Influence of protons on backbending

Backbending in (at least the first half of) the rare earth nuclei seems to be determined by the alignment of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron pair. This is supported by the disappearance of backbending due to the blocking of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ level by an odd neutron for example in ¹⁶⁵Yb. Contrary to expectations backbending disappears also by adding an odd $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$,proton to ₇₀¹⁶⁶Yb in ₇₁¹⁶⁷Lu for this state (but is present if the odd proton is in the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ level). A theory is presented which explains the odd neutron and the odd proton nuclei. It turns out that the odd proton in ¹⁶⁷Lu serves only as a type of catalyst for the alignment of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron pair. The odd proton changes the deformation and moves the Fermi surface nearer ($\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$) or farther away ($\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$) from the nearest $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron level. In one case one finds backbending and in the other case no backbending in ¹⁶⁷Lu.     

Backbending behaviour of rotational bands in 163,165,167Yb

Several rotational bands in ^163,165,167Yb are observed in (HI,xnγe^?) experiments. The $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ and $\text{3}\text{2}{}^{\mathrm{?}}\text{[521]}$ bands do not backbend, whereas the $\text{5}\text{2}{}^{\mathrm{?}}\text{[523]}$ bands do, indicating additional processes besides the rotational alignment of one $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron pair that are responsible for the backbending.     

Particle pairs in the cranked Hartree-Fock-Bogoliubov approximation and the interacting boson model

The number projected HFB wave function is analyzed in terms of particle pairs. It is found that the S(J = 0) and D(J = 2) pairs have dominant probabilities in this wave function before the occurrence of backbending, which is clarified from the behaviour of the O(J = 12) and M(J = 10) pairs arising from the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ level. After backbending the wave function can be described mainly in terms of the O and M pairs plus the core made of S and D pairs.     

Connection between backbending and high-spin isomer decay in 179W

A new 710 ns isomer in ¹⁷⁹W is found to decay directly into backbending region of the $\text{7}\text{2}{}^{\mathrm{-}}\text{(514)}$ gorund-state band. The $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ band is observed up to spin $\text{41}\text{2}$ and shows no evidence for backbending at core rotational frequencies, where the effect is observed in the ¹⁷⁹W and ¹⁸⁰W ground-state bands.     

Influence of Coriolis anti pairing and alignment on the rotational states in nuclei

The inclusion of both Coriolos anti pairing (CAP) and alignment in the simple $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ model is studied. It is found that “backbending” occurs for too small angular frequencies in such a model.     

Magnetic moments of (νi132)−n isomers in neutron-deficient lead isotopes

The magnetic moments of the 12⁺ isomers in ^{192, 196, 198, 200, 206}Pb and of the $\text{33}\text{2}{}^{\mathrm{+}}$ isomer in ²⁰⁵Pb have been measured using the PAD technique. The results for the g-factors are: g(192) = ?0.173(2), g(196) = ?0.1600(15), g(198) = ?0.1552(15), g(200) = ?0.1512(15), g(206) = ?0.1496(18), and g(205) = ?0.148(5). As all states have a rather pure $\text{(νi}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?n}}$ configuration, the values reflect directly the $\text{νi}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ orbital. They show a decrease towards the more neutron-deficient isotopes attributed to the reduced core polarisation as a result of decreasing occupation of the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron shell. The measured systematics are discussed regarding core polarisation, mesonic corrections, and small admixtures of core-excited states to the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ wave function.     

Neutron and proton alignment at high spin in 168W

Excited states in the neutron-deficient nucleus ¹⁶⁸W, populated in the ¹⁴⁸Sm(²⁴Mg, 4n)¹⁶⁸W reaction, have been studied using γ-ray spectroscopy. The yrast band, which is identified up to about spin 28, shows a very strong backbend at low frequency, $\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{= 0.235}\text{MeV}$, attributed to the $\text{(i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}\text{)}{}^2$ neutron alignment. Evidence for a second backbend is also observed. A strongly populated odd-spin (probably negative-parity) sideband is also identified to the spin, and shows several band-crossing anomalies. The characterisation of the anomalies is made by comparison with CSM calculations. Proton and neutron alignments are probably present in the sideband, and the second backbend in the yrast sequence may be due to alignment of $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ protons.     

