Tests of interacting boson model wave functions from measured gyromagnetic ratios of states in the even Os isotopes

The gyromagnetic ratios of the 2₁⁺, 2₂⁺, and 4₁⁺ states in ^188,190,192Os were experimentally measured. It is shown that the hamiltonians of standard interacting boson models (IBM-1 and -2) fit to level spectra and B(E2) rates fail to account for either the intra-nucleus or mass-dependent g-factor variations of these states in these Os isotopes.     

Electric quadrupole and magnetic dipole moments of the first excited 2+ states of186Os and188Os

The spectroscopic quadrupole moments and the magnetic dipole moments of the lowest 2⁺ states in¹⁸⁶Os (137 keV) and¹⁸⁸Os (155 keV) have been determined by Mößbauer transmission experiments. The electric quadrupole momentsQ ₂₊(Os 186)=? (1.80±0.22) b andQ ₂₊(Os 188)=?(1.81±0.24) b as well as their ratioQ ₂₊(Os 188)/Q ₂₊(Os 186)=1.00±0.07 within the limits of error agree withB(E2) data, if a comparison on the basis of the rotational model is made. For the g-factors and their ratio g₂₊(Os 186)=0.281±0.008, g₂₊(Os 188)=0.305±0.015 andg ₂₊(Os 188)/g ₂₊(Os 186)=1.08±0.05 was obtained. All results are compared with recent model calculations.     

Mössbauer studies and nuclear quadrupole moments of186, 188, 189, 190 Os

Mössbauer transmission experiments with the 137, 155, 69 and 187 keV gamma rays of^{186, 188, 189, 190}Os, respectively, yielded the electric quadrupole splitting of these gamma resonance lines in OsO₂ and OsP₂. From the results the following ratios of quadrupole moments were derived:Q ₂ ⁺(¹⁸⁶Os, 137 keV):Q ₂ ⁺(¹⁸⁸Os, 155keV):Q ₂ ⁺(¹⁹⁰Os, 187 keV):Q _3/2 ^?(¹⁸⁹Os, g.s.)=(+1.100±0.020): 1.0:(+0.863±0.051): (?0.586±0.011) andQ _5/2 ^?(¹⁸⁹Os, 69 keV)/Q _3/2 ^?(¹⁸⁹Os, g.s.)=?0.735 ±0.012. The ratios for^{180, 188, 190}Os are, within their limits of error, in agreement with the expectation of the rotational model, indicating that the pairing-plusquadrupole model calculations of Kumar and Baranger predict too rapid a transition form rotational to vibrational nuclei. Applying this argument to¹⁸⁶Os in particular and using the measured ratios, one obtains a set of values for the quadrupole moments themselves, namelyQ ₂ ⁺ (¹⁸⁶Os)=?(1.50 ± 0.10)b,Q ₂ ⁺(¹⁸⁸Os)=?(1.36± 0.09) b,Q ₂ ⁺ (¹⁹⁰Os)=?(1.18 ± 0.08) b,Q _3/2 ^?(¹⁸⁹Os)=+ (0.80 ± 0.06) b, andQ _5/2 ^? (¹⁸⁹Os)=? (0.59 ± 0.05) b. For the electric field gradient at Os nuclei in Re metal a value ofV _zz=?(3.3 ± 0.6) · 10¹⁷ V/cm² was found. A measurement with a magnetically split source yielded δ=+ 0.685 ± 0.025 for theE2/M1 mixing parameter of the 69 keV transition of¹⁸⁹Os,g _5/2 ^?/g _3/2 ^?=0.895 ± 0.006 for the ratio of theg-factors of the 69 keV state and the groundstate, andH _i=?(1135 ± 20) kOe for the hyperfine field at Os nuclei in an iron matrix.     

Dependence of nuclear deorientation on nuclear spin for recoils in vacuum

Time-integral measurements have been made of the vacuum deorientation of the 2⁺ and 4⁺ states in ¹⁵⁰Sm and the 6⁺ and 8⁺ states in ¹⁵⁶Gd Coulomb-excited by 133 MeV ³⁵Cl ions. The ¹⁵⁰Sm results were deduced from γ-ray angular distributions measured in coincidence with backscattered ³⁵Cl ions. In the ¹⁵⁶Gd measurements, a fixed counter array and a sandwich target were used to measure directly the differences between the γ-ray angular distributions from nuclei recoiling in vacuum and the unperturbed γ-ray angular distributions from nuclei stopped in a thick ¹⁵⁶Gd target. The measured deorientation time constants in ps are τ₂(2⁺) = 27±4; τ₂(4⁺) = 14±4; τ₂(6⁺) = 24±3; τ₂(8⁺) = 23⁺¹⁰_?6; τ₄(2⁺) = 12±2; τ₄(4⁺) = 5±3; τ₄(6⁺) = 7.6±2.5. The 8⁺ data were analyzed assuming τ₂/τ₄ = $\text{10}\text{3}$ as predicted by the Abragam-Pound theory for $\text{I ≧ 4}$ essentially independently of the degree of quadrupole admixture. The other results are consistent with this except for the 2⁺ level which shows some quadrupole effect. The present results, which show strong deorientation of high spin levels, are in contrast to earlier work on neutron deficient Er isotopes. In light of our findings we suggest that the failure to observe deorientation in the high spin states in Er is primarily due to anomalously low g-factors associated with the backbending observed in these nuclei.     

