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Multiplicatively interacting stochastic process consists of many particles having their own values and they do binary interactions to exchange their values multiplicatively. It is known that the pr...

A growing system with weighted and multiplicatively interacting particles is investigated. Each particle has a quantity that changes multiplicatively after a binary interaction, with its growth rate controlled by a weight parameter in a homogeneous symmetric kernel. We consider the system using moment inequalities and analytically derive the log-normal-type tail in the probability distribution function of quantities when the parameter is negative, which is different from the result for single-body multiplicative processes. We also find that the system approaches a winner-take-all state when the parameter is positive.

The z-transform technique is used to analyze Smoluchowski equations of aggregation–fragmentation processes where the selection of aggregation clusters, a decomposed cluster and a generated cluster is entirely random and independent of cluster size. An analytic form of asymptotic behavior for a cluster size distribution function is derived on the basis of approximation where lower-order terms in the average cluster size are neglected. The obtained results agree well with numerical ones.

For neutron-deficient 124,125,127-130 La, Q EC measurement has been performed by determining β + -ray maximum energies. The radioactive sources were prepared by on-line mass-separation following the fusion-evaporation reactions 92, nat Mo( 36 Ar, 3 p x n ). The β + -rays were measured with an HPGe detector in β-γ coincidence mode in which γ-rays were detected with another HPGe detector for specifying an excited state in daughter nucleus. By unfolding the β + -ray spectra using experimental response functions, the Q EC -values of 124, 125, 127, 130 La were newly obtained, and those of 128, 129 La were improved in their accuracy. The Q EC -values obtained and the resulting atomic masses are compared with theoretical predictions. The results of half-life calculation and two-neutron separation energies using the experimental Q EC -values are also discussed.

The DAS 7×7 surface structure is known to be the most stable on Si(111), and we investigated its formation mechanism by scanning tunneling microscopy. Triangular narrow unreconstructed-regions (“1×1”), prepared on terraces by quenching, are chosen for in situ observation of the formation of the unit cell of the DAS 7×7 at about 250°C. It is demonstrated that the single stacking-faulted half of the unit cell is formed or annihilated dynamically in a structural sequence of “1×1”↔5×5↔7×7↔9×9. The faulted half is stabilized when another neighboring faulted-half of the same size is formed during its lifetime. We propose a formation model for the 7×7 unit cell.

The level structure of 153 Pm has been studied from the decay of 153 Nd. The radioactivities of 153 Nd were separated from the fission products of 235 U using the upgraded KUR-ISOL. A precise decay scheme of 153 Nd has been constructed up to 2 MeV and 115 γ-rays and 36 levels were involved in the decay scheme, in which 107 γ-rays and 28 levels were newly observed. The multipolarities and E2/M1 mixing ratios of 11 γ-transitions were deduced from the measurement of internal conversion electrons. From the results of the angular correlation measurements, the spin values of 450.5, 105.4 and 32.3 keV levels were deduced to be 3/2 + , 7/2 + and 5/2 + , respectively and the previous assignments were confirmed. The half-lives of 32.3 and 105.4 keV levels were determined to be 1.2(1) ns and 0.44(2) ns, respectively and the enhanced E1 transitions with B ( E1)=10 -3 ∼10 -4 W.u. were observed. The 153 Pm level structure was compared with the result of a calculation with a rotation-vibration coupling model (RVCM) and ...

A new neutron-rich isotope 166 Tb produced in 16 MeV proton-induced fission of 238 U has been identified using the JAERI on-line isotope separator (JAERI-ISOL) coupled to a gas-jet transport system. Dy KX-rays and γ rays originating from the decay of 166 Tb were found in both mass-166 and 182 fractions, where the 166 Tb nuclides were mass-separated as elemental ions 166 Tb + and monoxide ions 166 TbO + , respectively. The half-life of 166 Tb has been determined as 21±6 s, which is much shorter than theoretical predictions. A decay scheme of 166 Tb has been proposed and a probable spin assignment for the 166 Tb ground state has been discussed.

