Octupole Phonon Research Articles

Quadrupole and octupole collectivity in Ba143

Author(s): Morse, C; MacChiavelli, AO; Crawford, HL; Zhu, S; Wu, CY; Wang, YY; Meng, J; Back, BB; Bucher, B; Campbell, CM; Carpenter, MP; Chen, J; Clark, RM; Cromaz, M; Fallon, P; Henderson, J; Janssens, RVF; Jones, MD; Khoo, TL; Kondev, FG; Lauritsen, T; Lee, IY; Li, J; Potterveld, D; Santamaria, C; Savard, G; Seweryniak, D; Stolze, S; Weisshaar, D | Abstract: The neutron-rich barium nuclei have been the subject of intense interest due to the enhanced octupole correlations they are predicted to exhibit. The observation of enhanced octupole collectivity in Ba144,146 as measured in sub-barrier Coulomb excitation, consistent with static octupole deformation, has further heightened this interest. In the present work, these studies are extended to the neighboring odd-mass Ba143 to investigate the interplay between single-particle and collective octupole degrees of freedom. A new measurement of the first 92 - state lifetime is also presented. Reflection-Asymmetric Triaxial Particle Rotor Model calculations indicate that the negative-parity bands in Ba143 can be understood as a decoupled structure of νh9/2 parentage, while the positive-parity bands are built on a decoupled octupole phonon. No evidence for E3 excitation is observed in this work, but an upper limit is placed on the E3 matrix element to the lowest octupole band.

A solvable model for octupole phonons

A solvable model is proposed for the description of octupole phonons in closed-shell nuclei, formulated in terms of shell-model par\-ticle--hole excitations. With some simple assumptions concerning single-particle energies and two-body interactions, closed expressions are derived for the energy and wave function of the octupole phonon. In particular, it is shown that the components of the octupole phonon are proportional to Wigner $3j$ coefficients. This analytic wave function is proven to be exactly valid in light nuclei, which have $LS$ shell closures that coincide with those of the three-dimensional harmonic oscillator, and to be valid to a good approximation in heavier nuclei, which have $jj$ shell closures due to the spin--orbit interaction. The properties of the solvable model are compared with the results of a realistic shell-model calculation for $^{208}$Pb.

Evidence of octupole-phonons at high spin in 207Pb

A lifetime measurement of the 19/2− state in 207Pb has been performed using the Recoil Distance Doppler-Shift (RDDS) method. The nuclei of interest were produced in multi-nucleon transfer reactions induced by a 208Pb beam impinging on a 100Mo enriched target. The beam-like nuclei were detected and identified in terms of their atomic mass number in the VAMOS++ spectrometer while the prompt γ rays were detected by the AGATA tracking array. The measured large reduced transition probability B(E3,19/2−→13/2+)=40(8) W.u. is the first indication of the octupole phonon at high spin in 207Pb. An analysis in terms of a particle-octupole-vibration coupling model indicates that the measured B(E3) value in 207Pb is compatible with the contributions from single-phonon and single particle E3 as well as E3 strength arising from the double-octupole-phonon 6+ state, all adding coherently. A crucial aspect of the coupling model, namely the strong mixing between single-hole and the phonon-hole states, is confirmed in a realistic shell-model calculation.

Decay properties of the level in 96Mo

The first excited level of 96Mo was investigated in a high-statistics experiment using the 95Mo(n, γγ) cold neutron capture reaction. The measurements used the high cold neutron flux from the research reactor at Institut Laue-Langevin and employed the highly-efficient EXILL array to detect γ-ray coincidences. The recorded statistics allow identification of decay branches with only a small relative intensity including the E3 decay. With the knowledge of the newly measured branching ratio and the known transition probability, the lifetime of the level was determined and, subsequently, the strength of the other decay branches of the octupole phonon were calculated. The extracted electromagnetic decay strengths are compared to the systematics of the stable even–even molybdenum isotopes and values calculated in a Skyrme-force based quasiparticle random phase approximation and in a cluster approach. Additionally, the decay branch to the low-lying quadrupole isovector level was observed.

