Precise Quadrupole Moment of the Doubly Closed Shell Plus One Proton Nucleus 41Sc

In order to precisely determine the |eqQ(⁴¹Sc)/h| of ⁴¹Sc(I ^π=7/2⁻, T _1/2=0.596 s) implanted in a TiO₂ single crystal the electric field gradient tensor and anisotropic chemical shift were determined by detecting the Fourier Transformed Pulse-NMR of ⁴⁵Sc(I ^π=7/2⁻, stable) in the crystal at a high field of 7.0 T and 9.4 T. Combining the new |eqQ(⁴¹Sc)/h| value with the Q(⁴⁵Sc)=−(23.6±0.2) fm², also renewed by using the known atomic hyperfine interaction constants and Sternheimer polarization effect, the |Q(⁴¹Sc;I ^π=7/2⁻,T _1/2=0.596 s)|=(15.6±0.3) fm² has been precisely determined. The value is compared with the theoretical Q(⁴¹Sc) given by a shell model code. This revised version was published online in September 2006 with corrections to the Cover Date.     

Quadrupole moment of the doubly closed shell +1 nucleon nucleus41Sc(Iπ=7/2−)

The nuclear electric quadrupole moment of⁴¹Sc(I^π=7/2⁻) was experimentally determined by use of the NMR detection in which the asymmetric β-ray distribution from spin polarized nuclei was monitored. The magnetic interaction of the state with high external magnetic field and the nuclear quadrupole interaction with the electric field gradient obtained in TiO₂ crystal were studied. The field gradient seen to the implanted⁴¹Sc was measured independently by the high field NMR detection on the stable isotope⁴⁵Sc located in the equivalent⁴¹Sc site with. |Q(⁴¹Sc;I^π=7/2⁻)|=(0.120±0.006) b was determined.     

Precise measurement of magnetic moment of short-lived β-emitting nuclei12B ( I π=1+, T 1/2=20.18 ms)

The spin polarized β-emitting nuclei¹²B (I ^π=1⁺,T _1/2=20.18 ms) were produced by the nuclear reaction¹¹B(d, p)¹²B and by the selection technique of the incident deuteron energy and the¹²B recoil angle following the nuclear reaction. The nuclear magnetic moment of the short-lived nuclei¹²B was measured by β-NMR with the β-NMR and β-NQR setup established for the first time in China. The nuclear magnetic moment of¹²B was determined to be μ=0.99993±0.00048 nm org=0.99993±0.00048 after the precise correction of the Knight shift.     

Precise measurement of the magnetic moment of17F(I x =5/2+,T 1/2=64.5 s) and its hyperfine interactions in ionic crystals

Hyperfine interactions of β-emitting¹⁷F implanted in single crystals of NaF and CaF₂ were studied. The nuclear magnetic moment of theT ^π=5/2⁺ state was determined with an improved precision to be |μ(¹⁷F;π=5/2⁺,T _1/2=64.5s|=4.72130±0.00025. nm. Isoscalar magnetic moments of the doubly closed shell ±1 nucleon nuclei around mass number 16 were derived and the effective nucleon mass in the nucleus was discussed.     

Magnetic moment of beta-emitting41Sc(Iπ=7/2−) and knight shift in Pt metal

The nuclear magnetic moment of⁴¹Sc(I^π=7/2⁻, T_l/2=0.59sec) was remeasured, and the precision of the value was improved about 10 times compared with the previously known one. The value was determined to be |μ(⁴¹Sc;I^π=7/2)|=(5.4305±0.0018) nm. Comparing the value with the previously known NMR of the nuclei in Pt, the knight shift, K=−(0.4±5.3)·10⁻⁴ was determined.     

Precise Nuclear Quadrupole Moments of 8B and 13B

The electric quadrupole coupling constants eqQ/h of ⁸B (, T _1/2 = 769 ms) and ¹³B (, T _1/2 = 17.4 ms) in single crystal TiO₂ have been precisely measured by the β-NQR technique. The ratios of these Q moments to Q(¹²B) were determined as ∣Q(⁸B)/Q(¹²B)∣ = 4.882(32) and ∣Q(¹³B)/Q(¹²B)∣ = 2.768(24).     

