Microscopic determination of nuclear deformation energy surfaces at very high spins

The deformation energy surfaces of a number of rare-earth nuclei are calculated microscopically as a function of the Bohr-Mottelson deformation parameters (β,γ), for the very high spin states $\text{(30}\text{h}\text{?}\text{?J?70}\text{h}\text{?}\text{)}$ and compared with semiphenomenological Strutinsky based calculations. The possibility of rotational isomers (yrast traps) is discussed.     

Second backbending in the yrast line of 156Er

High spin yrast states of ¹⁵⁶Er were investigated using the reactions ¹⁴¹Pr(¹⁹F,4nγ) and ¹²³Sb(³⁷Cl, 4nγ), the latter in connection with a sum-crystal. In addition to the backbending at $\text{I = 12}\text{h}\text{?}$, a second one is found at $\text{I = 26}\text{h}\text{?}\text{;}$ and the yrast band is extended up to $\text{I = 32}\text{h}\text{?}\text{;}$. These results are interpreted in terms of a Hartree-Fock-Bogolyubov Cranking (HFBC) method. It is demonstrated that for deformations in the vicinity of the Strutinsky equilibrium deformation, both a 2qp proton band crossing the yrast band or a 4qp neutron band crossing the yrast band can cause strong secondary backbending.     

High-spin states in 24Mg and upper limits for particle spectroscopy of high spins by heavy-ion compound reactions

High-spin states in ²⁴Mg have been investigated by the reaction ¹⁰B(¹⁶O, d)²⁴Mg up to $\text{E}{}^1\text{≈ 24}\text{MeV}$. High-spin states with $\text{I ≧ 9}$ have been identified at $\text{E}{}^1\text{= 19.20, 20.26, 20.8, 21.6, 23.1,}\text{and}\text{23.5}\text{MeV}$. The 10⁺ yrast state in ²⁴Mg is probably located at 20.26 MeV. The upper limits with respect to spin and excitation energy of the applicability of heavy-ion compound reactions for particle spectroscopy of high-spin states are discussed. The main limitations result from the increasing continuum and from a decrease of the high-spin selectivity when the final spins approach the critical angular momentum for compound-nucleus formation. It will be shown that the difficulty in the analysis of the experiments arising from the decreasing probability of finding isolated yrast states at high excitation energies, i.e. from the increasing level density, can be overcome in such experiments. The decrease in the high-spin selectivity of the total cross section is compensated for spins up to J_max by the fact that the shape of the angular distributions depends on the final spin for states with I ～ J_max. This is caused by the decreasing alignment of the final nucleus with decreasing values of |I ? J_max| and can be used for high-spin spectroscopy.     

The yrast bands in 77Kr and 76Kr

High-spin states of both parities in ⁷⁷Kr have been studied in the reaction ⁶³Cu(¹⁶O, pn). On the basis of γγ- and nγ-coincidence experiments, we extended the yrast bands up to spin $\text{I}{}^{\mathrm{\pi }}\text{=}\text{25}\text{2}{}^{\mathrm{+}}$ and $\text{21}\text{2}$^t-. Doppler-shift attenuation and recoil-distance measurements have been performed for some fifteen states. In addition, lifetimes of some yrast states in ⁷⁶Kr have been determined in the reaction ⁶³Cu(¹⁶O, p2n). Transition energies and E2 strengths in ⁷⁶Kr have been interpreted with the IBA-2 and different collective and microscopic triaxial rotor models, those in ⁷⁷Kr with the triaxial rotor plus quasiparticle model.     

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.     

A microscopic classification of high-spin states in 56Fe

A large-scale shell-model calculation on ⁵⁶Fe including positive parity states with spins up to J = 15 shows that several states in the yrast region may be of a particular nature. These states can be locd in groups of which the gamma decay and quadrupole moments show a collective behaviour. The signature of each group is the $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ hole structure. This structure is coupled to a definite J_hole and T_hole with the spin J_hole being as large as possible. The level density above the yrast region turns out to be largely independent of J.     

