Signature Splitting Research Articles

Generalization of the variable-moment-of-inertia model to description of rotation of odd-odd nuclei

The most complete compilation of rotational bands of odd-odd nuclei with masses 40 ≤ A ≤ 254 has been developed on the basis of the ENSDF 2006 file of evaluated nuclear data. To describe the observed energies of rotational levels, generalization of the variable-moment-of-inertia model, taking into account the signature splitting in the bands with K = 0 and 1, has been proposed. An adequate description of the energy behavior of majority of rotational bands is obtained and systematic behavior of the model parameters in all regions of deformed nuclei is demonstrated. The model description is used to combine fragments of rotational bands, as well as to exclude unnecessary and recover missed energy levels.

Band properties of the transitional nucleusPt187

High-spin states in $^{187}\mathrm{Pt}$ have been studied experimentally using the $^{173}\mathrm{Yb}$($^{18}\mathrm{O}$, $4n$) reaction at beam energies of 78 and 85 MeV. The previously known bands based on the $\ensuremath{\nu}{i}_{13/2},\ensuremath{\nu}7/{2}^{\ensuremath{-}}[503]$, and $\ensuremath{\nu}{i}_{13/2}^{2}\ensuremath{\nu}j$ configurations have been extended to high-spin states, and new rotational bands associated with the $\ensuremath{\nu}3/{2}^{\ensuremath{-}}[512]$ and $\ensuremath{\nu}1/{2}^{\ensuremath{-}}[521]$ Nilsson orbits have been identified. The total Routhian surface calculations indicate that the transitional nucleus $^{187}\mathrm{Pt}$ is very soft with respect to $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ deformations. The band properties, such as level spacings, band crossing frequencies, alignment gains, and signature splittings, have been compared with the systematics observed in neighboring nuclei and have been interpreted within the framework of the cranked shell model. The rotational bands show different band crossing frequencies, which can be explained by the alignment either of ${i}_{13/2}$ neutrons or of ${h}_{9/2}$ protons. Importantly, evidence is presented for a $\ensuremath{\pi}{h}_{9/2}$ alignment at very low frequency in the $\ensuremath{\nu}7/{2}^{\ensuremath{-}}[503]$ band. The proton nature of the band crossing is strongly suggested by comparing the measured $B(M1;I\ensuremath{\rightarrow}I\ensuremath{-}1)/B(E2;I\ensuremath{\rightarrow}I\ensuremath{-}2)$ ratios with the theoretical values from the semiclassical D\onau and Frauendof approach.

High-K band in 140Gd

High-spin states in the neutron-deficient140Gd nucleus have been studied with the 92Mo(54Fe,a2p) reaction at a beam energy of 240 MeV. The level scheme of 140Gd was considerably extended from what was previously known. In this work we concentrate on one of the 9 bands observed, which presents relatively strong M1 transitions and negligible signature splitting, and has an isomeric band-head, indicating a strongly coupled or high-K configuration. We compare this band to the Kp = 8- bands observed in N=74 isotones and propose a similar configuration assignment, but with a somewhat larger deformation.

Nuclear shape and structure in neutron-richTc110,111

The high-spin nuclear structure of Tc isotopes is extended to more neutron-rich regions based on the measurements of prompt \ensuremath{\gamma} rays from the spontaneous fission of $^{252}\mathrm{Cf}$ at the Gammasphere. The high-spin level scheme of $N=67$ neutron-rich $^{110}\mathrm{Tc}$ ($Z=43$) is established for the first time, and that of $^{111}\mathrm{Tc}$ is extended and expanded. The ground band of $^{111}\mathrm{Tc}$ reaches the band-crossing region, and the new observation of the weakly populated $\ensuremath{\alpha}=\ensuremath{-}1/2$ member of the band provides important information on signature splitting. The systematics of band crossings in the isotopic and isotonic chains and a CSM calculation suggest that the band crossing of the ground band of $^{111}\mathrm{Tc}$ is due to alignment of a pair of ${h}_{11/2}$ neutrons. The best fit to signature splitting, branching ratios, and excitations of the ground band of $^{111}\mathrm{Tc}$ by the rigid triaxial rotor plus particle model calculations result in a shape of ${\ensuremath{\varepsilon}}_{2}=0.32$ and $\ensuremath{\gamma}=\ensuremath{-}{26}^{\ifmmode^\circ\else\textdegree\fi{}}$ for this nucleus. Its triaxiality is larger than that of $^{107,109}\mathrm{Tc}$, which indicates increasing triaxiality in Tc isotopes with increasing neutron number. The identification of the weakly populated $K+2$ satellite band provides strong evidence for the large triaxiality of $^{111}\mathrm{Tc}$. In $^{110}\mathrm{Tc}$, the four lowest-lying levels observed are very similar to those in $^{108}\mathrm{Tc}$. At an excitation of 478.9 keV above the lowest state observed, ten states of a $\ensuremath{\Delta}I=1$ band are observed. This band of $^{110}\mathrm{Tc}$ is very analogous to the $\ensuremath{\Delta}I=1$ bands in $^{106,108}\mathrm{Tc}$, but it has greater and reversal signature splitting at higher spins.

