Boson Core Research Articles

Particle-type states in 137Ba

The study of the 137Ba level scheme has been extended in the framework of the interacting boson-fermion model. Two categories of negative-parity states up to excitation energies of 5 MeV were found. One is associated with the h112 hole-type family and another with the particle-type configurations placed above the N = 82 boson core. The calculated SU(5) energy spectrum as well as cumulative (d, p) cross sections are in good agreement with experimental data.

On N=3 super Korteweg–de Vries equation

A one-parameter family is constructed of N=3 supersymmetric and SO(3) symmetric extensions of the Korteweg–de Vries (KdV) equation as a Hamiltonian flow on a N=3 superconformal algebra and it is argued that it is nonintegrable for any choice of the parameter. Then a modified N=3 super KdV equation is proposed which possesses the higher order conserved quantities and so is a candidate for an integrable system. Upon reduction to N=2, it yields the recently discussed ‘‘would-be integrable’’ version of the N=2 super KdV equation. In the bosonic core it contains a coupled system of the KdV-type equation and a three-component generalization of the mKdV equation. A Hamiltonian formulation of the new N=3 super KdV equation as a flow on some contraction of the direct sum of two N=3 superconformal algebras is given.

Spectral anomalies of even-mass Hg isotopes.

The $^{184--200}\mathrm{Hg}$ isotopes are studied in the interacting-boson-approximation-plus-fermion-pair model. In general, energy levels up to I=22 can be reproduced quite well. In the low excitation energy region both the shape evolution and the (${8}^{+}$,${10}^{+}$,${12}^{+}$) triplet structure can be reproduced. The (${8}^{+}$,${10}^{+}$,${12}^{+}$) triplet structure can be understood as the saturation of isospin 1 fermion-pair interaction at the high spin end. The termination of triplet structure at I=12 strongly supports the (${\mathit{i}}_{13/2}$${)}^{2}$ band crossing. Striking agreements between the observed energy gaps of (${14}_{1}^{+}$,${12}_{1}^{+}$) and (${2}_{1}^{+}$,${0}_{1}^{+}$) states are considered as an indication of weak coupling between the boson core and the fermion pair. The B(E2,I\ensuremath{\rightarrow}I-2) are calculated and the spin dependence of the B(E2) values can be reproduced qualitatively. However, the detailed mass dependence is not correctly reproduced.

Interacting-boson-fermion-approximation description of negative-parity states in even-odd Yb isotopes.

The negative-parity energy levels of the even-odd Yb isotopes, $^{163}\mathrm{Yb}$, $^{165}\mathrm{Yb}$, $^{169}\mathrm{Yb}$, $^{171}\mathrm{Yb}$, and $^{173}\mathrm{Yb}$, are studied systematically within the framework of the extended interacting-boson-fermion-approximation (IBFA) model in which one odd fermion is couplied with a boson core. The boson core is described with the IBA model but allowing one boson to break into a quasifermion pair. The odd fermion is assumed to be in one of the ${\mathit{f}}_{7/2}$ and ${\mathit{p}}_{3/2}$ single-particle orbitals while the fermion pair is allowed to occupy the single-particle orbit ${\mathit{i}}_{13/2}$. It was found that the negative-parity energy levels of these even-odd Yb isotopes and the values of transition quadrupole moments for the ground-state rotational band of $^{173}\mathrm{Yb}$ can be reproduced in fairly good agreement with the observed data.

Structure of the Triplet of low-lying states in101Mo

The properties of the triplet of low-lying states in101Mo have been studied through spectroscopy of theγ radiation following thermal neutron capture in100Mo and β− decay of101Nb and through a measurement of the proton angular distributions in the100Mo(d,p) reaction with 14 MeV deuteron energy. The half-lives of the 13.5 keV state and the 57.0 keV 5/2+ state have been measured as 226(7) and 133(7)ns, respectively. These values and the quadrupole/dipole mixing ratios of the 13.5 keV and 43.5 keV transitions yield spin and parity 3/2+ for the 13.5 keV level. The E2 components in the 13.5 (3/2+ →1/2+) and 43.5 keV (5/2+→3/2+) transitions are ≦ 8·10−4 and 54(9)%, respectively. The possibility of an additional state near to the 57.0 keV level is discussed. IBFM/PTQM calculations, taking into consideration the transitional character of the100Mo boson core, account for the electromagnetic-transition and transfer-reaction pattern of the triplet of states.

Two- and four-quasiparticle states in the interacting boson model: Strong-coupling and decoupled band patterns in the SU(3) limit.

