Intrinsic <Emphasis Type="Italic">g</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> factors of odd-mass <Superscript>167–179</Superscript>Lu isotopes

In this paper, g _K -factors of the intrinsic magnetic moments and effective spin gyromagnetic factors (g _s^eff) of the ^167–179Lu isotopes have been studied within the Tamm-Dancoff approximation (TDA) (Kuliev et al, Sov. J. Nucl. Phys. 9, 185 (1969)) by using a realistic potential such as Woods-Saxon potential for the first time. The effects of the spin-spin and spin-isospin interactions on magnetic moments were investigated. The results of the theoretical calculations are compared with the experimental data for related nuclei. The experimental values of g _K and g _s^eff were computed from the observed magnetic moments (Georg et al, Eur. Phys. J. A3, 225 (1998)) using the spin matrix elements. The theoretical predictions for the g _K factors exhibit good agreement with the experimental g _K factors with increasing mass number A of the lutetium isotopes. The strongest influence of the neutron-proton spin interaction occurs at q = −1. Sufficient agreement between the calculated and the experimental values of g _K is obtained for κ = (45/A) MeV and q = −1.     

Hyperfine structure and nuclear magnetic moments of some neutron-deficient thallium isotopes

Using the atomic-beam magnetic resonance method, hyperfine structure (h.f.s.) measurements have been performed in the²P_1/2 electronic ground state of the neutron-deficient thallium isotopes^193–202Tl. In the doubly odd isotopes, the magnetic dipole hyperfine interaction constantsa were determined, while in the odd-A isotopes, direct measurements of the nuclearg-factors,g _I , were made. The electronicg-factor was measured in¹⁹⁸Tl. The magnetic dipole moments of the doubly odd isotopes have been evaluated by a direct comparison with known values in the stable isotope²⁰³Tl. The moments of the odd-A isotopes are in agreement with pervious measurements by optical spectroscopy. A discussion of the magnetic dipole moments in terms of different nuclear models is included. The moments of the 2^? nuclear ground states of the doubly odd isotopes may be interpreted as arising from a combination of the configurations 2^? (πs_1/2 vf_5/2) and 2^? (πs_1/2 vp_3/2).     

Experimente und Berechnungen zur Hyperfeinstruktur der 3d 9 5g-Konfiguration im Kupfer II-Spektrum

The 3d ⁹ 5g-configuration in the Cu II-spectrum is an example for extreme(j _d l _g )K-coupling. It is shown how under these circumstances experimental hyperfinestructure separations can be explained and calculated by means of the concept of intermediate coupling between two basic coupling schemes. The basic schemes used are built on the vectorK coupled either to the spins of the outer 5g-electron or to the nuclear spinI. The value of the experimental magnetic separation factorya _j (3d) can be understood as the consequence of the core polarization of the inners-electrons by the spin of the unfilled 3d-shell. — The measured effective spin-orbit-constantζ _5g is three times larger than the theoretical result. Reasons for this discrepancy will be discussed.     

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.     

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).     

Magnetic properties of the υj15/2 intruder orbital in the superdeformed minimum of 197Pb

This work has established eight cross-talk transitions between the two signature partner superdeformed (SD) bands in ¹⁹⁷Pb with the EUROBALL IV spectrometer. Directional correlations from oriented states measurements confirm the ΔI = 1 character of these transitions. The flat behaviour of the dynamical moment of inertia and the agreement between the experimental and microscopic HF+BCS values of (g _K - g _R)K/Q ₀ suggest that the configuration of the SD bands is based upon the υ[752]5/2^- neutron intruder orbital. The derived effective spin gyromagnetic factor g _s ^eff is found to be not quenched, and is close to the theoretical g _s ^free value. Received: 14 June 2000 / Accepted: 14 September 2000     

gR and gK factors in deformed nuclei

The static and dynamic magnetic dipole moments of odd-mass and even-mass nuclei with 150R and intrinsic g-factors g_K.     

Energies and electromagnetic moments of deformed nuclei in the rare-earth region

Strutinsky-type cranking calculations with inclusion of pairing correlations have been performed for the rare-earth nuclei ^{156, 158, 164}Dy and ¹⁶⁴Er. The pairing effects contribute significantly and with their inclusion the calculated yrast spectra agree very well with experiments. Using Hartree-Fock-Bogouliubov cranking wave functions we have calculated the magnetic moments and quadrupole moments for states up to spin $\text{I = 20}\text{h}\text{?}$. The quadrupole moments are found to be constant over the whole spin range. The gyromagnetic factors g(I) show a strong I-dependence for ^{156, l58}Dy, a weaker one for ¹⁶⁴Er and none for ¹⁶⁴Dy. The sensitivity of this spin dependence on the single-particle occupation and the pairing degrees of freedom is studied. It is found that the spin variation of the gyrofactors is a rotational alignment effect.     

