Broken Pair Model Research Articles

Three-quasiparticle rotational bands in 101Rh: IBFBPM description and signature inversion of the πg9/2 orbital

High- and intermediate-spin level structures of the 101Rh nucleus have been studied using the reaction 70Zn+ 36S at 130 MeV bombarding energy. γ-rays were detected with the EUROGAM II detector array. Three new ΔI=1 rotational bands have been observed in this nucleus. The deduced level scheme is compared with results of calculations using Interacting Boson–Fermion plus Broken Pair Model. The model calculations give a consistent description of the one- and three-quasiparticle states providing fair agreement between the observed and calculated level energies and branching ratios. Experimental Routhians of the new high-spin bands and the πg 9/2 νh 11/2 bands in the neighbouring Rh and Ag nuclei have been found to exhibit signature inversion. This signature inversion can be interpreted qualitatively as the inversion of the two signatures of the proton g 9/2 orbital caused by triaxial nuclear shape with large positive γ parameter.

Lifetime measurements of high-spin states in101Agand their interpretation in the interacting boson fermion plus broken pair model

Lifetimes of 20 high spin states in Ag-101 in the range between 0.2 and 200 ps have been measuredand interpreted within the boson fermion plus broken pair model.

High-spin structure and electromagnetic transition strengths in104Cd

The recoil distance Doppler shift and Doppler shift attenuation techniques were employed to determine for the first time lifetimes of high spin states in Cd-104in the time range 0.3 ps less than equal to tau less than 1.2 ns. The new experimental results are discussed in the frame of the interacting boson plus broken pair model.

Collective and broken pair states of65,67Ga

Excited states of 65Ga and 67Ga nuclei were populated through the 12C(58Ni,αp) and 12C(58Ni,3p) reactions, respectively, and investigated by in-beam γ-ray spectroscopic methods. The NORDBALL array equipped with a charged particle ball and 11 neutron detectors was used to detect the evaporated particles and γ rays. The level schemes of 65,67Ga were constructed on the basis of γγ-coincidence relations up to 8.6 and 10 MeV excitation energy, and Iπ=27/2 and 33/2+ spin and parity, respectively. The structure of 65,67Ga nuclei was described in the interacting boson-fermion plus broken pair model, including quasiproton, quasiproton-two-quasineutron, and three-quasiproton fermion configurations in the boson-fermion basis states. Most of the states were assigned to quasiparticle + phonon and three quasiparticle configurations on the basis of their electromagnetic decay properties.

Level structure of99Nb

The $\ensuremath{\beta}$ decay of ${}^{97}\mathrm{Sr}$ to ${}^{97}\mathrm{Y}$ has been investigated using ion-guide on-line mass separation and a 10 Ge-detector array to record $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ coincidences to a detection limit well below that of former studies. Similarities are found in the $\ensuremath{\beta}$-decay patterns of ${}^{99}\mathrm{Zr}$ and of its isotone ${}^{97}\mathrm{Sr}$ and also in the $\ensuremath{\gamma}$-ray decay rates and branchings of the corresponding levels in their respective daughters ${}^{99}\mathrm{Nb}$ and ${}^{97}\mathrm{Y}$. This indicates a persisting influence of the ${d}_{5/2}$ neutron shell closure for ${}^{99}\mathrm{Nb}$. The level structure of ${}^{99}\mathrm{Nb}$ and the $\ensuremath{\beta}$-feeding pattern are discussed in the frame of the interacting boson-fermion plus broken pair model and the microscopic quasiparticle phonon model.

Nuclear structure of97Yin the interacting boson fermion plus broken pair model and the nature of the 3.523 MeV high-spin isomer

Nuclear structure of ${}^{97}\mathrm{Y}$ is described in the interacting boson fermion plus broken pair model, including quasiproton and quasiproton-two-quasineutron configurations in the basis states. In particular, the yrast bands and the decay of the ${27/2}^{\ensuremath{-}}$ high-spin isomer are accounted for in this approach.

Nucleon-pair shell model: Formalism and special cases

A formalism is described for a nucleon-pair shell model (NPSM) for even-even and even-odd nuclei. The building blocks of the model space are collective nucleon pairs of angular momenta J = 0,2,… for an even system, and nucleon pairs plus one unpaired nucleon for an odd system. Analytical formulas are given for the matrix elements of a general Hamiltonian. Without any space truncation, the NPSM is equivalent to the shell model in full space, while with a special choice for the building blocks and Hamiltonian it reduces to the broken pair model, the favored-pair model of Hecht and the fermion dynamical symmetry model.

Study of 116sn via neutron pickup and proton stripping reactions

The nucleus 116Sn has been studied via the neutron pickup reactions 117Sn(d,t) 116Sn and 117Sn( 3He, α) 116Sn, and via the proton stripping reactions 115In( 3He, d) 116 and 115In(α,t) 116Sn. Spectroscopic factors have been deduced from the 117Sn(d,t) and the 115( 3He, d) reactions for final states in 116Sn below E x = 3.8 MeV. By combining the ( l-transfers, observed in these reactions, spin assignments for various states can be given or limits on them can be set. Notably an unambiguous assignment of I π = 3 + can be made for the states at 2.997, 3.180, 3.416 and 3.709 MeV. Spectroscopic factors and their fragmentation are compared with those derived from the broken pair model and from a large-basis shell-model calculation involving both neutron quasi-particle excitations and proton 1p1h excitations.