Backbending in 167Hf and 168Hf and the band-crossing picture

Using two Compton-suppression spectrometers in an E_γ?E_γ coincidence experiment, the yrast bands in ^167,168Hf were extended up to $\text{49}\text{2}$ and 28 ?, respectively. The i ${}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ positive parity band in ¹⁶⁷Hf experiences backbending at a higher frequency than the first backbending in ¹⁶⁸Hf, and no second backbending is obseerved in ¹⁶⁸Hf. New information is threby obtained on the nature and interaction strength of the crossing bands in the vicinity of N = 96.     

The g-factor of the 132+ state in 207Po and the mesonic contribution to the moment of the i132-neutron

The magnetic moment of the $\text{13}\text{2}{}^{\mathrm{+}}$ state in ²⁰⁷Po was determined to be μ = ?0.910 ± 0.014 n.m. An analysis of this value and other known moments of $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron states around ²⁰⁸Pb supports the existence of a mesonic contribution of at least ?0.3 n.m. to the moment.     

Evidence for triaxial shapes in Pt nuclei

Positive parity levels in ¹⁹¹Pt obtained from (α, xnγ) reactions and β-decay are presented as a first example of a rather complete $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ level family. The spectrum confirms triaxial shapes found before from $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ proton structures in this mass region. In addition to the usual decoupled yrast band, a second ΔI = 2 band within the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ family, built on a low-lying $\text{j?1 =}\text{11}\text{2}$ state, is observed in agreement with theory.     

Magnetic moments in the backbending region of 158Dy

Yrast levels in the backbending region of ¹⁵⁸Dy were Coulomb excited with a 4.7 MeV/u ²⁰⁸Pb beam. Employing the transient field technique with a thin magnetized iron foil, the precessions of the angular correlations of decay γ-rays from levels up to spin I^π = 16⁺ were measured. The results show a clear reduction of the g-factor for states in the backbending region relative to that of the low-spin levels, thus demonstrating that the backbending in ¹⁵⁸Dy is mainly caused by the alignment of $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutrons. In a similar experiment, precession measurements on Coulomb excited low-spin levels of ¹⁶⁴Dy served to determine the static hyperfine field of Dy in Fe and the g-factor of the 6⁺ state in ¹⁶⁴Dy.     

Magnetic moment of the 10−, 2.53 ms state in 208Bi measured by in-beam NMR-PAD

The g-factor of the 10^? isomeric state in ²⁰⁸Bi has been measured by the method of inbeam NMR-PAD. From the experimental value $\text{¦g¦= 0.2666(27)}$ the magnetic moment of the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron hole state is deduced. The result is compared with experimental values of neighbouring nuclei and theoretical predictions.     

High-spin level systematics in 177–182W: Yrast band anomaly in 180W

High-spin levels in ^177–182W have been populated in (α,χnγ) reactions. Backbending-type behavior appears most prominently in ¹⁸⁰W. The role of $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutrons and $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ protons in the ¹⁸⁰W yrast behavior is examined. A strongly-coupled K^π = 10⁺ band structure is identified in ¹⁸²W, the first seniority-two $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ configuration to be characterized in a deformed nucleus.     

Two- and three-quasiparticle states in the interacting boson model and a unified description of even- and odd- mass Hg isotopes

The formalism of the interacting boson-fermion approximation is extended to include two- and three-quasiparticle states. This model is used in a systematic study of the high-spin states in even- and odd-mass ^189–198Hg isotopes. The positive-parity states in these nuclei are described by coupling $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron states to an O(6) core, which offers a simple and parameter-free test of the boson-fermion interaction. Good agreement is obtained between the recent experimental results and the calculated energies, transition rates and g-factors.     

Self-consistent field description of high spin states in rare earth nuclei

The Hartree-Fock-Begoliubov cranking equations are solved for ^{168, 170}Yb and ¹⁷⁴Hf. Deformation and pairing properties are both obtained with a G-matrix derived from the Reid soft-core potential. The high spin anomalies are attributed to the disappearance of the neutron pair gap in ¹⁶⁸Yb, the realignment of an $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$. neutron pair in ¹⁷⁰Yb, and a combination of these two mechanisms in ¹⁷⁴Hf. Two bands intersecting at high spin are found for ¹⁷⁴Hf.     