Surface demagnetizing field as a source of uniaxial surface anisotropy in GdCoMo thin amorphous films

Surface magnetic anisotropy energy was studied for (Gd_0.26Co_0.74)_0.96Mo_0.04 and (Gd_0.29Co_0.71)_0.96Mo_0.04 thin amorphous films by means of microwave spectroscopy at the X-band within the temperature range 4–295 K. Excitations of surface spin waves were observed in the spin wave resonance spectra. The experiment was performed in a rotating external magnetic field. The angular dependence of the resonance field for the uniform mode (spin wave vector k=0) and the surface mode made it possible to determine the surface uniaxial anisotropy constant K_s and its temperature dependence. An inhomogeneity of the saturation magnetization M_s within a close-to-surface layer of thickness d can generate the surface anisotropy energy with anisotropy constant K_s given by the formula: K_s=4πM^b_s (M^b_s−M^surf_s)d, where the indexes b and surf correspond to the bulk and surface values, respectively. The temperature dependence of K_s calculated by means of the formula agrees qualitatively with temperature dependence of K_s found in the experiment.     

Electric quadrupole moments of the K π = 8− and 23/2− isomeric states in 170, 171, 172Hf

The spectroscopic quadrupole moments of the K ^π = 8^? isomers in ¹⁷⁰Hf and ¹⁷²Hf, Q _s ?=?4.91(17) b and 5.40(19) b, respectively and Q _s ?=?4.92(17) b for K ^π ?=?23/2^? in ¹⁷¹Hf have been measured using the time differential perturbed angular distribution technique. The nuclear reaction ¹⁶⁰Gd(¹⁶O, xnγ) was used to excite the respective isomeric states and for the recoil implantation of Hf nuclei into the Hf foil. The quadrupole deformation for the 8^? isomer and the ground state has the same value. The deformation corresponding to 23/2^? isomeric state is observed to be reduced with respect to the ground state due to the i _13/2 neutron alignment. The results are in good agreement with the multi-quasiparticle calculations.     

Dependence of electron spin g-factor on magnetic field in quantum wells

The dependence of electron spin g-factor on magnetic field has been investigated in GaAs/AlGaAs quantum wells. We have estimated the electron g-factor from spin precession frequency in time-resolved photoluminescence measurements under a magnetic field in different configurations; the magnetic field perpendicular (g_⊥) and parallel (g_∥) to the quantum confinement direction. When the angle between the magnetic field and the confinement direction is 45°, we have found that g-factor varies depending on the direction of magnetic field and the circular polarization type of excitation light (σ⁺ or σ^?). These dependences of g-factor exhibit main features of Overhauser effect that nuclear spins react back on electron spin precession. The value of g_⊥ and g_∥ corrected for the nuclear effects agree well with the results of four-band k·p perturbation calculations.     

Magnetic moments of negative parity baryons from the effective Hamiltonian approach to QCD

The magnetic moments of the S ₁₁(1535) and S ₁₁(1650) baryons are studied in the framework of the relativistic three-quark Hamiltonian derived in the Field Correlation Method. The baryon magnetic moments are expressed via the average current quark energies which are defined by the fundamental QCD parameters: the string tension σ, the quark masses, and the strong coupling constant α _s . The resulting magnetic moments for the J ^P = 1/2^? nucleons are compared both to model calculations and to those from lattice QCD.     

Hyperfine structure and isotope shifts in the 5d6s2 a2D3/2--5d6s(a3D)6p z4F5/2 ° transition of Hf II

The hyperfine structure and isotope shifts of the transition between the 5d6s² a²D_3/2 ground state and the 5d6s(a³D)6p z⁴F_5/2 ^° excited state of singly ionized hafnium at \lambda=340 nm have been investigated by laser spectroscopy using a radio-frequency quadrupole ion trap. The magnetic dipole coupling constant A and electric quadrupole coupling constant B of the two atomic levels for both stable isotopes ¹⁷⁷Hf and ¹⁷⁹Hf are determined. The changes of mean square nuclear charge radii \delta[ r²] of the stable Hf isotopes and the radioactive isotope ¹⁷²Hf (T_1/2=1.87a) have been extracted from the data. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electric quadrupole moments and strong interaction effects in pionic atoms of 165Ho, 175Lu, 176Lu, 179Hf and 181Ta

The effective quadrupole moments Q_eff of the nuclei of ¹⁶⁵Ho, ¹⁷⁵Lu, ¹⁷⁶Lu, ¹⁷⁹Hf and ¹⁸¹Ta were accurately measured by detecting the pionic atom 5g-4f X-rays of the elements. The spectroscopic quadropole moments, Q_spec, were obtained by correcting Q_eff for nuclear finite size effect, distortion of the pion wave function by the pion-nucleus strong interaction, and contribution to the energy level splittings by the strong interaction. The intrinsic quadrupole moments, Q₀, were obtained by projecting Q_spec into the frame of reference fixed on the nucleus. The shift, ε₀, and broadening, Γ₀, of the 4f energy level due to the strong interaction between the pion and the nucleons for all the elements were also measured. Theoretical values of ε₀ and Γ₀ were calculated and compared to the experimental values. The measured values of Q₀ were compared with existing results in muonic and pionic atoms. The measured values of ε₀ and Γ₀ were also compared with existing values.     

