Paramagnetic Correction Research Articles

Interaction of a relativistic electron beam with a laser pulse in the presence of a magnetized plasma medium

Significant progress has been made using plasma channels to guide relativistic e-beams in magnetostatic wiggler free-electron lasers (FELs). In this regard, we study the interaction of an intense laser pulse (as a laser wiggler) with a relativistic electron beam embedded in a background of magnetized plasma. The short wavelength of the laser wiggler ( ∼ µm) allows a higher radiation frequency to be obtained than from conventional magnetostatic wigglers. Laser-plasma interaction in a magnetized plasma channel has been studied. Numerical results reveal that the laser self-focusing and self-compression can be enhanced with increasing the external axial magnetic field strength, which leads to a decrease in the spot size of the laser beam. Hence, we employ the laser beam as a suitable laser wiggler in a FEL-device. Injection of plasma in the interaction region of a laser-wiggler-FEL suggests the possibility of producing short wavelengths ( ∼ x-ray) using lower energy beams ( ∼ O(10) MeV). Furthermore, this configuration has a higher tunability by controlling the plasma density in addition to the e-beam energy tunability of the conventional FELs. Effects of the external axial guide magnetic field and plasma medium on the gain of the FEL have been studied. It is found that by increasing the plasma frequency the FEL-gain increases. The effects of e-beam self-electric and self-magnetic fields on the laser gain have also been investigated in the presence of various plasma frequencies. The results indicate that in the presence of beam self-fields, the sensitivity of the gain increases in the vicinity of resonance regions. Besides, the normalized wiggler-induced self-magnetic field has been obtained which reveals that it is a positive parameter, i.e., it can act as a paramagnetic correction to the wiggler magnetic field, therefore, the gain enhancement can be due to the paramagnetic effect of the self-magnetic field. This concept opens a path toward a new source of soft x-ray pulse based on table-top plasma loaded laser wigglers.

Magnetic moment of the 3/2 + state in 165Ho

The Larmor precession for the 362 keV state in 165Ho(Iπ = 3/2 + , T1/2 = 1.512 μs) in Dy2O3 with an external magnetic field of 0.3 T was determined to be − 32.3 ± 0.6 MHz by use of the perturbed angular correlation technique, intending to determine the magnetic moment and apply it to the measurement of the hyperfine field at Ho in Fe. The magnetic moment for this state was tentatively deduced under the assumption that the paramagnetic correction factor for a free Ho3 + ion is applicable to the present case. The independent A22 measurement for the 633 − 362 keV γ cascade for the sign assignment of the Larmor frequency is inconsistent with that from known multipolarities and mixing ratios for this cascade, implying that the mixing ratios may be different from the reported values.

London penetration depth in single crystals of F- and Co-doped RFeAsO (R = La, Nd) superconductors

The in-plane magnetic penetration depth, λ(T), has been measured in single crystals of NdFe1−xCoxAsO, NdFeAsO1−xFx, and LaFeAsO1−xFx. In the Nd compounds we found an upturn in λ(T) below 4K and attribute it to the paramagnetic contribution from the Nd3+ ions. After the correction for this contribution, the in-plane temperature dependent London penetration depth, λL(T), in F-doped crystals was found to follow a power-law dependence, ΔλL(T)∝Tn, n≈2. Similar power-law behavior was found in direct measurements of non-magnetic LaFeAsO1−xFx with n≈2. In NdFe1−xCoxAsO, on the other hand, after the paramagnetic correction, we found n≈3. Our results indicate unconventional pairing in the pnictides, incompatible with a single isotropic gap or a gap with line nodes. The power-law behavior is observed down to T/Tc=0.02 indicating significant gap anisotropy.

