Bestimmung der Kernmomente des Ho165 aus der Hyperfeinstruktur des Grundzustandes im Ho I-Spektrum

In an atomic beam magnetic resonance experiment, the hyperfine interaction constantsA andB of the⁴ I _2/15-groundstate of Ho¹⁶⁵ were found to beA=800,58389 (50) MHz,B=?1667,997 (50) MHz. Using an effective value for 〈r ^?3〉, the magnetic moment of the Ho¹⁶⁵ nucleus was calculated to beμ=4·1(4)μ _n . The quadrupolement was determined by use of the 〈r ^?3〉 given byWatson andFreeman. The result isQ=2·4·10^?24 cm².     

Verzweigungsverhältnisse und Konversionskoeffizienten von angeregten Zuständen des208Tl

The branching ratios of theγ rays of the second and fourth excited states of²⁰⁸Tl have been investigated by coincidence measurements between the α rays of²¹²Bi and subsequent 40keVγ ray. The detectors employed were a silicon surface barrier counter for α particles, and a 1.5 in ×2 mm NaJ (Tl) crystal forγ rays. It has been found that (75.6±3.7)% of all transitions of the 328 keV state and (94±7)% of all transitions of the (492 keV+473 keV) states populate the first excited state of²⁰⁸Tl. The 40 keV state is excited to (3.4±0.3)% by transitions of higher excited states relative to the direct excitation by α particles. The number of α particles with energyE _α = 6.047 MeV and the number of subsequent 40keVγ rays resulted in a conversion coefficient α(40keV)=22.55± 0.46. Similarly coincidence measurements between Tl-x rays and α particles have been used to determine theK- conversion coefficients α_K(328 keV)=0.31±0.03 and α_K(492 keV+ 473keV)=0.100±0.015. The experimental results are in good agreement with the theoretical values ofSliv.     

Der mittlereg-Faktor der ersten angeregten Rotationszustände der geraden Wolframisotope in natürlichem Wolfram

The average gyromagnetic ratio of the first excited 2⁺ states of the Tungsten isotopes was measured using a target of natural Tungsten. An external magnetic field of 40950±200 Gauss was employed for observing the precession of the angular distribution of the 115 keV deexcitationγ-rays following Coulomb-excitation with an atomic hydrogen beam of 2·18 MeV. The measurement of the angular distribution was carried out with a proton beam at 6 different energies between 1·5 and 3·7 MeV, and was found to be slightly perturbed by internal fields. The measured attenuation coefficients areG ₂=0·966±0·049,G ₄=1·07±0·15. The gyromagnetic ratio was found be\(\bar g = 0 \cdot 264_{ - 0 \cdot 019}^{ + 0 \cdot 023}\), in agreement with the average value of the measurements ofGoldring andVager and the average theoretical value ofNilsson andPrior, but lower than the measurements ofBodenstedt et al.     

Regularisierende Deltafunktionen

In the Laurent Schwartz theory of distributions the integral∫ δ(r)f(r)dτ _r is only defined for a certain class of test functions. Unfortunately, in physics, we obtain test functionsf(r) likee ^ikr /r, e ^?kr /r, ?(e ^ikr /r) and so on, which are not belonging to the Laurent Schwartz class (§1). Here, we want to extend the class of test functions so that it includes physically meaningful functions with poles of finte order inr=0. For this purpose we replaceLaurent Schwartz's axiomatic method defining theδ-distribution by a constructive one consideringδ(r) as a given set of sequences of functions (§2). First we prove that the redefinedδ-function satisfy the equations, axiomatically assumed byLaurent Schwartz (§3). Then we obtain well defined and finite results even in the case of test functions with poles atr=0 (§4). The Fourier components of the newδ-function are given (§5). Finally we show why theδ-function is Lorentz invariant (§6).     

Winkelkorrelationsmessungen an >30y Holmium 166 und Bestimmung desg R -Faktors des 4+-Rotationsniveaus von Erbium 166