The β + -ray maximum energies of neutron-deficient 121,123,125 Ba and 121–124,126 Cs isotopes were measured using single HPGe-detector method, which does not need an annihilation-photon detection system. The radioactive sources were produced by bombarding Mo targets with 32 S 10+ and 35 Cl 11+ ions, followed by on-line mass-separation. The analysis of the experimental β + -ray spectra using response functions to monoenergetic positrons yielded β + -ray maximum energies and Q -values of orbital-electron capture ( Q EC -values) in the decay of these nuclides. The present experiment has extended the Q EC determination to 121,123 Ba isotopes in addition to improving the accuracy for the other nuclides.

The systematic Q β measurements of 14 neutron-rich nuclei in the mass region from A =147 to A =152 have been performed with an HPGe detector. Neutron rich nuclei were mass separated from the thermal neutron induced fission of 235 U using a He-jet type on-line isotope separator which has been developed at the Kyoto University Reactor (KUR). From β-ray singles and β-γ coincidence measurements, the Q β values of 147 La, 147-150 Ce, 147-152 Pr, 152 Nd and 152 Pm have been determined. The Q β values of 152 Pr and 152 Nd have been measured for the first time. The atomic masses derived from the Q β values are compared with the predictions of theoretical mass calculations.

This paper reports the experimental results of the Shubnikov–de Haas (SdH) effect and angular-dependent magnetoresistance oscillation (AMRO) for the organic conductor β′′-(ET)(TCNQ). We observed several two dimensional (2D) SdH frequencies, whose cross-sectional areas of the Fermi surfaces (FSs) correspond to only a few percent of the first Brillouin zone. Such small 2D FSs are not predicted by band-structure calculations, suggesting that these FS pockets are created by an imperfect nesting of FSs at low temperatures. It is found that the AMRO consists of a long-period oscillation and a short-period one. The long-period oscillation is associated with the Yamaji oscillation corresponding to the α orbit, whose shape and area are consistent with previous magneto-optical measurement. The short-period oscillation is not caused by peaks instead but dips. The dip structure is discussed in terms of the AMRO of a quasi-2D electron system with a periodic potential caused by the possible density-wave related to the ...

The β-decay of 151 59 Pr 92 to the levels in 151 60 Nd 91 has been studied from the fission products of 235 U using an on-line isotope separator (KUR-ISOL). Gamma-rays and conversion electrons have...

The level structure of 147 Nd has been studied from the decay of 147 Pr. The radioactive sources of 147 Pr were separated from the fission products of 235 U using the on-line isotope-separator KUR-ISOL and chemical separation techniques. A decay scheme has been constructed involving 93 γ-rays and a newly observed 1261.1 keV level. The half-lives of 49.9, 127.8 and 214.6 keV levels were determined to be 1.0 ±0.3 ns, 0.4 ±0.1 ns and 4.53 ±0.06 ns, respectively. Conversion coefficients of 15 transitions were determined. The parities for the levels at 49.9, 127.8, 214.6, 314.7 and 463.5 keV are deduced to be odd. Spins and parities for the 769.3 and 792.6 keV levels are deduced to be 3/2 + . The properties of transition probabilities between the low-lying triplet hole states are similar to that of three particle states in the N =85 isotones.

Level energies and γ-transition properties in the low-lying states of 123 Ba have been investigated through the decay of 123 La. From γ-ray singles and γ-γ coincidence measurements of the 123 La produced in the 35 Cl+ 92 Mo reaction and an on-line mass-separation technique, 12 new levels haye been assigned in the level scheme of 123 Ba. The [411]1/2 + band, consisting of 6 members, has been proposed.