The low temperature quadrupole orientation of103Ru in ruthenium

The quadrupole frequencyv _Q =e ² qQ/h of¹⁰³Ru (Z=44,N=59) in a ruthenium single crystal has been measured using the technique of low temperature quadrupole orientation to bev _Q (¹⁰³RuRu)=−14.7(5) MHz. Temperatures below 2 mK were reached in this experiment using a PrNi₅ demagnetization stage attached to a³He−⁴He dilution refrigerator. Using the measured magnitude of the RuRu electric field gradient (EFG) at low temperatures |eq(RuRu)|=1.02(3)×10¹⁷ V.cm⁻² [1] and adopting the sign ofeq(RuRu) to be negative from systematics, this result yields a value for the ground-state electric quadrupole moment of¹⁰³Ru ofQ(¹⁰³Ru)=+0.59(2) b. This moment may be interpreted using the weak coupling model of de-Shalit [2]. A Korringa constant for¹⁰³RuRu ofC _K=39(6) Ks was measured in this experiment. Taking advantage of a small iridium contamination of the ruthenium single crystal, the quadrupole moment of the¹⁹²Ir ground state was determined to beQ(¹⁹²Ir)=+2.12(25) b. The sign of the IrRu electric field gradient was found to be negative as a result of this work.     

Measurement of the Electric Quadrupole Moment of the 9/2− and 21/2− Isomers in 173Ta

The electric quadrupole moments of the 9/2⁻ and 21/2⁻ isomeric states of ¹⁷³Ta at 165.8 keV and 1713.2 keV, respectively, were measured as Q(9/2⁻)=2.92(15) b and Q(21/2⁻)=6.23(18) b for the first time using the TDPAD technique. A 66 MeV pulsed ¹²C ion beam from the 15UD pelletron accelerator facility of the Nuclear Science Centre at New Delhi was used in the reaction ¹⁶⁵Ho(¹²C, 4nγ)¹⁷³Ta. The experimental values of equilibrium deformations β₂(9/2⁻)=0.251(7) and β₂(21/2⁻)=0.391(7) were extracted. This revised version was published online in July 2006 with corrections to the Cover Date.     

Q 2 dependence of the measured asymmetry A 1: A test of the Bjorken sum rule

We analyze the proton and deutron data on the spin-dependent asymmetry A ₁(x, Q ²), supposing that the DIS structure functions g ₁(x, Q ²) and F ₃(x, Q ²) have a similar Q ² dependence. As a result, we have found that Λ ₁ ^p −Λ ₁ ⁿ =0.190±0.038 at Q ²=10 GeV² and Λ ₁ ^p −Λ ₁ ⁿ =0.165±0.026 at Q ²=3 GeV²; these values are in the best agreement with the Bjorken sum rule predictions. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 1, 9–14 (10 January 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

A Possible Nuclear Spin Dewar. Hyperfine Interactions of Short-Lived β Emitter 8Li and 12B in TiO2

It was confirmed by detecting the β-NMR of ¹²B (I ^π=1⁺, T _1/2=20.2 ms) in a TiO₂ (rutile) crystal that the nuclear spin polarization of ¹²B was totally maintained in the crystal as produced through a nuclear reaction before implantation. Two locations, site 1 and site 2, were found with the relative populations 9 and 1, respectively, and the electric field gradients (EFGs) at those sites were obtained to be q(site 1)=+(37.1±0.5)10¹⁵ V/cm², η(site 1)<0.03, q(site 2)=+(185±5)10¹⁵ V/cm² and η(site 2)=0.62±0.02. We also found that about 30% of the initial polarization of ⁸Li (I ^π=2⁺, T _1/2=838 ms) was maintained in the crystal. Since the polarizations of other β emitting nuclei, ^12,16N, ^13,19O, and ⁴¹Sc were also totally maintained in the crystal, the crystal can be a “Spin Dewar” in which many short-lived nuclides can be implanted with their polarizations totally maintained during their lifetimes for the studies not only on the electronic structure of impurities in it but also on the nuclear properties. This revised version was published online in September 2006 with corrections to the Cover Date.     

