Der Einflu\ einer Spin-Spinwechselwirkung auf das magnetische Moment schwerer Atomkerne

The corrections to the magnetic moments of heavy nuclei on account of a spindependent two-body-interaction of the form (σ ₁ σ ₂)V(r ₁–r ₂) are determined in the Fermi model calculating the second order contribution for the selfenergy part. It is shown using conservation laws that this contribution is connected to the local Vertex T ^ω [σ] of Migdal's theory of finite Fermi systems.     

The Ruderman-Kittel-Kasuya-Yosida interaction in amorphous La80Au20 alloys with dilute Gd impurities

From magnetization measurements on some amorphous dilute La_80?xGd_xAu₂₀ alloys with x ? 1 we have shown that the magnetic behavior follows the scaling laws of a spin-glass system, characteristic of the 1/r³ dependence of the pairwise interaction. We have also determined the strength of the Ruderman-Kittel-Kasuya-Yosida interaction V(r) = (V₀cos 2k_Fr)/r³, to be V₀ = 0.20 × 10^?37 ergcm³. The corresponding value of the s-f exchange integral is |J_sf| = 0.14 eV, which is compared with values determined from other experiments.     

Phase transition and phonon-drag conductivity in quasi-unidimensional systems

We investigate the properties of a quasi-unidimensional system which exhibits Peierls instability at T_c(μ), where μ is the Fermi energy as measured from the middle of the conduction band. T_c(μ) decreases as 6μ6 increases. The phonon-drag diagrams contribute to fluctuation conductivity, which is proportional to $\text{(T ? T}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$, if |μ| > 1.056 T_c(0). The Kohn Anomalies do not occur at 2k_F unless μ = 0 or |μ| ? T.     

Extrapolation from positive to negative energy of the Woods-Saxon parametrization of the n-208Pb mean field

The real part V(r); E) of the nucleon-nucleus mean field is assumed to have a Woods-Saxon shape, and accordingly to be fully specified by three quantities: the potential depth U_v(E), radius R_V(E) and diffuseness a_v(E). At a given nucleon energy E these parameters can be determined from three different radial moments [r^q]_v = (4π/A) ∝V(r; E)r^q dr. This is useful because a dispersion relation approach has recently been developed for extrapolating [r^q]_V(E) from positive to negative energy, using as inputs the radial moments of the real and imaginary parts of empirical optical-model potentials V(r; E) + iW(r; E). In the present work, the values of U_v(E), R_v(E) and a_v(E) are calculated in the case of neutrons in ²⁰⁸Pb in the energy domain −20 < E < 40 MeV from the values of [r^q]_V(E) for q = 0.8, 2 and 4. It is found that both U_V(E) and R_v(E) have a characteristic energy dependence. The energy dependence of the diffuseness a_a(E) is less reliably predicted by the method. The radius R_V(E) increases when E decreases from 40 to 5 MeV. This behaviour is in agreement with empirical evidence. In the energy domain −10 MeV < E < 0, R_V(E) is predicted to decrease with decreasing energy. The energy dependence of the root mean square radius is similar to that of R_V(E). The potential depth U_v slightly increases when E decreases from 40 to 15 MeV and slightly decreases between 10 and 5 MeV; it is consequently approximately constant in the energy domain 5 < E < 20 MeV, in keeping with empirical evidence. The depth U_v increases linearly with decreasing E in the domain −10 MeV < E < 0. These features are shown to persist when one modifies the detailed input of the calculation, namely the empirical values of [r^q]_v(E) for E > 0 and the parametrization [r_q]_w(E) of the energy dependence of the radial moments of the imaginary part of the empirical optical-model potentials. In the energy domain −10 MeV < E < 0, the calculated V(r; E) yields good agreement with the experimental single-particle energies; the model thus accurately predicts the shell-model potential (E < 0) from the extrapolation of the optical-model potential (E > 0). In the dispersion relation approach, the real part V(r; E) is the sum of a Hartree-Fock type contribution V_HF(r; E) and of a dispersive contribution ΔV(r; E). The latter is due to the excitation of the ²⁰⁸Pb core. The dispersion relation approach enables the calculation of the radial moment [r^q]_ΔV(E) from the parametrization [r^q]_w(E): several schematic models are considered which yield algebraic expressions for [r^q]_ΔV(E). The radial moments [r^q]_HF(E) are approximated by linear functions of E. When in addition, it is assumed that V_HF(r; E) has a Woods-Saxon radial shape, the energy dependence of its potential parameters (U_HF, R_HF, a_HF) can be calculated. Furthermore, the values of ΔV(r; E) can then be derived. It turns out that ΔV(r; E) is peaked at the nuclear surface near the Fermi energy and acquires a Woods-Saxon type shape when the energy increases, in keeping with previous qualitative estimates. It is responsible for the peculiar energy dependence of R_V(E) in the vicinity of the Fermi energy.     