Vector boson in the constant electromagnetic field

The propagator and the complete sets of in-and out-solutions of the wave equation, together with the Bogoliubov coefficients relating these solutions are obtained for the vector W-boson (with the gyromagnetic ratio g=2) in a constant electromagnetic field. When only the electric field is present, the Bogoliubov coefficients are independent of the boson polarization and are the same as for the scalar boson. For the collinear electric and magnetic fields, the Bogoliubov coefficients for states with the boson spin perpendicular to the field are again the same as in the scalar case. For the W ^? spin parallel (antiparallel) to the magnetic field, the Bogoliubov coefficients and the one-loop contributions to the imaginary part of the Lagrange function are obtained from the corresponding expressions for the scalar case by the substitution m ² → m ²+2eH (m ² → m ²-2eH). For the gyromagnetic ratio g=2, the vector boson interaction with the constant electromagnetic field is described by the functions that can be expected by comparing the scalar and Dirac particle wave functions in the constant electromagnetic field.     

Total nuclear photoabsorption cross sections in the region 150 < A < 190

The curves of the total gamma-absorption cross sections (σ_tot) in the E1 giant resonance energy range for the nuclei ¹⁵⁴Sm, ¹⁵⁶Gd, ¹⁶⁵Ho, ¹⁶⁸Er, ¹⁷⁴Yb, ¹⁷⁸Hf, ¹⁸⁰Hf, ¹⁸¹Ta, ¹⁸²W, ¹⁸⁴W, ¹⁸⁶W and ¹⁹⁷Au have been measured using the absorption method. Parameters of the Lorentz curves fitting the measured cross sections σ_tot are given. Quadrupole moments (Q₀) and nuclear deformation parameters (β) were obtained.For deformed nuclei in the ～ 155 < A < ～ 180 region a violation of the correlation between giant resonance widths (Γ) and nuclear deformation parameters was found. Γ₁ and Γ₂, the widths of the resonances corresponding to vibrations of nucleons along and across the nuclear deformation axis, were observed to decrease with the increase of A which could be accounted for by the presence of an N = 108 subshell.     

Theg R -factor of rare-earth nuclei in the Geometric Collective Model

A parameter-free expression for the collective magnetic dipole operator ofee-nuclei is derived within the Geometric Collective Model. Using this result we give an analytical formula for the (g _R ?Z/A)-value of the lower spin groundstate band members foree-nuclei. The general procedure is explained discussing the results (energies, B(E2)-values and quadrupole moments) for^166–170Er-isotopes extensively. The groundstate bandg _R -factors of the isotopes^166–170Er,^153–160Gd,^160–164Dy,^170–174Yb are calculated and compared with experimental data and results of other models.     

Search for macroscopic CP violating forces using a neutron EDM spectrometer

The search for CP violating forces between nucleons in the so-called axion window of force ranges λ between 2 × 10^?5 m and 0.02 m is interesting because only little experimental information is available there. Axionlike particles would induce a pseudo-magnetic field for neutrons close to bulk matter. A laboratory search investigates neutron spin precession close to a heavy mirror using ultracold neutrons in a magnetic resonance spectrometer. From the absence of a shift of the magnetic resonance we established new constraints on the coupling strength of axion-like particles in terms of the product g _s g _p of scalar and pseudo-scalar dimensionless constants, as a function of the force range λ, g _s g _p λ² ≤ 2 × 10^?21 [cm²] (C.L.95%) for 10^?4 cm < λ < 1 cm. For 0.1 cm < λ < 1 cm previous limits are improved by 4 to 5 orders of magnitude.     

Positive parity low spin states of odd-mass tellurium isotopes

In this work, we analyse the positive parity of states of odd-mass nucleus within the framework of interacting boson fermion model. The result of an IBFM-1 multilevel calculation with the lg_9/2, 2d_5/2, 2d_3/2, 3s_1/2 and one level, 1h_11/2 with negative parity, single particle orbits is reported for the positive parity states of the odd mass nucleus ^123-125Te. Also, an IBM-1 calculation is presented for the low-lying states in the even-even ^124-126Te core nucleus. The energy levels and B (E2) transition probabilities were calculated and compared with the experimental data. It was found that the calculated positive parity low spin state energy spectra of the odd-mass ^123-125Te isotopes agree quite well with the experimental data.