Fragment mass dependence of angular anisotropy in 15 MeV proton-induced fission of 244Pu

Angular distributions of fission fragments with mass number A=97-159 have been measured by the radiochemical recoil-catcher method in the proton-induced fission of ²⁴⁴Pu with the incident energy of 15 MeV. Angular anisotropies of extreme asymmetric mass division products even up to the fragment mass ratio of A _H /A _L ∼ 1.85 are found not any different from those of the typical asymmetric mass division products with A∼ 138, which indicates that no clear evidence is observed for the existence of an additional saddle point configuration in the extreme asymmetric mass division. The correlation between the saddle point state evaluated from the angular anisotropy and the mass division mode is discussed.     

Fragment angular distributions in fission and fission-like reactions

Fragment angular distributions in fission is one of the oldest and well understood aspects of fission theory. However, recent heavy ion-induced fission and fission-like reactions have added a new dimension to this problem. We review here our present understanding of the fragment angular distribution theory in fission and fission-like reactions.     

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included.We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei ²⁷⁰110, ²⁷⁸110, ²⁹⁸114, ²⁹²118 and ³²²128, which have been tried to form in krypton and argon induced heavy ion reactions.     

Fragment angular distributions in electron-induced fission of 232Th

Fission fragment angular distributions have been observed in electron-induced fission of ²³²Th for electron energies 8.7 MeV ≦ E_e ≦ 30 MeV. For low energies (though above the fission threshold) the angular distributions contain both a dipole and a quadrupole component. The (90°/0°) anisotropy decreases rapidly for higher electron energies but reveals smaller peaks after the onset of second-, third- and fourth-chance fission suggesting that the effective fission barriers for ²³¹Th and ²²⁹Th in second- and fourth-chance fission, respectively, are both characterized by $\text{K =}\text{1}\text{2}$.     

Coulomb effects in low energy fission

The structures in the total kinetic energy (TKE) distributions in cold fission of²³⁴U and²³⁶U are interpreted in terms of the Coulomb interaction energy (C) between fragments at the scission point. The maximal value ofC, C _max, corresponding to the most compact scission configuration, is calculated for several mass fragmentations. It is shown that withQ being constant,C _max increases if one increases the charge asymmetry for a given primary fragmentation. This condition produces oscillations with a period of approximately 5 amu ofC _max as a function of the light fragment mass which are correlated with the observed oscillations of the maximal value of TKE. Moreover, the enhancement of the yields of the more asymmetric charge fragmentation for a given fragmentation is explained.     

Distribution of angular momenta in shell-model configurations

Zeitschrift für Physik A Hadrons and nuclei - It is shown how the number ofJ-states in a configuration can be calculated approximately. A particularly simple method for obtaining the moments...     

Kinetic energy and angular distributions of instantaneous fission fragments in a classical model

The process of instantaneous fission in deep inelastic collisions is investigated in a classical model. Kinetic energies and angular distributions of the fragments are calculated for the proposed reaction Pb+U atE _cm ^inc =750 MeV; an experimental setup for the separation of the fragments originating from instantaneous fission from the fragments of thermal fission is explained. We also discuss fusion following instantaneous fission as a mechanism for the production of superheavy elements and arrive at rather promising estimates.     

Anomalous angular momenta in a quantised theory of monopoles

In this paper a gauge theory with a classical solution corresponding to a magnetic monopole is quantised. By careful handling of the zero frequency modes it is shown that the monopole is capable of absorbing both momentum and charge. The angular momentum operator is considered and it is shown that if the original theory contains an isodoublet scalar field, the quantum excitations may be half odd integer eigenvalue eigenstates of this operator.     

