Internal Excitation Energy Research Articles

Collisions of UF−6 ions with Ar, Xe, SF6, and UF6

Electrostatic energy analysis has been performed on the products of collisions of up to 200 eV (lab) UF−6 ions with Ar, Xe, SF6, and UF6. Negative ions of UF6 containing internal excitation energy up to ∼5 eV have been observed and their distributions as functions of scattering angle and internal excitation recorded. The behavior of the fragment ions F− and UF−5 was investigated and found to be in accord with a simple statistical model of the collision dynamics.

Estimation of Neutron Yield from Individual Fragment in Medium-Excitation Fission

A method of calculation is described to estimate the average number of neutrons emitted per fragment in medium-excitation fission from published experimental data on neutron emission in thermal-neutron induced fission, average total kinetic energy as a function of fragment mass and mass yield in low- and medium-excitation fission reactions. Use is made of a relation of fragment excitation energy with internal excitation and deformation energies, and the difference in kinetic energy between the fission reactions at two-excitation energies. A tentative calculation is made for the fission of 238U induced by 12 MeV protons. The results are in good agreement with experimental data. The method developed in the present work may make it possible to predict the average number of neutrons emitted from individual fragment in medium-excitation fission which has not yet been measured experimentally.

Dynamic excitation in the fission ofPu240

The excitation mechanism of the fission process is studied in terms of a model of particles moving in a deformed time-dependent potential. A residual interaction of the pairing type is incorporated by means of the BCS approximation. No limitations are imposed on the number of quasiparticles. The calculations of the dynamical variables are done by solving numerically the equation of motion of the quasiparticle density and pairing matrices. The set of quasiparticle states is truncated by an energy cutoff. The effects of this cutoff on the results are negligible. Comparison with calculations for $^{240}\mathrm{Pu}$ which were restricted to two-quasiparticle excitations only shows that this restriction results in an appreciable underestimate of the total excitation energy. The estimated collective energy is found to be at least one order of magnitude smaller than the dissipated energy for an oscillatory motion of the collective coordinates.NUCLEAR REACTIONS, FISSION, $^{240}\mathrm{Pu}$ internal excitation energy at scission. Time dependent mean field and pairing, equations of motion of quasiparticle density and pairing matrices integrated numerically.

Collisional ionization of atomic cesium by UF6 and WF6

Collisional ionization of Cs by UF6 and WF6 has been studied in crossed-beam geometry. Product UF−6 and WF−6 contain ≈3 eV of internal excitation energy even at the lowest Cs laboratory impact energy of 7 eV.

Estimation of neutron yield from individual fragment in medium-excitation fission.

A method of calculation is described to estimate the average number of neutrons emitted per fragment in medium-excitation fission from published experimental data on neutron emission in thermal-neutron induced fission, average total kinetic energy as a function of fragment mass and mass yield in low- and medium-excitation fission reactions. Use is made of a relation of fragment excitation energy with internal excitation and deformation energies, and the difference in kinetic energy between the fission reactions at two-excitation energies. A tentative calculation is made for the fission of 238U induced by 12 MeV protons. The results are in good agreement with experimental data. The method developed in the present work may make it possible to predict the average number of neutrons emitted from individual fragment in medium-excitation fission which has not yet been measured experimentally.

Measurement of the Energy Division versus Mass in Highly Damped Reactions

Nuclear charge, mass, and kinetic energies were measured for fragments from the reactions of $^{86}\mathrm{Kr}$+ $^{124}\mathrm{Sn}$ at 440- and 720-MeV bombarding energies. From these data it was deduced that the internal excitation energy of the strongly damped products divides proportionally with the mass.

Modified one-body nuclear dissipation

We study a modification of the one-body dissipation mechanism for the conversion of energy of collective nuclear motion into internal single-particle excitation energy. One-body nuclear dissipation is a consequence of the long mean free path of nucleons inside a nucleus, and arises from nucleons colliding with the moving boundary of the nucleus rather than with other individual nucleons. In our modification, which attempts to incorporate self-consistency, the dissipation rate is proportional to an integral over the nuclear surface of the square of the normal component of the normal derivative of the velocity. The resulting properties of this dissipation are qualitatively similar to those of ordinary two-body viscosity rather than to those of the original one-body dissipation. In particular, for small oscillations about a sphere the dissipation rate increases with increasing multipole degree, and in fission this dissipation leads to more elongated scission shapes and to decreased fission-fragment kinetic energies. By adjusting the parameter that specifies the magnitude of this dissipation, we are able to reproduce adequately the experimental most probable fission-fragment kinetic energies for the fission of nuclei throughout the Periodic Table.[NUCLEAR REACTIONS, FISSION Calculated dependence of fission-fragment kinetic energies upon modified one-body dissipation. Dynamics of large-scale nuclear collective motion, nuclear dissipation, hydrodynamical model, Werner-Wheeler method.]