Decays of 118In, 120In isomers to levels in 118Sn, 120Sn, and 122Sn.

The nuclear excited states of $^{118}\mathrm{Sn}$, $^{120}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$ were studied by means of the decays of 4.45-min $^{118}\mathrm{In}$ isomer, 46.2-sec and 47.3-sec $^{120}\mathrm{In}$ isomers, and 10.3-sec and 10.8-sec $^{122}\mathrm{In}$ isomers, respectively. The In activities were produced by the (n,p) reaction with 14-MeV neutrons on enriched samples of $^{118}\mathrm{Sn}$, $^{120}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$. The \ensuremath{\gamma} rays, measured with a Ge(Li) detector, were incorporated into separate level schemes, each resulting from the decay of an individual In isomer. The experimental level schemes of $^{118}\mathrm{Sn}$, $^{120}\mathrm{Sn}$, and $^{122}\mathrm{Sn}$ were compared with level schemes calculated on the basis of a broken-pair model that includes up to two broken pairs in the 50<N<82 shell. This model is reasonably successful in explaining the experimental data for these nuclides.

Application of realistic meson-exchange forces in the broken-pair model

A G-matrix, derived from a meson-exchange potential in nuclear matter, is applied to finite, semi-magic nuclei. For the open shell the broken-pair model, which can accommodate many single-particle levels, is used. The excitations of the closed shell are treated as particle-hole states. Energy spectra and electromagnetic transition densities are calculated for 88Sr and 58Ni. The energies of the non-collective states are well described. Pairing correlations in the ground state have almost the correct strength in a multishell model space. To improve the energies of the collective 2 + and 3 −1 states the inclusion of core-polarisation effects in the force is required. Transition charge densities for collective states become strongly surface-peaked by core-polarisation effects, as is observed in experiments. The effects of pairing correlations and core polarisation on the magnetic form factor of the 3.486 MeV 1 + state in 88Sr are found to be important.

Do we understand IBM parameters?

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.

Correlated-pair structure in nuclei and possible relation to IBM-2

The broken-pair model is used to study the nature of collective pair structure in even nuclei and a possible connection with the interacting-boson model IBM-2. In our self-consistent treatment there is no particle-hole ambiguity, such as has been reported in recent literature.

Remarkable properties of the broken-pair model: (II). Relation with the quasiparticle scheme

A non-spurious quasiparticle scheme is presented, its number-projection being exactly the broken-pair model. From this property, quantities needed in the broken-pair approach are easily evaluated by making use of the extreme simplicity of the quasiparticle algebra. Applications to the hamiltonian operator and to one-body operators are presented for seniority υ = 0, 1 and 2.

Remarkable properties of the broken-pair model: (I). The differential structure

The differential structure of the broken-pair model is exhibited. As a consequence, matrix elements of any operator acting in the k-broken-pair subspace (or between states with different broken-pair numbers) can be evaluated by making use of effective operators defined in the 0-broken-pair subspace only.

Analysis of IBFA-model assumptions with the broken-pair model

Assuming a correspondence of boson-model states and fermion-pair states, we use the broken-pair model to compute quantities Γ ab , Λ ab j and A j and check whether these numbers fulfill the relations adopted in IBFA-model fits. Results are shown for 125Xe and 131Xe. The part of the IBFA hamiltonian which changes the number of d-bosons by one, parametrized by Γ ab , can very well be represented in its usual form as a single-particle matrix element of the quadrupole operator. The part parametrized by A j seems to be also well justified. For the part parametrized by Λ ab j , a similarity is found between our computed numbers and IBFA-model fit prescriptions. A small class of terms is missing in IBFA-model fits however.

The broken-pair model versus the quasi-particle scheme: Two different formalisms?

The particle-number conserving Broken-Pair Model (BPM) and the Quasi-Particle Scheme (QPS) are shown to be nothing but two aspects of the same formalism. As a consequence, the old problem of the number-projection becomes elementary and BPM is algebraically as simple as QPS. Furthermore, owing to the existence of simple recursion formulas, BPM is also numerically as tractable as QPS.

Neutron excitations in even mass Sn nuclei

Abstract High-spin neutron quasi-particle excitations in the even-mass 110–118Sn 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 Jπ = 6+ state at 2480 keV in 110 Sn(T 1 2 = 8.3±0.4 ns ) , the Jπ = 8− state at 3440 keV in 112 Sn(T 1 2 = 0.58±0.06 ns ) , the Jπ = 8− state at 3190 keV in 114 Sn (T 1 2 = 0.35±0.20 ns ) and the Jπ = 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 110–114Sn 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 Eλ 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.

A broken-pair description of89Y,91Nb and93Tc

The low-energy properties of89Y,91Nb and93Tc are described in a broken-pair model. The shell model space for the protons consists of one major shell and for the neutrons particle-hole states within two major shells are taken into account. The effective interaction is assumed to be a simple Gaussian Serber force, which has proved to be the most successful in adjacent even nuclei.