Measurement of the nuclear magnetic dipole moments of 177Hf and 179Hf with the atomic beam magnetic resonance method

The nuclear ground-state magnetic dipole moments of ¹⁷⁷Hf and ¹⁷⁹Hf have been determined with the atomic beam magnetic resonance method. The results are: $\text{μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{177}\text{Hf}\text{= 0.7836(6)μ}{}_{\mathrm{<mtext>N</mtext>}}\text{, μ}{}_{\mathrm{<mtext>I</mtext>}}\text{(}{}^{179}\text{Hf) = ?0.6329(13) μ}{}_{\mathrm{<mtext>N</mtext>}}$ (uncorrected for diamagnetic shielding).     

High-spin positive-parity states in 179Hf studied by the 180Hf(τ, α)179Hf reaction AT 32 MeV

Full angular distributions are presented for states populated in the reaction ¹⁸⁰Hf(τ, α)¹⁷⁹Hf at 32 MeV beam energy. Positive-parity states associated with the i_{$\text{13}\text{2}$} unique parity intruder orbital are given special attention. Thus, angular distributions for the five first members of the [624$\text{9}\text{2}$] groundstate sequence are given, as well as for a number of more highly excited states, some being new assignments. The distribution of l = 6 transfer strength is quite characteristic, two $\text{13}\text{2}$⁺ states being substantially more populated than the rest. The characteristic features of the data are explained by a quasiparticle-rotor calculation employing deformed Woods-Saxon orbitals, but only if the hexadecapole shape parameter of the nuclear potential is β₄ ～ ?0.08. The often anomalous differential cross sections for $\text{I}{}^{\mathrm{\pi }}\text{≠}\text{13}\text{2}{}^{\mathrm{+}}$ band members are well accounted for by a rotor model CCBA calculation employing transfer form factors extracted from the orbitals of the deformed Woods-Saxon field, and including non-adiabatic Coriolis mixing effects.     

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.     

Magnetic moments of high-spin states above the rotational band of 168Hf and 172Hf

The transient magnetic field IMPAC technique was used to measure the magnetic moments of high-spin states above the rotational band of ¹⁶⁸Hf and ¹⁷²Hf, populated in the reactions ^{156, 160}Gd(¹⁶O, 4n). The average g-factors of these prerotational feeding states were deduced to be 0.07 ± 0.04 and 0.14 ± 0.04 for ¹⁶⁸Hf and ¹⁷²Hf, respectively. These results are in agreement with a reduction of the collective g-factors due to a neutron phase transition.     

The decay properties of 3.25 min 169Hf and 2.05 min 167Hf

The decays of 3.25 min ¹⁶⁹Hf and 2.05 min ¹⁶⁷Hf have been studied with high-resolution Ge(Li) and Si(Li) detectors. The total decay energy of ¹⁶⁹Hf determined from our experimental $\text{K}\text{β}{}^{\mathrm{+}}$ ratio is 3.29^+0.05_?0.13 MeV. The allowed unhindered character of the main β-branches in the decay of both isotopes allows unique Nilsson model assignments.     

High-spin states and rotation-particle coupling in 179W

The ¹⁷⁸Hf(α, 3n)¹⁷⁹W and ¹⁸¹Ta(p, 3n)¹⁷⁹W reactions are used to populate rotational states in ¹⁷⁹W. Particular attention is paid to the strongly perturbed positive-parity bands. The rotational energies within these bands are successfully explained within the unified model with pairing and Coriolis interactions included if the theoretical Coriolis matrix elements are reduced. The wave functions are calculated from a fit to the experimental energies and the theoretical and experimental transition probabilities are compared. Rotational bands built on the $\text{7}\text{2}$^?[514], $\text{1}\text{2}$^?[521] and $\text{5}\text{2}$^?[512] intrinsic states are also observed.     