Ion-molecule reaction of CH 3+, C 2H 5+, C 3H 5+ and C 3H 7+ with unsaturated C 2, C 3 and C 4 hydrocarbons

The reaction rate constants and product distributions for reaction of CH 3 + and C 2H 5 + with ethylene, C 2H 5 + with propene and cyclopropane, and C 3H 5 + and C 3H 7 + with the four butene isomers are reported here. The results were obtained using a Dempster-ion cyclotron resonance tandem mass spectrometer which mass analyzes and decelerates the reactant ions to less than 0.1 eV. The internal excitation energy of all but the methyl reactant ions may be varied through unreactive collisions in the first stage of the instrument. Deuterated reactant ions have been used in an attempt to classify reaction channels according to models such as hydride abstraction, proton transfer or complex formation. Most of the major reaction channels studied here are best described as proceeding through a short-lived intermediate complex. The reactions of C 2H 5 + with propene and cyclopropane are particularly interesting since the major product, C 4H 9 +, is produced through both direct proton transfer and complex formation.

Calculation of compound-nucleus cross sections for symmetric very-heavy-ion reactions

Cross sections for forming compound nuclei in symmetric very-heavy-ion reactions are calculated by use of the criterion that the dynamical trajectory for the fusing system must pass inside the fission saddle point in a multidimensional space in order to form a compound nucleus. The dynamical trajectory is obtained by solving numerically the modified classical Lagrange equations of motion for a system whose shape is specified in terms of smoothly joined portions of three quadratic surfaces of revolution. This restriction to nuclear shapes that are axially symmetric (about an axis that is in general rotating in space) is a good approximation for systems with small angular momentum, but it may be seriously deficient for systems with large angular momentum. The nuclear potential energy of deformation is determined by means of a macroscopic model that includes the Coulomb energy and the nuclear macroscopic energy. This latter quantity is calculated in terms of a double volume integral of a Yukawa two-body interaction potential, which includes the surface energy of the liquid-drop model but also takes into account the lowering in energy due to the finite range of the nuclear force. For systems with angular momentum, we include a centrifugal pseudopotential calculated for rigid-body rotation. The kinetic energy of collective motion is calculated for nuclear flow that is a superposition of incompressible, nearly irrotational collective-shape motion and rigid-body rotation. Nuclear dissipation (the transfer of energy of collective motion into internal single-particle excitation energy) is included in the formulation by means of Rayleigh's dissipation function. However, to emphasize that compound-nucleus cross sections become small for very heavy systems even in the absence of dissipation, our current results are presented for the case of zero dissipation. For nuclear systems lighter than about $^{110}\mathrm{Pd}$ + $^{110}\mathrm{Pd}$ \ensuremath{\rightarrow} $^{220}\mathrm{U}$ and for relatively low angular momentum, the fission saddle point lies outside the point of hard contact in heavy-ion reactions, which permits the compound-nucleus cross section at relatively low bombarding energy to be calculated in terms of a one-dimensional interaction barrier, as is customarily done. For heavier nuclear systems and/or for high angular momentum, the fission saddle point lies inside the contact point, which reduces the compound-nucleus cross section compared with that calculated for a one-dimensional interaction barrier.NUCLEAR REACTIONS $^{100}\mathrm{Mo}$ + $^{100}\mathrm{Mo}$ \ensuremath{\rightarrow} $^{200}\mathrm{Po}$, $^{110}\mathrm{Pd}$ + $^{110}\mathrm{Pd}$ \ensuremath{\rightarrow} $^{220}\mathrm{U}$, $^{124}\mathrm{Sn}$ + $^{124}\mathrm{Sn}$ \ensuremath{\rightarrow} $^{248}\mathrm{Fm}$. Calculated compound-nucleus cross sections. Liquid-drop model, hydrodynamical model, nuclear potential energy of deformation, nuclear inertia, dynamical trajectory, compound-nucleus formation, heavy-ion fusion, quasifission, highly inelastic heavy-ion collisions.

Blast waves in real gases

Real gas effects of compressibility, vibrational excitation, dissociation, ionization and electronic excitation are taken into account in blast wave formulation. Residual property concepts, as well as those of equilibrium quantum statistical thermodynamics, are utilized to relate the different microscopic internal energy excitation levels to macroscopic thermodynamic properties. Jump conditions across the shock front are then evaluated and a non-self-similar quasi-similar solution is obtained for the adiabatic point explosion problem. From the results it appears that temperature profiles are affected most by the real gas properties of the medium. Some of their effects are evident in density profiles, while pressure and particle velocity are relatively unaffected. Finally, the shock front decays slower than in the perfect gas case, especially during the initial stages of propagation.