Pairing and signature splitting in pf-shell nuclei

A comparative study of light pf shell nuclei using cranked Nilsson–Strutinsky model and the spherical shell model indicates that some of the signature splitting between the partner bands in odd-A nuclei originates from a gradual decrease in the contents of the pairing energy as spin increases.

First observation of excited states inCs114: Spectroscopy of the yrastν(h11/2)⊗π(h11/2)band

Excited states have been observed for the first time in the very neutron-deficient ${}_{55}^{114}{\mathrm{Cs}}_{59}$ nucleus. The assignment to $^{114}\mathrm{Cs}$ was made by detecting $\ensuremath{\gamma}$ rays in coincidence with evaporated charged particles and with recoiling evaporation residues. A rotational band has been observed up to spin $21\ensuremath{\hbar}$ (tentatively $25\ensuremath{\hbar}$). Excitation-energy systematics and a study of quasiparticle alignments suggest that the band is based on the $\ensuremath{\nu}({h}_{11/2})\ensuremath{\bigotimes}\ensuremath{\pi}({h}_{11/2})$ configuration. Unlike bands based on this configuration in heavier cesium isotopes, only one signature partner is observed, and there is no evidence for signature inversion. These observations agree with theoretical calculations which predict that Coriolis-induced signature splitting should dominate at $N=59$.

Cranked Nilsson-Strutinsky vs the spherical shell model: A comparative study ofpf-shell nuclei

A comparative study is performed of a deformed mean field theory, represented by the cranked Nilsson-Strutinsky (CNS) model, and the spherical shell model. Energy spectra, occupation numbers, B(E2)-values, and spectroscopic quadrupole moments in the light pf shell nuclei are calculated in the two models and compared. The result is also compared to available experimental data which are generally well described by the shell model. Although the Nilsson-Strutinsky calculation does not include pairing, both the subshell occupation numbers and quadrupole properties are found to be rather similar in the two models. It is also shown that ``unpaired'' shell model calculations produce very similar energies as the CNS at all spins. The role of the pairing energy in the description of backbending and signature splitting in odd-mass nuclei is also discussed.

Table of three-quasiparticle rotational bands in deformed nuclei, 153 ⩽ A ⩽ 187

The experimentally observed level structures based on three-quasiparticle (3qp) states are classified according to their intrinsic structures, and other properties are deduced from measurements such as B( M1)/ B( E2) ratios, | g K − g R| values, lifetimes, etc. The present table lists data for a total of 168 such structures which have been extracted from the literature for 55 nuclides in the mass region A = 153–187 ( Z = 63–78, N = 88–112), with the majority of these bands in the A = 180 region (28 bands in seven Re isotopes alone). Nuclear models used for the interpretation of 3qp structures, generalization of the Gallagher–Moszkowski (GM) rules to 3qp states, and high-spin features such as t-bands, high- K isomers, signature splitting, signature inversion, alignment, etc., are discussed briefly. The literature cutoff date for extraction of data for known 3qp structures is July 15, 2005.