The decay of 11.6 min 152 Nd to levels of odd-odd 152 Pm has been studied with HpGe, Ge(Li) detectors, LEPS, and a plastic scintillation detector by γ-ray singles, time dependent γ-ray singles, γ-γ coincidence and β-γ delayed coincidence measurements. Sources were prepared by a rapid chemical separation method from the fission products of 235 U. Ten γ-rays were observed and five of them are newly observed (19.5, 25.0, 44.4, 545.6 and 570.7 keV). Half-lives of the 16.1 and 28.5 keV transitions were measured to be 2.1±1.0 ns and ≤1.0 ns, respectively. A decay scheme of 152 Nd involving 2 new levels at 25.0 and 570.7 keV in 152 Pm and spin-parities are proposed. The Nilsson configurations of excited states in 152 Pm are discussed.

The asymptotic power-law behavior of the distribution function P(X) for X clusters is analyzed for aggregation and weighted-chipping processes. Here, chipping off of a cluster of size n takes place with the probability function ∼1/nσ. An exact value of a noninteger power-law index is obtained, that is, P(X) ∼ 1/Xα with α = σ in the case of 1 < σ ≤ 2. This gives thresholds of σ = 2 for the emergence of a condensed cluster and σ = 1 for the appearance of a power-law distribution. Numerical analysis supports well this result.

We report the magnetic properties of Ce 2 CuGe 6 and Pr 2 CuGe 6 , both of which exhibit a ferrimagnetic order around 15 K. Hysteretic curves with small residual magnetization, 7.8×10 -4 µ B / f.u. and 1.1×10 -2 µ B / f.u., are observed for Ce 2 CuGe 6 and Pr 2 CuGe 6 , respectively. The peak of specific heat and the sharp decrease of electrical resistivity near their ordering temperature are consistent with observed magnetic orders.

A gradual change from the Kondo lattice to the impurity Kondo regime has been observed in Ce 1- x La x FeGe 3 ( x =0, 0.1, 0.3, 0.5, 1.0). CeFeGe 3 exhibits a greatly reduced resistivity below about 100 K corresponding to the coherent state of the Kondo lattice. Ce 0.5 La 0.5 FeGe 3 , on the other hand, shows a resistance minimum around 30 K which is consistent with the impurity Kondo regime. The ground state of CeFeGe 3 turns out to be very stable against the La substitution and no magnetic instability is induced in the present diluted system. Magnetic susceptibility at 0 K per mole of Ce, χ(0), and the linear term of the specific heat, γ increase by 24% and 15% from x =0.0 to 0.5, respectively. The Kondo temperatures T K 's estimated from χ(0) and γ decrease accordingly by 20 and 13% in the same range of La content. This decrease in T K is explained by the lattice expansion caused by the substitution of La for Ce.

We performed 13 C-NMR measurements in the metallic state of α-(BEDT-TTF) 2 I 3 under pressure to determine the local spin susceptibility at each BEDT-TTF molecular site. We found that the local susceptibility becomes quite different from molecule to molecule in a unit cell with approach to the zero-gap state (ZGS) under pressure. This is related to the charge disproportionation among molecular sites [named A (A'), B, and C]. We confirmed that the most/least positively charged site, the B/C molecule, carries the smallest/largest local susceptibility. We also confirmed the linear temperature dependence of the local susceptibility at low temperatures. These results are consistent with the theoretical calculation [Eur. Phys. J. B 67 (2009) 139] and should be considered as the characteristics of the ZGS.

We present the optical conductivity, infrared- and Raman-active charge-sensitive phonon modes, and the x-ray diffraction superlattice spots of β''-(ET)(TCNQ) [ET = bis(ethylenedithio) tetrathiafulv...

We investigated the magnetoresistance effect on an organic conductor, (ET) 3 Cl(DFBIB), which has a quasi-two-dimensional electron system. The out-of-plane resistivity in transverse magnetic fields...

The half-life and the multipolarity for the 213 keV transition in 95 Sr have been determined to be (4.6±0.3) ns and E2 (≤ 15%Ml) from β-γ delayed and x-γ coincidences, respectively. The half-life for the 204 keV transition in 95 Sr was also determined to be (20.9±0.5) ns. The reduced transition probabilities are deduced as B (E2)=(261 -43 +17 )e 2 fm 4 for the 213 keV transition and B (E2)=(71±2)e 2 fm 4 for the 204 keV transition. These B (E2) values are comparable to the Weisskopf estimates and to those for the similar transitions in the neighbouring nuclei.