Die relativen Quadrupolmomente der ersten angeregten 2+-Zustände von Os188, Os190 und Os192

The angular distributions of the deexitationγ-rays following Coulomb-excitation of the first excited 2⁺-states in Os¹⁸⁸, Os¹⁹⁰ and Os¹⁹² were measured using a metallic Target of natural Osmium. The measured attenuation coefficients areG ₂(Os¹⁸⁸)=0.798±0.013,G ₂(Os¹⁹⁰)=0.917±0.030 andG ₂(Os¹⁹²)=0.940±0.030. As a general test the angular distribution of the 330 keV-γ-rays of Pt¹⁹⁴ was also measured. This distribution was found to be completely undisturbed. Assuming pure electric quadrupole interaction with the internal crystalline fields one obtains an interaction frequency ofΔv _Q =eQ V _zz /h=278±32 MHz for the 155 keV-state of Os¹⁸⁸. Because the electric field gradients acting on the decaying nucleus are the same for all isotopes, one can deduce the ratio of the quadrupole moments of the excited states. The result isQ(Os¹⁸⁸)∶Q(Os¹⁹⁰)=1.11 _?0.19 ^+0.28 andQ(Os¹⁹⁰)∶Q(Os¹⁹²)=1.03±0.30. The effects of the uncertainties in the effective field gradients and their possible asymmetries on the integral attenuation factors are discussed. For 1≧G ₂?0.75 these effects are found to be small.     

Measurements of the radiative widths of the first T = 1, 2+ state of 20Ne and their relationship to analog β-decays

The radiative widths for decays of the ²⁰Ne T = 1, 2⁺ (10.27 MeV) state were measured by resonance α-capture in the reaction ¹⁶O(α, γ)²⁰Ne. A special windowless gas-cell target yielded a low-background spectrum enabling six γ-branches to be observed with a Ge(Li) detector. The six branches correspond to decays from the 10.27 MeV level to the following levels: 2⁺(7.83 MeV), 2⁺(7.42 MeV), 3^?(5.62 MeV), 2^?(4.97 MeV), 2⁺(1.63 MeV) and 0⁺(g.s.). The branching ratios and radiative widths Γ_γ to these levels are: 7.83 MeV [(0.22 ± 0.06)%, 0.008 ± 0.002 eV], 7.42 MeV [(6.9 ± 0.4)%, 0.31 ± 0.04 eV], 5.62 MeV [(2.1 ± 0.2)%, 0.097 ± 0.014 eV], 4.97 MeV [(1.3 ± 0.1)%, 0.060 ± 0.008 eV], 1.63 MeV [(88.9 ± 0.5)%, 4.08 ± 0.43 eV] and 0.0 MeV [(0.64 ± 0.14)%, 0.029 ± 0.008 eV]. The radiative widths to the 1.63 MeV and 7.42 MeV levels are used to determine the CVC predictions of the weak magnetism form factors and their effects on certain β-decay observables are evaluated.     

Magnetic moment measurements of the first-excited 2+ states in even Nd isotopes

The g-factors of the first-excited 2⁺ states of ^{144, 146, 148}Nd were deduced from precession measurements in which the excited nuclei recoil through (TF IMPAC) or stop in (IMPAC) magnetized iron. The transient and static hyperfine fields which are active in these cases have been calibrated. The results for the g-factors, combined with previous data which were reanalyzed in the present work, are: g₁₄₄ = 0.15 ± 0.02, g₁₄₆ = 0.25 ± 0.04, g₁₄₈ = 0.32 ± 0.04. The g-factor for ¹⁴⁴Nd, which is abnormally low for a collective 2⁺ state, cannot be accounted for theoretically.     