Angular distributions,relative orbital angular momenta,and spins of fragments originating from the binary fission of polarized nuclei

The angular distributions of fragments originating from the binary fission of odd and odd-odd nuclei capable of undergoing spontaneous fission that are polarized by a strong magnetic field at ultralow temperatures and from the low-energy photofission of even-even nuclei that is induced by dipole and quadrupole photons are investigated. It is shown that the deviations of these angular distributions from those that are obtained on the basis of the A. Bohr formula make it possible to estimate the maximum relative orbital angular momentum of fission fragments, this estimate providing important information about the relative orientation of the fragment spins. The angular distributions of fragments originating from subthreshold fission are analyzed for the case of the ²³⁸U nucleus. A comparison of the resulting angular distributions with their experimental counterparts leads to the conclusion that the maximum relative orbital angular momentum of binary-fission fragments exceeds 20, the fragment spins having predominantly a parallel orientation. The possibility is considered for performing an experiment aimed at measuring the angular distributions of fragments of the spontaneous fission of polarized nuclei in order to determine both the spins of such nuclei and the maximum values of the relative orbital angular momenta of fission fragments.     

Angular momenta of fission fragments in the α-accompanied fission of 252Cf

For the first time, average angular momenta of the ternary fission fragments ^{100, 102}Zr, ¹⁰⁶Mo, ^{144, 146}Ba and ^{138, 140, 142}Xe from the α-accompanied fission of ²⁵²Cf were obtained from relative intensities of prompt γ-ray transitions with the use of the statistical model calculation. Average values of the angular momenta were compared with the corresponding values for the same fission fragments from the binary fission of ²⁵²Cf. Results indicate the presence of a decreasing trend in the average values of angular momenta induced in ternary fission fragments compared to the same binary fission fragments. On the average, the total angular momentum extracted for ternary fission fragments is ∼1.4 ℏ lower than in binary fission. Consequently, results indicate that the mechanism of the ternary α-particles emission may directly effect an induction of angular momenta of fission fragments, and possible scenarios of such mechanisms are discussed. Further, the dependence of the angular momenta of ¹⁰⁶Mo and ¹⁴⁰Xe on the number of emitted neutrons from correlated pairs of primary fragments was obtained also showing a decreasing dependence of average angular momenta with increasing number of emitted neutrons. Consequences are briefly discussed.     

Yield ratio for the two 241Pu fission isomers in the 242(γ, n) reaction

The half-lives and yield ratios for the two ²⁴¹Pu fission isomers have been measured in the ²⁴²Pu(γ, n) reaction. The observed half-life for the long-lived isomer $\text{(T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 20.5 ± 2.2 μs)}$ is in agreement with previous data, and the existence of a short-lived 34 ± 7 ns isomer in ²⁴¹Pu could be confirmed. The measured yield ratios are Y_iso/Y_pr = (9.2 ± 0.8) × 10^?5 and Y_iso/Y_pr = (3.7 ± 0.7) × 10^?5, respectively. From a statistical model analysis of the isomeric fission yield ratio, Y^long_iso/Y^short_iso = 2.5 ± 0.6, a spin assignment for the two isomers is attempted. Possible spin combinations are compared with single-particle shell-model calculations and with available spectroscopic data for the other even-odd Pu isotopes.     

Correlation between fractional independent yields and neutron-to-proton ratio of fission products in low energy fission

Fractional independent yields of fission products in the thermal neutron-induced fission of²³³U,²³⁵U,²³⁹Pu,²⁴¹Pu and in the spontaneous fission of²⁵²Cf have been correlated with the neutron-to-proton ratio of the fission products. The yields of the products from a fissioning system, when plotted as a function of neutron-to-proton (N/Z) ratio of fission preducts, fall on two Gaussian distribution corresponding to light and heavy fission products. The centroids of the distribution or the most probable value of neutron-to-proton ratio is found to be very close to theN/Z of the fissioning nucleus. From the most probable value ofN/Z the various parameters of charge distribution e.g. most probable massA _p, most probable chargeZ _p, the mass dispersionσ _Aand the charge dispersionσ _Zhave been obtained and are in good agreement with the experimental values ofA _pandZ _p.     

Fragment mass and kinetic energy distribution in isomeric fission of 240Pu

Fragment mass and kinetic energy distributions have been measured for isomeric fission of ²⁴⁰Pu. The mass distribution is asymmetric with the average heavy fragment mass nearly equal to that found for ground state spontaneous fission of ²⁴⁰Pu, but slightly lower than for n_th + ²³⁹Pu-fission. The average total fragment kinetic energy appears to be higher in isomeric fission (179.5_?0.7^+1.5 MeV) than in spontaneous fission from the ground state (176.8 ± 1.8 MeV).     