Triaxial shape and onset of high-spin bands in 129Ba

High-spin states in ¹²⁹Ba have been studied by the ¹²⁰Sn(¹²C, 3n)¹²⁹Ba reaction. The onset of a system of bands parallel to the yrast band is observed. The negative parity states ($\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}\text{system}$) break up into two substructures based upon the lowest $\text{I = j =}\text{11}\text{2}\text{and the}\text{I = j ? 1 =}\text{9}\text{2}$ states. In addition to the $\text{h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ system, a new positive parity structure is seen which is built on the $\text{g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{shell}$. The results are in qualitative agreement with the triaxial core model.     

High-spin structure in 169W and 170W

High-spin states in ^{169, 170}W have been populated in ${}^{154}\text{Gd}\text{(}{}^{20}\text{Ne}\text{, x}\text{n}\text{)}$ reactions. In-beam γ-ray spectroscopic techniques with multi-detector set-ups, multiplicity filters and an anti-Compton shield have been used. Levels up to about spin 30 (tentatively up to 36) in ¹⁷⁰W and up to $\text{57}\text{2}$ (tentatively up to $\text{61}\text{2}$) in ¹⁶⁹W have been identified. The data are interpreted within the framework of a pairing-selfconsistent cranking model. The nuclear shape evolution with increasing spin is studied theoretically within a configuration-controlled shell correction approach and also pairing effects are studied. The behaviour of the yrast states around 28⁺ in ¹⁷⁰W can be related in a model-dependent way to a reduction of the neutron-pairing correlations.     

Investigation of i132 excitations in 197Hg and 191Pt

The level schemes of the odd-neutron nuclei ¹⁹⁷Hg and ¹⁹¹Pt have been studied using in-beam spectroscopic methods. Energies, intensities, angular distributions and coincidences of the γ-rays following (α, 2n) reactions were measured. Also conversion electrons and delayed γ-ray spectra were recorded. Most of the levels in both nuclei are de-populated via the $\text{13}\text{2}{}^{\mathrm{+}}$ isomers. Besides the yrast states, several additional states with spin values between $\text{13}\text{2}$ and $\text{21}\text{2}$ were identified. The negative parity of a side band in ¹⁹⁷Hg starting with an $\text{f =}\text{21}\text{2}$ state was proved by the conversion electron measurement. The families of positive-parity states were compared with model calculations where the core was described as rigid triaxial rotor or anharmonic vibrator. For ¹⁹⁷Hg both models give similarly good results for the energy spectrum and the branching ratios of electromagnetic transitions. Several negative-parity states found in ¹⁹⁷Hg are compared with the predictions of a pairing-plus-quadrupole model.     

High-spin states in 208Rn

The yrast decay scheme of ²⁰⁸Rn has been investigated up to spin $\text{≈ 20}\text{h}\text{?}$ and an excitation energy of ≈ 6 MeV. Several different γ-ray spectroscopic techniques were used to determine the properties of excited states and transitions in the nucleus. Significant changes to the previously established level scheme are proposed, based on the existence of an unobserved 3.1 keV transition. Simple empirical shell-model calculations of level energies aided in the assignment of shell-model configurations to excited states and the decay scheme is discussed in terms of these configurations. The energy level systematics for the even radon isotopes, from A = 206 to 212 are discussed, as are core polarization effects in the even radon isotopes (A = 204 to 210) and polonium isotopes (A = 202–208).     

Proton 1h112 excitations in odd-mass N = 82 nuclei

The structure of negative-parity states in odd-mass N= 82 isotones (135 ≦ A ≦ 145) is investigated in the framework of a model which is based on coupling one $\text{1h}{}_{\mathrm{<mtext>11</mtext><mtext>2</mtext>}}$ proton to π = + 1 states of the appropriate doubly-even isotonic core. It is shown that an effective model-space truncation can be achieved if only core states in the vicinity of the yrast line are taken into account. These have been selected from the several hundreds or even thousands of states obtained from shell-model calculations, where the $\text{1g}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$, $\text{2d}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{3s}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ single- are assumed to be occupied. Spectroscopic data are calculated and predictions on the structure of low-lying π = ? 1 states are discussed and compared as far as possible to experimental findings. Thereby, the particle-core coupling approach is shown to be capable of describing essential properties of negative-parity levels in the N = 82 nuclei considered.     