An extension of the interacting boson approximation model is proposed by allowing for two- and four-quasiparticle excitations out of the boson space. The formation of band patterns based on two- and four-quasiparticle states is investigated in the SU(3) limit of the model. For hole-type (particle-type) fermions coupled to the SU(3) prolate (oblate) core, it is shown that the algebraic K-representation basis, which is the analog of the strong-coupling basis of the geometrical model, provides an appropriate description of the low-lying two-quasiparticle bands. In the case of particle-type (hole-type) fermions coupled to the SU(3) prolate (oblate) core, a new algebraic decoupling basis is derived that is equivalent in the geometrical limit to Stephens’ rotation-aligned basis. Comparing the wave functions that are obtained by diagonalization of the model Hamiltonian to the decoupling basis, several low-lying two-quasiparticle bands are identified. The effects of an interaction that conserves only the total nucleon number, mixing states with different number of fermions, are investigated in both the strong-coupling and decoupling limits. All calculations are performed for an SU(3) boson core and the h11/2 fermion orbital.

K representation for odd-odd nuclei in the interacting boson-fermion-fermion model. II. Band mixing in the normal and conflicting case and electromagnetic properties.

The formation of band patterns in odd-odd nuclei is investigated in the SU(3) limit of the interacting boson-fermion-fermion model. For two holes (particles) coupled to the SU(3) prolate (oblate) core, we study the algebraic {ital K}-representation basis which is the analog of the strong-coupling basis of the geometrical model. In the case of a particle and a hole coupled to the SU(3) core, we derive a new algebraic basis which, in the limit of the large boson number, becomes equivalent to the semi-decoupling basis of the particle-rotor model. For a simple demonstration case which was proposed in the first part of this work, the interacting boson-fermion-fermion-model Hamiltonian is explicitly diagonalized in these algebraic bases and all bands, which derive their parentage from the (2{ital N},0) representation of the SU(3) boson core, are identified. Electromagnetic properties of low-lying bands are calculated and compared to the predictions of the geometrical model of Bohr and Mottelson. We also present an illustrative calculation for the realistic case ({pi}{ital h})(11/2,{nu}{ital i} 13/2) and identify several low-lying bands.

Signature property of odd- A nuclei in the interacting boson-fermion model

The signature dependence of energy levels and electromagnetic transitions (E2 and M1) in odd- A nuclei is studied in terms of the interacting boson-fermion model (IBFM). The odd- A nucleus is treated in the IBFM as a system of odd particles (fermions) coupled with boson cores described by the interacting boson model (IBM). There are three dynamical-symmetry limits in the IBM, and the boson cores in such limits are shown to produce different signature dependences in the IBFM. We also discuss the effects of the boson-fermion quadrupole-quadrupole and exchange interactions on the signature dependence. We then apply the IBFM to the nuclei 173Yb, 157Ho, 165Lu and 163Dy. The signature dependence observed in some of these nuclei resembles the one obtained with the boson core in one of the dynamical-symmetry limits. Including such cases, the IBFM describes various signature dependences in a unified way. The nucleus 173Yb is characterized by the SU(3) core, while the other three nuclei show situations between the O(6) and the SU(3) limits. The single-particle orbit π h 11 2 or ν f 7 2 is considered for the odd particle, except 163Dy where two single-particle orbits h 9 2 and f 7 2 are introduced. The results are compared with those of the rotating shell model and the particle-rotor model.

Mixed-symmetry states in lighter odd nuclei

In the interacting boson-fermion model for odd nuclei it is shown that mixed- symmetry boson states may occur at low excitation when neutrons and protons occupy the same shell-model orbits. In any of the forms of the interacting boson model (l, 21 IBM~, -3 or -4 in which there is more than one type of boson, it is possible to have states which are less than fully symmetric in the separate orbital and intrinsic spaces. Such states are said to be of mixed symmetry and are labelled by a partition of the boson number N. Calculations for even-even nuclei show that low-lying states are dominated by full symmetry and that the lowest states of mixed symmetry have the partition (N- 1, 11. These states of mixed symmetry have been identified experimentally, mainly through their Ml properties, and examples are the I+ states (3) at 3.08 MeV excitation in lshGd and the 2+ state (4) at 1.99 MeV in 14Ba. The boson model (5) for an odd nucleus (IBFM) consists of a single nucleon coupled to the boson structure for the even-mass core. In the IBM~ version of the model, which is appropriate for heavy nuclei with valence neutrons and protons in different orbits, each nucleus has a unique assignment of neutron and proton boson numbers N, and N, and a unique charge for the single nucleon. In this situation the states of the odd nucleus in which the bosons have mixed symmetry would be expected to lie at about the same excitation as in even-even nuclei (see above). However, in lighter nuclei, with valence neutrons and protons filling the same orbits, it is necessary to extend the boson model to IBM~ by introducing a third type of boson composed of a neutron and a proton in order to preserve isospin symmetry. Odd nuclei may also be described (6) in this region (IBFM~) but the single nucleon must now be vector coupled, in isospin, to the bosons. This implies that, in an odd-neutron nucleus, for example, the single nucleon spends part of its time as a neutron with an even-even boson core and part of its time as a proton with an odd-odd boson core. The question of the excitation energy of the mixed-symmetry states in the odd nuclei is then a more delicate one. Here we explore that question and show that in certain odd nuclei the mixed-symmetry states are at lower excitation than in the even-even nuclei. Consider a nucleus with an odd number n of nucleons beyond a double closed shell such as 40Ca or 56NNi. The number of bosons is then N= f(n - 1) and we shall discuss states with full symmetry (NI and with the lowest mixed symmetry (N- 1, 11. The possible total isospin may take the values T=tn, 3n- 1, in-2, . . ., and, from