Nonexponential London Penetration Depth of FeAs-Based SuperconductingRFeAsO0.9F0.1(R=La, Nd) Single Crystals

The superconducting penetration depth, $\lambda(T)$, has been measured in RFeAsO$_{0.9}$F$_{0.1}$ (R=La,Nd) single crystals (R-1111). In Nd-1111, we find an upturn in $\lambda(T)$ upon cooling and attribute it to the paramagnetism of the Nd ions, similar to the case of the electron-doped cuprate Nd-Ce-Cu-O. After the correction for paramagnetism, the London penetration depth variation is found to follow a power-law behavior, $\Delta \lambda_L(T)\propto T^{2}$ at low temperatures. The same $T^2$ variation of $\lambda(T)$ was found in non-magnetic La-1111 crystals. Analysis of the superfluid density and of penetration depth anisotropy over the full temperature range is consistent with two-gap superconductivity. Based on this and on our previous work, we conclude that both the RFeAsO (1111) and BaFe$_2$As$_2$ (122) families of pnictide superconductors exhibit unconventional two-gap superconductivity.

Self-fields in a free-electron laser with helical wiggler and axial magnetic field

An analysis of self-fields associated with charge and current densities of the electron beam in a free-electron laser with helical wiggler and axial magnetic field is presented. The self-electric field is derived from Poisson's equation. A more detailed analytical model for the self-magnetic field is determined from Ampere's law. Mutual influence of the electron velocity and self-magnetic field is considered to account for the total self-magnetic field. It is shown that for group I orbits, the self-magnetic field acts as a diamagnetic correction to the wiggler magnetic field; for group II orbits, it acts as a paramagnetic correction. Both diamagnetic and paramagnetic effects become stronger near the transverse velocity resonance. An important effect of the self-fields on the electron trajectories is the creation of unstable orbits for group II, which are not found in the absence of self-fields.

Measurement of the g-Factor of the 27− High-Spin Isomer State of 152Dy

The g-factor of the 27− isomer state of 152Dy has been measured using the Time- Integral Perturbed Angular Distribution (TIPAD) method. The high-spin states of 152Dy have been populated by 141Pr(16O,p4n)152Dy reaction at E = 115 MeV from the AVF cyclotron at CYRIC. The paramagnetic correction factor of Dy ions in Pr has been determined to be 4.2(5) by the Time- Differential Perturbed Angular Distribution (TDPAD) measurement of the 21− state of 152Dy. As a result, the g-factor of the 27− isomer state of 152Dy has been obtained to be +0.09(5). This shows the smaller value than the expected one of +0.39 deduced from a fully aligned configuration of π(h 11 2/2 ) ⊗ v(f 7 2/2 h 9/2 i 13/2).

Orbital Paramagnetism of Electrons in Proximity to a Superconductor

We consider the magnetic response of a normal layer (N) coating a superconducting cylinder (S). The diamagnetic response of the normal layer (proximity effect) is related to the formation of Andreev levels. At low energies, the density of such states goes linearly to zero which enhances the various scattering mean-free paths. As a consequence, the low-energy glancing states, which can skip along the outer boundary, can have relatively large magnetic moments that lead to a low-temperature paramagnetic correction to the Meissner result.

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2− state in145Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency ωL=gNμNħ1 β(T)Bext. The paramagnetic correction factor β strictly follows the Curie-Weiss relation β=1+C/(T-θ), withC=−50(2) K and θ=−29(5) K. This is compatible with a hyperfine field ofBint(0)=−25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.

The g-Factor of the First Excited State in 95Mo

The g-factor of the first 3/2+ excited level in 95Mo was determined by perturbing the angular correlation of the 582-204 keV and the 835-204 keV γγ-cascades in three different external fields. A cubic metal lattice (Ag-95Tc) was used in the g-factor experiment as there are no interfering perturbation effects due to quadrupole interactions and no paramagnetic correction of the applied magnetic field in such sources. The result for the g-factor is g = -0.246±0.010.

Hyperfine paramagnetic corrections in the actinides

The paramagnetic correction factors (β) for actinide ions are calculated, using relativistic expressions for the orbital contribution and a phenomenological expression for the core polarization contribution to the hyperfine field. Numerical results for β are given for ions ranging from Th2+ to Cf4+ in various ionization states. The approximations used in the calculations and the validity of the results are discussed. The results of previous PAC experiments on actinide nuclei are re-examined in the light of the present calculations.

