Shell-correction approach to nuclear state densities and the competition between fission and neutron emission of 210Po

Starting from the Hartree-Fock approximation to the grand canonical partition function we formulate a consistent renormalization of the ground-state energy and the intrinsic state density as a function of deformation. The competition between fission and neutron emission, $\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{(E)}$, of ²¹⁰Po is studied within the framework of the statistical theory as an example. Calculations using renormalized state densities are compared with usual shell-model calculations and experimental data. We find that the usual calculations reflect the incorrect uniform deformamation dependence of the shell-model spectral function. As important changes due to renormalization we find: there is a rapid change of the shape of the transition state at ≈ 45 MeV excitation energy, $\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{(E)}$ remains smaller than unity for all excitation energies and the deformation of the transition state increases after the “shape transition” at 45 MeV monotonically towards the liquid drop saddle-point deformation.     

Mass dependence of statistical fission parameters

Statistical fission parameters B_f and $\text{a}{}_{\mathrm{<mtext>f</mtext>}}\text{a}{}_{\mathrm{\nu }}$ are extracted from analyses of recently measured heavy-ion induced fission and evaporation residue excitation functions for medium mass systems using a formalism with spin dependent level densities and multiple particle/fission competition. Results are compared with those of the less rigorous s-wave approximation as treated in the code ALICE.     

Muon-induced prompt fission of uranium

The prompt-fission probabilities of muonic ²³⁸U in radiationless dipole and quadrupole transitions of the muon are calculated. The 3d → 1s transition is found to dominate, in agreement with experiment. A measured drastic enhancement in the $\text{Γ}{}_{\mathrm{<mtext>n</mtext>}}\text{Γ}{}_{\mathrm{<mtext>f</mtext>}}$ ratio compared to photofission data is reproduced in terms of the increase of the fission barrier in the presence of the muon.     

γ-Ray multiplicity in 239Pu fission induced by resonance neutrons: experimental evidence for the (n, γf) reaction

The fission γ-ray multiplicity measurement in the ²³⁹Pu resonances has been carried out, using the Saclay 60 MeV electron linac as a neutron source. Large fluctuations are observed from resonance to resonance, in correlation with the number $\text{}\text{?}$Gn of prompt neutrons, the total energy of these γ-rays and the fission width Γ_f. The results are interpreted in terms of a competition between the fission and the radiative capture during the de-excitation of the compound nucleus. They are the first experimental evidence of the (n, γf) reaction. Some parameters like the width $\text{Г}{}_{\mathrm{\gamma f}}$ are deduced.     

A pair approximation of the spin fluctuation theory of itinerant-electron ferromagnets

We discuss a pair approximation of the spin fluctuation theory, which is an extension of the single-site theory proposed by the present author and can include the effect of the short-range magnetic order (SRMO). Numerical calculations of b.c.c. iron show that SRMO for neighbouring sites j and l, $\text{Γ≡}\text{〈m}{}_{\mathrm{j}}\text{m}{}_{\mathrm{l}}\text{〉}\text{〈m}{}^2{}_{\mathrm{j}}\text{〉}$, is about 0.21–0.14 at $\text{T}\text{T}{}_{\mathrm{c}}\text{=1.0?2.0}$. This is considerably smaller than the value (Γ～0.8) proposed by Korenman, Murray and Prange for an analysis of sloppy spin waves of iron, while it coincides with the value (Γ≌0.12–0.18) given by Shastry, Edwards and Young with the use of the spherical Heisenberg model with exchange interactions extending to far nearest neighbours.     

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

(p, γ) reaction studies on 60Ni

The γ-ray spectra from the ⁶⁰Ni(p, γ)⁶¹Cu reaction were measured for 27 isolated resonances. From these studies the J^π assignment of the compound states in ⁶¹Cu were made. Moreover, a value for the El photon strength function k(El) = 1.03 × 10^?9 MeV^?3 was obtained from seven l = 0 resonances to the 16 low-lying states. This value was then compared with the theoretical estimates of El strengths as predicted from the s.p. and giant dipole resonance models. The distribution of partial radiative widths about their mean value was determined from a Monte Carlo technique and was found to be consistent with the Porter-Thomas distribution when the Γ_{γ, ij} were divided by the E_γ⁵ energy dependence.Values for the coefficients of the correlation R between Γ_{λ, p} and Γ_{λ, γj} and T between Γ_{λ, yj} and $\text{Γ}{}_{\mathrm{\lambda ,\; \gamma ?}}$ where f ≠ j, were computed with the values R = 0.14 and T = 0.39, respectively. Also the correlation coefficients C(〈 Γ_{λ, yj}〉, I₃He, d, j) and $\text{C(〈Γ}{}_{\mathrm{\lambda ,\; y?}}\text{〉 I}{}_{\mathrm{<mtext>d,\; n</mtext><mtext>,\; ?</mtext>}}\text{)}$ yielded the values ρ = 0.87 and ρ = 0.80 respectively. All these correlations which are found to be statistically significant, imply that the (p, γ) reaction in ⁶⁰Ni is partly due to direct capture such as given by valence and doorway state contributions.     