The spins of several excited states of Er¹⁶⁶ have been investigated byγγ-angular correlation measurements. The spin sequence 0+, 2+, 4+, 6+ for the ground state rotational band was presumed to be correct. Unique assignments were derived for the states of 1076 keV, 1377 keV and 1785 keV asI=5, 7 and 6 respectively. These results are in agreement with the spins proposed byGallagher jr. andSoloviev. The multipolarities of theγ-transitions of 408 keV, 709 keV, 811 keV and 831 keV were derived as 95%E1+(5±1)%M2, 99·6%E1+(0·4±0·5)%M2, 99·1%E2+(0·9±0·3)%M1, and 96·1%E2+(3·9±1)%M1 respectively. The unusual mixing ratios of the transitions of 811 keV and 831 keV can be understood as a consequence of theK-selection rule. Eachγ-transition from the 1785 keV state should be stronglyK-forbidden and one expects a half-life ofT _1/2≈3·10^?9s. A measurement of the time spectrum of the coincidences between theβ-radiation and the high energyγ-lines gave however:T _1/2(1785 keV state)≦3·10^?10s. The rotation of the angular correlation between the 184 keV line and theγ-group at 820 keV has been measured in an external magnetic field of 53000 gauss as:ω·τ(4+)=0·083±0·006. This value contains small corrections for an additional rotation of the angular correlation of the 831 keV–184 keV triple cascade in the 6+state and for a small attenuation by internal fields. WithT _1/2(4+state)=1·23·10^?10s, andβ=7·08 one gets for theg-factorg _R=+0·266±0·024 in good agreement with recent results for the 2+ state.     

TheK-conversion coefficient of the 321 keVE1 transition in Hf177

TheK-conversion coefficient of the 321 keVE1 transition in Hf¹⁷⁷ has been measured by means of an iron free double focusing beta-ray spectrometer, using the internalexternal conversion method. The result obtained for α _K (321)=0.162±0.016 is in disagreement with the theoretical values for pureE1 transition (α _K =0.0154) calculated bySliv andBand. The large anomaly observed in theK-conversion process of the inhibitedE1 transition is compatible with a largeM2 admixture or, more probable with the presence of penetration matrix elements.     

Untersuchungen zur Mehrfach-Emission von Sekundärelektronen

CuBe- and NaCl-targets are bombarded by single electrons (100–600 eV). The secondary electrons accelerated by 40 kV strike the crystal of a scintillation counter, backed by a multichannel analyser. The probabilityP _n of emission ofn=0, 1, 2, 3, ... secondaries can be found from the pulse height distribution. The probability distributionP _n =f(n) shows a characteristic deviation from aPoisson's distribution. There was no evidence that there is a preference for even numbers ofn as found byBarrington andAnderson.     

Messungen derK-Konversionskoeffizienten und der Aktivierungsquerschnitte der isomeren Atomkerne Se77m,Se79m,Ge75m und Ge77m

TheK-conversion coefficients α _K of the nuclear isomers Se^77m , Se^79m , Ge^75m and Ge^77m have been measured by detecting theK-röntgen- andγ-radiation from neutron-irradiated Se- and GeO₂-samples with the aid of scintillation counters to be α _K =0.79±0.06, 7.4±0.6, 1.44±0.13, and 1.2±0.6, respectively. In all cases, the values obtained, are in agreement with those taken from the tables ofRose under the assumption of anE3-transition, thus confirming this assignment which was proposed earlier by other authors. In addition, the cross sectionsσ for inducing the activities by slowed down neutrons have been measured to beσ=22±2, 0.40±0.04, 0.20±0.02, and 0.12±0.03 barns, respectively, and are compared with earlier data of several authors.     

The spin cut-off factor for60Co

Nine experimental isomeric cross-section ratios for the reactions⁵⁹Co(n, γ)⁶⁰Co,⁶⁰Ni(n,p)⁶⁰Co, and⁶³Cu(n,α)⁶⁰Co are analysed in terms of statistical theory by means of the method ofHuizenga andVandenbosch. Theγ-cascades are treated by a new model which was recently published. The results confirm the energy dependence of the spin cut-off factor for⁶⁰Coσ～U^1/4 which should not be neglected. As a mean value (σ=4.3±0.3 is obtained forU=B _n =7.5 MeV in good agreement with a nuclear moment of inertia for a rigid sphere.     

Diekll-Auger-Spektren von Eisen und Vanadium

The relative intensities of theKLL-Auger transitions of Fe (Z=26) und V (Z=23) were measured with an iron free, double focusing β-spectrometer. The results obtained are in good agreement with those measured bySokolowski andNordling forZ=29 andZ=32. This confirms the discrepancies between the nonrelativistically calculated intensities and the experimental values in the region of lowerZ. A summary is given about all known measurements of theKLL-Auger intensities. Also theKLL∶KLX-ratio of Fe was measured to be 1·0∶(0·19±0·01). The energy of the 14·4-keVγ-transition of Fe⁵⁷ was evaluated to be (14389±6) eV.     

