The probability of prompt and delayed fission of muonic237Np

Fission fragments from the reaction²³⁷Np(μ ^?,γ,f) have been measured in coincidence with muonic X-rays. The efficiency of the fission fragment detector is determined from (μ ^?,γ,f)-data of the same experiment. The total fission probability perμ-stopP _t has been measured as well as the fission probabilities P_f of the non-radiative muonic (3d→1s)- and (2p→1s)-transitions; the latter has been divided into two parts leading to different mean excitation energiesE:P _t =(54±17)%,P _f (3d→1s)=(41±21)%,P _f (2p→1s,E=6.218 MeV)=(61±19)%, andP _f (2p→1s,E=6.525 MeV)=(57±18)%. The influence of the muon on the fission barrier is discussed. The fission probability after muon capture is compared with a calculated value using a distribution of nuclear excitation energies following muon capture and the fission probability as measured in a²³⁸U(³He,αf)-reaction.     

Fine structure and isotope shift of the 3s4d 3 D-3s3p 3 P, 3s5d 3 D-3s3p 3 P and 3p 2 3 P-3s3p 3 P Transitions of MgI

Summary We report the measurements of the³ D(3s4d)-³ P(3s3p)³ D(3s5d)-³ P(3s3p), and³ P(3p ²)-³ P(3s3p) transition frequency of MgI, the fine-structure separation and isotope shift between²⁴Mg and²⁶Mg. The measurements have been performed in a metastable atomic beam; a good agreement is found for data already existing in the literature. The accuracy of the measurements reported in this paper is mainly limited by the Doppler broadening of theI ₂ transitions used as a reference and by the precision in the knowledge of the related wavelengths.     

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve

The relationship between the transition voltage of the I–V curve of the ferroelectrics and the coercive field of the P–V hysteretic curve is calculated. The first mathematical analysis to explain the relation between the transition voltage V_t and the coercive voltage V_c is obtained. The origin of the interrelation between the transition voltage of the I–V curve and the coercive field is that the height of the boundary barrier is inversely proportional to the effective dielectric constant of the near-boundary region, which is dependent on a derivative of polarization on the electric field, ∂P/∂E. The term ξ(eV_t) plus the term (en_b²δ/dN_dP_s)(eV_c) equals a constant. V_t is the function of E_g, P_s, V_c, and E. There is a linear relation between V_c and V_t. This relationship will induce the matchable relations between the I–V curve and the E–P loop. As long as the V_c of the V–P loop exists, the correspondent V_t of I–V curve will certainly exist. It will be the foundation of a new ferroelectric memory, which operates by the I–V characteristics. These relations are the conditions that can enable nonvolatile memory and nondestructive readout.     

Das Kernquadrupolmoment des Mn55

With a recording photoelectric Fabry-Perot spectrometer and an atomic-beam light source the hyperfine structure of the Mn I-resonance linesλ=4031 Å,λ=4033 Å,λ=4034 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁶ P _7/2,5/2,3/2 ⁰)and of the inter-combination linesλ=5395 Å andλ=5433 Å (3d ⁵4s ² a ⁶ S _5/2?3d ⁵4s4p z ⁸ P _7/2,5/2 ⁰) was measured. Furthermore the resonance lines have been measured with a pulsed atomic-beam in absorption. In this case the quotient (I ₀(ν)?I(ν))/I ₀(ν) was recorded, whereI(ν)=I ₀(ν) exp(?α(ν)d) is the observed intensity with absorption andI ₀(ν) the intensity of the light source. From the hyperfine structure splitting the value of the electric quadrupole moment of Mn⁵⁵ was derived to be:Q(Mn⁵⁵)=+(0.35±0.05)·10^?24 cm².     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Pole approximation in the quasi-free t + p scattering and the t(p,d)d reaction via the t + d interaction

The t(p,p)t and t(p,d)d channels have been investigated in an indirect way through the ²H(t,tp)n and ²H(t,dd)n three-body reactions performed at E _t = 35.5?MeV in quasi-free kinematics. The agreement with direct data supports the pole approximation at energies above the Coulomb barrier.     

In beam gamma spectroscopy of62Zn

The decay scheme of⁶²Zn has been investigated by studying the yield functions, angular distributions and coincidence relation-ships of theγ-rays emitted in the⁶³Cu(p, 2nγ) and⁶⁰Ni(α, 2nγ) reactions. Spins up to7? were assigned to the observed states. Nuclear Reactions ⁶⁰Ni(α, 2nγ)⁶²Zn,E _α=28–35 MeV and⁶³Cu(p, 2nγ)⁶²Zn,E _p = 22–31 MeV; measuredE _γ,I _γ(θ),I _γ(E _p , andI _γ,E _α-γ coincidences,⁶²Zn deduced decay scheme. Enriched target, Ge(Li) detectors.     

