The kinetic energy of fission fragments

The Coulomb energy is calculated for the nucleus in the process of fission (in the general case asymmetrical) into two spherical fragments and for ellipsoidal deformations. In the first case the calculation has been done on an M-20 electronic computer. Conclusions are drawn on the form of the nucleus in symmetrical fission at the moment of fragmentation and its effect on the kinetic energy of the fragments.We wish to express our thanks to Yu. Volkov for making the numerical calculations.     

Quantum coherence between states with even and odd numbers of electrons

Systems with variable numbers of electrons are described in which the states representing coherent superpositions of states with even and odd numbers of electrons may occur. An experiment is suggested which generalizes the experiment of Nakamura et al. and may provide direct evidence of such coherence and, thereby, justify the reality of a superspace.     

Comparison of the spontaneous fission of 244Cm and 252Cf: (I). Fragment masses and kinetic energies

The energy of both fission fragments of ²⁴⁴Cm and ²⁵²Cf, respectively, was measured in coincidence with the prompt neutrons (see part II). Energy calibration of the surface-barrier detectors was done after the method of Schmitt et al. with the ²⁵²Cf fragments. Mean values and rms widths of the mass and energy distributions of both isotopes are calculated and compared with the results of other authors. The total kinetic energy of ²⁴⁴Cm fragments is at least as high as that of ²⁵²Cf fragments.     

On the analytical unfolding of generator coordinate kernels for unequal fragments

The generator coordinate formalism breaks down for scattering and reactions involving fragments of unequal size. Analytical expressions are given through which, even in that case, the resonating group kernels can be extracted from those of the generator coordinate method. The possibility of defining a generator coordinate density matrix is discussed.     

On Hamilton systems with even and odd poisson brackets

We present a new bound for the decay rate of a metastable state (in the context of the Fokker-Planck equation) and indicate circumstances under which this bound provides a good estimate. The estimate is used to study the conjectured relation =k Im F between decay rate and free energy analytic continuation. A counterexample as well as an explanation for the relation's usual validity are provided.     

Fission-fragment energy correlation measurements for 252Cf(sf) and structures in far-out asymmetric fission

Fragment-mass and kinetic-energy distribution measurements for ²⁵²Cf(sf) have been extended to the far-out asymmetric low-yield fission region of M_H = 190 compared with the existing data that go up to M_H ≈ 168. The mass yield Y(m) shows a shoulder for M_H ≈ 163 and an important enhancement for M_H ? 176. The 〈E_K〉(m), σ_EK(m) and, to a lesser extent, Y(m) distributions show strong and correlated amplitude fluctuations for M_H ? 170. These data indicate strong and rapid changes in deformation of the nascent fragments and the coexistence of more than one deformed-shell stabilized scission configuration for the same mass splits. These structures and those present in the relatively high-yield regions are discussed in terms of the static macro-microscopic potential-energy calculations.     

On spontaneous fission of neutron-deficient isotopes of elements 103, 105 and 107

Experiments are described on the determination of the spontaneous fission probability for the isotopes of elements 103, 105 and 107 produced by bombarding Tl, Pb and Bi targets with ⁵⁰Ti, ⁵¹V, ⁵⁴Cr, ⁵⁵Mn and ⁵⁸Fe ions. The upper limit of the spontaneous fission probability is established to be 2% for the isotopes ^{252, 253}103. A new isotope of element 105 with mass number $\text{257(T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 5}\text{s}\text{)}$ has been produced. In bombardment of ²⁰⁹Bi with ⁵⁴Cr ions a new spontaneous fission activity with $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{≈ 1–2}\text{ms}$ has been observed. The experimental data permit identification of this activity as the isotope of the new element 107 with mass number 261, which mainly undergoes α-decay (≈ 80%) resulting in the formation of the isotope ²⁵⁷105. The values of the partial α-decay and spontaneous fission half-lives of the isotopes ²⁵⁷105 and ²⁶¹107 are compared with the systematics of the properties of transfermium nuclei.     

Investigation of the maximum accessible kinetic energy of fragments in the neutron-induced fission of 238U nuclei

The masses, total kinetic energies (TKE), and emission angles of fragments originating from the fission of ²³⁸U nuclei that was induced by 5- and 6.5-MeV neutrons were measured by using digital methods for processing signals. A detailed analysis of the shape of digital signals made it possible to reduce substantially the contribution of fragments whose TKE values were distorted because of a superimposition of signals from recoil protons and from alpha particles produced in the spontaneous decay of uranium. The total statistics exceeded two million events for either neutron energy, and this permitted performing a detailed analysis of fission-fragment yields in the region of the highest attainable TKE values. An analysis of fragment yields made it possible to draw specific conclusions on the structure of the potential surface of fissile nuclei.     

Zeta function continuation and the Casimir energy on odd and even dimensional spheres

The zeta function continuation method is applied to compute the Casimir energy on spheresS ^N. Both odd and even dimensional spheres are studied. For the appropriate conformally modified Laplacian the Casimir energy is shown to be finite for all dimensions even though, generically, it should diverge in odd dimensions due to the presence of a pole in the associated zeta function (s). The residue of this pole is computed and shown to vanish in our case. An explicit analytic continuation of (s) is constructed for all values ofN. This enables us to calculate exactly and we find that the Casimir energy vanishes in all even dimensions. For odd dimensions is never zero but alternates in sign asN increases through odd values. Some results are also derived for the Casimir energy of other operators of Laplacian type.     

Total kinetic energies and mass yield distributions of Cf fission fragments

The variation in the mass yield distribution of the spontaneous fission of ²⁵²Cf as a function of the total kinetic energy (TKE) of the two fragments is investigated. With increasing TKE the peaks of the mass yield distributions become narrower.     