High-frequency EPR of Cr<Superscript>2+</Superscript> ions in CdGa<Subscript>2</Subscript>S<Subscript>4</Subscript>

High-frequency broad-band (65–240 GHz) EPR is used to study impurity centers of bivalent chromium in a CdGa₂S₄ crystal. It is found that the EPR spectra correspond to tetragonal symmetry. The spin Hamiltonian H = βB · g · S + B ₂ ⁰ O ₂ ⁰ + B ₄ ⁰ O ₄ ⁰ + B ₄ ⁴ O ₄ ⁴ with the parameters B ₂ ⁰ =23659±2 MHz, B ₄ ⁰ =1.9±1 MHz, |B ₄ ⁴ |=54.2±2 MHz, g_‖=1.93±0.02, and g_⊥=1.99±0.02 is used to describe the observed spectra. It is concluded that chromium ions occupy one of the tetrahedrally coordinated cation positions.     

DasL/K-Einfangverhältnis von51Chrom

We have investigated theL/K-capture ratio of⁵¹Cr. The values obtained for the transitions to the first excited state of⁵¹V and for both transitions to the first excited state and the ground state of⁵¹V are(N _L /N _K )_A=0.1044±2% and (N _L/N_K)_G=0.1033±3% respectively. They are in fairly good agreement with theoretical results which take exchange corrections into account. But there still remains a dependence of the results on the method used to obtain the capture numbers from the measured spectrum.     

Paramagnetische Resonanz von Zentren mit den Symmetrienn,\bar n undn/mundn/m

The consequences of applying the spin-Hamiltonians ofAbragam andPryce to paramagnetic centers with the low symmetriesn,\(\bar n\) andn/m(C _n ,C _nh ,S _n ) are examined. The asymmetry of theg- and the hfs-tensors, described in an earlier paper, is considered in this context. The point is that for the symmetries under consideration the coordinate systems are not determined by the symmetry elements. For this reason it is possible to introduce separate coordinate systems for the magnetic field, the electron spin and the spins of the nuclei and this allows the symmetrisation of the tensors under certain conditions. This procedure also leeds to an understanding of the independent parameters found in the Hamiltonians. Ambiguities between the spin-Hamiltonians and the esr-spectra indicate the limits of theAbragam andPryce formalism. The application of the theory to paramagnetic centers under the influence of external, electrical fields is discussed and reveals interesting aspects.     

Bestimmung der Atomspinkorrelationszeiten der Fe3+-Ionen in FeNH4(SO4)2·12 H2O mit Hilfe des Mössbauereffektes

The Mössbauer effect studies of⁵⁷Fe in the paramagnetic salt FeNH₄(SO₄)₂·12 H₂O reported byObenshain et al. were extended to higher values of the applied external magnetic fieldH _a. The results are discussed in terms of the theoretical calculations given byWegener. The data can be fitted using a maximum internal fieldH _max=(598±10) kOe and two atomic spin correlation times τ_c=2,4 · 10^?9 sec andτ′ _c=2,1 · 10^?9 sec.τ _c andτ′ _c are independent ofH _a and the temperatureT. It is assumed in the analysis that the distribution w(H) of the internal fields can be described by a continuous function of the Boltzmann factor type with two parameters. These two parameters are determined by the normalization and the macroscopic magnetization.     

Possible violation of the δS=δQ selection rule in leptonic decays of σ+-hyperons

We have found a possible example of the rare decayσ ⁺ →nΜ ⁺ Ν, which violatesδS=δQ. The positive decay track of theσ ⁺ comes to rest in the hydrogen bubble chamber and decays into ane ⁺. This track has all the characteristics of a stoppingΜ ⁺. The decay neutron fortuitously scatters twice, producing two recoil protons. The only other possible interpretation of the event isσ ⁺→nγ(π ⁺ →Μ ⁺ Ν), where theπ ⁺ →Μ ⁺ Ν decay produces no deflection (θ<0.1 rad) and no significant change in curvature. Using thep-wave radiative decay predictions ofBarshay et al. we calculate that the integrated branching ratio for such “accidental” events isγ(σ ⁺ →nγ(π ⁺ →Μ _stop ⁺ Ν))/γ(σ ⁺ →nπ ⁺)=1.6×10^?6. Most of the contribution to this “accidental” branching ratio comes from radiative decays where theπ ⁺ mesons have ranges less than 1 mm (p _π<20 MeV/c). If one excludes thoseΜ's with ranges less than 1.2 cm the above “accidental” branching ratio becomes 5.5×10^?7. With this figure we estimate that we should have seen 6.5×10^?2 events of this type thusfar in our experiment. The neutron momentum does not help in deciding between the two hypotheses. We therefore assign a confidence level of 7% for the radiative hypothesis. For the leptonic hypothesis we obtain an estimate of the branching ratio,γ(σ ⁺ →nΜ ⁺ Ν)/γ(σ ⁺ →nπ ⁺)=5×10^?5. If one further accepts theσ ⁺ →nπ ⁺ Ν event reported byBarbaro-Galtieri et al. and theσ ⁺ →ne ⁺ Ν event reported byNauenberg et al., one obtains theδS=?δQ leptonic branching ratio [γ(σ ⁺ →nΜ ⁺ Ν)+γ(σ ⁺ →ne ⁺ Ν)]/γ(σ ⁺ →nπ ⁺)=(4±3)×10^?5.     