Die Isotopieverschiebung von151Eu,152Eu,153Eu,154Eu und die Kernmomente der radioaktiven Isotope152Eu und154Eu

The isotope shift of the stable¹⁵¹Eu,¹⁵³Eu, and the radioactive¹⁵²Eu,¹⁵⁴Eu isotopes and the hyperfine splitting of the¹⁵²Eu isotope was investigated using a digital recording Fabry-Perot-spectrometer. From isotope shift measurements on the line λ 5 765 Å (4f ⁷ 6s 6p z⁶P_7/2-4f ⁷ 6s² a⁸S_7/2) the relative isotope shift was derived:¹⁵¹Eu:0;¹⁵²Eu: 0.923(8);¹⁵³Eu: 1;¹⁵⁴Eu: 1.197(8). The results show that there is a strong increase in the change of the mean square nuclear charge radius δ〈r²〉 when only one neutron is added to the 88 neutrons of the¹⁵¹Eu nucleus, whereas the change of δ〈r²〉 between¹⁵²Eu and¹⁵³Eu is of the same order of magnitude as that between¹⁵³Eu and¹⁵⁴Eu. From the hyperfine splitting of the radioactive isotope¹⁵²Eu in the line δ 6865 Å (4f ⁷ 6s 6p z ¹⁰ P _9/2-4f ⁷ 6s² a⁸S_7/2) the sign of the magnetic dipole moment μ_I(¹⁵²Eu) was found to be negative, and with this result and earlier experimental data the signs of the nuclear quadrupole momentsQ(¹⁵²Eu) andQ (¹⁵⁴Eu) could be determined to be positive.     

Winkelverteilung der Polarisation der Neutronen aus der Reaktion14C(d,n 0)15N bei Deuteronenenergien zwischen 1,3 und 1,9 MeV

Polarization distributions of ground state neutrons emitted from the¹⁴C(d,n ₀)¹⁵N reaction were investigated over the angular range from 15 ° (lab) to 150 ° (lab) at bombarding energies of 1.28, 1.55 and 1.88 MeV. Scattering of neutrons from helium served as polarization analyzer. The experimental results show a large variation with energy of the polarization ranging betweenP(Θ_lab=130 °)=?21% andP(Θ_lab=130 °)=+50% at 1.28 and 1.88 MeV respectively.     

Isotope shifts and energies of the 1s 2p states in helium

The specific mass shift (SMS) and energies of the (1s2p)^{1, 3} P states in helium are evaluated using wave functions expressed in terms of radial “pair functions” which are obtained by numerical solution of inhomogeneous two-particle differential equations. The results obtained when including successively higher angular symmetries in the wave function indicate that the SMS converges asl _max ^?3 for the singlet state and betweenl _max ^?5 andl _max ^?6 for the triplet state. These convergence rates are considerably slower than thel _max ^?5 andl _max ^?7 behaviours found for the singlet and triplet energies. The total energies,E(2¹ P)=?2.123835 a.u. andE(2³ P)=?2.133155 a.u., are about 0.00001 a.u. above the “exact” non-relativistic results obtained with perimetric coordinates and also the SMS between³He and⁴He, SMS(2¹ P)=0.4533 cm^?1 and SMS(2³ P)=?0.6356 cm^?1, are very close to the “exact” results.     

The energy dependence of nuclear reaction cross sections

The reaction cross section σ_R^pA(E) for proton-nucleus collisions varies with energy as the total cross section σ_t^pN(E) does for proton-nucleon scattering in the energy regime 100 MeV ? E ?400 GeV. We propose several empirical relations, and test them by a χ² analysis of various data. Within the framework of Glauber theory, the parameters in the relations can be linked to the cross section for a single inelastic collision.     

On the invariants of the complex Ginzburg-Landau equation

Using Lie group theory, both the invariants and the similarity variables of the complex Ginzburg—Landau equation V_xx = a(V_t + bV) + cV|V|^2kwherea,b,c?Iandk?I are constructed.     

Study of the reactions 118Sn(d,t) and98Mo(d,t): (I). Spectroscopy of 117Sn and 97Mo

