Two-phonon Octupole Research Articles

Search for the two-phonon octupole vibrational state in 208Pb

We have performed an experiment to search for the two-phonon octupole vibrational state in 208Pb. Thick targets of 208Pb, 209Bi, 58,64Ni, and 160Gd were bombarded with 1305 MeV beams of 208Pb supplied by the ATLAS accelerator facility at Argonne. Gamma rays were measured using the Argonne-Notre Dame BGO gamma ray facility, consisting of 12 Compton suppressed Ge detectors surrounding an array of 50 BGO scintillators. We have identified some 30 known γ rays from 208Pb in coincidence spectra gated on low-lying transitions in 208Pb. In addition, after unfolding these spectra for Compton response, we observe broad coincident structures in the energy region expected for the decay of 2-phonon states. Furthermore, we have confirmed the placement of a previously observed 2485 keV γ ray in 207Pb and find no evidence consistent with the placement of this line in 208Pb.

Direct and multiple excitations in 96Zr from inelastic-scattering experiments

The excitation of doubly closed subshell 96Zr is studied in polarized d, d') as well as in unpolarized (p, p') and (d, d') reaction experiments at bombarding energies near 20 and 60 MeV. All excited states known from previous γ-spectroscopic studies have been resolved up to 4.1 MeV excitation energy. The data confirm that the low-lying spectrum is dominated by two-quasiparticle excitations, with the excitation strength being concentrated on the lowest states for each spin. The high collectivity of the 3 − 1 state is most remarkable and in line with recent level-lifetime results. The excitation energies and extracted isoscalar strengths compare well with QRPA results. Coupled- channel calculations, used to distinguish between one-step (two-quasiparticle) and two-step (four- quasiparticle) excitations, give only partial evidence concerning the existence of two-phonon octupole and quadrupole-octupole vibrational states.

One- and two-phonon octupole states in nuclei near 146Gd

Recent in-beam and other experiments have identified one- and two-phonon octupole excitations in nuclei with up to three valence particles outside 146Gd. It is shown that the observed deviations from harmonic vibration in complex multiparticle × octupole spectra as well as the anharmonicities of the two-phonon octupole states in 147Gd and 148Gd are quantitatively related to the one-particle × phonon anharmonicities observed in 147Tb and 147Gd.

Application of the Holstein-Primakoff boson expansion to two-phonon octupole states in 208Pb

Taking the coupling between the quadrupole and octupole interaction into account, the splitting of two-phonon octupole states in 208Pb and quadrupole moment Q(3-) are studied by using the generator coordinate method (GCM) and the Holstein-Primakoff boson expansion method (1940). The authors find that the energy splitting is small and depends more sensitively on the multipole force strength chi lambda ( lambda =2,3) than the quadrupole moment Q(3-).

Fast E1 transitions and evidence for octupole-octupole and quadrupole-octupole excitations in 144Sm.

The nucleus $^{144}\mathrm{Sm}$ has been studied with the (n,n'\ensuremath{\gamma}) reaction and lifetimes of many states have been extracted from the observed Doppler shifts of the deexciting \ensuremath{\gamma} rays. A large number of fast E1 transitions have been observed and have led to the identification of possible members of the octupole-octupole and the quadrupole-octupole multiplets. Substantial fragmentation of the two-phonon octupole strength is indicated.

An octupole two-phonon multiplet in 96Zr and its description within the spdf interacting boson model

Abstract Members of a two-phonon octupole vibrational multiplet in 96Zr and their mixing with other positive parity levels are discussed. Calculations within the spdf boson version of the interacting boson model which includes intruder configuration mixing are compared with the experimentally observed properties.