Band crossing and the prealignment B(E2) anomaly in 126Ba

A theoretical interpretation of the reduction in E2 strengths in ¹²⁶Ba prior to backbending is presented. A shell model basis is built from normal parity orbilals organized into multiplets of a pseudo SU(3) symmetry coupled to $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ configurations restricted to states of seniority zero and two. Within the framework of the model the scattering of a pair of protons from normal parity to the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ orbital produces band crossing and a corresponding reduction in E2 transition strengths prior to pair alignment which is the principal mechanism of the backbending.     

g-Factors of high-spin isomers in 194Hg and 196Hg

The g-factors of the 10⁺ isomeric states in ¹⁹⁴Hg and ¹⁹⁶Hg have been measured using the in beam IPAD method. The results $\text{g(}{}^{194}\text{Hg}\text{) = ?0.24(4)}$ and $\text{g(}{}^{196}\text{Hg}\text{) = ?0.18(9)}$ are in agreement with the value expected for an ($\text{i}{}_1\text{3}\text{2}$^?2) neutron satructure and clearly contradict the previous assignment as ($\text{h}{}_{\mathrm{<mtext>1</mtext><mtext>1</mtext><mtext>2</mtext>}}{}^{\mathrm{?2}}$) proton configurations. Cranking model calculations show that the neutron excitation energies in the rotating frame agree satisfactorily with the experimental energies and that the proton excitations are expected ≈2 MeV above the experimental yrast line     

Structure of 186Ir and decoupling phenomena in doubly-odd deformed nuclei

States of ¹⁸⁶Ir, excited through several (HI, xn) reactions, were studied using in-beam γ-ray spectroscopy techniques. A completely new high-spin level scheme, comprising several rotational bands, is presented. The positive-parity ΔI = 2 ground-state band is possibly a first example of a hitherto unreported scheme called double decoupling associated with a proton and neutron both occupying $\text{Ω =}\text{1}\text{2}$ orbits of decoupling parameters larger than unity. A prominent ΔI = 1 negative-parity structure is interpreted as the $\text{π}\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{?}\text{ν}\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ band known in Tl isotopes but in a prolate-deformed situation.     

Structural connections between 148Sm and 149Sm nuclei

The ^{146, 148}Nd(α, χn) and ^{148, 150}Nd(³He, χn) reactions at E_α = 20–43 MeV and E_3He = 19–27 MeV, are used to study excited states in the ¹⁴⁹Sm₈₆ and ¹⁴⁹Sm₈₇ nucleides and consequently the low-spin odd-parity excitation. The mixing ratios and multipolarities of the most prominent transitions are deduced from the combined evidence of angular distribution and electron conversion data. The spin-parity assignments for most of the levels observed are established. In ¹⁴⁸Sm the ground state band extending to I^π = 10⁺ is predominantly populated. A negative-parity odd-spin band extending from I^π = 3^?through 11^? is also observed. The bands in ¹⁴⁸Sm are interpreted within the framework of the interacting boson approximation model. In ¹⁴⁹Sm positive-parity levels with spin up to $\text{25}\text{2}$ and negative-parity levels with spins up to $\text{21}\text{2}$ are observed. The predominant γ-decay proceeds via transitions associated with $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$, $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$, $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ intrinsic configurations. The branching ratios B(E1)/B(E2) are calculated and compared in both ¹⁴⁸Sm and ¹⁴⁹Sm nucleides. The B(E1)/B(E2) dependence on the value of Z for some N = 86 (as well as 88 and 84) isotones showing a minimum of Z = 64 was noted. A 4 ns high-spin isomer mainly decaying into the positive-parity band based on the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ state in ¹⁴⁹Sm is found. Experimental evidence is presented to interprete the $\text{1}\text{2}{}^{\mathrm{+}}$, $\text{15}\text{2}{}^{\mathrm{+}}$, … and $\text{9}\text{2}{}^{\mathrm{?}}$, $\text{13}\text{2}{}^{\mathrm{?}}$, …, ΔI = 2, sequences in ¹⁴⁹Sm as arising from the coupling of an $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ neutron to the octupole and quadrupole modes of the ¹⁴⁸Sm core nucleus. The absolute reaction cross sections for the ^{146, 148, 150}Nd(³He, χn) reactions have been determined for different bombarding energies. The mixing of the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ and $\text{h}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}$ shells is discussed in the framework of an axial-particle-rotor model calculation.