Measurement of thegFactor for the1.1−μsecShape Isomeric State inPu237

The spin precession of the $1.1\ensuremath{-}\ensuremath{\mu}sec$ shape isomeric state in $^{237}\mathrm{Pu}$ has been measured by the perturbed angular correlation method. From a measurement of the spin rotation frequency as a function of temperature of the target, the paramagnetic correction factor $\ensuremath{\beta}$ has been determined to be in agreement with the theoretical value of 2.86 at room temperature for a ${4}^{+}$ ionic state. The deduced value for $g$ is +0.14 \ifmmode\pm\else\textpm\fi{} 0.02.

Role of Field-Induced-Surface Current in the Landau Diamagnetism

By assuming an infinite potential barrier at the surface of the semi-infinite system, the field-induced surface current is evaluated within the linear response to the magnetic field applied parallel to the surface. It is shown that the surface current determines the entire diamagnetic susceptibility of the system which is composed of the Landau value of the susceptibility and the negligible paramagnetic correction term proportional to the surface area. When the field is applied perpendicularly, it is found that the surface current vanishes and that no screening of the field strength occurs at all. By this difference the role of the surface-modified cyclotron orbits in the Landau diamagnetism is stressed.

Search for atomic after-effects of the β-decay of 160Tb in insulating and semiconducting compounds

Abstract The hyperfine fields at 160 Dy nuclei immediately following the β − decay of 160 Tb have been examined at room temperature in anhydrous terbium fluoride and in Eu 1 − x Tb x S for several values of x . Integral-rotation perturbed angular correlation (PAC) measurements on cascades proceeding through the 2.9 nsec first excited state show that the paramagnetic correction factor β is close to the free-ion value for the daughter Dy 3+ ion, and is independent of the number of available lattice electrons over the entire range of conductivity from semimetal to ionic insulator. Calculations based on a simple model show that the source of the electrons needed for atomic-shell recovery may be trace impurities at a level available even in the purest of insulating materials. At room temperature in zero applied magnetic field, the character of the fluctuating hyperfine field at the 160 Dy nucleus is found via time-differential and time-integral PAC measurements to be principally magnetic in character, arising from the rapid relaxation of the 4f shell.

Determination of the paramagnetic correction factor of ytterbium

The Larmor precession of the first excited state of172Yb has been measured by perturbedγγ-angular correlations in a liquid source at two different temperatures. By a comparison with theg-factor of this state directly obtained by other experiments the corresponding paramagnetic correction factors were deduced to beβ(20 °C)=2.61±0.27 andβ(33 °C)=2.43±0.27. For the ions Sm3+, Dy3+ and Er3+ the paramagnetic correction factors have been calculated from experimental data given in literature.

The nuclear g-factors of the [formula omitted] states in 237Np and 239Np and the level structure of 237Np

The nuclear g-factors of the 59 keV level in 237Np and the 75 keV level in 239Np were measured by the α-γ perturbed angular correlation technique in a differential and integral measurement, respectively. Liquid sources were used to minimize perturbation by internal fields. The ratio of the g-factors is g 5 2 − ( 239 Np)/g 5 2 − ( 237 Np = 1.04±0.09 . The Np ions are expected to be in the 6 + valency state (5f 1). With a paramagnetic correction factor β estimated to be 1.68±0.11, ifg 5 2 − ( 237 Np) = 0.762±0.060 and g 5 2 − ( 239 Np) = 0.793±0.097 . The experimental values of the g-factors are in good agreement with the theoretical predictions of the Nilsson model. The γ-spectrum following the decay of 241Am was studied with a Ge(Li) detector. The new results are discussed.

The magnetic moment of the first excited state of 143Pr

A value of 1.03±0.08 was found for the gyromagnetic ratio of the 57 keV level of 143Pr from measurements of the perturbation of the angular correlation of the 293-57 keV γ-ray cascade of 143Pr in external magnetic fields. Measurements were carried out with 143Ce sources in the form of dilute solutions at room temperature and with a CeO 2 source at 1400° K, where the paramagnetic correction β is relatively small. The measurements indicate that the Pr ion in aqueous solutions reaches the 3 + state in a time shorter than 4 ns after the β-decay.