Octupole phonon model based on the shell model for octupole vibrational states

A model is proposed for a description of the octupole vibrational states based on the nuclear shell model. In this model, a one-octupole-phonon representing the collective octupole vibration across the magic core is introduced onto the shell-model states that are microscopically calculated within the valence nucleon space. With this model, a unified description is now possible for the pure shell-model states made by valence nucleons, and the octupole-phonon states excited on the shell-model states. The model is applied to various nuclei around the $^{208}\mathrm{Pb}$ nucleus. Energy levels and electric octupole transition probabilities are well reproduced for both the pure shell-model states and the octupole vibrational states.

The γ-ray spectroscopy studies of low-spin structures in 210Bi and 206Tl using cold neutron capture reactions

The γ-coincidence studies of low-spin structures of 210Bi and 206Tl are presented. The 210Bi nucleus, populated in thermal neutron capture reaction, was investigated using EXILL HPGe array at Institut Laue-Langevin in Grenoble. The experimental results were compared to the shell-model calculations allowing to draw the conclusions on the nature of the low-spin excitations populated below the neutron binding energy in 210Bi (4.6 MeV). It has been found that some levels cannot be described by the valence proton and neutron couplings, but may arise from couplings of valence particles to the 3- octupole phonon of the doubly magic 208Pb core. Moreover, preliminary results of a low-spin structure measurements of 206Tl by the γ-coincidence technique, making use of the 205Tl(n,γ)206Tl reaction at the FIPPS prompt γ-ray spectroscopy facility of ILL are shown. The population of a large number of excited states of 206Tl above the ground state up to the neutron binding energy (at 6.5 MeV), within a few units of spin is expected. The analysis involving double and triple γ-coincidences and γγ-angular correlations will allow to significantly extend the experimental information on the energy and spin-parity of the levels in 206Tl. This will help shedding light on the proton-hole and neutron-hole couplings near the doubly magic core 208Pb.

Level lifetimes and the structure of Xe134 from inelastic neutron scattering

The level structure of $^{134}\mathrm{Xe}$ was studied with the inelastic neutron scattering reaction followed by $\ensuremath{\gamma}$-ray detection. A number of level lifetimes were determined for the first time with the Doppler-shift attenuation method and the low-lying excited states were characterized. From this new spectroscopic information, the third excited state, a ${0}^{+}$ level which had only been observed in a previous inelastic neutron scattering study, was verified. Reduced transition probabilities were calculated; comparisons were drawn with a vibrational description of the nucleus and found lacking. The ${3}^{\ensuremath{-}}$ octupole phonon has been confirmed, and the complete negative-parity multiplet resulting from the $\ensuremath{\nu}(1{h}_{11/2}2{d}_{3/2})$ configuration has also been tentatively identified for the first time in the $N=80$ isotones.

Shell evolution of stable N = 50-56 Zr and Mo nuclei with respect to low-lying octupole excitations

.For the N = 50-56 zirconium (Z = 40) and molybdenum (Z = 42) isotopes, the evolution of subshells is evaluated by extracting the effective single-particle energies from available particle-transfer data. The extracted systematic evolution of neutron subshells and the systematics of the excitation energy of the octupole phonons provide evidence for type-II shape coexistence in the Zr isotopes. Employing a simplistic approach, the relative effective single-particle energies are used to estimate whether the formation of low-lying octupole-isovector excitations is possible at the proposed energies. The results raise doubts about this assignment.

Role of triple phonon excitations in large angle quasi-elastic scattering of very heavy mass systems

We study the effect of multi-phonon excitations on large-angle quasi-elastic scattering of massive systems using the full order coupled-channels formalism. We especially investigate the role of triple phonon excitations of the target and projectile nuclei on the quasi-elastic scattering cross-section as well as the barrier distribution for [Formula: see text]Cr, [Formula: see text]Fe, [Formula: see text]Ni and [Formula: see text]Zn + [Formula: see text]Pb systems. It is shown that the calculations taken into account, the triple octupole phonon excitations of the target and triple quadrupole phonon excitations of the projectile for these systems can explain the experimental data of the quasi-elastic cross-section and the quasi-elastic barrier distribution. These results indicate that the coupled-channels formalism is still valid even for the very heavy mass systems.