Low-Lying Excited States in213Rn and215Ra

Gamma rays from low-lying levels in 213 Rn and 215 Ra have been studied following the 208 Pb( 9 Be, 4n) 213 Rn and 206 Pb( 12 C, 3n) 215 Ra reactions. Spins and parities were determined by means of the measurements of γ ray angular distributions, linear polarizations and lifetimes. Enhanced E3 transitions have been observed between the ground and the first excited state. The enhancements were as high as 38±5 for 213 Rn and 34±2 for 215 Ra in Weisskopf unit. The enhancement is qualitatively explained by the particle-vibration coupling model. Cascade E3 transitions have been observed in both nuclei. The role of the two-phonon octupole vibration has been examined in relation to these cascade E3 transitions.

E0 decays of 0+ states in 146Gd: Search for two-phonon octupole excitations.

Conversion-electron measurements following the $^{144}(\mathit{\ensuremath{\alpha}}$,2n) and $^{144}\mathrm{He}$,n) reactions reveal high-energy E0 transitions at 3020, 3485, and 3639 keV. The lowest of these deexcites the known two-neutron pairing vibrational state in $^{146}\mathrm{Gd}$. It is not clear whether either of the others can be associated with the ${0}^{+}$ member of the ${3}^{\mathrm{\ensuremath{-}}}$\ifmmode\times\else\texttimes\fi{}${3}^{\mathrm{\ensuremath{-}}}$ two-phonon octupole multiplet.

Study of the shift of two-phonon poles in deformed nuclei by the method of boson expansions

The situation with regard to two-phonon collective states in even-even deformed nuclei is obscure. According to the Bohr-Mottelson model deformed nuclei must have two-phonon collective states; this was recently pointed out once more in [i]. According to the interacting boson model the low-lying states must include states with large two-boson components [2]. In the framework of the quasiparticle-phonon nuclear model [3] the study of the twophonon states showed [4] that allowance for the Pauli principle, i.e., allowance for the exact commutation relations between the phonons, leads to a shift of the two-phonon poles to higher energies. In [5], the corresponding secular equations were solved. Allowance for the Pauli principle leads to a shift of the centroids of the energy of the collective two-phonon states by 1-2 MeV. At excitation energies of 3-4 MeV the strength of the collective two-phonon states must be distributed over many nuclear levels. It was concluded on this basis in [5] that in even-even deformed nuclei there are no collective twophonon states. In the description of two-phonon collective states in deformed nuclei there is a contradiction between the quasiparticle-phonon model and the Bohr-Mottelson and interacting boson models. As is shown in [6], there is a contradiction between the quasiparticle-phonon model and the interacting boson model in the description of a number of other nonrotational states in deformed nuclei. We note that according to [7] allowance for the Pauli principle in even-even spherical nuclei does not lead to a large shift in the energies of the two-phonon states, in agreement with the experimental data on the twophonon collective states in spherical nuclei. An analysis of experimental data led to the conclusion in [8] that there are no twophonon collective states in deformed nuclei. New experimental data on 1~SEr in [9,10] showed that the levels previously treated as two-phonon levels have a dominant one-phonon component. The absence of two-phonon quadrupole states with energy less than 2 MeV in 168Er is explained in [i,Ii] by the large anharmonicity of the $ and ~ vibrations due to the shape of the nucleus in the form of a triaxial ellipsoid. The absence of two-phonon octupole states in a number of Ra, Th, and U isotopes [12] is explained in many studies by the existence of a stable octupole deformation. We note that the new experimental data on 168Er [9,13] agree well with calculations in the quasiparticle-phonon model and with the calculations in [14] of the structure of the single-phonon states and do not agree with the calculations in the interacting boson model. In view of the importance of clarifying the situation with regard to two-phonon collective states of even-even deformed nuclei, it is necessary to study the behavior of the two-phonon states by a different mathematical formalism. Since allowance for the Pauli principle in the two-phonon components of the wave functions plays a decisive role, it is expedient to make the calculations with phonons constructed from the operators of "true" bosons. It is necessary to establish whether there is a large shift of the twophonon poles in the problem when formulated in this way. The present paper is devoted to