The electromagnetic properties of Tm 169

The rotations of the angular correlation of the 198-118 keV and of the 177-130 keV cascades observed in the decay of Yb 169 into Tm 169 have been measured in an external magnetic field. A source of YbCl 3, dissolved in water was used. With a paramagnetic correction factor of 5.31 for the enhancement of the magnetic field at the nuclear site, and the experimental values for the lifetimes of the 5 2 and 7 2 rotational states in Tm 169, the magnetic moments μ 5 2 = 0.61±0.12 n.m. and μ 7 2 = 1.31±0.18 n.m. have been derived. An analysis of all experimentally known electromagnetic properties of the ground state rotational band in Tm 169 is presented and it is found that fifteen measured electromagnetic quantities can be represented by one set of the four rotational parameters Q 0, g K, g R and b 0 .

Effective Magnetic Field and Gradient of Electric Field Acting on the Nucleus of Eu in Europium Iron Garnet

The internal effective magnetic field (${\mathrm{H}}_{\mathrm{eff}}$) and the electric field gradient acting on europium nuclei in europium iron garnet has been calculated. The nondiagonal matrix elements connected with the admixture of states produced by the exchange interaction give the main contribution to these fields. The temperature dependence of these fields is compared with the dependence of the magnetic moment of the ion as caclulated by Wolf and Van Vleck. The effective magnetic field at 0\ifmmode^\circ\else\textdegree\fi{}K turns out to be 7\ifmmode\times\else\texttimes\fi{}${10}^{5}$Oe, whereas, the electric field gradient at 0\ifmmode^\circ\else\textdegree\fi{}K is $\frac{\mathrm{eq}}{h}=\ensuremath{-}555$ Mc/sec per b. In an Appendix the paramagnetic correction for the internal magnetic field acting on the nucleus of Eu in the presence of an external magnetic field is also calculated as a function of temperature. At room temperature ${H}_{\mathrm{int}}=1.54{H}_{0}$.

Theory of Lattice Magnetic Susceptibility of Semiconductors

The motion of a Bloch electron in a static uniform magnetic field is calculated exactly up to second order in the magnetic field in terms of the crystal momentum representation. The magnetic energy of an intrinsic semiconductor at zero temperature is calculated. An explicit expression of the lattice magnetic susceptibility, which consists of the Larmor-like diamagnetic term, the paramagnetic correction term, and additional terms, is presented. As a by-product, the Hamiltonian for the cyclotron motion of a free carrier is obtained in a form which is applicable for arbitrary symmetry and for bands with degeneracies.

The gyromagnetic ratio of the 80 keV rotational state of erbium 166

The angular correlation of the (1380 keV) - (80 keV) gamma-gamma cascade in the decay of 27 h Holmium 166 has been measured in an external magnetic field of 13 550 G. The observed rotation yields for the nuclear g-factor of the 80 keV 2+ rotational state g R = +0.260±0.034 . A paramagnetic correction factor of β = 8.36 ( B eff = β B ext) has been applied in the calculation of this value. There is a strong attenuation of the (1380 keV) - (80 keV) angular correlation by internal fields. The attenuation factors for a liquid source of HoCl 3 in aqueous solution were determined as G 2 = 0.80±0.08, G 4 = 0.56±0.04 . A measurement of the (1380 keV) - (80 keV) angular correlation for different delays showed agreement with a time dependent attenuation A k(t) = A k(0) e −λ k t , where the λ k are λ 2 = 0.09×10 9 sec −1, λ 4 = 0.30×10 9 sec −1 . The ratio of λ 4/ λ 2 suggests that the attenuation is caused mainly by magnetic interaction between the 4f electron shell and the magnetic moment of the nucleus. The spin relaxation time for the 4f electron shell was calculated as τ J = (3.4±0.9) × 10 −13 sec .