Study of band crossings in 182Os

High-spin states in ¹⁸²Os have been populated by the (¹⁸O, 4n) reaction and studied using in-beam spectroscopy methods. Seven side bands have been established for the first time. Three of the side bands show a band crossing. The features of the bands have been interpreted in the framework of the cranking model considering the motion of independent particles in a rotating deformed potential. The band crossings of the yrast band and of these three side bands can be explained by the rotation-alignment of a pair of $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ quasineutrons.     

Electromagnetic transitions in 51Mn

The nuclear structure of ⁵¹₂₅Mn was studied by γ-ray spectroscopy in the ⁵⁴Fe(p, α)⁵¹ Mn reaction (E_p = 9.0–13.2 MeV) and the ¹⁴N+³⁹K, ¹⁶O+⁴⁰Ca and ¹⁴N+⁴⁰Ca fusion-evaporation reactions (E_beam = 36 MeV). In the ⁵⁴Fe(p, αγ)⁵¹Mn reaction γ-rays were detected in coincidence with α-particles emitted near 180°; mean lifetimes and γ-ray mixing and branching ratios were deduced from Doppler shift attenuation and α-γ angular correlation measurements, respectively. Definite spin assignments are: 237 and 2416 keV, $\text{J}{}^{\mathrm{\pi }}\text{=}\text{7}\text{2}{}^{\mathrm{?}}$; 1140 keV, $\text{9}\text{2}$^?; 1488 keV, $\text{11}\text{2}$^?; 1825 and 2140 keV, $\text{3}\text{2}$^?. The results for other states below 3 MeV are consistent with the existence of rotational bands (/kh²/2/OI/t~ 95 keV) built on the ($\text{3}\text{2}$⁺) 1817 keV and $\text{1}\text{2}$⁺ 2276 keV hole states. The various measurements together with an earlier value for the lifetime of the first-excited state determine unambiguously the B(M1) and B(E2) values for all of the decay branches of the $\text{7}\text{2}$^?, $\text{9}\text{2}$^? and $\text{11}\text{2}$^? lowest three excited states. From the γ-singles and γ-γ coincidence observations with fusion-evaporation reactions, the yrast cascade proceeds through these three states and higher states at 2957, 3250,3680 and 4139 keV which are suggested to have $\text{J}{}^{\mathrm{\pi }}\text{=}\text{13}\text{2}{}^{\mathrm{?}}$, $\text{15}\text{2}$^?,$\text{15}\text{2}$^? and $\text{19}\text{2}$^?, respectively. The various experimental results for the $\text{5}\text{2}$^? → ($\text{19}\text{2}$^?) yrast states are in good overall agreement with shell-model calculations in the (f_{$\text{7}\text{2}$}¹ space.     

Intrinsic states,high-spin rotational bands and rotation alignment in 177Os and 179Os

Low-lying intrinsic states and their associated rotational bands have been identified in ¹⁷⁷Os and ¹⁷⁹Os. They are the mixed i_{$\text{13}\text{2}$} neutron states and the $\text{1}\text{2}$^?[521] states in ¹⁷⁷Os and ¹⁷⁹Os, as well as the $\text{5}\text{2}$^?[512] state in ¹⁷⁷Os and the $\text{7}\text{2}$^?[514] state in ¹⁷⁹Os. The $\text{1}\text{2}$^? sta is assumed to be the ground state, the other intrinsic states giving rise to isomers. The in-band decay properties of the $\text{7}\text{2}$^?[514] band, and the i_{$\text{13}\text{2}$} bands show the effect of mixing. In the rotational bands in ¹⁷⁷Os a low frequency backbending anomaly is observed but no anomaly is observed in the i_{$\text{13}\text{2}$}. band. In ¹⁷⁹Os the i_{$\text{13}\text{2}$} band does backbend but at a higher frequency than in the yrast bands of the even neighbours. The systematics of the backbending frequencies, and the effects of blocking, are discussed. The rotation aligned angular momentum is deduced, and a comparison made between the i_{$\text{13}\text{2}$} bands and the s-bands in the even neighbours. The results broadly support the identification of the s-bands with the aligned (i_{$\text{13}\text{2}$})² configuration.     