New neutron-rich 179Yb and 181,182Lu isotopes produced in reactions of 9 MeV/u 136Xe ions on tantalum and tungsten targets

The new neutron-rich isotopes ¹⁷⁹Yb and ^181,182Lu were produced in multinucleon transfer reactions by irradiating ^natW/Ta targets with 9 MeV/u ¹³⁶Xe ions, and identified by mass separation and decay spectroscopy. The measured half-lives of ¹⁷⁹Yb, ¹⁸¹Lu and ¹⁸²Lu are 8.1±0.8, 3.5±0.3 and 2.0±0.2 min, respectively. The properties of the excited states of ^181,182Hf are discussed. The possibility of studying neutron-rich nuclei outside the classical fission-product regions is demonstrated.     

High-spin states and two-quasiparticle structure in 172Hf

Five rotational bands in ¹⁷²Hf have been observed to high spin following the ¹⁶⁰Gd(¹⁶O, 4n)¹⁷²Hf reaction, using γ-γ coincidence techniques. The ground-state band is extended to spin 20⁺ without backbending, in contrast to the neighbouring even-even isotones. The most strongly populated side-band, consisting of separated odd-spin and even-spin sequences, appears to result from the partial decoupling of an i_{$\text{13}\text{2}$} neutron. Three other bands are identified with the following band-heads: an 8^? state at 2006 keV with 163 ns half-life; a 6⁺ state at 1685 keV with a half-life < 16 ns; and a level at 1857 keV with spin 4, 5, 6 or 7 and a half-life < 16 ns. The differences between the bands are discussed in terms of the influence of Coriolis forces and the two-quasiparticle level structure.     

High-spin rotational bands and pairing reduction in 166Hf

Rotational properties of the ¹⁶⁶Hf nucleus have been studied by in-beam spectroscopic methods using the ¹⁵⁰Sm(²⁰Ne, 4n)¹⁶⁶Hf reaction. The ground band was observed up to the I^π = 18⁺ level, the s-band from the I^π = 12⁺ up to I^π = 22⁺ level; in addition two side bands were found. The results are interpreted in terms of the pairing-self-consistent Hartree-Fock-Bogolyubov cranking model. Quantitative agreement between theory and experiment is obtained for the crossing of the ground band and s-band. The calculations predict a reduction of about 50 % in the neutron pairing energy gap of yrast states in the crossing region. The kinematical ($\text{I}$⁽¹⁾) and dynamical ($\text{I}$⁽²⁾) moments of inertia are analysed.     

The 181Ta(γ, π+)181Hf reaction

Yields for the reaction ¹⁸¹Ta(γ, π⁺)¹⁸¹Hf have been measured by an activation method using bremsstrahlung radiation with end-point energies in the range 150–360 MeV. The data have been unfolded to give cross section results corresponding to bombarding with monoenergetic photons. A comparison is made with respect to previous results and a semiclassical cascade-model calculation.     

Absolute E1, ΔK = 1 transition probabilities between multi-quasiparticle high-spin states in 176Hf and 178Hf

Applying the generalized centroid shift method in (α, 2n) reactions, the half-lives of the 3080 keV 15⁺ state in ¹⁷⁶Hf and of the 1637 keV 5^? state in ¹⁷⁸Hf have been measured as $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.20}{}^{\mathrm{+0.12}}{}_{\mathrm{?0.08}}\text{ns}$ and $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.40 ± 0.10}\text{ns}$, respectively. B(El) values of K-allowed E1 transitions $\text{n}\text{9}\text{2}{}^{\mathrm{+}}\text{[624]→}\text{7}\text{2}{}^{\mathrm{?}}\text{[514]}$ are derived, and together with other data on similar transitions in odd-A nuclei, compared with predictions of the Nilsson plus pairing model. In ¹⁷⁶Hf, the 15⁺ and 14^? states at 3080 and 2866 keV, respectively, appear as quite pure deformed 4QP configurations. In the 2QP state at 1637 keV in ¹⁷⁸Hf, possible strong mixing of vibrational components is discussed coupled via 2QP K-admixtures arising from the partial alignment of the $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ neutron.     