Magnetic hyperfine interaction in muonic indium,osmium and mercury

The magnetic hyperfine interaction in several muonic atoms has been measured. The magnetic splittings of the 1s _1/2, 2s _1/2 and 2p _1/2 muon states in the 9/2⁺ ground state of¹¹⁵In, determined by measuring muonic X rays areΔE _mag(1s _1/2,¹¹⁵In 9/2⁺)=3580±70 eVΔE _mag(2s _1/2,¹¹⁵In 9/2⁺)=525±120 eVΔE _mag(2p _1/2,¹¹⁵In 9/2⁺)=850±180 eV. The magnetic splitting of nuclearγ rays in the presence of a muon in the 1s _1/2 state yields for the 1/2^? ground state in¹⁹⁹HgΔE _mag(1s _1/2,¹⁹⁹Hg 1/2^?)=468±115 eV and the following values for the first excited 2⁺ states in the nuclei^190,192Os and²⁰⁰Hg:ΔE _mag(1s _1/2,¹⁹⁰Os 2⁺)=665± ₄₀ ⁸⁰ eVΔE _mag(1s _1/2,¹⁹²Os 2⁺)=800±80 eVΔE _mag(1s _1/2,²⁰⁰Hg 2⁺)=655± ₇₅ ¹⁰⁵ eV. These data are compared with calculations using different nuclear models.     

The quadrupole moment of 26Mg as a test of shell-model interactions

The static quadrupole moment Q_21⁺, and the B(E2; 0₁⁺ → 2⁺₁) value of the first excited state of²⁶Mg have been measured using the reorientation effect in Coulomb excitation of ²⁶Mg projectiles. It is found that Q_21⁺ = ?13.6±3.0 (?9.5±3.0) e ·fm² and B(E2; 0⁺₁ → 2⁺₁) = 322±16 (328±16) e² ·fm⁴ for constructive (destructive) interference from higher states. The result for Q₂ clearly differentiates among several alternative effective interactions which have been used in shell-model calculations.     

Collective states in even Sn nuclei

0⁺, 2⁺, 4⁴ and 3^? states in ^112–124Sn have been studied with the (p, p′γ) reaction and in Coulomb excitation. Absolute E2 transition rates between these levels have been extracted with the aid of the Winther-de Boer code. For ^116,118Sn, B(E2; 4₁⁺ → 2₁⁺) ≈ 20 W.u., suggesting a two-phonon character of the 4₁⁺ states. For the lighter and heavier isotopes, this value is significantly smaller. All observed values of B(E2; 2₂⁺ → 2₁⁺) and B(E2; 2₃⁺→ 2₁⁺) are about 5 W.u. Also. values of B(E3; 0₁⁺ → 3^?₁) have been measured for all stable even Sn nuclei. In ¹¹⁶Sn the branching ratio (3₁^? → 0₁⁺)/(3₁^? → 2₁⁺) has been measured. From this we obtain a half-life of 0.34±0.07 ps for the first 3^? level in ¹¹⁶Sn and B(E1; 3₁^? → 2₁⁺) = (1.4±0.3) × 10^?5'e² · b, corresponding to a hindrance factor of 10³.     

Transient field measurements of g-factors for 24Mg AND 26Mg

The g-factors of the first-excited J^π = 2⁺ states of ²⁴Mg and ²⁶Mg have been measured with the ion-implantation perturbed angular correlation technique (IMPAC). The precession of the spins of nuclei recoiling into a magnetized iron backing is predominantly caused by the transient magnetic field for these very light and short-lived (τ_m ≈ 1 ps) nuclei. The transient field, which attains a value of 200 T for the Mg isotopes, is present only during the slowing-down of the recoiling nucleus and results in average precession angles of about 1.5 mrad. The experimental results are treated in the framework of the transient field theory of Lindhard and Winther. This yields g-factors of g = +0.42b ± 0.09 and g = +1.3 ± 0.3 for ²⁴Mg and ²⁶Mg, respectively. The results are compared with theoretical predictions and for ²⁴Mg also with a recent time-differential deorientation experiment.     

Disparity of measured gyromagnetic ratios of ground- and excited-band states in184W

Gyromagnetic ratios of levels in the ground-band and of the 2 ₂ ⁺ state in¹⁸⁴W were measured by means of the transient magnetic field perturbedγ-ray angular distribution technique. The levels of interest were Coulomb excited by beams of 220-MeV⁵⁸Ni and⁶³Cu ions. The results show theg-factor of the 2 ₂ ⁺ state to be approximately half the effectively constant value found for the ground-band levels. This disparity is compared with those previously obtained for the corresponding states in^188–192Os and¹⁸⁶W; these are discussed in the context of the interacting boson model.     

Gyromagnetic ratios of excited states in186W

The gyromagnetic ratios of the 4 ₁ ⁺ , 6 ₁ ⁺ , and 2 ₂ ⁺ states in¹⁸⁶W were measured relative to that of the 2 ₁ ⁺ level by means of the transient field implantation perturbedγ-ray angular distribution technique. The nuclei in the states of interest were Coulomb excited using a beam of 220-MeV⁶³Cu projectiles and recoiled swiftly through a thin, polarized Fe foil. The present measurements yielded ratiosg(4 ₁ ⁺ )/g(2 ₁ ⁺ )=1.04±0.07,g(6 ₁ ⁺ )/g(2 ₁ ⁺ )=1.03 ±0.20 andg(2 ₂ ⁺ )/g(2 ₁ ⁺ )=0.63±0.13. The sizable disparity between the measuredg-factors of the ground- and excited-band is examined within the context of the interacting boson approximation model.     