Shape trends and triaxiality in neutron-rich odd-mass Y and Nb isotopes

New level schemes of odd-Z 99,101Y (Z = 39) and 101,105Nb (Z = 41) are established based on the measurement of prompt gamma rays from the fission of 252Cf at Gammasphere. Bands of π5/2+[422], π5/2−[303] and π3/2−[301] are observed and extended to provide spectroscopic information concerning nuclear shapes in this important odd-Z region. In combination with the level structure of the odd-Z Tc (Z = 43), Rh (Z = 45) and the neighbouring even-Z isotopes the level systematics, signature splittings and kinematic and dynamic moments of inertia of the bands in the Y and Nb isotopes are discussed in terms of shape transition and triaxiality. The pronounced difference observed in the signature splittings between Y and Tc, Rh isotopes is interpreted as evidence of the axially symmetric deformed shape in the Y isotopes, and, as previously reported, large and near maximum triaxiality in Tc–Rh isotopes. The likely lowering of crossing frequencies of the ground-state bands in Tc and Rh isotones in comparison with those in Y isotones also implies a shape transition from axially symmetric deformed shapes in Y nuclei to triaxiality in Tc and Rh isotones. Triaxial-rotor-plus-particle model calculations strongly support a pure axially symmetric shape with large quadrupole deformation in Y isotopes. The model calculations yielded γ values ranging from −19° to −13° for the 5/2+[422] ground-state bands of 101,103,105Nb and of −5° for the two negative-parity bands in 101Nb. The fact that Nb isotopes have intermediate values of signature splitting and band crossing frequencies between those of Y and Tc, Rh isotopes is interpreted as that the Nb isotopes are transitional nuclei with regard to triaxial deformation. A correlation of quadrupole deformations and of triaxiality is seen in the neutron-rich nuclei with Z = 39–45.

High-spin states and band structures in the doubly odd 136La nucleus

High-spin states of 136La have been investigated with the reaction 130Te( 11B, 5n) at a beam energy of 60 MeV. The level scheme with three collective bands has been updated with spin up to 20 ℏ. The observed πh 11/2 ⊗ νh 11/2 band shows γ-instability with increasing spin according to the TRS calculations. The band crossing and the signature splitting and inversion have been discussed. Other two collective bands based on 12-and 16+ levels were proposed as oblate deformation with γ ∼ -60°. They most probably originate from four- and six-quasiparticle configurations, that is, πh 11/2 ⊗ νg 7/2 h 11/2 2 and πg 7/2 ⊗ νg 7/2 2 d 5/2 h 11/2 2 respectively.

New level schemes with high-spin states ofTc105,107,109

New level schemes of odd-$Z$ $^{105,107,109}\mathrm{Tc}$ are proposed based on the $^{252}\mathrm{Cf}$ spontaneous-fission-gamma data taken with Gammasphere in 2000. Bands of levels are considerably extended and expanded to show rich spectroscopic information. Spin/parity and configuration assignments are made based on determinations of multipolarities of low-lying transitions and the level analogies to the previously reported levels, and to those of the neighboring $\mathrm{Rh}$ isotopes. A non-yrast negative-parity band built on the $3∕{2}^{\ensuremath{-}}[301]$ orbital is observed for the first time in $^{105}\mathrm{Tc}$. A positive-parity band built on the $1∕{2}^{+}[431]$ intruder orbital originating from the $\ensuremath{\pi}({g}_{7∕2}∕{d}_{5∕2})$ subshells and having a strong deformation-driving effect is observed for the first time in $^{105}\mathrm{Tc}$, and assigned in $^{107}\mathrm{Tc}$. A positive-parity band built on the excited $11∕{2}^{+}$ level, which has rather low excitation energy and predominantly decays into the $9∕{2}^{+}$ level of the ground state band, provides evidence of triaxiality in $^{107,109}\mathrm{Tc}$, and probably also in $^{105}\mathrm{Tc}$. Rotational constants are calculated and discussed for the $K=1∕2$ intruder bands using the Bohr-Mottelson formula. Level systematics are discussed in terms of the locations of proton Fermi levels and deformations. The band crossings of yrast positive-parity bands are observed, most likely related to ${h}_{11∕2}$ neutron alignment. Triaxial-rotor-plus-particle model calculations performed with $\ensuremath{\epsilon}=0.32$ and $\ensuremath{\gamma}=\ensuremath{-}22.5\ifmmode^\circ\else\textdegree\fi{}$ on the prolate side of maximum triaxiality yielded the best reproduction of the excitation energies, signature splittings, and branching ratios of the positive-parity bands (except for the intruder bands) of these $\mathrm{Tc}$ isotopes. The significant discrepancies between the triaxial-rotor-plus-particle model calculations and experiment for the $K=1∕2$ intruder bands in $^{105,107}\mathrm{Tc}$ need further theoretical studies.

