Rb Nuclei Research Articles

On the “contact” hyperfine interaction

When Enrico Fermi analyzed the magnetic interaction between the electron and Na, Cs, and Rb nuclei in 1930, he used the Dirac equation to compute the energy of an electron interacting with a point charge and magnetic dipole (the nucleus) fixed at the origin. After the mathematical dust had settled, he found an interaction that appeared to act only at a single point: the center of the electron wavefunction; it has been called a contact interaction. In 1936, Casimir analyzed the magnetic interaction of proton and neutron spins in the ground state of the deuteron using the Schrödinger equation and classical electrodynamics. Using symmetries appropriate only to s states, and performing an integration by parts, he found that they, too, seemed to interact only at a single common point of the proton and neutron: their center-of-mass. When applied to hydrogen, his result agreed with Fermi's. We present an expanded version of Casimir's important but little-known calculation.

Trial for the long neutron counter TETRA using 96,97Rb radioactive sources

The TETRA long neutron counter is operated at ALTO ISOL facility behind the PARRNe mass separator. TETRA has been proven to be a unique instrument for measurements of β-decay properties of short-lived neutron-rich nuclei having applications for the nuclear structure and/or astrophysical r-process calculations. A proper calibration of TETRA can allow validation of the experimental procedure used for determination of β-delayed one-neutron emission probabilities (P1n). It requires the use of a well-known β-neutron decaying radioactive source which can be only produced and measured on-line due to its short half-life. Thus, the present paper reports on measurements of P1n and T1/2 of 96,97Rb nuclei using TETRA . The results obtained are in a good agreement with the values available in the literature. This proves that the developed techniques can be applied to unknown P1n and T1/2 of neutron-rich species.

Shape evolution and coexistence in neutron-deficient Kr, Rb, Sr and Zr nuclei

The potential energy surfaces of the isotopes of Kr, Rb, Sr and Zr and the isotones N=40 in the A∼80 region of the nuclear landscape display interesting shape variations with N and Z. The shape evolution and the possible shape coexistence are discussed within the cranked Nilsson-Strutinsky (CNS) framework for the isotopic and isotonic chains. The results indicate an oblate shell gap at Z=36 and 37 and a prolate shell gap at Z=38 and 40 with deformation ϵ2∼0.4. Our calculations show a well deformed prolate shell gap at N=40 so that it is determinant in the nuclear shape in this mass region.

Isomeric levels in92Rb and the structure of neutron-rich92,94Rb isotopes

The medium-spin structure of the ${}^{92}$Rb nucleus, populated in spontaneous fission of ${}^{248}$Cm and ${}^{252}$Cf, has been studied using the EUROGAM2 and the GAMMASPHERE Ge arrays, respectively. Two isomers have been found in ${}^{92}$Rb at 284.2 and 1958.2 keV with half-lives of ${T}_{1/2}=54(3)$ ns and ${T}_{1/2}=7(2)$ ns, respectively. A measurement of neutron-induced fission of ${}^{235}$U, at the PF1B cold-neutron beam facility of the Institut Laue Langevin, Grenoble, has been performed to confirm the assignment of the ${T}_{1/2}=54(3)$ ns, 284.2-keV isomeric level to the ${}^{92}$Rb nucleus. Excited levels in ${}^{92}$Rb and ${}^{94}$Rb nuclei have been calculated in a large-scale shell-model framework. Isomers observed in these two nuclei have been interpreted as proton-neutron configurations involving the high-$j$ $\ensuremath{\nu}1{h}_{11/2}$ and $\ensuremath{\pi}1{g}_{9/2}$ orbitals.