s- and p-wave neutron spectroscopy: Part VII. Widths of Neutron Resonances

Neutron reduced widths Γ_n⁰ and Γ_n¹ are reported for about 200 resonances observed in neutron total cross sections of Ca^{40, 44}, Ti⁴⁸, Cr^{50, 52, 54}, Fe^{54, 56}, Ni^{58, 60}, Sr⁸⁸, Y⁸⁹, Sn¹²⁴, Te¹³⁰, Ba^{136, 138}, and Pb^{206, 207, 208}, in the energy region 1 to 200 ^kev. Average parameters $\text{Γ}{}_{\mathrm{n}}{}^0$, $\text{Γ}{}_{\mathrm{n}}{}^0\text{D}$, and $\text{Γ}{}_{\mathrm{n}}{}^{\mathrm{(1)}}\text{D}$ have been derived and the Wigner distribution for local spacings and the Porter-Thomas distribution for reduced widths are verified for the resonances in the even-even nuclei Ca⁴⁰, Fe⁵⁶, Ni⁵⁸, and Ni⁶⁰. A simple method of area analysis which is less tedious and time consuming than the method reported before in Part III is also described.     

Fission of muonic 232Th and 239Pu

The neutron emission is studied following the formation of muonic atoms of ²³²Th and ²³⁹Pu. Energy and time distributions are measured. Various processes which contribute to the measured spectra are considered. A collective resonance model of the muon capture is used to calculate the nuclear excitation function. The probability of the radiationless nuclear excitations and the influence of the presence of the bound atomic muon on the fission barrier are discussed. The existing data for the $\text{Γ}{}_{\mathrm{n}}\text{Γ}{}_{\mathrm{f}}$, are analysed. As a result of the analysis the rates of the prompt and delayed fission events (due to the radiationless mu-atomic transitions and the nuclear muon capture, respectively) are deduced from the experimental data to be 0.006/muon and 0.045/muon for ²³²Th and 0.10/muon and 0.49/muon for ²³⁹Pu, respectively. The increase of the fission barrier for muonic atoms is confirmed. The experimental neutron rates can be consistently explained only if it is assumed that in both nucleides the K_α radiationless transitions do not induce fission. The increase of the fission barrier for ²³⁹Pu is hence deduced to be not less than 1.2 MeV. The fate of the atomic muon after the nuclear fission is briefly discussed. Its influence on the interpretation of the present results is found to be small.     

Anomalous shape of cyclotron resonance line in n-GaP in high magnetic fields

Cyclotron resonance in n-GaP has been observed at 119 μm in pulsed magnetic fields up to 410 kG. From the experiments with the magnetic field parallel to the 〈100〉, 〈110〉 and 〈111〉 axes, it is concluded that the transverse effective mass for electron is and that the anisotropy factor of the conduction band is K = 7.9^+3.2_?2.0. An anomalous shape of the absorption curve was found in the magnetic field directions parallel to the crystal axes 〈110〉 and 〈111〉.     

The irreducible Raman scattering tensor operator for the 32 crystallographic point groups and its application to the resonance and electronic Raman effect

The irreducible components of the Raman scattering tensor operator $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ under the symmetry of a general point group are calculated. The unitary transformations U(Γ_γΓ_ksΓ_k′s′, ρσ) from the Cartesian $\text{α}\text{?}{}_{\mathrm{\rho \sigma }}$ and spherical $\text{α}\text{?}{}_{\mathrm{Q}}{}^{\mathrm{K}}$ components, respectively, to the irreducible components $\text{α}\text{?}{}_{\mathrm{\gamma }}{}^{\mathrm{<mtext>\Gamma </mtext>}}\text{(}\text{Γ}{}_{\mathrm{ks}}\text{Γ}{}_{\mathrm{k\prime s\prime }}\text{)}$ for the 32 crystallographic point groups are collected in tables. As an example the unitary transformation U(Γ_γΓ_ksΓ_k′s′, ρσ) is used to discuss the behavior of the scattering tensor in a resonance Raman experiment. With the help of the general formalism the scattering tensor for electronic Raman transitions of transition metal ions is calculated. As an example the scattering tensors of electronic Raman transitions within the ⁵T₂ state of the high-spin trigonal distorted octahedral Fe²⁺ are calculated and the refinement of the selection rules is discussed.     

Analysis of topological cross sections in pp interactions at 22.4 GeVc

The multiplicity distribution for 11558 events in $\text{p}\text{p}$ interactions at 22.4 $\text{GeV}\text{c}$ was analyzed. The average charged multiplicity 〈n_ch〉 for inelastic events was found to be 4.69 ±0.05 and $\text{〈n}{}_{\mathrm{ch}}\text{〉}\text{D=2.04 ± 0.05}$. The early KNO scaling of normalized topological cross sections has been tested.     