Approaching complete low-spin spectroscopy ofBi210with a cold-neutron capture reaction

The low-spin structure of the 210Bi nucleus was investigated in the neutron capture experiment 209Bi(n,γ )210Bi performed at ILL Grenoble at the PF1B cold-neutron facility. By using the EXILL multidetector array, consisting of 46 high-purity germanium crystals, and γγ-coincidence technique, 64 primary γ rays were observed (40 new) and a total number of 70 discrete states (33 new) were located below the neutron binding energy in 210Bi. The analysis of the angular correlations of γ rays provided information about transitions multipolarities, which made it possible to confirm most of the previously known spin-parity assignments and helped establish new ones. The obtained experimental results were compared to shell-model calculations involving one-valence-proton, one-valence-neutron excitations outside the 208Pb core. It has been found that while up to the energy of ∼2 MeV each state observed in 210Bi has its calculated counterpart; at higher excitation energies some levels cannot be described by the valence particle couplings. These states may arise from couplings of valence particles to the 3− octupole phonon of the doubly magic 208Pb core and may serve as a testing ground for models which describe single particle-phonon excitations.

Decay of quadrupole-octupole1−states inCa40andCe140

Background: Two-phonon excitations originating from the coupling of two collective one-phonon states are of great interest in nuclear structure physics. One possibility to generate low-lying $E1$ excitations is the coupling of quadrupole and octupole phonons. Purpose: In this work, the $\gamma$-decay behavior of candidates for the $(2_1^+\otimes 3_1^-)_{1^-}$ state in the doubly-magic nucleus $^{40}$Ca and in the heavier and semi-magic nucleus $^{140}$Ce is investigated. Methods: $(\vec{\gamma},\gamma')$ experiments have been carried out at the High Intensity $\gamma$-ray Source (HI${\gamma}$S) facility in combination with the high-efficiency $\gamma$-ray spectroscopy setup $\gamma^3$ consisting of HPGe and LaBr$_3$ detectors. The setup enables the acquisition of $\gamma$-$\gamma$ coincidence data and, hence, the detection of direct decay paths. Results: In addition to the known ground-state decays, for $^{40}$Ca the decay into the $3^-_1$ state was observed, while for $^{140}$Ce the direct decays into the $2^+_1$ and the $0^+_2$ state were detected. The experimentally deduced transition strengths and excitation energies are compared to theoretical calculations in the framework of EDF theory plus QPM approach and systematically analyzed for $N=82$ isotones. In addition, negative parities for two $J=1$ states in $^{44}$Ca were deduced simultaneously. Conclusions: The experimental findings together with the theoretical calculations support the two-phonon character of the $1^-_1$ excitation in the light-to-medium-mass nucleus $^{40}$Ca as well as in the stable even-even $N=82$ nuclei.

A particle-number conserving microscopic approach to octupole deformation of normal deformed and superdeformed states in 194Pb

The left–right asymmetric deformation of normal deformed (ND) and superdeformed (SD) states of 194 Pb has been investigated in the framework of the parity-symmetry projection of the highly truncated diagonalization approach (HTDA), which is suited to treat the correlations in an explicitly particle-number conserving microscopic approach. A Skyrme energy density functional using the SIII and SkM* interactions has been considered to treat the particle–hole channel, whereas a density-independent δ force has been adopted for the residual interaction. The obtained results are compared with previous approaches. The calculated octupole phonon excitation energy is found to be in good qualitative agreement with available data in the ND state.

Core excitations across the neutron shell gap in 207Tl

The single closed-neutron-shell, one proton–hole nucleus 207Tl was populated in deep-inelastic collisions of a 208Pb beam with a 208Pb target. The yrast and near-yrast level scheme has been established up to high excitation energy, comprising an octupole phonon state and a large number of core excited states. Based on shell-model calculations, all observed single core excitations were established to arise from the breaking of the N=126 neutron core. While the shell-model calculations correctly predict the ordering of these states, their energies are compressed at high spins. It is concluded that this compression is an intrinsic feature of shell-model calculations using two-body matrix elements developed for the description of two-body states, and that multiple core excitations need to be considered in order to accurately calculate the energy spacings of the predominantly three-quasiparticle states.