Local spin fluctuations in iron-based superconductors:Se77andRb87NMR measurements on Tl0.47Rb0.34Fe1.63Se2

We report nuclear magnetic resonance (NMR) studies of the intercalated iron selenide superconductor ${(\text{Tl},\text{Rb})}_{y}{\text{Fe}}_{2\ensuremath{-}x}{\text{Se}}_{2}$ (${T}_{c}=32$ K). Single-crystal measurements up to 480 K on both ${}^{77}$Se and ${}^{87}$Rb nuclei show a superconducting phase with no magnetic order. The Knight shifts $K$ and relaxation rates $1/{T}_{1}T$ increase very strongly with temperature above ${T}_{c}$, before flattening at 400 K. The quadratic $T$-dependence and perfect proportionality of both $K$ and $1/{T}_{1}T$ data demonstrate their origin in paramagnetic moments. A minimal model for this pseudogap-type response is not a missing density of states, but rather two additive contributions from the itinerant electronic and local magnetic components, a framework unifying the $K$ and $1/{T}_{1}T$ data in many iron-based superconductors.

High-spin states and level structure inRb84

High-spin states in $^{84}\mathrm{Rb}$ have been studied by using the $^{70}\mathrm{Zn}$($^{18}\mathrm{O},p3n)$$^{84}\mathrm{Rb}$ reaction at beam energy of 75 MeV. The $\ensuremath{\gamma}$-$\ensuremath{\gamma}$ coincidence, excitation function, and ratios for directional correlation of oriented states were determined. A new level scheme was established in which the positive- and negative-parity bands have been extended up to ${17}^{+}$ and ${17}^{\ensuremath{-}}$ with an excitation energy of about 7 MeV. The signature splitting and signature inversion of the positive-parity yrast band were observed. To understand the microscopic origin of the signature inversion in the yrast positive-parity bands of doubly odd Rb nuclei, as an example, we performed calculations using the projected shell model to describe the energy spectra in $^{84}\mathrm{Rb}$. It can be seen that the main features are reproduced in the calculations. This analysis shows that the signature splitting, especially its inversion, can be reproduced by varying only the $\ensuremath{\gamma}$ deformation with increasing spin. To research the deformation of $^{84}\mathrm{Rb}$ carefully, we calculate the total Routhian surfaces of positive-parity yrast states by the cranking shell model formalism. In addition, the results of theoretical calculations about the negative-parity yrast band in $^{84}\mathrm{Rb}$ with configuration $\ensuremath{\pi}({p}_{3/2},{f}_{5/2})\ensuremath{\bigotimes}\ensuremath{\nu}{g}_{9/2}$ are compared with experimental data, and a band diagram calculated for this band is also shown to extract physics from the numerical results.

R 87 b and C133s nuclear magnetic resonance study of the structural properties of mixed RbxCs2−xZnCl4 (x=, 1, and 2) crystals

The structures of mixed RbxCs2−xZnCl4 (x=0, 1, and 2) single crystals grown by using the slow evaporation method were determined with x-ray diffraction. In addition, the NMR spectra and the spin-lattice relaxation times, T1, of the R87b and C133s nuclei of the three crystals were determined by using nuclear magnetic resonance (NMR) spectroscopy. The spin-lattice relaxation times, T1, of the Cs-based compounds are very much longer than those of the Rb-based compounds. The differences between the T1 values of the Rb and Cs nuclei are due to the difference between their electric quadrupole moments. Further, we analyzed the crystallographic structures of these crystals by considering the occupation probabilities (Rb or Cs) of the two cationic sites. Our NMR experimental results confirm that there are two crystallographically inequivalent Rb sites, Rb(1) and Rb(2), in Rb2ZnCl4 and two crystallographically inequivalent Cs sites, Cs(1) and Cs(2), in Cs2ZnCl4. And, only one Rb site and only one Cs site in RbCsZnCl4 was obtained. The Cs and Rb occupation rates of each of the two available sites, A1 and A2, were determined from the NMR signals.

