Octupole Boson Research Articles

Quadrupole and octupole states in 152Sm using the proton–neutron interacting boson model

A scheme of solving the proton–neutron interacting boson model (IBM-2) in terms of the SU(3) basis is introduced, by which the IBM-2 coupled with an octupole boson is applied to describe the low-energy structure of the critical point nucleus, 152Sm. The results indicate that the spectral properties of both the positive-parity bands and negative-parity bands in this nucleus can be well captured by the IBM-2 calculations through a simple Hamiltonian, thus providing an example of the IBM-2 in a unified description of quadrupole and octupole states in a transitional system. In addition, a statistical analysis of the low-spin states in the model is also provided.

Coherent state model extension for the description of positive and negative parity bands in even-odd nuclei

A particle-core Hamiltonian is used to describe the lowest parity partner bands $K^{\pi}=1/2^{\pm}$ in $^{237}$U and $^{239}$Pu. The quadrupole and octupole boson Hamiltonian associated to the core is identical to the one previously used for the description of four positive and four negative parity bands in the neighboring even-even isotopes. The single particle space for the odd nucleon consists of three spherical shell model states, two of positive and one of negative parity. The particle-core Hamiltonian consists of four terms: a quadrupole-quadrupole, an octupole-octupole, a spin-spin and a rotational $\hat{I}^2$ interaction, with $\hat {I}$ denoting the total angular momentum. The parameters involved in the particle-core coupling Hamiltonian were fixed by fitting four particular energies in the two bands. The calculated excitation energies are compared with the corresponding experimental data as well as with those obtained with other approaches. Also, we searched for some signatures for a static octupole deformation in the considered odd isotopes.

New results for the missing quantum numbers labelling the quadrupole and octupole boson basis

The many $2^k$-pole boson states, $|N_kv_k\alpha_k I_kM_k>$ with $k=2,3$, realize the irreducible representation (IR) for the group reduction chains $SU(2k+1)\supset R_{2k+1}\supset R_3\supset R_2$. They have been analytically studied and widely used for the description of nuclear systems. However, no analytical expression for the degeneracy $d_v(I)$ of the $R_{2k+1}$'s IR, determined by the reduction $R_{2k+1}\supset R_3$, is available. Thus, the number of distinct values taken by $\alpha_k$ has been so far obtained by solving some complex equations. Here we derive analytical expressions for the degeneracy $d_v(I)$ characterizing the octupole and quadrupole boson states, respectively. The merit of this work consists of the fact that it completes the analytical expressions for the $2^k$-pole boson basis.

Unified description of three positive and three negative parity interacting bands

The coherent state model (CSM) is extended so that three negative parity bands are treated on equal footing with three positive parity bands. The six rotational bands are generated by projecting out angular momenta and parities from three intrisic orthogonal states which exhibit both quadrupole and octupole deformations. The projected states are, by construction, mutually orthogonal. In the space of projected states, a sub-space of a quadrupole and octupole multi-boson states, an effective quadrupole and octupole boson Hamiltonian is solved. The eigenstates of the model Hamiltonian are linked by multipole transition operators for which lowest order boson expressions are considered. The calculations involve 6 structure coefficients and two deformation parameters. All of them are fixed by a least square fit of the known experimental energies. Applications are made to Gd158, Yb172, Ra218, Ra226, Th232, U238, Pu238. Very good agreement is obtained for both excitation energies and transition probabilities. New signatures for octupole deformation, manifested in excited bands, are pointed out.

Interrelation between the isoscalar octupole phonon and the proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei

The interrelation between the octupole phonon and the low-lying proton–neutron mixed-symmetry quadrupole phonon in near-spherical nuclei is investigated. The one-phonon states decay by collective E3 and E2 transitions to the ground state and by relatively strong E1 and M1 transitions to the isoscalar 2 + 1 state. We apply the proton–neutron version of the interacting boson model including quadrupole and octupole bosons ( sdf -IBM-2). Two F -spin symmetric dynamical symmetry limits of the model, namely the vibrational and the γ -unstable ones, are considered. We derive analytical formulae for excitation energies as well as B( E1) , B( M1) , B( E2) and B( E3) values for a number of transitions between low-lying states.