Is KNO scaling proved or postulated?

Assuming Feynman's scaling law, Koba, Nielson and Olesen had shown that as s → ∞, (i) 〈n^q〉/〈n〉^q → d_q where d_q is independent of s and $\text{(ii)}\text{σ}{}_{\mathrm{n}}\text{(s)/σ}{}^{\mathrm{(s)}}{}_{\mathrm{<mtext>incl</mtext>}}\text{→ (}\text{1}\text{〈n〉)}\text{Ψ(n/〈n〉)}$. The derivation of the latter result is, however, not rigorous and it does not follow, as a necessary consequence, from the scaling law.     

Exact approach to equilibrium for the glauber model of a one-dimensional Ising system with random ±J bonds

The (discrete-time) Glauber model is considered for a one-dimensional system of spins s_j = ±1 with nearest-neighbor Ising interaction $\text{H}\text{= -Σ}{}_{\mathrm{j}}\text{J}{}_{\mathrm{j}}\text{s}{}_{\mathrm{j}}\text{s}{}_{\mathrm{j+1}}$. The J_j = ±J are treated as random variables with an arbitrary joint probability p(J). The exact time-dependent average 〈s_j〉_t is determined, and from it the “quenched” average $\text{〈〈s}{}_{\mathrm{j}}\text{〉}{}_{\mathrm{t}}\text{〉}{}_{\mathrm{<mtext>av</mtext>}}\text{=Σ}{}_{\mathrm{<mtext>J</mtext>}}\text{p}\text{(}\text{J}\text{)〈s}{}_{\mathrm{j}}\text{〉}{}_{\mathrm{t}}$ is explicitly found.     

Multiplicity distribution in antiproton-proton interactions

In a compilation of $\text{p}\text{p}$ interactions we present evidence for KNO scaling in the primary momentum region up to 7 GeV/c. The average multiplicity in $\text{p}\text{p}$ interactions and annihilations has a logarithmic increase with energy. The reduced statistical momenta of multiplicity distribution $\text{c}{}_{\mathrm{q}}\text{=}\text{〈n}{}^{\mathrm{q}}\text{〉}\text{〈n〉}{}^{\mathrm{q}}$ are energy independent and for all final states have practically the same values as in proton-proton interactions. In annihilations the c_q to appear to be different from those in pp interactions and the KNO scaling function is also different.     

Submillimetre cyclotron resonance of electrons in GaP

The first observation of cyclotron resonance in n-type GaP is reported. The electrons were thermally excited at a temperature of 100 K and the resonance was observed at submillimetre wavelengths (337 μm) using a pulsed magnetic field of 0–300 kG. From experiments with B∥〈100〉, 〈110〉 and 〈111〉 it was found that the transverse effective mass for electrons is $\text{m}{}^1{}_{\mathrm{\perp }}\text{= 0.25 ± 0.01 m}{}_0$ and that the anisotropy factor for the conduction band ellipsoids is K = 20⁺¹⁰_-6.     

α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

The β− decay of 102Mo

The ¹⁰²Mo activity was obtained by photofission of natural U and thermal-neutron induced fission of ²³⁵U, with subsequent chemical separation of the molybdenum fraction. In addition, nuclei with mass 102 were separated from fission products of ²³⁵U(n_th, f) using the mass separator LOHENGRIN. A decay scheme and absolute γ-intensities are deduced from measured γ-ray, X-ray and γ-coincidence spectra. Logftvalues are calculated. Shell-model calculations for a $\text{(πlg}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^3$$\text{(νlg}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}\text{)}{}^3$ multiplet have been carried out using effective nucleon-nucleon interactions. The γ-decay between low-lying, low-spin members of this multiplet was studied in detail and compared with the experimental data.     

The decay of uranium shape isomers investigated by photonuclear reactions

The half-life of the ²³⁸U shape isomer and its yield ratio in a (γ, γ') reaction have been measured by pulsed beam techniques at a bremsstrahlung endpoint energy of 12 MeV. From the results $\text{(T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 146 ± 22}\text{ns}\text{, Y}{}_{\mathrm{<mtext>iso</mtext>}}\text{/Y}{}_{\mathrm{<mtext>pr</mtext>}}\text{= (6.6 ± 1.0) × 10}{}^{\mathrm{?6}}\text{)}$ the isomeric fission cross section has been deduced. Combining this information with the results of a previous ²³⁸U(γ, xnγ) study, an upper limit for the branching ratio Γ_γ/Γ_f|II < 13 for the decay of ^238mU can be obtained. The decay properties of the ²³⁶U and ²³⁸U shape isomers are discussed.