Study on the paramagnetic relaxation mechanisms by R87b nuclear magnetic resonance in Rb2MnCl4 crystals of A2BX4 type

The spin-lattice relaxation time, T1, for R87b nuclei in Rb2MnCl4 crystals was investigated, and a phase transition was found near 383 K (=TC). The R87b spectrum changes near TC from two central resonance lines due to Rb(1) and Rb(2) to one Rb central resonance line, and this change is due to changes in the local symmetry of the Rb sites near TC. The central resonance lines for Rb nuclei in Rb2MnCl4 crystals are shifted to higher frequencies by the paramagnetic ions. Further, the relaxation times for the Rb(1) and Rb(2) nuclei in Rb2MnCl4 crystals are more or less continuous near TC. Below TC, the spin-lattice relaxation rates, T1−1, for Rb(1) and Rb(2) are proportional to T−2, which implies that these relaxations occur mainly via Raman processes. We also compare our results for Rb2MnCl4 with those reported previously for Rb2BCl4 (B=Co and Zn) and CsBCl3 (B=Mn, Cu, Zn, and Cd) crystals.

A nuclear magnetic resonance study of the phase transitions and electric quadrupole Raman processes of M 5H 3(SO 4) 4·H 2O (M=Na, K, Rb, and Cs) single crystals

The spin–lattice relaxation times and spin–spin relaxation times for 1H and M in M 5H 3(SO 4) 4·H 2O (M=Na, K, Rb, and Cs) single crystals grown using the slow-evaporation method were measured as functions of temperature. Two kinds of protons were identified in the M 5H 3(SO 4) 4·H 2O structure: acid protons and water protons. Our experimental results show that the acid and water protons in Cs 5H 3(SO 4) 4·H 2O are involved in phase transitions of this crystal, whereas neither type of proton is involved in the phase transitions of the other three crystal type (M 5H 3(SO 4) 4·H 2O; M=Na, K, and Rb). Moreover, the relaxation times for the M (=Na, K, and Rb) nuclei in these crystals were found to decrease with increasing temperature and can be described with T 1 - 1 ∝ T k ( k=2). The T 1 results for M (=Na, K, and Rb) in M 5H 3(SO 4) 4·H 2O crystals can be explained in terms of a relaxation mechanism in which the lattice vibrations are coupled to the nuclear electric quadrupole moments.

Relaxation mechanisms of Rb 2Co(SO 4) 2 ⋅ 6H 2O single crystals studied by 1H and 87Rb nuclear magnetic resonance

The spin-lattice relaxation time, T 1 , and the spin–spin relaxation time, T 2 , for 1 H and 87 Rb nuclei in Rb 2Co(SO 4) 2⋅6H 2O crystals were investigated. The phase transitions occur near 370 K ( = T C 1 ) , 402 K ( = T C 2 ) , 413 K ( = T C 3 ) , and 458 K ( = T C 4 ) . The 87 Rb spectrum changes near T C 1 from Rb(1) and Rb(2) central resonance lines to one Rb central resonance line, and this change is due to the structural phase transition. The change in the 1 H T 1 near T C 1 and the changes in T 1 and T 2 for Rb(1) and Rb(2) near T C 1 and T C 2 are also due to the phase transitions, and are related to changes in the symmetry of the octahedra of water molecules and slight rotations of the SO 4 tetrahedra surrounding Rb +. Further, below T C 1 the spin-lattice relaxation rates, T 1 − 1 , for Rb(1) and Rb(2) are proportional to T − 2 , which implies that these relaxations occur mainly via Raman processes.

Precise atomic masses of neutron-rich Br and Rb nuclei close to the r-process path

The Penning trap mass spectrometer JYFLTRAP, coupled to the Ion-Guide Isotope Separator On-Line (IGISOL) facility at Jyvaskyla, was employed to measure the atomic masses of neutron rich 85 to 92Br and 94 to 97Rb isotopes with a typical accuracy less than 10 keV. Discrepancies with the older data are discussed. Comparison to different mass models is presented. Details of nuclear structure, shell and subshell closures are investigated by studying the two-neutron separation energy and the shell gap energy.