The decay of 24 min 146 Pr has been studied with Ge(Li), pure Ge, NaI(Tl) and plastic detectors in singles and coincidence modes. Sources were prepared by the chemical separation, called a rapid paper electrophoresis, from the fission products of 235 U. A total of 104 γ-ray transitions, 64 of them not reported before, have been observed and 88 transitions of them are incorporated into a level scheme comprising 32 excited states of 146 Nd. Observed Q β value was 4.15±0.15 MeV. Gamma-gamma directional angular correlation measurements in 146 Nd have been performed with 12 cascades each including 453.9 keV 2 + →0 + ground state transition. Spin assignments of 13 levels in 146 Nd were deduced. The low lying-states in 146 Nd are discussed in terms of the quasi band.

The decay of 148 Pr to levels on 148 Nd has been investigated with Ge(Li) and plastic detectors in singles and coincidence modes. Sources were prepared by a chemical separation from the fission products of 235 U. Forty γ-rays associated with 148 Pr decay have been observed and thirty four of them are incorporated into a level scheme including six new levels at 723.7, 1275.0, 1512.4, 1687.5, 2543.0 and 3129.6 keV. In comparison with the decay study of 148 Pr produced by the 148 Nd(n, p) reaction, this work, for the first time, could make clear the existence of 148 Pr isomers by γ-ray intensity ratios and their half-lives which are 2.27 ±0.04 and 2.0 ±0.1 min. A low lying level at 723.7 keV is assigned as a 0 + state from the γ- γ anisotropy measurements and low lying levels in the transitional nuclide 148 Nd are discussed in terms of the quasi band description.

The decay of a short lived nucleus 144 La to levels of 144 Ce was investigated with Ge(Li), NaI(Tl) and plastic detectors in singles and coincidence modes. Radioactive sources were prepared by the chemical separation, a rapid paper electrophoresis, from the fission products of 235 U. The half-life of 144 La is 40.6 ±1.0 sec. Fifty-four γ-rays, including 17 new ones, were observed and 46 of them are incorporated in a decay scheme of 144 La including 11 new levels. The Q β value was deduced to be 4.3 ±0.1 MeV on the basis of the results of the γ- β coincidence measurements.

The Zeeman effect of the R-lines in alexandrite was investigated by using pulsed high magnetic fields up to 400 kOe. Well separated Zeeman splitting of R-lines was observed below liquid nitrogen temperature. Different from the R-lines in ruby, all the transitions with Δ S z =0, ±1 and ±2 are observed in alexandrite reflecting the lower symmetry on the Cr 3+ ion site. The excited state g -values along the a -, b - and c -axes are experimentally determined as 1.6, 1.4 and 1.3 for the A '-state (R 1 ) and 2.0, 1.4 and 1.4 are obtained for the A ''-state (R 2 ), respectively.

Decay of 178m,g Lu has been studied by using Ge(Li), NaI(Tl) and plastic detectors. Sources were prepared by the 179 Hf(γ, p) 178m,g Lu reaction. Thirty-nine of forty γ-rays are assigned to the 178 Hf level scheme, which includes six newly observed levels at 1174.4( I π K =2 + 2), 1199.3(0 + 0), 1276.8(2 + 0) and 1322.4(3 - 2) keV in the 178g Lu decay and at 1364.04(9 - 8) and 1601.6(10 - 8) keV in the 178m Lu decay. Q β values are 2.05±0.05 MeV for 178g Lu and 2.25±0.03 MeV for 178m Lu. The most probable spin-parity assignments of 1 + and 9 - are proposed for the ground and isomeric states of 178 Lu, respectively. There is reasonable agreement between the experimental β branching ratios from 178m Lu to the 8 - band at 1147 keV and the Alaga rules. Discussions on the 178 Hf levels are made mainly on the basis of log f t values.