Nuclear g-factor of the 172+ isomeric state in 63Cu

The nuclear g-factor of the 4498 keV $\text{17}\text{2}$⁺ isomeric state in ⁶³Cu was measured with the in-bearn perturbed angular distribution method, through the ⁶²Ni(α, p2nγ)⁶³Cu reaction, to be g_exp = 0.184 ± 0.012. This value is in good agreement with a semiempirical g-factor for the three-quasiparticle configuration [π2p_{$\text{3}\text{2}$}(v1f_{$\text{5}\text{2}$}, 1g_{$\text{9}\text{2}$})₇]_{$\text{17}\text{2}$⁺} calculated using the experimental single-particle g-factors of neighbouring nuclei. At the same time the internal magnetic field at the Cu nuclei in Ni metal was obtained to be B_int = ?46.6 ± 1.3 kG.     

E0 transitions in 70Ge and shape-coexistence interpretation of even-mass Ge isotopes

The branching ratios of E0 and E2 transitions depopulating the 0⁺₂ and 0⁺₃ states in ⁷⁰Ge have been studied using conversion-electron and γ-ray spectroscopy, as well as a new internal-pair measurement technique. A value of 3.7 (2) ns has been obtained in a remeasurement of the half-life of the 0⁺₂ state. Two new E0 transitions, 0⁺₃ → 0⁺₂ and 0⁺₃ → 0⁺₁, have been observed. A comparison of the measured X(E0/E2), ρ²(E0) and B(E2) values for the excited 0⁺ states in ⁷⁰Ge with the corresponding ¹⁵⁰Sm data supports a recent shape-coexistence interpretation of the even-mass Ge isotopes.     

A measurement of B(E3;0+ → 31−) and some E2 transition probabilities in 132, 134, 136, 138Ba using Coulomb excitation

Reduced transition probabilities, B(E2) and B(E3), have been measured for low-lying 2⁺ and 3^? states in ^{132, 134, 136, 138}Ba using Coulomb excitation by 40 MeV ¹²C ions. The B(E2) values are in general consistent with previous measurements and the B(E3;0⁺ → 3₁^?) values are 0.176 ± 0.022, 0.148 ± 0.018, 0.155 ± 0.018 and 0.133 ± 0.013 e² · b³ for ^{132, 134, 136, 138}Ba respectively. These B(E3) values correspond to about 24 to 17 W.u. and such enhancements suggest that these 3^? states have an essentially collective character which may be attributed to octupole vibrations.     

g-Faktoren und Multipol-Mischungsverhältnisse in156Gd

By integral perturbedγ-γ-angular correlation the gyromagnetic ratios of a 2-quasi-particle state at 1,513 keV and the 4⁺ state of the ground state rotational band in¹⁵⁶Gd were measured, using sources prepared by¹⁵⁹Tb(γ, 3n) and¹⁵⁶Gd(d, 2n) reactions:g _{1;513 keV} ⁴⁺ =0.78±0.05;g _R ⁴⁺ =0.37±0.05. In addition we obtain the multipole mixing ratiosδ _{535 keV}(M2/E1)=?0.09±0.01;δ _{1,225 keV}(E2/M1)=+1.83±0.10 for the 535 keV and 1,225 keVγ-rays. The classification of the 1,513 keV state is discussed. The internal field of Gd in Tb metal at 77 °K was found to beH=(?192±16)kOe.     

Magnetic moments of the 12+ isomeric states in 194, 196, 198Pb

The g-factor of the 12⁺ isomeric state in lead isotopes with A = 194, 196, 198 was measured using the time-differential perturbed angular distribution method (TDPAD). The values obtained are respectively g(194) = ?0.158(6); g(196) = ?0.157(7); g(198) = ?0.144(11). A more precise determination of the 12⁺ level half-life is also made. The g-factprs of these nuclear states, which are described with v(i_{$\text{13}\text{2}$})^?2 as the main configuration, are surprisingly constant over a large mass range (between A = 206 and 194). A core polarization analysis explains this trend: the polarization induced on neutrons in i_{$\text{13}\text{2}$} orbit decreases with the mass number A (blocking effect), but a compensation is provided by the other spin-orbit partners f_{$\text{7}\text{2}$}-f_{$\text{5}\text{2}$} and P_{$\text{3}\text{2}$}-P_{$\text{1}\text{2}$}.