Spin-lattice relaxation below superprotonic phase transition in Rb 3H(SeO 4) 2

In order to investigate the proton dynamics and the mechanism of the relatively high-electrical conductivity observed even below T c in Rb 3H(SeO 4) 2, we have measured the 1H spin-lattice relaxation rate. From the measurement of the 1H spin-lattice relaxation rate T 1 − 1 , it is found that the temperature dependence of T 1 − 1 takes a peak at around 345 K. The analysis of the temperature dependence of T 1 − 1 shows that T 1 − 1 in Rb 3H(SeO 4) 2 is described well by the dipole–dipole relaxation between proton and Rb nuclei. Moreover, it was also found that not only the proton dynamics described by a hopping motion of proton between two equivalent sites in the hydrogen bond but also a new process of proton transfer appears above around 338 K. This new process is a hopping motion of proton accompanied by the breaking and rearrangement of hydrogen bond. From these results it is deduced that the increase of the electrical conductivity observed even below T c is caused by the proton transfer between possible stable sites accompanied by the breaking and rearrangement of hydrogen bond, and that electrical conductivity in Rb 3H(SeO 4) 2 is dominated by protons motion even below T c.

Transferred hyperfine field of Rb 2CoCl 4 single crystals in the ferroelectric–incommensurate–normal phase by 87Rb NMR

The molecular susceptibility and paramagnetic shift of Rb 2CoCl 4 single crystals grown using the slow evaporation method were measured, and from these experimental results we obtained the transferred hyperfine interaction due to the transfer of spin density from Co 2+ ions to Rb + ions. The transferred hyperfine field was obtained for the ferroelectric, incommensurate, and normal phases. In the case of Rb(I), the transferred hyperfine interaction decreases with increasing temperature in the incommensurate phase, and increases with increasing temperature in the normal phase. The value of H hf in the incommensurate and normal phases increases abruptly with increasing temperature in the case of Rb(II). These results indicate that the effects due to the transfer of spin density from Co 2+ ions to the Rb(I) and Rb(II) ions are large above T i. In particular, the effect due to the transfer of spin density to Rb(II) ions in the normal phase is very large; the variations with temperature of the transferred hyperfine interactions of the Rb(I) and Rb(II) nuclei are more or less continuous in T c1 and T i, and are not affected by the ferroelectric–incommensurate–normal phase transitions.

Transferred hyperfine interaction for Rb87 and Cs133 in AMnCl3 (A=Rb and Cs) single crystals

The transferred hyperfine interactions at the A nuclei in AMnCl3 (A=Rb and Cs) crystals were measured on both sides of their corresponding Néel temperatures, TN. The changes in the curves of the transferred hyperfine field, Hhf, near 94.6 and 67 K for the Rb and the Cs nucleis, respectively, were associated with paramagnetic-to-antiferromagnetic transitions in these crystals. The Hhf due to transfer of the spin density from the Mn2+ ion to the A ion was obtained in the paramagnetic and the antiferromagnetic regions. The change in the Hhf for Rb and Cs nuclei may be due to differences in the contributions of the Mn2+ ions. Also, the temperature dependences of Hhf for Rb and Cs nuclei in RbMnCl3 and CsMnCl3 change abruptly in the antiferromagnetic phase, and the abrupt increase in the Hhf is large enough to allow transfer of the spin density from the Mn2+ ion to the A ion for TN>T. This result is consistent with the increases in the spin-lattice relaxation times, which were observed in previous research, for both crystals.

NMR study of Rb clusters in zeolite LTA

The features of 27 Al and 87 Rb NMR in Rb-loaded LTA-type zeolite are discussed in comparison with K-loaded one. Broadening of 27 Al spectrum by magnetic origin is observed and the difference from the K case is pointed out for the shape of spectrum. These facts suggest that the configurations of electrons are not identical in the cases of Rb and K. For 87 Rb the mass center of the spectrum shifts clearly to higher frequency side below 10 K . The existence of Fermi contact interaction between s electron and Rb nuclei is suggested.

Reintroducing anisotropic interactions in magic-angle-spinning NMR of half-integer quadrupolar nuclei: 3D MQMAS.

