V ≦ 2 shell model. Particle number projection is the main effect in improving spectra. The parameters ua, va which minimize the ground state energy were found to be not the most suitable to calculate excited states.

Selectivity of the {16}O(e,e'pp) reaction to discrete final states.

16 O in this reaction, whereas other states mostly arise by the removal of a 3 P pair. This theoretical prediction has been supported recently by an analysis of the pair momentum distribution of the experimental data @1#. In this paper we present results of reaction calculations performed in a direct knockout framework where final-state interaction and one- and two-body currents are included. The two-nucleon overlap integrals are obtained from a calculation of the two-proton spectral function of 16 O and include both long-range and short-range correlations. The kinematics chosen in the calculations is relevant for recent experiments at NIKHEF and Mainz. We find that the knockout of a 3 P proton pair is largely due to the ~two-body !D current. The 1 S0 pair knockout, on the other hand, is dominated by contributions from the one-body current and therefore sensitive to two-body short-range correlations. This opens up good perspectives for the study of these correlations in the 16 O(e,e8 pp ) reaction involving the lowest few states in 14 C. In particular the longitudinal structure function f 00 , which might be separated with superparallel kinematics, turns out to be quite sensitive to the NN potential that is adopted in the calculations. @S0556-2813~98!00904-2#

Do we understand IBM parameters

Abstract A 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.

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.