Magnetic moments of picosecond high-spin states: experimental status and future developments

Magnetic moments are among the most sensitive experimental quantities reflecting the structure of individual excited nuclear states because they are able to distinguish between the nature and the spin coupling of the valence particles. To explore the abilities and limitations of different theoretical models of the nucleus, it is therefore very desirable to determine g-factors with the highest possible reliability. From the experimental point of view, the accuracy achievable is limited by the fact that the effect that has to be measured is extremely small. In addition, when heavy-ion fusion-evaporation reactions are used to populate the nuclei of interest, the complex feeding mechanism inherent in this type of reaction leads to further systematic uncertainties. To overcome these difficulties a new experimental technique called recoil distance transient field technique is introduced allowing for the first time to measure g-factors of individual high-spin states with lifetimes as short as a few picoseconds populated in fusion reactions. For this γγ coincidence technique, the use of highly efficient γ-ray spectrometers is mandatory. This revised version was published online in August 2006 with corrections to the Cover Date.     

The AΠu state of : Electric properties, fine and hyperfine coupling constants, and magnetic moments (g-factors). A theoretical study

Several properties are calculated for A²Π_u of —the majority for the first time—including electric and magnetic moments, and fine/hyperfine structure (fs/hfs) parameters. The new results are compared with our previous ones for X² and B² of [P.J. Bruna, F. Grein, J. Mol. Spectrosc. 227 (2004) 67–80]. The electric quadrupole Θ and hexadecapole Φ moments, polarizability α, and hfs constants a, b, c, d, eQq₀, eQq₂ are evaluated at the density functional theory (DFT) level [B3LYP/aug-cc-pVQZ]. The fs constants (spin–orbit coupling A_Π, Λ-doubling p, q, spin-rotation γ_Π), and magnetic moments (g-factors) are obtained via 2nd-order sum-over-states expansions, using wavefunctions and matrix elements obtained with a multireference configuration interaction (MRDCI) method, and the Breit–Pauli Hamiltonian. At equilibrium, 2nd-order properties of A²Π_u are dominated by its coupling with B². For the A state, two independent components are reported for traceless tensor properties (multipoles Θ and Φ; hfs parameters c/d and q₀/q₂) and three for traced properties (polarizability α and g-factors), i.e., one more component than for axially symmetric Σ states. The currently available experimental data on — limited to A_Π, p, and q—are well reproduced by our theoretical results.     

The tilted-multifoil hyperfine interaction and nuclear spectroscopy

Ions emerging from a stretched foil with their velocity vectorv at an oblique angle to the normaln (tilted foil geometry) are known to be polarized along the axisv×n. The electronic polarization of atomic configurations can influence the nucleus during flight in vacuum via the hyperfine interaction. For a large number of polarizing foils and for very short interaction times, the resulting effects resemble a pure precession in an external magnetic field and have been used to measureg-factors of short-lived nuclear high-spin levels. For long interaction times, a net nuclear polarization is induced and has so far been utilized to determine signs of nuclear quadrupole moments of high-spin isomers and to investigate parity nonconservation effects in⁹³Tc.     

Kinetics of the polarization transfer in spatially disordered spin systems: Depolarization of impurity beta-active nuclei

We performed theoretical and experimental studies of the delocalization of the nuclear polarization of impurity beta-active nuclei ⁸Li in the spatially disordered system of ⁶Li nuclei in LiF single crystals. The process is controlled by the dipole-dipole interaction of nuclear magnetic moments with other nuclei (⁷Li, ¹⁹F) in the crystal. It is effective in a wide range of magnetic fields H ₀ = 150–3000 G as a result of a unique proximity of the g-factors of ⁸Li and ⁶Li nuclei: (g(⁸Li) − g(⁶Li))/g(⁶Li) = 0.0057. The kinetics of the ⁸Li depolarization is measured for an ⁶Li concentration of 0.15%–10.06% and in the field H ₀ of 200, 692 and 1210 G. A satisfactory explanation of the results is obtained on the basis of a numerical-analytical simulation of the process.     

Magnetic dipole moment of the doubly-closed-shell plus one proton nucleus ^{49}sc

The nucleus ^{49}Sc, having a single f_{7/2} proton outside doubly magic ^{48}Ca (Z=20, N=28), is one of the very few isotopes which makes possible testing of the fundamental theory of nuclear magnetism. The magnetic moment has been measured by online β NMR of nuclei oriented at milli-Kelvin temperatures to be (+)5.616(25) μ_{N}. The result is discussed in terms of a detailed theory of the structure of the magnetic moment operator, showing excellent agreement with calculated departure from the f_{7/2} Schmidt limit extreme single-particle value. The measurement completes the sequence of moments of Sc isotopes with even numbers of f_{7/2} neutrons: the first such isotopic chain between two major shells for which a full set of moment measurements exists. The result further completes the isotonic sequence of ground-state moments of nuclei with an odd number of f_{7/2} protons coupled to a closed subshell of f_{7/2} neutrons. Comparison with a recent shell-model calculation of the latter sequence is made.     