Selective reintroduction of anisotropic interactions such as the chemical shift anisotropy (CSA) and homonucler dipolar (HMD) coupling were implemented in a high-resolution NMR spectroscopy for half-integer quadrupolar nuclei. Rotary resonance recoupling (R(3)) combined with the multiple-quantum magic-angle spinning (MQMAS) in a three-dimensional (3D) experiment provides not only site-specific high-resolution spectra to yield the quadrupolar interaction parameters but also the CSA or HMD interaction parameters. This 3D experiment provides an avenue for the complete local structural information of half-integer quadrupolar nuclei. Three-dimensional MQMAS experiments incorporating R(3) of HMD and CSA interactions were demonstrated on model compounds containing (11)B, (23)Na, and (87)Rb nuclei.

Nuclear quadrupole moments from molecular microwave data: The quadrupole moment of85Rband87Rbnuclei and survey of molecular data for alkali-metal nuclei

The ``molecular'' values of the quadrupole moment of the Rb and Na nuclei have been obtained by using spectroscopic values of nuclear coupling constants and high-level-correlated relativistic calculations of the electric-field gradients in fluorides and chlorides. The recommended value for the ${}^{85}\mathrm{Rb}$ nucleus which follows from the present study is about 276 mb, with expected error bars of the order of about 1 mb. This value agrees with the atomic spectroscopy data, and suggests that the quadrupole coupling constant measured for the RbCl molecule is in error. The present calculations for ${}^{23}\mathrm{Na}$ confirm the earlier molecular result for its electric quadrupole moment, and combined with recent atomic calculations lead to the recommended value in the range 104--105 mb. The molecular results for nuclear quadrupole moments of the alkali-metal nuclei are reviewed leading to a list of the corresponding recommended values.

Sensitivity enhancement of the MQMAS NMR experiment by fast amplitude modulation of the pulses

We report here an improved way of doing the multiple-quantum magic-angle spinning (MQMAS) NMR experiment that relies on the use of amplitude modulated pulses. These pulses were found to yield MQMAS NMR signals that are considerably stronger (≈200–300%) than the ones arising from the usual continuous wave pulse schemes by virtue of a superior efficiency of the triple- to single-quantum conversion process. Numerical simulations and experimental results taking 23 Na and 87 Rb nuclei as examples are presented that corroborate the usefulness of this approach.

87,85Rb NMR spectra and relaxation in Rb 3C 60

85,87Rb NMR spectra and relaxation are reported in the temperature range 4–300 K, for samples of C 60 intercalated with Rb through a direct-reaction technique at the nominal composition Rb 3C 60. The NMR spectrum is characteristic of the second-order quadrupole powder distribution of the central line, indicating a local non-cubic symmetry at the Rb site and a very small Knight shift. The relaxation rate is found to follow a T 2 law above 30 K. This result, together with the ratio of the relaxation for the two Rb isotopes, points towards a quadrupole relaxation mechanism by phonons. Two contributions were found in the nuclear magnetization recovery which have been attributed to the Rb nuclei in the tetrahedral site and in the octahedral site, respectively, with the nucleus in the T-site coupled more strongly to the lattice dynamics. No detectable change in the NMR spectrum and/or relaxation rates was found at the superconducting transition located at T c = 27.5 K.

EPR of S2- in RbCl and RbBr

An EPR study of a new S2- defect in RbCl is presented. A comparison with the S2- centre in RbBr, previously found by Vannotti et al. is made. For both salts a clearly resolved superhyperfine structure was observed, which has not yet been reported. The interpretation of the spectra was complicated by the simultaneous presence of the 85Rb (I=5/2) and 87Rb (I=3/2) nuclei. An excellent quantitative agreement between simulation and the experimental data was obtained, using only two parameters, i.e. the linewidth for a single superhyperfine component and the 85Rb (I=5/2) splitting. The analysis is based on the interaction of the unpaired electron on the S2- ion with four equivalent Rb nuclei. The model is consistent with an S2- ion replacing a single Cl-, respectively Br-, ion.