Special analytic properties of the amplitude for scattering on the Woods-Saxon potential

It is shown that the s-wave partial amplitude f(k) for scattering on the real-valued Woods-Saxon potential V(r)=?V ₀/[1+exp((r?R)/d)] has very special analytic properties: the trajectories of the poles of the function k cotδ [of the zeros of the amplitude f(k)] coincide with the lines of the dynamical singularities [spurious poles of f(k)], so that the zeros and the poles compensate each other. In contrast to what is obtained for Yukawa-like potentials, the scattering length does not vanish here at zero energy. The results reported in this article were obtained analytically under the assumption that exp(-R/d)?1. The problem of revealing the poles of the function k cotδ in a partial-wave analysis of neutron scattering on nuclei is discussed.     

Evolution of spin susceptibility from the Pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ～T^?1 appears in the expression for the spin susceptibility χ_ac(T) of the system after the transition point at finite temperatures. The behavior of χ_ac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature T _f is close to zero is discussed. The results are compared with the available experimental data.     

Analyticity of the partition function for finite quantum systems

The partition functionZ(β,λ)=Tre ^-β(T+λV) for a finite quantized system is investigated. If the interactionV is a relatively bounded operator with respect to the kinetic energyT withT-boundb<1,Z(β,λ) is shown to be a holomorphic function of β and λ for $$\left| {\arg \beta } \right|< arctg\frac{{\sqrt {1 - b^2 \left| \lambda \right|^2 } }}{{b\left| \lambda \right|}}and\left| \lambda \right|< b^{ - 1} .$$ Forb=0Z(β,λ) is an entire function of λ and holomorphic in β for Re β>0.     

On the normalization of the Gamov resonant wave function in the configuration space

The regularization of the normalization integral for the resonant wave function, proposed by Zeldovich, is valid only when |Req _res| > |Imq _res|. A new normalization procedure is proposed and implemented, which is valid when this condition fails. First, an arbitrarily normalized vertex function g(k) is calculated using the formula with the potential V(r) in the integrand. This Fourier integral converges for a potential with the asymptotics V(r) → constr ^?n exp(?μr) if |Imq _res| < μ/2. Then the function g(k) is normalized using the generalized normalization rule, which is independent of the resonance pole position. The proposed method is approved by the example of calculation for a virtual triton.     