Rotational bands in neutron-richEr169,171,172

The neutron-rich $^{169,171,172}\mathrm{Er}$ nuclei were populated by few-neutron transfer reactions between $^{170}\mathrm{Er}$ and $^{238}\mathrm{U}$ at a near barrier energy. The spectroscopy of these $\mathrm{Er}$ isotopes was studied using prompt $\ensuremath{\gamma}$ rays correlated with delayed transitions or events involving at least three prompt transitions. The ground-state band of $^{172}\mathrm{Er}$ was populated up to spin ${22}^{+}$ at an excitation energy of $5528\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. Rotational bands built on the $1∕{2}^{\ensuremath{-}}[521]$, $5∕{2}^{\ensuremath{-}}[512]$, and $7∕{2}^{+}[633]$ neutron configurations in $^{169,171}\mathrm{Er}$ were extended to substantially higher spins than previously known. The signature splitting observed in these rotational bands is addressed within the framework of the particle-rotor model in terms of triaxiality and Coriolis attenuation. The signature inversion observed in the $5∕{2}^{\ensuremath{-}}[512]$ band is well reproduced by including the triaxial degree of freedom in the calculation. Attenuating the Coriolis interaction in the calculation is found to be necessary to reproduce the signature splitting observed in the $7∕{2}^{+}[633]$ band. A similar Coriolis attenuation also is needed to account for the signature splitting as well as the $B(M1)∕B(E2)$ ratios in the $7∕{2}^{+}[633]$ ground-state band in the neighboring $N=99$ isotones, $^{167}\mathrm{Er}$ and $^{169}\mathrm{Yb}$.

Level structures ofRh110,111,112,113from measurements onCf252

Level schemes of $^{111}\mathrm{Rh}$ and $^{113}\mathrm{Rh}$ are proposed from the analysis of $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence data from a $^{252}\mathrm{Cf}$ spontaneous fission source with Gammasphere. These schemes have the highest excitation energies and spins yet established in these nuclei, as well as weakly populated bands not reported in earlier fission-$\ensuremath{\gamma}$ work. From these data, information on shapes is inferred. By analogy with lighter $Z=45$ odd-even isotopes, tentative spins and parities are assigned to members of several rotational bands. In this region triaxial nuclear shapes are known to occur, and we carried out calculations for $^{111}\mathrm{Rh}$ and $^{113}\mathrm{Rh}$ with the triaxial-rotor-plus-particle model. The $7∕{2}^{+}\ensuremath{\pi}{g}_{9∕2}$ bands of both nuclei, as well as lighter isotopes studied by others, show similar signature splitting. Our model calculations give a reasonable fit to the signature splitting, collective sidebands, and transition probabilities at near-maximum triaxiality with $\ensuremath{\gamma}\ensuremath{\approx}28\ifmmode^\circ\else\textdegree\fi{}$. For the $K=1∕{2}^{+}[431]$ band, experiment and model calculations do not fit well, which is accounted for by greater prolate deformation of the $K=1∕{2}^{+}$ band, a case of shape coexistence. Our data on $^{110,112}\mathrm{Rh}$ show no backbending and thus support the idea of the band crossing in the ground band of the odd-A neighbors being due to alignment of an ${h}_{11∕2}$ neutron pair. In $^{111,113}\mathrm{Rh}$ above the band crossing (spins $\ensuremath{\approx}21∕2\ensuremath{\hbar}$) the ground band appears to split, with two similar branches. We consider the possibility that chiral doubling may be involved, but there are not enough levels to determine that.

Triaxiality and the alignedh11∕2neutron orbitals in neutron-rich Zr and Mo isotopes

Neutron-rich Zr and Mo isotopes were populated as fission fragments produced by the $^{238}\mathrm{U}(\ensuremath{\alpha},\mathit{f})$ fusion-fission reaction. The level schemes of these nuclei have been extended beyond the first band crossing region, which can be ascribed to the ${h}_{11∕2}$ neutron pair alignment. The spin alignment and signature splitting for the $\ensuremath{\nu}{h}_{11∕2}$ orbitals in term of triaxiality is addressed. The crossing frequency of the aligned bands in even Zr and Mo isotopes can be reproduced well by calculations using the cranked shell model. Compared to the Zr isotopes, band crossings in Mo isotopes shift to a lower rotational frequency due to the emerging importance of the $\ensuremath{\gamma}$ degree of freedom. Within the framework of particle-rotor model, the difference in the signature splitting observed for the $\ensuremath{\nu}{h}_{11∕2}$ bands between the odd Zr and Mo isotopes can be attributed to the triaxial degree of freedom in the Mo isotopes. The surprising shift of the band crossing to a higher rotational frequency in $^{106}\mathrm{Mo}$ is interpreted as a manifestation of the deformed subshell closure at $N=64$.