The decay of 187Pt: Comparison of the levels of 187Ir with those of heavier odd mass iridium isotopes

The decay scheme of 2.35 h ¹⁸⁷Pt has been investigated using isotopically separated samples produced by the ISOLDE facility at CERN. A total of 20 excited levels in ¹⁸⁷Ir have been established. For many of these levels, spin, parity and absolute probabilities of depopulating transitions have been determined. The results indicate that the ¹⁸⁷Ir nucleus can be described in terms of a single particle Nilsson model including Coriolis coupling between bands ($\text{3}\text{2}{}^{\mathrm{+}}\text{[402],}\text{1}\text{2}{}^{\mathrm{+}}\text{[400]}$).     

Investigation of polar emission in 252Cf and 235U + nth fission

The energy distributions and relative intensities of protons, deuterons, tritons and α-particles emitted along the fission axis during spontaneous fission of ²⁵²Cf were measured simultaneously with both fission fragment energies. The absolute intensity of particles, the mass distribution of fragments, the total kinetic energy and total excitation energy of both fragments were subsequently deduced from the experimental data. Statistical model calculations based on a hypothesis that the polar particles are evaporated from fission fragments have been performed for ²⁵²Cf and ²³⁶U fission. Although some experimental results agree remarkably well with the evaporation hypothesis, the considered model cannot describe many features of the polar emission phenomenon.     

High-resolution measurements of beta-delayed protons from 37Ca and 41Ti

Protons with energies from 870 keV to 5.4 MeV have been observed following bombardment of a ⁴⁰Ca target with ³He at beam energies of 29.5, 36.5 and 60 MeV, as well as from 40 MeV ³He bombardment of an ³⁶Ar gas target. These data, and those resulting from 20 MeV proton bombardment of ⁴⁰Ca, permit accurate identification of proton unbound levels in ⁴¹Sc, ³⁷K, and ⁴⁰Ca fed by allowed beta decay from ⁴¹Ti, ³⁷Ca or ⁴⁰Sc, respectively. Absolute ft values have been determined for beta decay to these levels. The half-life of ⁴¹Ti has been remeasured to be 80±2 ms and the log ft for its superallowed decay branch has been found to be 3.35±0.02, indicating an isospin purity for the lowest $\text{T =}\text{3}\text{2}\text{state in}{}^{41}\text{Sc of}\text{≈ 91 \%}$. The $\text{ft}\text{values for}{}^{37}\text{Ca}\text{β}{}^{\mathrm{+}}$ decay are compared to shell-model calculations for beta-decay in A = 37 nuclei.     

Nucleus shape at the scission point at different kinetic energies of fission fragments

Deformations of fission fragments at fixed kinetic energies of a light fragment have been calculated within the droplet model. The calculations performed demonstrate the existence of a spherical shape with A ₁ = 76 and A _h = 134 (β₁, β_h ≈ 0). Fragments with A ₁ < 76 and A _h < 130 pass from the spherical to flattened shape. Fragments with A _h < 126 again acquire an elongated shape.     

Nonequilibrium thermodynamics of stochastic systems with odd and even variables

The total entropy production of stochastic systems can be divided into three quantities. The first corresponds to the excess heat, while the second two comprise the housekeeping heat. We denote these two components the transient and generalized housekeeping heat and we obtain an integral fluctuation theorem for the latter, valid for all Markovian stochastic dynamics. A previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal, which restricts consideration of directional variables such as velocity.     

偶奇相干态的q-类比

在偶奇相干态的基础上,构造出偶、奇q-相干态,并讨论了它们的光统计特性.计算分析表明:偶奇q-相干态的光统计特性,是完全不相同的.     

Determination of fragment isotopic yields in the fission of 252Cf accompanied by light charged particles

High resolution measurements of prompt γ-rays emitted from fission fragments accompanied by light charged particles (LCP) and those emitted from normal binary fission fragments in ²⁵²Cf fission were simultaneously carried out using a 30 cm³ Ge(Li) detector. A “sandwich” type of arrangement in the source-detector assembly was used to eliminate Doppler broadening of the γ-ray lines in both cases. About thirty γ-ray lines were assigned to specific fission fragments by comparison with the published results for binary fission, and the ratios of intensities of these γ-ray lines in LCP fission and binary fission were determined. Assuming that 2⁺ → 0⁺ transition intensities of doubly even isotopes are a measure of their yields, the yields of several such isotopes in LCP accompanied fission relative to that in binary fission were obtained.     

Fine structures by deformation in the mass energy distribution of fission fragments

It is shown within a seission point model that for a fixed mass and charge fragmentation the potential energy of the scission configuration has several minima as a function of the deformation parameters of the fragments. The scission at these minima leads to a relatively enhanced yield of the fragments with a certain TKE and creates fine structures in the TKE-mass distribution which are different from those produced by the odd-even effect.     

On nonlinear irreversible processes II: The case of even and odd variables

The nonlinear generalization of the theory of Onsager and Machlup presented in a previous paper is extended to the case in which both of even and odd variables exist simultaneously.The generalization of Onsager's principle of least dissipation for the general nonlinear process is presented based on the diffusion and the semi-classical approximations.     

Magic numbers and low energy nuclear transmutation by protons in host metals

The observed nuclear transmutations by protons or deuterons in host metals at low reaction energies are evaluated. Reaction probabilitiesN(Z) depending on the atomic numberZ show maxima close to the magic numbers with the exception ofZ=20. The exponential decay of the maxima onZ have an incrementZ′=10. Exactly this empirically derived relation fits a sequence of the magic numbers of 3 ⁿ , where the basis value 3 reminds of the threefold scheme of the quarks. Dedicated to Prof. Dr. D. Sc. Drs. h.c. Arthur Sharmann to his 70th birthday, 26 January 1998.