Influence of collective rotational degrees of freedom in medium energy fission

In the present work rms angular momenta have been deduced for the fission fragments corresponding to¹³¹Te^m,g and¹³³Te^m,g in²³²Th(α _{40 MeV},f) and²³⁸U(α _{40 MeV},f) systems from the radiochemically determined independent isomeric yield ratios and statistical model based analysis. For¹³¹Te and¹³³Te the rms angular momenta deduced are 5.9±1.0 and 7.9±1.2 ? respectively in²³²Th(α _{40 MeV},f) and 7.2±0.6 and 8.0±0.8 ? respectively in²³⁸U(α ₄₀ MeV,f). Comparison of the present data with the literature data for these fragments in the same compound nuclei²³⁶U^* and²⁴²Pu^* at lower excitation energies shows increase in the fragment angular momentum with increasing excitation energy and angular momenta of the fissioning nuclei. Fragment angular momentum deduced theoretically for asymmetric and deformed fragments on the basis of thermal equilibration of the collective rotational degrees e.g., rigid rotation, wriggling, tilting, bending and twisting modes considering the effect of multichance fission, are in good agreement with the experimental observations.     

Quantum generation of angular momenta of crystallites in a nanocrystalline material

It is shown that, under the effect of a point force, ordered deformation states of the Fermi type can arise in a nanocrystal. These states are characterized by an angular momentum whose magnitude (estimated in the units of Planck’s constant) depends on the number of atoms in the deformed nanocrystals and can accept macroscopic values. A qualitative explanation is given to the evolution of the strength, diffusive, and damping properties of compact nanocrystalline materials based on the assumption that the quantum generation of angular momenta of crystallites can result in states of rotational motion.     

Fission instability of nuclei at very high angular momenta

Deformation energy surfaces at high angular momenta ($\text{I ≧ 30?}$) are calculated for different nuclear shapes characterized by the deformation β and a neck parameter r. This parametrization has the advantage that it is a natural extension of the Bohr-Mottelson shape parameters β and γ. This choice allows one to study the neck degree of freedom near the fission instability at high angular momenta and also the sudden change of the nuclear shape from an oblate deformation (β > 0; γ = ?60°) to a prolate one (β > 0, γ = 0°) which gives rise to the so called giant backbending (g.b.b.). The deformation energy surface is calculated using the Strutinsky approach with the rotating liquid-drop model (RLDM) and the shell corrections based on a cranked Saxon-Woods potential. The heights of the first and, if present, the second barrier are studied at γ = 0° as a function of the total angular momentum for even mass rare earth and actinide nuclei. The critical angular momenta at which the fission barriers vanish are often higher than that predicted by the RLDM.     

Pseudodipole interaction of ions with nonzero orbital angular momenta

It is shown that the direct exchange interaction of ions possessing electrons (holes) with orbital angular momenta L and ℓ always contains a contribution , where is a unit vector along the bond connecting the ions. As a result, taking the spin-orbit interaction into account gives rise to a pseudodipole interaction of the spins (total angular momenta) of the ions under study and to uniaxial anisotropy. The possibility of using this pseudodipole interaction to explain the magnetic properties of cuprates is discussed. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 67–72 (10 July 1998)     

Structures in far-out asymmetric mass distributions in low energy fission

The far-out asymmetric mass distributions for ²³⁵U(n_th, f), ²³⁹Pu(n_th, f), ²⁴³Am(n_th, f) and ²⁵²Cf(sf) have been determined. The structures in these data and those in the existing results on ²³⁸U, ²³⁴Np and ²³⁵Np have been analysed in a systematic way in terms of the static scission-point model of Wilkins et al. The model explains well all the structures seen in very asymmetric fission.     

The target asymmetry in hard vector-meson electroproduction and parton angular momenta

The target asymmetry for electroproduction of vector mesons is investigated within the handbag approach. While the generalized parton distribution (GPD) H is taken from a previous analysis of the electroproduction cross section, we here construct the GPD E from double distributions and constrain it by the Pauli form factors of the nucleon, positivity bounds and sum rules. Predictions for the target asymmetry are given for various vector mesons and it is discussed how experimental data on the asymmetry will further constrain E and what we may learn about the angular momenta the partons carry.