Spectroscopic properties of Nd<Superscript>3+</Superscript>:CaNb<Subscript>2</Subscript>O<Subscript>6</Subscript> crystal

The absorption spectra, fluorescence spectrum and fluorescence decay curve of Nd³⁺ ions in CaNb₂O₆ crystal were measured at room temperature. The peak absorption cross section was calculated to be 6.202×10⁻²⁰ cm² with a broad FWHM of 7 nm at 808 nm for E//a light polarization. The spectroscopic parameters of Nd³⁺ ions in CaNb₂O₆ crystal have been investigated based on Judd-Ofelt theory. The parameters of the line strengths Ω _t are Ω ₂=5.321×10⁻²⁰ cm²,Ω ₄=1.734×10⁻²⁰ cm²,Ω ₆=2.889×10⁻²⁰ cm². The radiative lifetime, the fluorescence lifetime and the quantum efficiency are 167 μs, 152 μs and 91%, respectively. The fluorescence branch ratios are calculated to be β ₁=36.03%,β ₂=52.29%,β ₃=11.15%,β ₄=0.533%. The emission cross section at 1062 nm is 9.87×10⁻²⁰ cm².     

Hyperfine Interaction of 140Ce(←140La) in CaB6

A ¹⁴⁰La(I ^π=3⁻, T _1/2=40.3 h)-doped layer has been produced in CaB₆ by means of radioactive isotope (RI) beam technique: ¹⁴⁰Cs(I ^π=1⁻, T _1/2=63.7 s) was implanted into CaB₆ and the radioactive equilibrium of ¹⁴⁰Ba–¹⁴⁰La was achieved. The concentration of La in CaB₆ was La/Ca ∼0.001. Obtained TDPAC spectra of the 2083 keV level of ¹⁴⁰Ce (I ^π=4⁺, T _1/2=3.4 ns, μ=+4.35±0.10 μ _N ) followed by the β decay of ¹⁴⁰La showed the existence of hyperfine magnetic fields: B _hyp=−15.0±0.5 T and −1.00±0.15 T. This revised version was published online in September 2006 with corrections to the Cover Date.     

Anharmonic force constants of GaSb from the measured third order elastic constants at 300°K

The third-order elastic constants of single crystal GaSb are determined using ultrasonic pulse interferometer at 10 MHz. The constants at 300°K, in units of 10¹¹ N.m.⁻², are C_l11 = ™ 4 ·75 ± 0·06 C₁₄₄ = + 0·50 ± 0·25 C₁₁₃ = ™ 3 ·08 ± 0·02 C₁₆₆ = ™ 2·16 ± 0·13 C₁₂₃ = ™ 0 ·44 ± 0·29 C₄₅₆ = ™ 0·25 ± 0·15 These constants are used to evaluate the three anharmonic first and second neighbour force constants based on modified Keating’s model. The constants are (in units of 10¹¹ N.m⁻²)γ=− 2·406;δ=0·407;ε=−0·222.     

Magnetic moment measurement of the 15/2+, 3578 keV level in67Ga

The magnetic moment μ=−(1.69±0.47) μ_N of the 15/2⁺, 3578 KeV level in⁶⁷Ga was determined from measurements of the integral perturbed angular distributions in implanted sources. The excited levels were populated by the reaction⁵⁶Fe(¹⁶O, αp)⁶⁷Ga.     

Beta-gamma-gamma directional correlation in103Rh

β-γ-γ directional correlation studies for the cascades (i)β-rays ofE _max=0.12 MeV,γ-rays of 557 keV andγ-rays of 53 keV and (ii)β-rays ofE _max=0.21 MeV,γ-rays of 444 keV andγ-rays of 53 keV have been made. The triple correlation functionsW(θ) were obtained to beW(θ)=1+(−0.153±0.031)P ₂(cosθ)+(0.004±0.035)P ₄(cosθ) forβ-rays ofE _max 0.12 MeV→557→53 keV cascade andW(θ)=1+(0.163±0.042)P ₂(cosθ)+(−0.035±0.058)P ₄(cosθ) forβ rays ofE _max=0.21 MeV→444 keV→53 keV cascade. Spins and parities of the 650, 537 and 93 keV levels of¹⁰³Rh are deduced by triple angular correlation and the internal conversion coefficient studies. Multipolarities of the transitions are also determined.     

Critical point phenomena in the electrical resistivity of binary liquid systems: CS2 + CH3CN and CS2 + CH3NO2

Electrical resistance measurements are reported on the binary liquid mixtures CS₂ + CH₃CN and CS₂ + CH₃NO₂ with special reference to the critical region. Impurity conduction seems to be the dominant mechanism for charge transport. For the liquid mixture filled at the critical composition, the resistance of the system aboveT _c follows the relationR=R _c−A(T−T _c) ^b withb=0·6±0·1. BelowT _c the conductivities of the two phases obey a relation σ₂−σ₁=B(T _c−T)^β with β=0·34±0·02, the exponent of the transport coefficient being the same as the exponent of the order parameter, an equilibrium property.     