One-phonon octupole vibrational states in 211At, 212Rn, 213Fr and 214Ra with N = 126

Excited high spin states in 211At, 212Rn, 213Fr and 214Ra with N = 126 are reorganized and interpreted in terms of the stretched weak coupling of an octupole 3− phonon. Nearly identical sequences of levels with ΔI = 3 and the parity change are found, for the first time, up to 25− for 20 states of 214Ra, up to 35− for 36 states of 212Rn and up to 53/2+ for 16 states of 213Fr. The stretched weak coupling of an octupole phonon is extended up to the highest excitation energy of 11355 keV for 212Rn which has the largest experimental B(E3) value of 44.1(88) W.u. for the 11− → 82+ transition. The stretched weak coupling of an octupole 3− phonon needs to be considered when single particle configurations are assigned to high spin states. Average octupole excitation energies of 657(51) keV for 211At, 1101(28) keV for 212Rn, 667(25) keV for 213Fr, and 709(25) keV for 214Ra are obtained. The calculated level enegies are in a good agreement with the experimental level energies within the error limit of 4.3%.

One-phonon octupole vibrational states in 136Xe, 137Cs, 138Ba, 140Ce and 142Nd with N = 82

Excited high spin states in 136Xe, 137Cs, 138Ba, 140Ce and 142Nd with N = 82 are reorganized and interpreted in terms of the weak coupling mode of an octupole 3− phonon. Nearly identical sequences of levels with ΔI = 3 and Δπ = yes built on 17/2+ and 23/2− states are found, for the first time, up to 29/2+ and 35/2−, respectively, for 22 states of 137Cs . Also, nearly identical sequences of levels with ΔI = 3 and Δπ = yes built on the 6+ and 9− states are found, for the first time, up to 14+ and 17−, respectively, for 18 states of 136Xe, up to 14+ and 17−, respectively, for 24 states of 138Ba and up to 11+ and 14−, respectively, for 14 states of 140Ce. New spins and parities are assigned, tentatively, to the high spin states of these nuclei based on the weak coupling mode of an octupole 3− phonon. The weak coupling of an octupole 3− phonon needs to be considered when single particle configurations are assigned to high spin states. Neutron particle-hole states (νh 11/2 −1 f 7/2 +1 ) with weak coupling of an octupole 3− phonon are proposed, for the first time. The νh 11/2 −1 f 7/2 +1 excitation energies (E ext(1p1h)) are nearly constant with increasing of Z. One-phonon excited states in 136Xe, 137Cs, 138Ba and 140Ce have the stretched weak coupling configurations of ΔI = 3. But one-phonon excited states in 142Nd show the non-stretched weak coupling configurations of an octupole phonon with ΔI = 3 and 2.

Search for possible one- and two-phonon octupole vibrational states in 134Sb, 134, 135Te, 135, 136I, 137Xe and 139Ba near 132Sn

High spin states of 134Sb, 134, 135Te, 135, 136I, 137Xe and 139Ba near 132Sn are reanalysed in order to search for octupole phonon vibrational states. New spins and parities are tentatively assigned to the 2203.9 keV state in 137Xe and the 1976.6 and 2091.7 keV states in 139Ba from the state energy plots of the N = 82 and 83 nuclei. High spin states of 134Sb, 134, 135Te, 135, 136I, 137Xe and 139Ba connected by E1, E3/M2 and E3 transitions are proposed, for the first time, as zero-, one- and two-phonon octupole vibrational (POV) states. One- and two-POV states in 134Sb and 135Te are built on a 7− (πg7/2νf7/2) state and a 19/2− (νf7/2 ⊗ 6) state, respectively. One-POV states built on the 19/2− (νf7/2 ⊗ 6) and the 21/2− (νh9/2 ⊗ 6) states coexist in 137Xe. Then, one- and two-POV states in 139Ba are built only on the 21/2− (νh9/2 ⊗ 6) state. One- and two-POV states in 134Te are built on the 6 state with some mixing with the 6 state.