Coulomb excitation in 180Hf

Coulomb excitation studies have been performed to measure transition probabilities of collective quadrupole vibrational states in ¹⁸⁰Hf. The I = 2 level of the K^π = 2⁺ collective γ-band is established at 1200.5 keV with B(E2)_exc = (11.0 ± 1.1) × 10^?50e² · cm⁴ (3.6 ± 0.4 s.p.u.). The angular distribution of the de-exciting γ-rays from this level yields δ = 9.6⁺²²_?5.8 or, less likely, 0.7 ± 0.2 for the 1107.2 keV 2_γ⁺ → 2_g⁺ transition. The B(E2)_exc for any K^πI = 0⁺2 stateorother 2⁺ states up to 1500 keV is less than 5 × 10^?51e² · cm⁴ (< 0.2. s.p.u.).     

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.     

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.     

Atomic beam magnetic resonance investigations in the3 F 2 Ground State of177Hf,179Hf and180Hf

The 5d ²6s ^{2 3} F ₂ ground state of¹⁷⁷Hf,¹⁷⁹Hf and¹⁸⁰Hf has been studied using the atomic beam magnetic resonance method. The atomic beam was produced by an universal evaporation technique described in a previous paper. The results are¹⁸⁰Hfg _j (³ F ₂)=0.695812 (10)¹⁷⁷Hf Δv(³ F ₂;F=11/2?F=9/2)=991.7917 (10) MHz Δv(³ F ₂;F=9/2?F=7/2)=477.0081 (10) MHz Δv(³ F ₂;F=7/2?F=5/2)=162.8890 (10) MHz¹⁷⁹HfΔv(³ F ₂;F=13/2?F=11/2)=82.1320 (10) MHz Δv(³ F ₂;F=11/2?F=9/2)=392.8498 (10) MHz. The magnetic dipole and electric quadrupole moments of the¹⁷⁷Hf and¹⁷⁹Hf nuclear ground states as calculated from these hyperfine structure measurements are the following: μ(177)=0.75(8)μ _k , Q(177)=4.34 (65) barns μ(179)=?0.61 (6)μ _k , Q(179)=4.90 (75) barns.     

Three- and five-quasiparticle isomers,rotational bands and residual interactions in 175Hf

Two 3-quasiparticle isomers with spins, parities and half-lives of $\text{19}\text{2}$⁺, 1.1 μs and $\text{23}\text{2}$^?, 1.2 ns have been identified at 1433 and 1766 keV in ¹⁷⁵Hf. A third isomer, possibly $\text{35}\text{2}$^? with a 1.2 μs half-life, is found at 3015 keV. The first two are characterised as a $\text{7}\text{2}$⁺ [633] neutron coupled to the known 6⁺ and 8^? 2-proton isomers of the core nuclei. Rotational bands based on the 3-qp isomers are highly perturbed, due to Coriolis mixing, and their structure is reproduced in a band mixing calculation. The energy depression of the 3-quasiparticle states relative to the 2-quasiproton core states is attributed mainly to the residual proton-neutron interaction, and possibly also to blocking effects through neutron admixtures.     

Hyperfine field at 181Ta nuclei in ferromagnetic ZrZn2

A sample of ZrZn₂ containing 2% Hf has been studied by differential perturbed angular correlations of the gamma rays of ¹⁸¹Hf. A value of -15.1 ± 0.6 kOe was found for the hyperfine field at the ¹⁸¹Ta nuclei.     