The vector analyzing power and differential cross section have been measured at a deuteron energy of 12.0 MeV for ${}^{118}\text{Sn}\text{(}\text{d}\text{,}\text{t}\text{)}$ transitions to six states of ¹¹⁷Sn (E_x = 0.0, 0.16, 0.31, 0.71, 1.02 and 1.18 MeV), for ${}^{98}\text{Mo}\text{(}\text{d}\text{,}\text{t}\text{)}$ transitions to eight states of ⁹⁷Mo (E_x = 0.0, 0.68, 0.72, 0.89, 1.12, 1.28, 2.39 and 2.52 MeV), and for ${}^{118}\text{Sn}\text{(}\text{d}\text{,}\text{d}\text{)}\text{and}{}^{98}\text{Mo}\text{(}\text{d}\text{,}\text{d}\text{)}$. Deuteron optical model potentials were obtained from analysis of the elastic scattering measurements, and were used in a DWBA analysis of the $\text{(}\text{d}\text{,}\text{t}\text{)}$ results. Comparison of the measurements and DWBA predictions for σ(θ) and for iT₁₁(θ) allows unambiguous determination of tl_n and j_n for all ¹¹⁸Sn(d, t) and most ⁹⁸Mo(d, t) transitions. Differences in the triton energy relative to the Coulomb barrier cause marked qualitative differences in the measured cross sections and analyzing powers between ${}^{118}\text{Sn}\text{(}\text{d}\text{,}\text{t}\text{)}\text{and}{}^{98}\text{Mo}\text{(}\text{d}\text{,}\text{t}\text{)}$ transitions of the same l_n and j_n.     

Einfaches Modell für monoatomare klassische Flüssigkeiten

A simple approximation for the conditional time-dependent pair distribution functionP(r′t ¦ rt) is proposed. With this approximation the van Hove-correlation-functionG _d (rt) is computed and compared with Ludwig's¹ computer results for liquid A1. Then we determine the velocity autocorrelationfunction ψ(t) under special assumptions for the particle motion. That function is compared with Rahman's² computer results for liquid Ar.     

Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s _x s _y 〉,x, y εZ ^d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ > 0.r(β) is ad-dependent function, analytic atβ = 0.c _n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Z^d limit of a finite number of finite lattice A spin-spin correlation functions 〈s₀s_x〉t>Afor a finite number ofx = (x ₁,x₂, ..., x_d), ¦x¦ = ∑ _i ^d 1¦x_i¦< R(n), where R(n) increases withn. Furthermore, there exists aβ' > 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]^d?1, of the fundamental particle of the associated lattice quantum field theory.     

Transport and equilibrium characteristics of γ-lithium vanadium bronze

The diffusion coefficient of Li⁺ in the γ-lithium vanadium bronze (Li_1+xV₃O₈) has been measured with the long-pulse galvanostatic technique. Values ranging from 1.7×10⁻⁷ cm²s⁻¹, at x=0.3, to 2.2×10⁻⁸ cm²s⁻¹, at x= 1.4, have been measured. The thermodynamic factors, d ln a/d ln c, determined from the OCV/x curve and from voltage relaxation after the current pulse, have a mean value of ∼15. The pseudo two-phase region observed in the OCV/x curve at high Li⁺ concentrations seems attributable to ordering of Li⁺ in specific sites and to alteration of the unit cell. This process is reversible as shown by X-ray diffractometry. Finally, from OCV/t plots at different x, the partial molar entropy of Li⁺ was determined. The values, on account of the large dE(x)/dt measured, are higher than those found for V₆O₁₃ or TiS₂.     

A field theory model for fixed angle proton-proton scattering

It is argued that the sum of the leading terms to each order in the coupling constant in massive Q.E.D. at fixed angle leads to the elastic cross-section dσ/dt = A(θ)s^?2exp (a ln²s + b(θ)lns). This gives good agreement with the data for wide angle proton-proton scattering.     

Measurements of elastic scattering in alpha-alpha and alpha-proton collisions at the CERN intersecting storage rings

We measured the elastic scattering of $\text{αα}\text{at}\text{s}\text{= 126}\text{GeV}$ and of αp at $\text{s}\text{= 89}\text{GeV}$. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV². At small |t| = 0.05?0.07 GeV², this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α_tot(αα) = 250 ± 50 mb and an integrated elastic cross section σ_e1(αα) = 45 ± mb. Another method of estimating σ_tot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV², and for 0.05 < |t| < 0.18 GeV² behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σ_tot(αp) = 130 ± 20 and σ_e1(αp) = 20 ± 4mb. Results on pp elastic scattering at $\text{s}\text{= 63}\text{GeV}$ agree with previous ISR experiments.     

Calculation of the hyperfine structure of the 42 S 1/2, 42 P 1/2, 42 P 3/2 states in the 3d 10 nl configuration of Cu

The hyperfine structure of the 4² S _1/2, 4² P _1/2, 4² P _3/2 states in the 3d ¹⁰ nl configuration of Cu has been evaluated using many-body perturbation theory. Polarisation effects were included in all orders and correlation to third-order. By the use of iteration methods, a large number of higher order diagrams were also included. The correlation effects between the valence electron and the 3d shell were found to be very important. The results forA(² S _1/2) andA(² P _1/2) 5827MHz and 440 MHz, respectively, are in good agreement with the experimental results, whereas the result forA(² P _3/2)=83 MHz is far from the experimental value. No explanation was found for the discrepancy. The quadrupole values were found to be ?206 mb for⁶³Cu and ?185 mb for⁶⁵Cu.