Configuration-dependent bands in 169Re

High-spin states in 169Re were studied and resulted in the identification of a strongly coupled band based on the 9/2-[514] Nilsson state and a decoupled band built on the h 9/2 1/2-[541] intruder proton orbit. The cranked-shell-model calculations present configuration-dependent deformations that can explain the different band crossing frequencies. The 9/2-[514] band in 169Re shows the largest signature splitting at low spin among the known odd-mass Re isotopes. After the alignment of a pair of i 13/2 neutrons, the phase of the splitting is inverted with a significantly reduced amplitude. For the 9/2-[514] bands in light odd-A Re isotopes, the signature splitting of the Routhians and its relation with the signature dependence of M1 transition matrix elements are investigated in connection with the deviation of nuclear shape from axial symmetry, suggesting an appreciable negative $ \gamma$ deformation for the very neutron-deficient odd-A Re isotopes. Additionally, a three-quasipariticle band was observed and assigned to be built likely on the $\pi 9/2^{-}[514] \otimes \mbox{AE}$ configuration.

Anomalous Signature Splitting of the πh 1/2 ⊗νi 3/2 Band in A~ 160 Odd–Odd Nuclei

Systematic features of anomalous signature splitting of the πh 11/2⊗νi 13/2 band in A~160 odd–oddnuclei have been investigated. It is shown that the mechanism ofanomalous signature splitting is similar to that of the normalsignature splitting which is essentially caused by the Coriolis mixingof Ω = 1/2 components into the nuclear wavefunction and theanomalous splitting in signature is mainly caused by the definition.The extensively observed anomalous signature splitting in this bandmight be an indication that the interaction between the h 11/2 proton and the i 13/2 neutron cannot be neglected. The newobservation of high- and low-K bands based onthe same πh 11/2⊗νi 13/2 configuration in164Tm is also discussed.

Negative Parity Bands and Signature Splitting Inversion in80Rb

High spin states in 80Rb were studied via the 65Cu+19F,66Zn+18O and 68Zn+16O reactions. The 75-MeV19F, 76-MeV 18O and 80-MeV 16O beams were provided by theCIAE HI-13 Tandem accelerator and the JAERI Tandem accelerator. The promptγ-γ coincidence and the directional correlation from orientednuclei (DCO) were measured by the detector arrays in CIAE and JAERI.Twenty-three new states with 28 new transitions have been assigned to80Rb. The states were observed up to spins of 20+ and 22− in theα = 0 branch for the positive and negative parity yrast bandsrespectively. The negative parity non-yrast bands were significantlyextended up to spins of 22− and 15−. The band crossingswith frequencies 0.51 MeV and 0.61 MeV in the α = 0 cascade were observed forthe first time. The signature splitting was observed in bothnegative parity bands. The signature inversions at spins of about7 ℏ and 15 ℏ were observed.

Configuration assignments of yrare high-spin structures in 126Cs

High-spin states in 126Cs were populated in the reaction 116Cd(14N, 4n) at a beam energy of 65 MeV. About 50 new transitions were placed in a level scheme that consists of six rotational structures, three of which have been observed for the first time. The newly observed bands and a previously reported but uninterpreted band were assigned configurations based on their population, aligned angular momentum, energy signature splitting and B(M1)/B(E2) ratios (for the strongly coupled bands).

Structure of the Semi-decoupled π 1/2[411] Band in OddProton Nucleus 169Ta

High spin states of the odd proton-nucleus 169Ta have beenpopulated in the reaction 155Gd(19F,5n) with beam energiesof 97 MeV. Rotational band based on d3/2 proton 1/2[411]Nilsson state has been pushed up to 39/2+ in the α = 1/2decay sequence. Its signature partner, the α = -1/2 decay sequence withfour link transitions has been established and 1/2[411] band in169Ta was reassigned to be a semi-decoupled band. Thesystematics of the signature splitting in the K = 1/2 bands in therear-earth region and the accidental degeneracy conclusion given by theangular projection shell model were discussed.

Projected shell model study of odd-oddf−p−gshell proton-rich nuclei

A systematic study of 2-quasiparticle bands of the proton-rich odd-odd nuclei in the mass A ~ 70-80 region is performed using the projected shell model approach. The study includes Br-, Rb-, and Y-isotopes with N = Z+2, and Z+4. We describe the energy spectra and electromagnetic transition strengths in terms of the configuration mixing of the angular-momentum projected multi-quasiparticle states. Signature splitting and signature inversion in the rotational bands are discussed and are shown to be well described. A preliminary study of the odd-odd N = Z nucleus, 74Rb using the concept of spontaneous symmetry breaking is also presented.