Hyperfine Interactions of 12B in CaB6

The hyperfine interactions of short-lived β-emitter ¹²B implanted into a CaB₆ crystal have been studied by means of the β-NMR technique. An electric quadrupole splitting has been observed at room temperature from which an electric field gradient of q=−(1.34±0.05)×10²¹ V/m² was determined. From the present result, it was found that the ¹²B nuclei are mainly implanted in the substitutional boron site. This revised version was published online in September 2006 with corrections to the Cover Date.     

Measurement and QCD analysis of the diffractive deep-inelastic scattering cross section at HERA

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep→eXY, where Y is a proton or a low mass proton excitation carrying a fraction 1-x_IP>0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t|<1 GeV². Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5≤Q²≤1600 GeV², triple differentially in x_IP, Q² and β=x/x_IP, where x is the Bjorken scaling variable. At low x_IP, the data are consistent with a factorisable x_IP dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α_IP(0)=1.118±0.008(exp.)^+0.029 _-0.010(model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q² and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q² range studied. Total and differential cross sections are also measured for the diffractive charged current process e⁺p→ν̄_eXY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q² at fixed x_IP and x or on x at fixed Q² and β.     

Renormalization of a Hard-Core Guest Charge Immersed in a Two-Dimensional Electrolyte

This paper is a continuation of a previous one [L. Šamaj, J. Stat. Phys. 120:125 (2005)] dealing with the renormalization of a guest charge immersed in a two-dimensional logarithmic Coulomb gas of pointlike ± unit charges, the latter system being in the stability-against-collapse regime of reduced inverse temperatures 0 ≤ β < 2. In the previous work, using a sine-Gordon representation of the Coulomb gas, an exact renormalized-charge formula was derived for the special case of the pointlike guest charge Q, in its stability regime β |Q| < 2. In the present paper, we extend the renormalized-charge treatment to the guest charge with a hard core of radius σ, which allows us to go beyond the stability border β|Q| = 2. In the limit of the hard-core radius much smaller than the correlation length of the Coulomb-gas species and at a strictly finite temperature, due to the counterion condensation in the extended region β|Q| > 2, the renormalized charge Q _ren turns out to be a periodic function of the bare charge Q with period 1. The renormalized charge therefore does not saturate at a specific finite value as |Q| →∞, but oscillates between two extreme values. In the high-temperature Poisson-Boltzmann scaling regime of limits β→ 0 and Q→∞ with the product β Q being finite, one reproduces the Manning-Oosawa type of counterion condensation with the uniform saturation of β Q _ren at the value 4/π in the region β|Q| ≥ 2. The obtained results disprove the “regularization hypothesis” of the previous work about the possibility of an analytic continuation of the formula for Q _ren from the stability region β |Q| < 2 to β |Q| ≥ 2.     

Electromagnetic moments of short lived β emitters 21F, 23Mg, 27Si and 39Ca

The β-NMR spectra of ²¹F, ²³Mg, ²⁷Si and ³⁹Ca which were produced in heavy ion collisions and implanted in various crystals have been observed. The magnetic moments of ²¹F and ²⁷Si were determined to be |μ(²¹F)| = 3.9194 ± 0.0012 μ_N and |μ(²⁷Si)| = 0.8653 ± 0.0003 μ_N, respectively. The electric quadrupole coupling constants were determined for the first time to be |eqQ(²¹F in MgF₂)/h|= 9.94 ± 0.09 MHz, |eqQ(²³Mg in MgF₂)/h|= 1.96 ± 0.06 MHz, |eqQ(²⁷Si in Al₂O₃)/h|= 1.90 ± 0.12 MHz, |eqQ(³⁹Ca in CaCO₃)/h|= 0.60 ± 0.04 MHz. From the present eqQ/h, the Q moments were deduced as |Q(²¹F)|= 110 ± 22 mb, |Q(²³Mg)|= 114 ± 3 mb, |Q(²⁷Si)|= 60 ± 13 mb and |Q(³⁹Ca)|= 36± 7 mb. The present data were compared with the theoretical values obtained by the OXBASH shell model code. This revised version was published online in August 2006 with corrections to the Cover Date.