Study of vibrational signatures in 102Ru

Abstract A Mo 100 ( α , 2 n ) Ru 102 fusion evaporation experiment, performed at the HORUS cube spectrometer at the Cologne FN-Tandem accelerator, is presented and discussed. Via the analysis of γγ coincidences, it was possible to extend the level scheme with 40 new levels and 81 decays. Several new spins and multipole mixing ratios were determined using the γγ angular correlation technique. In addition, a DSAM analysis was performed and 14 new effective lifetimes were determined in the femtosecond range. Thus, several effective transition strengths were determined. Investigating the phononic structure, candidates for the quadrupole–octupole phonon multiplet 2 1 + ⊗ 3 1 − were found. The data is compared to calculations within the Interacting Boson Model (IBM-1) in the U(5) limit, the O(6) limit as well as a transitional class U(5)–O(6). The low spin level energies show characteristics of multiphonon excitations and point towards 102Ru resembling an anharmonic vibrational nucleus. The B ( E 2 ) transition strengths do not exactly match this picture, and are described in a better way using the U(5)–O(6) calculation.

New Results on Octupole Collectivity

Octupole correlations play an important role in determining the level structure of nuclei throughout the periodic chart. Microscopically, octupole correlations are the result of the long-range, octupole-octupole interaction between nucleons occupying pairs of orbitals which differ in both orbital and total angular momentum by 3 units. A review of some of the most recent findings on octupole correlations is given. Emphasis is placed on new results from the actinide region, where two distinct collective modes have long been identified: octupole vibration and octupole deformation. These new results include negative-parity structures which appear to evolve from an octupole vibration into a static octupole deformed mode. In addition, newly observed rotational structures built on an excited 0+ state have been tentatively associated with a double-octupole phonon excitation. These newly observed properties can be successively described by calculations based on the concept of rotational-aligned octupole phonon condensation.

Coupled–Channels Analyses For Heavy–Ion Fusion Reactions of <sup>16</sup>O+<sup>92</sup>Zr,<sup>144,148</sup>Sm Systems

We study in detail the fusion reaction of 16 O with 92 Zr and 144,148 Sm at sub-barrier energies with coupled-channels framework using the error function potential for the nuclear potential. In particular, we investigate the effects of multiphonon excitations in target nuclei on experimental fusion cross section and barrier distributions for these reactions. We show that the present coupled-channels calculations well account for the experimental data of the fusion cross section as well as the fusion barrier distributions. It is shown that the coupled-channels calculations taking into account the coupling up to double quadrupole phonon excitations in 92 Zr well reproduce the experimental fusion cross section as well as fusion barrier distribution for 16 O+ 92 Zr. However, for 16 O+ 144 Sm, coupling to single quadrupole and octupole phonon states in 144 Sm can well explain the experimental data. And the coupling up to triple quadrupole phonon states and double octupole phonon excitations in 144 Sm are needed in order to reproduce the experimental data. Our study indicates the error function potential is adequate for analyses of the heavy-ion fusion reactions. Received: 20 November 2009; Revised: 17 April 2010; Accepted: 18 April 2010

StrongM1components in3i−→31−transitions in nearly spherical nuclei: Evidence for isovector-octupole excitations

An evaluation of data obtained in ($n,{n}^{\ensuremath{'}}\ensuremath{\gamma}$) experiments reveals strong $M1$ ${3}_{i}^{\ensuremath{-}}\ensuremath{\rightarrow}{3}_{1}^{\ensuremath{-}}$ transitions in nuclei near the $N=50$ ($^{92}\mathrm{Zr}$, $^{94}\mathrm{Mo}$, and $^{96}\mathrm{Mo}$), $Z=50$ ($^{112}\mathrm{Cd}$ and $^{114}\mathrm{Cd}$), and $N=82$ ($^{144}\mathrm{Nd}$) shell closures. The observed $\ensuremath{\langle}{3}_{1}^{\ensuremath{-}}||M1||{3}_{i}^{\ensuremath{-}}\ensuremath{\rangle}$ matrix elements scale with the $\ensuremath{\langle}{2}_{1}^{+}||M1||{2}_{\mathrm{ms}}^{+}\ensuremath{\rangle}$ matrix elements connecting the mixed-symmetric and symmetric quadrupole excitations. In accordance with a picture of a mixed two-component quantum system, the energy difference between the initial ${3}_{i}^{\ensuremath{-}}$ state and the ${3}_{1}^{\ensuremath{-}}$ octupole phonon is proportional to the $|\ensuremath{\langle}{3}_{1}^{\ensuremath{-}}||E3||{0}_{\mathrm{gs}}^{+}\ensuremath{\rangle}|$ matrix element. The possibility of assigning the ${3}^{\ensuremath{-}}$ states of interest as octupole isovector states is discussed.