Decay of 148 Pr has been studied with Ge(Li), NaI(Tl) and plastic detectors in singles and coincidence measurements of γ-rays and β-rays. Sources were prepared by the 148 Nd( n , p ) 148 Pr reaction at the neutron energy of about 15 MeV. Forty-one γ-rays were observed. A decay scheme of 148 Pr involving 4 new levels, is proposed for the first time, and twenty γ-rays were assigned in this decay scheme. Observed Q β value was 4.8±0.2 MeV. The half-life was measured to be 2.28±0.09 min.

A spectroscopic study of the decay of 152 Pm to the levels of 152 Sm was performed by using Ge(Li), NaI(Tl) and plastic detectors. The radioactive sources were produced from the (n, p) reaction with 14.8 MeV neutrons on enriched samarium targets. The half-lives of two 152 Pm isomers are 4.30±0.37 and 7.52±0.08 min. One hundred and twenty-nine γ-rays, including 96 new ones, were observed and 108 of them are assigned to the decay schemes for 152 Pm including 22 new levels. An observed Q β value for the 4.30 min 152 Pm was 3.50±0.10 MeV. Most probable spin assignments of 1 + and 4 - are proposed for the 4.30 and 7.52 min 152 Pm, respectively. The results are discussed in terms of the unified model.

Decay of 168 Ho has been studied with Ge(Li), NaI(Tl), and plastic detectors in singles and in coincidence. Sources were prepared by the 168 Er( n , p ) 168 Ho reaction with 14.8 MeV neutrons. Thirty-three gamma-rays were observed and twenty eight of them were assigned in a proposed decay scheme, including three new levels at 2192.7, 2254.4 and 2425.7 keV. The half-life was measured to be 2.98±0.09 min. The observation of a 1.92±0.10 MeV beta group in coincidence with a 821 keV gamma transition establishes the total beta-decay energy as 27.4±0.10 MeV. There is good agreement between beta-decay branching ratios to the gamma band and predictions from the adiabatic symmetric-rotor model. A value of 0.0313±0.0025 for the band-mixing parameter z 2 was calculated from the E2 branching ratios for transitions between the gamma band and the ground-state band in 168 Er.

Decay of 76 As was investigated by using a Ge(Li) detector and Ge(Li)-NaI(Tl) coincidence methods. Sixteen new gamma-rays were observed and eleven of them were assigned in a proposed decay scheme. Four new levels were found at 2026.4, 2365.1 and 2514 keV. Spins and parities of levels at 2026.4, 2655.7 and 2669.8 keV were estimated from log ft values of beta transitions which fed these levels. Existences of 563.4 and 772.1 keV gamma-rays emitted from the 0 + and 4 + levels which were considered to be levels of two-phonon triplet states and observed by the coulomb excitation and the inelastic scattering experiments were confirmed. Characters of the 1691.5 and 1788.1 keV levels as three phonon states were discussed.

Decay of 42 K was investigated by a Ge(Li) detector and a 5''φ×4'' NaI scintillation counter. Two gamma-ray peaks were newly observed at 0.692 and 1.228 MeV in the gamma-gamma coincidence spectrum. The 0.587 MeV gamma-ray, previously reported by McCullen et al. , could not be seen and the upper limit of the intensity of this gamma-ray relative to the 0.900 MeV gamma was 0.7%.

Radio-active sources of 165 Dy and 165m Dy were produced by neutron irradiation and the decay was investigated. Forty gamma-rays were observed in the decay of 165 Dy with a Ge(Li) detector and a Ge(Li)-NaI(Tl) coincidence apparatus. New gamma-rays were detected at the energy of 178 and 339 keV in the coincidence spectra. Seven gamma-rays were seen in the decay of 165m Dy. A delayed and a prompt coincidence measurements with the 361.8 keV gamma-ray were performed to confirm cascade relations with this gamma-ray. Decay schemes of 165 Dy and 165m Dy were proposed on the basis of the present experimental results.