Strongly damped heavy-ion collisions: Microscopic calculation of the kinetic-energy loss in rapid stretching

The internal excitation energy of two colliding heavy ions is calculated in a microscopic model based on the rapid stretching of two rotating heavy ions in weak contact. The excitation energies are calculated for various projectile-target combinations ($^{40}\mathrm{Ar}$, $^{84}\mathrm{Kr}$, and $^{136}\mathrm{Xe}$ as projectiles and $^{209}\mathrm{Bi}$ and $^{232}\mathrm{Th}$ as targets). The calculated energies in the rapid stretching mode are shown to be consistent with the experimentally observed kinetic-energy loss in the strongly damped collisions. A more definite experimental test of the concept of rapid stretching of two colliding heavy ions is suggested.NUCLEAR REACTIONS $^{40}\mathrm{Ar}$, $^{84}\mathrm{Kr}$, $^{136}\mathrm{Xe}$ as projectiles and $^{209}\mathrm{Bi}$, $^{232}\mathrm{Th}$ as targets; calculated kinetic-energy loss in strongly damped collisions.

Equilibrium properties of a mixture of reacting gases: A soluble model

We calculate exactly the equilibrium properties of a large system consisting of two kinds of Bose particles, a and b, that can be transformed into each other by an external field. The enhancement in the specific heat around the threshold (internal excitation) energy of the b particles is studied as a function of the external field strength, and the mass–action law is derived. Bose–Einstein condensation can occur in our mixture of reacting gases at a transition temperature lower than that of a one-component ideal gas. Also, the condensate occupancy increases faster than T3/2 as the temperature is lowered.

Effect of viscosity on the dynamics of fission

We study the effect of ordinary viscosity on nuclear fission by solving clasical equations of motion for the time evolution of fissioning nuclei. The collective potential energy is calculated both by means of the usual liquid-drop model and by means of a modified liquid-drop model that takes into account the lowering in the nuclear macroscopic energy due to the finite range of the nuclear force. The collective kinetic energy is calculated for incompressible, nearly irrotational hydrodynamical flow by use of the Werner-Wheeler method. The Rayleigh dissipation function, which describes the transfer of energy of collective motion into internal excitation energy, is calculated under the assumption that nuclear dissipation arises from individual two-body collisions. Prior to scission the nuclear shape is specified in terms of smoothly joined portions of three quadratic surfaces of revolution. After scission the fission fragments are represented by two spheroids with collinear symmetry axes. In addition to slowing the system down and converting some of the collective energy into internal energy, two-body viscosity hinders the formation of a neck. This leads to a more elongated scission configuration and consequently to a smaller final fission-fragment kinetic energy. From a comparison of calculated and experimental most probable fission-fragment kinetic energies for nuclei throughout the periodic table, we determine that at high excitation energies the average value of the viscosity coefficient $\ensuremath{\mu}$ is $\ensuremath{\mu}=0.015\ifmmode\pm\else\textpm\fi{}0.005 \mathrm{TP}=9\ifmmode\pm\else\textpm\fi{}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ MeV s/${\mathrm{fm}}^{3}$, provided that nuclear dissipation arises from two-body collisions. This is about 30% of the value that is required to critically damp the quadrupole oscillations of idealized heavy actinide nuclei.NUCLEAR REACTIONS, FISSION Calculated dependence of most probable fission-fragment kinetic energies on viscosity and compared with experimental values. Liquid-drop model, hydrodynamical model, nuclear potential energy of deformation, nuclear inertia, nuclear dissipation, numerical solution of classical equations of motion for fissioning nuclei.

Significance of limiting low pressure product yields from energetic atomic exchange reactions

The limiting low pressure yield behavior has been characterized for gas phase substitution reactions of energetic 3H and 18F atoms with aliphatic and alicyclic substances. The limiting yields correlate well with the respective critical energies for secondary unimolecular decomposition. The interpretation of this behavior leads to quantitative descriptions for the hydrogen-for-hydrogen and F-for-F primary product internal excitation energy distributions together with approximate descriptions of total energy disposal for the threshold hydrogen-for-hydrogen processes.

An estimate of the internal excitation energy in fission

A comparison of the potential energy at scission with experimental post-scission data yields an estimate of 7 MeV and an upper bound of 25 MeV for the internal excitation energy at scission. Complete damping during the descent to scission can be ruled out.