The p-40Ca and n-40Ca mean fields from the iterative moment approach

The real part V(r; E) of the p-⁴⁰Ca and n-⁴⁰Ca mean fields is extrapolated from positive towards negative energies by means of the iterative moment approach, which incorporates the dispersion relation between the real and imaginary parts of the mean field. The potential V(r; E) is the sum of a Hartree-Fock type component V^HF, (r; E) and a dispersive correction δV(r; E); the latter is due to the coupling of the nucleon to excitations of the ⁴⁰Ca core. The potentials V(r; E) and V_HF(r; E) are assumed to have Woods-Saxon shapes. The calculations are first carried out in the framework of the original version of the iterative moment approach, in which both the depth and the radius of the Hartree-Fock type contribution depend upon energy, while its diffuseness is constant and equal to that of V(r; E). The corresponding extrapolation towards negative energies is somewhat sensitive to the detailed parametrization of the energy dependence of the imaginary part of the mean field, which is the main input of the calculation. Moreover, the radius of the calculated Hartree-Fock type potential then increases with energy, in contrast to previous findings in ²⁰⁸Pb and ⁸⁹Y. A new version of the iterative moment approach is thus developed in which the radial shape of the Hartree-Fock type potential is independent of energy; the justification of this constraint is discussed. The diffuseness of the potential V(r; E) is assumed to be constant and equal to that of V_HF(r; E). The potential calculated from this new version is in good agreement with the real part of phenomenological optical-model potentials and also yields good agreement with the single-particle energies in the two valence shells. Two types of energy dependence are considered for the depth U_HF(E) of the Hartree-Fock type component, namely a linear and an exponential form. The linear approximation is more satisfactory for large negative energies (E < −30 MeV) while the exponential form is better for large positive energies (E > 50 MeV). This is explained by relating the energy dependence of U_HF(E) to the nonlocality of the microscopic Hartree-Fock type component. Near the Fermi energy the effective mass presents a pronounced peak at the potential surface. This is due to the coupling to surface excitations of the core and reflects the energy dependence of the potential radius. The absolute spectroscopic factors of low-lying single-particle excitations in ³⁹Ca, ⁴¹Ca, ³⁹K and ⁴¹Sc are found to be close to 0.8. The calculated p-⁴⁰Ca and n-⁴⁰Ca potentials are strikingly similar, although the two calculations have been performed entirely independently. The two potentials can be related to one another by introducing a Coulomb energy shift. Attention is drawn to the fact that the extrapolated energy dependence of the real part of the mean field at large positive energy sensitively depends upon the assumed behaviour of the imaginary part at large negative energy. Yet another version of the iterative moment approach is introduced, in which the radial shape of the HF-type component is independent of energy while both the radius and the diffuseness of the full potential V(r; E) depend upon E. This model indicates that the accuracy of the available empirical data is probably not sufficient to draw reliable conclusions on the energy dependence of the diffuseness of V(r; E).     

Magnetic properties and peculiarity of magnetic states in dilute antiferromagnets Mn1−x Zn x F2

The dependence of magnetic moment and susceptibility on temperature, magnetic field and frequency of some single crystals Mn_1?x Zn _x F₂ (x≈x _e=0.75—percolation limit) were experimentally investigated. Our experiments show that (Bazhan and Petrov 1984; Cowleyet al 1984; Villain 1984) in these crystals the nonequilibrium magnetic state of spinglass type with finite correlation length appears as temperature decreasesT<T in weak magnetic fields. This state is determined by fluctuation magnetic moments √nμ (wheren is the number of magnetic ions, corresponding to finite correlation length andμ the magnetic moment Mn⁺¹). In the experiments in low magnetic fields and frequencies there are no peculiarities in the magnetic susceptibility temperature dependence atT≠T _f. At temperaturesT>T _f andT<T _f magnetic susceptibility is determined by 1 $$\chi \left( {T > T_f } \right) = \frac{{N\left\langle \mu \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \frac{N}{n}\frac{{\left\langle {\sqrt n \mu } \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \chi \left( {T< T_f } \right)$$ . In strong magnetic fields and large frequencies there are peculiarities in thex(T) dependence atT=T _f. AtT<T _f and strong magnetic fieldsX(T)=x ₀ andT<T _f and at large frequenciesx(T)=x ₀+α/T. The dependences of magnetic susceptibility on the frequency are determined by the magnetic system relaxation. Calculations and comparison with experiments show that the relaxation of the investigated magnetic systems atT<T _f follows the relaxation lawM(t)=M(0) exp[?(t/τ) ^r ], suggested in Palmeret al (1984) for spin-glasses relaxation taking into account the time relaxation distributionτ ₀....τ _max in the system and its ‘hierarchically’ dynamics.     