Low-lying negative-parity bands in heavy nuclei: A phenomenological approach

A phenomenological analysis of theKπ=0−, 1−, 2− band spectra in actinides and few rare-earth nuclei is carried out within the coherent state model using an interacting boson Hamiltonian which includes quadrupole and octupole bosons. The bands are described as octupole boson excitations of intrinsic coherent wave functions associated to the model ground, beta and gamma bands. The calculation reproduces all available experimental energy spectra up to high angular momenta. Also theE1 branching ratios are fairly well reproduced. Different signatures of static octupole deformation are discussed.

Low-lying octupole bands in the coherent state model

The properties of the K π = 0 −, 1 −, 2 − octupole bands in actinides and few rare-earth nuclei are studied within the coherent state model using an effective Hamiltonian defined in a space spanned by six rotational bands. The octupole band head states are constructed as octupole boson excitations of the intrinsic coherent wave functions associated to the model ground, beta and gamma bands. The projected states have an aligned structure in the vibrational limit and a good K quantum number in the rotational regime. Energy spectra up to high angular momenta and E1 and E3 transition rates are computed. The results are in good agreement with the available experimental data.

Octupole bosons of negative parity in multi-level seniority boson mappings

The microscopic origin of the negative-parity f boson used in the interacting boson model for the description of low-lying collective octupole states is investigated by means of an approximate boson mapping procedure in the seniority scheme. The boson images of fermion pair and multipole operators are derived by preserving the computation relations of the associated Lie algebra. The physically interesting case of three shells with j1=j2-1=j3-3, the last shell having opposite parity to the other two, is studied in detail. Possibilities of calculations for realistic nuclei are discussed.

Octupole excitations in O(6) nuclei

The coupling is discussed of an octupole boson to an O(6) core in the interacting boson approximation, and the results are applied to several platinum isotopes.

A microscopic description of boson and fermion alignment in octupole bands of actinide nuclei

The rotational alignment of the octupole boson in negative-parity bands of actinide nuclei is investigated in the framework of the cranked random-phase approximation (CRPA).

Negative parity bands in 100Ru observed in the 100Mo(α, 4n)100Ru reaction

In the study of the 100Mo(α, 4n)100Ru reaction at Eα = 45 MeV the ground state band of 100Ru was excited up to Jπ = 10+ and a negative parity band up to Jπ = (15)−. In addition, two negative parity bands were observed, one of which probably has even and the other odd spin states. The experiments encompassed γ-ray angular distribution, coincidence, linear polarization and conversion electron measurements. New levels are reported at Ex = 5130, 5165 (Jπ = (13)−), 5280, 5717 and at 6201 keV (Jπ = (15)−). In addition spin or parity assignments were made for the Ex = 2529, 2953, 2965, 3141, 3356, 3505 and 4233 keV levels as Jπ = 5−, 7−, (6)−, 7−, (8)−, 9− and (11)−, respectively. A 3− state is for the first time observed at Ex = 2180 ± 20 keV in the 100Ru(α, α') reaction at Eα = 104 MeV. Multipolarities, conversion coefficients, branching and quadrupole/dipole amplitude mixing ratios have been determined for many transitions in 100Ru. From a detailed comparison of excitation energies and of the properties of many, even weak, transitions with the results of the interacting boson approximation model, it appears that this simple model provides a good overall parametrization. This supports the description of 100Ru as an anharmonic vibrator with quadrupole and octupole bosons as independent but interacting basic excitation modes. A negative parity band in 101Ru, of which a new level at Ex = 3474 keV is a candidate for the 272− member, is well described by coupling the h112 single particle to the 100Ru quadrupole excitation.

Negative parity bands in 100Ru and 150Sm and the interacting boson approximation

Ground-state band members up to J π = 10 + in 100Ru and up to 14 + in 150Sm and odd-spin negative parity states up to 15 − in both nuclei have been identified from (α, 4n) in-beam γ-ray and conversion electron spectra. The data are interpreted in terms of interacting quadrupole and octupole bosons.