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.     

Bremsstrahlung emission of photons in the case of scattering of neutrons by nuclei with arbitrary spins

In the Born approximation, expressions are obtained for the angular and energy distribution of bremsstrahlung photons emitted by relativistic neutrons in the field of a nucleus that has an electric quadrupole moment, and magnetic dipole and octupole moments. The expression obtained for the cross section (d=d_E+d_M) describes the total electromagnetic bremsstrahlung of the neutrons due to the interaction of the magnetic moment of the neutron with the electric (Ze, Q) and magnetic ( _I, ) multiple moments of the target nucleus. It is shown that in contrast to the bremsstrahlung of electrons the bremsstrahlung cross section of neutrons does not contain an infrared divergence. The application of the formulas to⁹Be and²⁷Al nuclei is considered. The results are used to investigate the electromagnetic emission of neutral Fermi particles with spin 1/2 and can be used to obtain additional information about the interaction of their magnetic moment with the multiple moments of a nucleus of arbitrary spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 60–69, December, 1974.We thank Professor D. D. Ivanenko for discussing the work.     

Nuclear Moment Studies with Polarized Radioactive Nuclear Beams

Magnetic dipole and electric quadrupole moments of nuclei in the light-mass neutron-rich region have been studied by taking advantage of spin-polarized radioactive nuclear beams that have been obtained from the projectile fragmentation reaction. Analyses of the results reveal a few interesting phenomena characteristic of nuclear structures in this region. In particular, we report in some detail the latest result on the magnetic moment of the ¹⁷C ground state. The distinctly small value of the g-factor obtained, |g(¹⁷C)|=0.5054±0.0025, clearly excludes a I ^π=1/2⁺ candidate for the spin-parity assignment of this marginally bound nucleus, providing a reasonable account of the non-halo nature reported in recent breakup reaction experiments. Finally, future plans at the upcoming radioactive beam facility presently under construction at RIKEN are briefly mentioned. This revised version was published online in September 2006 with corrections to the Cover Date.     

135Ba and137Ba Fourier transform NMR and NQR studies

¹³⁵Ba and¹³⁷Ba Fourier transform nuclear magnetic resonance and nuclear quadrupole resonance investigations are reported in liquids resp. solids. From these measurements ratios of g₁-factors, hyperfine structure anomalies, magnetic moments, atomic shielding constants and the ratio of the quadrupole moments are evaluated using also data from literature.     

Gyromagnetic ratios of first 2+ states in126, 128, 130, 132Xe

Gyromagnetic ratios of first 2⁺ states in^{126, 128, 130, 132}Xe were determined by implantation perturbed angular correlations (IMPAC). The effective hyperfine magnetic field together with the transient magnetic field at xenon nuclei in iron was utilized to obtain the precession of the angular correlation. The precession due to the transient field was taken from systematics to be /g=–36±6 mrad. The effective hyperfine magnetic field was determined in an experiment on¹²⁶Xe in iron to be 900±200 kG. The results for theg-factors areg(128)=0.41±0.07,g(130)=0.38±0.07 andg(132)=0.37±0.05. Theg-factor of the 2⁺ state in¹²⁶Xe was determined in a separate experiment using a radioactive source of¹²⁶I to beg(126)=0.37±0.07, and was used as calibration for the IMPAC-data.     

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.     

Magnetic dipole moments of collective quadrupole excited states

Magnetic dipole moments for low-lying collective quadrupole excitations are studied in heavy and medium-heavy nuclei within the framework of the Interacting Boson Model (IBM-2). In the present study, we concentrate mainly on the fully symmetric representations of the U(6) group and their magnetic dipole moments. We shortly discuss the lowest non-symmetric 1⁺ level. Comparison with other collective model calculations of g_R and microscopic studies as well as with experimental data is performed.The authors are most grateful to A.E.L.Dieperink and coworkers for the generous help and permission to quote largely from their recent results on magnetic dipole moments in nuclei.They are also indebted to A.Richter,O.Scholten and Iachello for many stimulating discussions. They thank the NFWO,IIKW and the IWONL for financial support.     