Dielectric response of the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 in the nonergodic state after a DC electric field is turned off

The Pb(Mg_1/3Nb_2/3)O₃ (PMN) relaxor system is used as an example to analyze the temperature dependences of the low-frequency dielectric permitivity (?′(T)) measured during zero-field heating (ZFH) from T = 10 K to T = 300 K after using different field cooling (FC) conditions. No changes in the temperature dependences of the permittivity have been detected during the transition from a nonergodic relaxor state (NERS) into an ergodic relaxor state (ERS) (at T _f ≈ 216 K). However, the difference Δ?′(T) between the curves corresponding to different field cooling conditions in the same electric field has different shapes and different values below and above T → (T _f + 9 K)^? (for E _dc = 1.52 kV/cm). The reduced permittivities ?′_r(T, f) recorded under different cooling conditions are shown to change their behavior when passing through T = T _f + 9 K. In NERS, these curves diverge: the stronger the field (0 ≤ E _dc ≤ 3 kV/cm), the larger the divergence. In ERS, however, the ?′_r(T, f) curves coincide under different cooling conditions irrespective of the field. The character of the changes in Δ?′(T) and ?′_r (T, f) during the NERS-ERS transition is frequency-independent. The difference in the behavior of the dielectric response during ZFH after cooling in different (ZFC, FC) modes (even in a weak field), for both transition through T _f and cooling down to T = 10 K, indicates different NERSs forming under these conditions. The contribution to ?′(T) from slowly relaxing regions (ω ～ 0.1 mHz), whose polarization is reoriented after the field is turned off, is responsible for the fact that, during the NERS-ERS transition, the ?′_r(T, f) curves coincide at a temperature that is higher than T = T _f.     

Energy dependence of effective nucleon-nucleon interaction and position of the nucleon drip line

A semimicroscopic version of the self-consistent theory of finite Fermi systems is proposed. In this approach, the standard theory of finite Fermi systems is supplemented with relations that involve the external values of the invariant components of the Landau-Migdal amplitude and which follow from microscopic theory. The Landau-Migdal amplitude at the nuclear surface is expressed in terms of the off-shell T matrix for free nucleon-nucleon scattering at the energy E equal to the doubled chemical potential of the nucleus being considered. The strong energy dependence of the free T matrix at low E changes the properties of nuclei in the vicinity of the nucleon drip line. It is shown that, upon taking into account the energy dependence of the effective interaction, the neutron drip line is shifted considerably toward greater neutron-excess values. This effect is illustrated by considering the example of the tin-isotope chain.     

|V<Subscript>ud</Subscript>| from T = 1/2 mirror transitions and the role of atom and ion traps

Precision correlation measurements in nuclear beta decay using atom and ion traps have made significant progress since the last ENAM2004 Conference. We review here the achievements and plans of different projects and discuss for each of them their potential to contribute to the determination of the V_ud element of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. This matrix element has traditionally been determined from the analysis of data in nuclear superallowed 0⁺ \( \rightarrow\) 0⁺ transitions, neutron decay and pion beta decay but can also independently be determined from data in nuclear mirror transitions. This requires the measurement of correlation parameters in such decays to determine the Gamow-Teller to Fermi mixing ratio which, in most cases, dominates the error on the extracted value of | V _ud| .     

Ultrasonic Studies of (CH3)2NH2Al(SO4)2 · 6H2O crystals irradiated by γ quanta and electrons

The temperature dependence of the longitudinal-ultrasound velocities in (CH₃)₂NH₂Al(SO₄)₂ · 6H₂O crystals was studied using the echo-pulse technique in the 90–300 K range. The measurements were carried out along mutually perpendicular crystallographic directions X, Y, Z on samples both unirradiated and irradiated to various doses by γ quanta and an electron beam. The ultrasound velocity V in this crystal was shown to be anisotropic, with V _YY >V _XX >V _ZZ . The V _XX =f(T), V _YY =f(T), and V _ZZ =f(T) curves exhibit anomalies in the form of breaks at the ferroelectric phase transition (PT) at T _c1=152 K, as well as in the region of T _c2=218 K. It was established that as the irradiation dose increases, the PT temperature T _c1 decreases and the anomalies in the temperature dependences of the ultrasound velocities are smeared.     