IBFFM yrast states in odd-odd nuclei associated withO(6) andSU(3) limits

In the Interacting Boson-Fermion-Fermion Model (IBFFM) for odd-odd nuclei the yrast states are calculated for\(\tilde j_\pi = \tilde h_{1 1/2} ,\tilde j_v = \tilde i_{1 3/2} \), proton-neutron configurations coupled to theO(6) andSU(3) boson core. The results are discussed in terms of the strongly coupled/ decoupled band type criterion and in comparison to the peaceful and conflicting case of asymmetric rotor model.

Band structure and determination of K quantum numbers for odd-odd systems in the interacting boson-fermion-fermion model.

A method of attributing K quantum numbers to the bands of odd-odd nuclei in the interacting boson-fermion-fermion model is presented. In a particular demonstration case with a j/sub 1/ = (3/2 proton and a j/sub 2/ = (5/2 neutron coupled to the SU(3) boson core in the interacting boson-fermion-fermion model, we show explicitly the formation of the band pattern and transformation of the interacting boson-fermion-fermion model wave functions to the truncated-weak-coupling basis and to the K-representation basis, which leads to the identification of exact or approximate K quantum numbers. The same method gives analogous results for any combination j/sub 1/ and j/sub 2/ of proton and neutron orbitals.

A coriolis-like effect of the dynamical boson-fermion interaction in the interacting boson-fermion model

It is shown that in a particular basis the dynamical interaction of IBFM for a boson core coupled to a single- j particle in the SU(3) limit takes a tridiagonal form, as does the Coriolis interaction. Interference between this Coriolis-like effect in the boson-fermion dynamical interaction and the genuine Coriolis effect results in interesting features of IBFM: For a particular ratio of the interaction strengths, depending only on the angular momentum of the odd particle, the K = j band exactly follows the rotational energy rule, is completely uncoupled from the other bands and has exactly the same moment of inertia as a ground-state band of the core. A possible interpretation of this feature in terms of spectrum-generating supersymmetry is suggested.

SpinBF ??(5) boson-fermion dynamical symmetry and supersymmetry for odd-odd nuclei associated withU b(5) boson limit and exemplification for62Cu

Boson-fermion dynamical symmetry associated withU (5) boson core is introduced for odd-odd nuclei. An algorithm is constructed for the subsequent reduction appropriate for the boson-fermion group chain associated with an odd proton and neutron inj=3/2 configurations and the corresponding energy formula is given and exemplified for62Cu in the case of an associated supersymmetry.

Analogs of Gallagher-Moszkowski bands in IBFFM ? A relation to spectrum-generating supersymmetry?

The quantal analogs of the Gallagher-Moszkowski bands in the Interacting boson-fermion-fermion model (IBFFM) withSU (3) boson core are associated with the exact quantum numberKjp+jn and approximate quantum numberK-¦jp-jn¦ of IBFFM. For characteristic ratiosГ/δ it is shown that theKc=0 band in even-even IBM system, theK=jp andK=jn bands in the corresponding odd-even (IBFM) systems and theK=jp+j band in the corresponding odd-odd IBFFM system exhibit the supermultiplet pattern.

Study of Pt isotopes in the core excited interacting boson model 1

The core exited IBM model was applied to the Pt isotopes. It was found that the energy spectra of the high-spin states as well as those of the low-spin states can be reproduced quite well. Also, it was found that there is a structure transition between 186Pt and 188Pt. The B(E2) values of 184Pt were calculated and compared with recent experimental data. It was found that the general features of the B(E2) values can be reproduced qualitatively. The need of more boson core excitations is also discussed.

Coriolis coupling in the interacting boson fermion model

The properties of a boson core coupled to a single- j particle are examined in the framework of the SU(3) limit of the interacting boson fermion model. It is shown that the Coriolis interaction arises in a natural way in this model. Excitation energies are calculated in the large boson number approximation. The analogy to the particle plus rotor model is discussed.

351-01351-01351-01Boson-fermion dynamical symmetry for hypernuclei

Boson-fermion dynamical symmetry is introduced for hypernuclei with odd proton, odd neutron and hyperon in j=3/2 configurations and with SO(6) boson core.

Extension of Boson-Fermion dynamical symmetry to hypernuclei

Boson-fermion dynamical symmetry is introduced for the states in hypernuclei associated with odd protons, odd neutrons and odd hyperons in j= 3 2 configurations, coupled to the boson core with U B(5) symmetry.

Three dynamical boson-fermion symmetries for odd-odd nuclei

For odd-odd nuclei we introduce three dynamical boson-fermion symnetries associated with jπ=3/2, jυ=3/2 and UB(5) symmetry of the boson core. The corresponding energy formulas and quantum numbers for low-lying states are explicitly given.