Single- and Double-Octupole Excitations inGd148

In the two-valence-neutron nucleus $^{148}\mathrm{Gd}$, in-beam $^{148}\mathrm{Sm}(\ensuremath{\alpha},4n)$ and ($^{3}\mathrm{He}$,$3n$) measurements have identified nine ${\ensuremath{\nu}}^{2}\ifmmode\times\else\texttimes\fi{}\mathrm{octupole}$ levels with $3<I<14$. The measured half-life of the ${(\ensuremath{\nu}{f}_{\frac{7}{2}}^{2}\ifmmode\times\else\texttimes\fi{}{3}^{\ensuremath{-}})}_{{9}^{\ensuremath{-}}}$ state gives $B(E3,{9}^{\ensuremath{-}}\ensuremath{\rightarrow}{6}^{+})=55(6){B}_{\mathrm{W}}$. A high-lying ${12}^{+}$ level, which decays by $E3$ to the ${9}^{\ensuremath{-}}$ state, as well as a ${14}^{+}$ level are shown to be two-phonon octupole excitations of stretched ${\ensuremath{\nu}}^{2}\ifmmode\times\else\texttimes\fi{}{3}^{\ensuremath{-}}\ifmmode\times\else\texttimes\fi{}{3}^{\ensuremath{-}}$ character. All these results can be quantitatively derived from the experimental data for the coupling of one neutron to the core octupole observed in $^{147}\mathrm{Gd}$.

In-beam studies of the shell model nuclei around146Gd

We will discuss multiparticle yrast states around146Gd and analyse their properties in terms of the empirical shell model. Furthermore, we will consider the first known example of a nuclear two-phonon octupole excitation which was recently identified in147Gd. Finally, we will present results on a collective ΔI=2 ground band level sequence in the spherical six-valence-particle nucleus152Dy.

Search for two-octupole-phonon states in 208Pb

A search for two-phonon octupole vibrational states in 208Pb was carried out using the 207Pb(n th, γ) reaction at the High Flux Reactor of the Institut Laue-Langevin. The conversion electron spectrum was scanned with the spectrometer BILL with a sensitivity of 20 μb in the 4–6 MeV interval. Coincidence and singles γ-ray measurements were performed at the end of the thermal neutron beam guide H22-F reaching a sensitivity of 80 μb for energies above 0.511 MeV. In addition the singles spectrum was investigated with the pair spectrometer at the tangential beam facility. Levels have been observed at (energies in keV and parenthesis for tentative level identification and spin-parity assignments): 2614.4, 3 −; 3997, (3 −); 4084.7, 2 +; 4253, (2 −, 3 −); 4704, (2 −, 3 −); (4882.0), (0 +); (4904.9), (0 +); 4935, 2 +; (6343), (2 +) and the 0 −, 1 − capture state at 7367.9 keV. The 4882.0 keV level probably corresponds to the known two-neutron pairing vibration. Possible candidates for two-phonon octupole excitations are the (0 +)(4904.9) and 2 + 4935 keV states. The nuclear field theory formalism is used to calculate branching ratios and energies for states in 208Pb under several assumptions. The most inimportant result of the comparison of theory and experiment is that the experimental properties of the 2 + 4935 keV state favour the interpretation of this state as a two-phonon octupole vibration rather than as a one-phonon non-collective quadrupole state.

Yrast Octupole Excitations in the 146Gd Region

Octupole excitations frequently occur in the yrast lines of nuclei above 146Gd. One-particle phonon exchange coupling identified in the Tb isotopes gives rise to low-lying ΔI = 2 octupole excitations; two-particle phonon exchange coupling in Dy isotopes causes ΔI = 1 octupole excitations in the yrast lines above 3 MeV which deexcite by E1 transitions of ≃ 1 MeV. The predominant octupole nature of the low-lying 13/2+ states in the N = 83 nuclei is emphasized, and the two-phonon octupole character of a 19/2- level in 147Gd which decays by E3 to the 13/2+ (νf7/2 × 3-) state is discussed.