Recent developments and new trends in NMR on oriented nuclei

Recent developments in nuclear magnetic resonance on oriented nuclei (NMR-ON) are reviewed with the following main topics: (i) Measurement of magnetic moments. In this context the resonance shift of NMR-ON resonances with an external magnetic field is discussed critically. (ii) Resonance techniques for the measurement of electric quadrupole moments. It is shown that — with hcp-Co as host matrix — the techniques QI-NMR-ON (quadrupole-interaction-resolved NMR-ON) and MAPON (modulated adiabatic passage on oriented nuclei) have a tremendous potential for the measurement of quadrupole moments of radioactive nuclei. Data are presented for medium (Zr, Nb) and heavy elements (Ir, Pt, Au, Hg). With results on the 11/2^– isomers in Au it is shown that MAPON yields highly precise quadrupole moments of states with half-lives of the order of seconds, for which no other technique with comparable precision exists up to now. In the case of⁹⁰Nb it is demonstrated that MAPON allows also the measurement of very small quadrupole moments with high precision. (iii) Electric field gradients in cubic Fe, fcc-Co and Ni. MAPON experiments show a strong magnetic-field dependence of the effective quadrupole interaction; the implications are discussed. (iv)-decay-induced lattice site change identified by a double-resonance NMR-ON measurement. The resulting change of the hyperfme interaction has severe consequences for the interpretation of time-integral and even time-differential nuclear orientation measurements on nuclei far off stability. (v) Spin-lattice relaxation for nuclei on non-substitutional lattice sites. Recent experiments support the global character of the spin-lattice relaxation, in contrast to the local character of the static magnetic hyperfine interaction. (vi) Magnetic-field dependence of the spin-lattice relaxation. Recent experiments with hcp-Co as host lattice strongly support the so-called enhancement factor model and disfavour the one-, two- or three-magnon processes postulated in the literature.     

Measurements of nuclear magnetic moments by transient field techniques

The intense transient magnetic fields have been applied tog-factor measurements of short-lived nuclear states. Significant data for discrete collective high-spin states in¹⁵⁸Dy and in the actinides²³²Th and²³⁸U can be understood by the rotational alignment of valent neutrons and protons, respectively. Measurements on excited states of the self-conjugate nuclei²⁰Ne and²⁴Mg are discussed. The controversial smallg-factor of the²⁰Ne(4⁺) state is particularly exciting since it contradicts all present theories.     

Particle-hole excitations in the208Pb mass region

Spectra, magnetic dipole moments and spectroscopic factors of a number ofA=205–209 nuclei as well asM1 transitions in²⁰⁸Pb are investigated in terms of large-scale shell-model calculations which include 1p ?1h excitations and for some nuclei 2p ?2h excitations. The calculated spectra agree well with the data. The calculatedg-factors are in fair agreement with the data in most cases. The predicted strength forM1 transitions to low-lying states in²⁰⁸Pb is less than that obtained from previous calculations. Spectroscopic factors forl=0 proton pick-up from²⁰⁸Pb and²⁰⁶Pb agree very well with recent experimental data from (e, e′p) reactions.     

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.     

Brute-force NMR-ON on 90NbCu, 101mRhCu and110mAgAg

Brute-force nuclear magnetic resonance on oriented nuclei (BF-NMRON) experiments have been performed for ⁹⁰NbCu, ^101m RhCu and ^110m AgAg at about 10mK. Narrow resonance spectra were detected. Using the known values of the g-factors, the Knight shift has been deduced: K(⁹⁰NbCu) = 0.62(24) %, K(^101m RhCu) = 0.87(27)%. The effective spin–lattice relaxation times were also measured.     

Nuclear structure and nuclear moments studied by the shell model and the interacting boson model

Magnetic dipole and electric quadrupole moments are discussed in terms of the interacting boson model (IBM) and the shell model. From the viewpoint of the IBM, systematic variations of magnetic moments will be discussed by analyzing data of Xe and Ba isotopes. Magnetic and quadrupole moments of various states of Sm and Os isotopes are discussed, pointing out an open problem in the magnetic moments of Os isotopes. The importance of measuring the quadrupole moment of O(6) or -unstable nuclei is emphasized by the example of¹²⁸Xe. The structure of neutron-rich unstable nuclei will be studied in terms of the shell model, by paying attention to the break-down of the closed shell structure, for instance, the collapse ofN=20 closed shell withZN=20. The magnetic moment of the anomalous ground state of¹¹Be is another topic of this discussion, and it is studied in terms of a new theoretical framework called variational shell model.