Chemical accelerator studies of reaction dynamics: Ar+ + CH4 → ArH+ + CH3

Chemical accelerator studies on isotopic variants of the reaction Ar+ + CH4 → ArH+ + CH3 are reported. Velocity and angular distributions of the ionic product as a function of initial translational energy have been measured over the energy range 0.39–25 eV center-of-mass (c.m.). The asymmetry of the product distribution with respect to the center of mass indicates that the reaction is predominantly direct over the energy range studied. The dynamics of the reaction are approximated by the spectator stripping model: The reaction exothermicity appears as product internal energy and product excitation increases with collision energy at the rate predicted by this model. The internal degrees of freedom of the neutral product have little effect on reaction dynamics, and product excitation appears to reside principally in the ionic product. Deviations from the spectator stripping model suggest the existence of a basin in the potential energy hypersurface for this reaction; the ArCH4+ complex which may be formed at low collision energies, however, preferentially decomposes via reaction channels other than that resulting in ArH+ formation.

Internal energy effects on the reaction of D3+with CH4

A tandem mass spectrometer has been used to measure the distribution of ionic products resulting from the reaction of D3+ with CH4 as a function of the average number of D3+-D2 collisions occurring in the source. These results provide information on the amount of internal excitation energy in D3+. It is shown that at least 69% of the D3+ ions are formed with 0.6 eV or more excitation energy. These results are compared with an approximate D3+ excitation energy distribution based upon a statistical model which assumes a random distribution of energy among the vibrational and translational states of the products of the reaction of D2+ with D2. Reasonable agreement was obtained.

Bimolecular reactions of trapped ions: IX. Effect of method of preparation on the rate of reaction of C 2H 5+

The ion—molecule reactions occurring in C 3H 8(CD 3) 2O, C 2H 4(CD 3) 2O and CD 4C 2H 4 mixtures have been studied by the ion trapping technique. The results indicate that C 2(H,D) 5 + ions produced by ion—molecule reactions in methane, by ion—molecule reactions in ethylene, and by dissociative electron impact ionization of propane react with the same rate coefficients in hydride transfer reactions (with C 3H 8), proton transfer reactions (with (CD 3) 2O) and proton transfer plus condensation (with C 2H 4). No significant effects are observed which can be traced to the method of preparation even though the various methods might be expected to produce ions of different internal excitation energy. Rate constants for a number of other reactions in the mixtures have been measured. Particularly noteworthy is the fact that C 2H 4D + and C 2D 5 + react with ethylene by both H +(D +) transfer and condensation to form C 3(H,D) 5 +, the reactions being of approximately equal importance.

A field ionization study of octan‐2‐one

AbstractH/D randomization is not observed within the octan‐2‐one‐1,1,1,3,3‐d5 molecular ion at times less than 7 × 10−10 sec following field ionization. Partial H/D randomization is observbed at 10−6 to 10−5 sec. It is deduced that the curves of microscopic rate constant k against internal excitation energy E for the reactions effecting randomization and for the McLafferty rearrangement intersect. The field ionization kinetics (FIK) for the McLafferty rearrangement in octan‐2‐one‐1,1,1,3,3‐d5 are investigated over a time range extending from 10−11 to 10−6 sec. The maximum microscopic rate constant k for the reaction is estimated as 5 × 1010 sec−1. It is suggested that FIK measurements with a double focusing mass spectrometer be made by sweeping the blade potential rather than by the alternative technique of sweeping the electric sector analyzer potential. The ‘normnal’ FI mass spectra of octan‐2 one and octan‐2‐one and octan‐2‐one‐1,1,1,3,3‐d5 are presented and discussed. It is proposed that the m/e 56 species in the ‘normal’ FI mass spectrum of octan‐2‐one represents a doubly charged ion formed by loss of oxygen in a surface process.

Angular spread of hydrogen atoms formed by electron capture and dissociation of H+, H2+ and H3+ in H2, H2O and C8F16 at energies of 2·5 to 15 keV

Data are presented on the angular spread of neutral atoms formed by electron capture and dissociation of H+, H2+ and H3+ in H2, H2O and C8F16 targets. Measurements were made at energies of 2·5 to 15 keV and for a range of target densities. The results are presented as the fraction transmitted through an aperture of a given half-angle. It is deduced that the angular spread of atoms from H2+ and H3+ molecular ion beams was predominantly due to the internal excitation energy of the molecular ions and not to simple scattering, even at the lower energies. The angular spread of atoms formed by electron capture by H+ in H2O varied with energy as E−0·6; this is compared with the cross section for single scattering of H+ on oxygen atoms obtained from the classical theory of Firsov, which varies as E−1.