Konversion der 238,6 keV-γ-Linie des ThB und Vergleich mit den Tabellen von Sliv und von Rose

The conversion ratiosK/L _I andK/L _II of the 238.6 keVγ transition of ThB have been measured with the new Heidelbergπ/2 √13Β-ray spectrometer. For this transition there are great discrepancies between the values as given bySliv andBand, and byRose. The experimental resultsK/L _I=5.96±0.26 andK/L _II=60.3±7.1 are in excellent agreement with the values ofSliv andBand.     

Die absolute Intensität der durch Elektronenstoß in einer dicken Wolfram-Antikathode erzeugtenL α -Strahlung

The number\(N_{L_\alpha }^{dir} \) (produced) ofL _α -photons produced by electron-bombardment in a thick target of tungsten per incident electron has been measured absolutely with the Ross-filter method and relatively with the crystal-spectrometer method in the energyregion up to the 3.6 times theL _III-ionization energy\(E_{L_{III} } \). The result can be presented in the following empirical form:\(N_{L_\alpha }^{dir} \) (produced)=4π·?·(U ₀?1) ⁿ with ?=0.52·10^?4±5% andn=1.44±0.02\((U_0 = E_0 /E_{L_{III} }< 3.6)\). Out of this the number\(n_{L_{III} } \) ofL _III-ionizations per electron which is slowed down to the energy\(E_{L_{III} } \) within the target, has been evaluated. The computation of\(n_{L_{III} } \) out of the elementary process by usingBethe's non-relativistic formulae for totalL _III-ionization cross sectionQ _L and energy loss-dE/ds is in full agreement with experiment in the region 2<U ₀<3.6, if the constants in\(Q_{L_{III} } \) are chosen as follows:\(B = 4E_{L_{III} } , b_{L_{III} } = 0.25 \cdot 5.89\). By comparison of this result for\(b_{L_{III} } \) with the corresponding value ofb _K in the totalK-ionization cross-sectionQ _K for copper (b _K=0.35·2.26) it is concluded that\(Q_{L_{III} } \) is considerably higher than predicted by theory. The necessary correction factors as e.g. loss ofL _III-ionizations by rediffusion of electrons and portion of indirectly producedL _α -radiation-radiation are determined for tungsten quantitatively.     

Auger spectra for elements of low atomic number

KLL Auger spectra for the light elements sodium (Z=11) and magnesium (Z=12) have been studied. All five lines predicted by the extremeLS coupling theory are observed. A comparison is made with intensities predicted by the inter-configuration interaction theory ofAsaad. Agreement is obtained for the transition intensities to the three differentKLL configurations; however, theory does not give correct relative intensities within the 2s ² 2p ⁴ configuration. The measured Auger energies are compared with those calculated from the semi-empirical expression ofAsaad andBurhop and modified byHörnfeldt et al. Good agreement is obtained when we use electron binding energies measured by the ESCA method.     

Relativistic Slater's integrals for theK andL shells

TheZ-dependent form of theSlater's integrals for electrons in theK andL shells is studied by expanding the relativistic hydrogenic radial wave functions in the manner explained byLayzer andBahcall. When screening is not taken into consideration, theseSlater's integrals can be put in the form AZ(1+a Z²) wherea is positive for all integrals considered except G¹(1s, 2p) and G²(2¯p, 2p). Values ofA anda are given.     

Paramagnetische Resonanz von Er3+ in Y2O3

The paramagnetic resonance absorption of trivalent erbium in single crystals of Y₂O₃ on sites of crystal field symmetry C_3i and C₂ is investigated at 4.2°K and 9.2 kMc/s. The values of theg-tensors and those of the hyperfine structure parallel to the axes of crystalline fields are:g _‖=12.176,g _⊥=3.319,A=426.4·10^?4 cm^?1, andg _z =12.314,g _x =1.645,g _y =4.892, andA _z =433.2·10^?4 cm^?1 for the C_3i-ions and the C₂-ions, respectively. For ions on sites of symmetry C₂ the principal axes ofg in the plane perpendicular toz are found ± 2° beside the [100]-directions. This is different from the result on Yb³⁺ in Y₂O₃. The dependency ofg on the angle of rotation is determined for the (001)-, (110)-, and (111)-plane.