Ground state hyperfine structure and nuclear magnetic dipole moments of177Hf and179Hf

Using the atomic beam magnetic resonance method the experimental hyperfine structure data of the 5d ²6s ^{2 3} F ₂ ground state of¹⁷⁷Hf and¹⁷⁹Hf described in a previous paper [1] have been completed. After applying corrections due to perturbations by other fine structure levels of the configuration 5d ²6s ² we got the following multipole interaction constants: $$\begin{gathered} ^{177} Hf:A = 113.43314 (7) MHz B = 624.3293 (13) MHz \hfill \\ C = 0.27 (18) KHz D = 0.045 (40) KHz \hfill \\ ^{179} Hf: A = - 71.42891 (9) MHz B = 705.5181 (24) MHz \hfill \\ C = - 0.43 (20) MHz D = 0.07 (6) KHz. \hfill \\ \end{gathered} $$ By measuring rf transitions at magnetic fields between 1100 and 1550 Gauss the nuclear ground state magnetic dipole moments were determined. The results are: $$\mu _I (^{177} Hf) = 0.7836 (6) \mu _N , \mu _I (^{179} Hf) = - 0.6329 (13) \mu _N $$ (uncorrected for diamagnetic shielding).     

Investigation of the low-lying levels of 179Hf with the (n, γ) and (n,e) reactions

The excited levels of ¹⁷⁹Hf are investigated using the thermal neutron capture γ-ray and conversion electron spectra measured with the bent crystal diffraction spectrometer in Risø and the β-spectrograph in Riga. The level scheme contains the odd parity rotational bands $\text{7}\text{2}{}^{\mathrm{?}}\text{[514],}\text{1}\text{2}{}^{\mathrm{?}}\text{[510],}\text{5}\text{2}{}^{\mathrm{?}}\text{[512],}\text{1}\text{2}{}^{\mathrm{?}}\text{[521],}\text{3}\text{2}{}^{\mathrm{?}}\text{[512]}$ and $\text{7}\text{2}{}^{\mathrm{?}}\text{[503]}$. The energies of these levels and the intensity ratios of the transitions between them are calculated taking into account the rotation-particle coupling (RPC). The following even parity levels are proposed: 859.0 and 942.2 keV $\text{(}\text{7}\text{2}{}^{\mathrm{+}}\text{and}\text{9}\text{2}{}^{\mathrm{+}}\text{of the}\text{7}\text{2}{}^{\mathrm{+}}\text{[633]}\text{band}\text{)}$; 1004.1 and 1079.2 keV $\text{(}\text{5}\text{2}{}^{\mathrm{+}}\text{and}\text{7}\text{2}{}^{\mathrm{+}}\text{of the}\text{9}\text{2}{}^{\mathrm{+}}\text{[624] + Q(22)}\text{band}\text{)}$; 1186.0, 1199.2 and 1296.4 keV $\text{(}\text{1}\text{2}{}^{\mathrm{+}}\text{,}\text{5}\text{2}{}^{\mathrm{+}}\text{and}\text{3}\text{2}{}^{\mathrm{+}}\text{of the}\text{1}\text{2}{}^{\mathrm{+}}\text{[651]}\text{band}\text{)}$. The levels at 1249.8, 1269.7, 1432.9, 1482.2 and 1755.5 keV, supported by the analysis of the γγ coincidence spectrum and Ge(Li) singles data, are discussed.     

The four quasi-particle 178Hf isomeric state,its excitation energy and multipolarities of deexciting transitions

The decay properties of the 31 y ¹⁷⁸Hf isomeric state have been investigated by means of a Ge(Li)-NaI(Tl) Compton suppression device and a Si(Li) detector, as well as with Ge(Li) and Ge(Li), intrinsic Ge and Si(Li) coincidence arrangements. From the E3 character of the unobserved isomeric transition (11.7 ≦ E_IT ≦ 16.7 keV), deduced from L-subshell and M/L ratios, I^π, K of the isomeric level was determined as 16⁺, 16. The {p[404] ↓ + p1514] ↑ + n[514] ↓ + n[624]↑}_16⁺ + four quasi-particle configuration was assigned to this level at 2447.5 ± 2.5 keV. As proposed earlier the isomeric E3 transition decays to the 13^? level of the band built upon the I^π = 8^? isomer. The |g_K?g_R| values derived from $\text{E}\text{2}\text{M}\text{1}$ ratios of interband transitions show that the 8^? isomer contains about 36 % of the p[404] ↓ + p[514] ↑ configuration and about 64 % of the n[624] ↑ + n[514] ↓ configuration.