In-beam γ-ray studies of complex band structures and of isomeric states in 152, 153Dy nuclei

The high-spin level structures of ¹⁵²Dy and ¹⁵³Dy were studied experimentally with ^{154, 155}Gd(α xnγ) in-beam reactions, and for ¹⁵²Dy also with ${}^{\mathrm{144,\; 146}}\text{Nd}\text{(}{}^{12}\text{C, x}\text{n}\text{γ)}$ reactions. The experiments included measurements of singles γ-ray and conversion-electron spectra, γ-ray angular distributions and E_γ-t and E_γ-E_γ-t coincidences. A multiplicity filter set-up was used to study the feeding and decay of isomeric states in ¹⁵²Dy. In ¹⁵²Dy about twenty so far unknown levels were found, including two high-spin isomeric states with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{≈ 60}\text{and}\text{≈ 13}\text{ns}$ at excitation energies E_x ≈ 5.04 and 6.08 MeV, respectively. These states are compared with recent calculations on yrast traps. The level scheme of ¹⁵³Dy contains 28 levels up to E_x = 4.1 MeV and $\text{J}{}^{\mathrm{\pi }}\text{= (}\text{37}\text{2}{}^{\mathrm{+}}\text{)}$. Band structures in both nuclei are discussed in comparison with other N = 86 and N = 87 isotones.     

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     

Semi-decoupled bands in the even Hg isotopes

The odd-parity yrast states of the isotopes ^190–200Hg are studied in a model of two quasiparticles coupled to an oblate rotor and interacting by a surface delta interaction. The experimental energy spectra and the enhancement of E2 transition probabilities are well explained by the model. The pure Coriolis coupling problem (i.e., the problem obtained when the residual interaction is suppressed) is investigated in detail. It is shown that the main effect of the Coriolis force is to decouple the high-spin quasiparticle originating in the neutron $\text{1}\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ subshell from the system of the rotor and the low-spin quasiparticle. We study the coupling of a particle to an axially symmetric rotor, which has an intrinsic spin along its symmetry axis, and derive a good approximate solution to the problem.     

Yrast levels of 220Ra populated in the 208Pb(14C, 2n) reaction

Yrast states in the nucleus ²²⁰Ra were studied by means of the ²⁰⁸Pb(¹⁴C, 2n) reaction at 61 and 64 MeV. A staggering sequence of levels of positive and negative parity has been observed up to spin and parity I^π = 16⁺ (18 ⁺) and from I^π = 5^? to I^π = 17^?, respectively. These states are connected by strong E1 transitions competing with the stretched E2 transitions, the $\text{B(}\text{E}\text{1)}\text{B(}\text{E}\text{2)}$ ratio being ~ 10 ^?6 fm^?2. The ratio of the excitation energy of the 4⁺ state to that of the 2⁺ state is close to the vibrational limit. The moment of inertia associated with the negative-parity yrast states is slightly increasing with the rotational frequency ω. It is considerably higher than that of the positive-parity states at lower spins, the difference decreasing monotonically with increasing ω. The data are discussed with reference to the octupole vibrational picture as well as to the results of recent models predicting reflection-asymmetric shapes in the Ra-Th region.     

Rotation of nuclei around a prolate symmetry axis at very high spin states

Classically one expects that nuclei rotate at very high spins (30≦I≦80) around an oblate symmetry axis. It is shown that strong shell correction energies yield for some nuclei at the end of the rare earth region and in the Pb-region yrast states for a rotation around a prolate symmetry axis. Like for the rotation around an oblate symmetry axis one expects also here yrast traps. The deformation energy surfaces for very high spin states are calculated by the Strutinsky method using a Saxon-Woods potential and by a microscopic method built on constraint Nilsson functions. Both methods agree qualitatively. Yrast traps are studied for these nuclei. It is shown that the MONA (Maximisation of theOverlap ofNuclear wave functions byAlignment) effect prefers at high spin rotation around the symmetry axis of a negative deformed shape at the beginning of the shell and of positive deformation at the end of the shell.