Exchange and correlation in finite-temperature TDDFT

We discuss the finite-temperature generalization of time-dependent density functional theory (TDDFT). The theory is directly analogous to that at temperature T = 0. For example, the finite-T TDDFT exchange-correlation kernel f_xc(T, n) in the local density approximation can again be expressed as a density derivative of the exchange correlation potential f_xc(T, n) = [?v_xc(T, n)∕?n]δ(r ? r′), where n = N∕V is the electron number density. An approximation for the kernel f_xc(T, n) is obtained from the finite-T generalization of the retarded cumulant expansion applied to the homogeneous electron gas. Results for f_xc and the loss function are presented for a wide range of temperatures and densities including the warm dense matter regime, where T ≈ T_F, the electron degeneracy temperature. The theory also permits a physical interpretation of the exchange and correlation contributions to the theory.     

Computable upper bounds for the adiabatic approximation errors

For a given Hermitian Hamiltonian H(s)(s∈[0,1])with eigenvalues Ek(s)and the corresponding eigenstates|Ek(s)(1 k N),adiabatic evolution described by the dilated Hamiltonian HT(t):=H(t/T)(t∈[0,T])starting from any fixed eigenstate|En(0)is discussed in this paper.Under the gap-condition that|Ek(s)-En(s)|λ0 for all s∈[0,1]and all k n,computable upper bounds for the adiabatic approximation errors between the exact solution|ψT(t)and the adiabatic approximation solution|ψadi T(t)to the Schr¨odinger equation i|˙ψT(t)=HT(t)|ψT(t)with the initial condition|ψT(0)=|En(0)are given in terms of fidelity and distance,respectively.As an application,it is proved that when the total evolving time T goes to infinity,|ψT(t)-|ψadi T(t)converges uniformly to zero,which implies that|ψT(t)≈|ψadi T(t)for all t∈[0,T]provided that T is large enough.     

Conductivity of heavily doped Si:P under uniaxial stress

Barely insulating, uncompensated Si:P samples have been tuned through the metal‐insulator transition applying uniaxial stress along the [100] direction. We find a critical exponent μ ≈︂ 1 of the electrical conductivity extrapolated to temperature T = 0, i.e. σ(T → 0,S) ∼ |S — S_c|^μ, in disagreement with earlier stress tuning studies along [123‐] where μ ≈︂ 0.5 was reported. Varying the stress or the concentration leads to a different T dependence of σ(T). Our stress‐tuning measurements obey finite‐T scaling with a dynamic exponent z = 3.     

Isospin impurity of 64Ga ground state

It is well known that the observation of a nonzero Fermi matrix element for a β-transition between states that differ in isospin can provide information about the relative isospin purity of the states involved. We have determined the log ft value for the 0⁺ → 0⁺ (ΔT ≠ 0) β-transition in ${}^{64}\text{Ga}\text{→}{}^{64}\text{Zn}$ decay as 6.516 ± 0.020. From this log ft value, we have deduced |M_F| = (43.4 ± 1.1) × 10^?3, |α| = (21.7 ± 0.6) × 10^?3 and |〈V_CD〉| = 41.7 ± 1.1 keV, where M_F,α² and 〈V_CD〉 represent the Fermi matrix element, isospin impurity and Coulomb matrix element, respectively. The Coulomb matrix element of 41.7 keV found for ⁶⁴Ga is one of the largest known from β-decay experiments. The experimental procedure involved a careful measurement of the intensity of the annihilation radiation relative to that of the other γ-rays from ⁶⁴Ga decay. As a by-product, we have obtained an improved ⁶⁴Ga decay scheme. We have also summarized the existing information on the isospin impurities of nuclear states as deduced from β-decay experiments.     

On the susceptibility exponent of random anisotropy magnets

The temperature dependence of the non-linear susceptibility ≈₂(T) of random anisotropy magnets in the Ising limit (speromagnets) is calculated for temperatures above the freezing temperature T_f within the framework of the correlated molecular field theory. For the effective susceptibility exponent λ_s(T) = (T?T_f)≈₂d^-1_≈2/dT a non-monotonic temperature dependence is found as for the case of spin glasses. This must be taken into account in order to obtain reliable values for the critical susceptibility exponent from experimental data.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.