New approximation of the energy dependences of total cross sections for proton-induced fission of actinide nuclei

The energy dependences of the cross sections for the fission of ²³²Th to ²³⁹Pu nuclei that is induced by protons of energy in excess of 50 MeV are proposed to be approximated by the sum of two functions. Of these, the first decreases exponentially with increasing proton energy. It represents the contribution of two-step fission, which competes with particle evaporation. The second function decreases exponentially as the energy grows to about 200 MeV, whereupon it increases up to an energy of 1 or 2.5 GeV. After that, it again decreases for ²³²Th to ²³³U nuclei or remains nearly unchanged for ²³⁷Np and ²³⁹Pu nuclei. This function is likely to represent the sum of the contributions from three modes of single-stage fission.     

Excitation energy division in the first 160 MeV of total kinetic energy loss for the reaction 684 MeV 80Kr+174Yb

The fraction of the total excitation energy imparted to the primary target-like fragment produced in the reaction 684 MeV ⁸⁰Kr+¹⁷⁴Yb has been determined for one charge asymmetry in the exit channel. This fraction was deduced from the kinetic energy cost of evaporating neutrons from the target-like fragment and is approximately 0.5 for total kinetic energy losses as large as 160 MeV. This result is consistent with the predictions of nucleon exchange models and indicates that for some exit channels thermal equilibrium has not been reached for energy losses corresponding to a sizeable fraction of the maximum kinetic energy relaxation.     

Monolayer K-films on Ni(100) — II. Electronic excitations

Electronic excitations in a K layer adsorbed on Ni(100) have been observed by means of electron energy loss spectroscopy. The observed excitation energy depends on the density of K atoms in the layer. In the low density range the loss energy decreases from 3.5 to 1.5 eV as the density increases from 6.10¹³ to 3.10¹⁴ K atoms per cm². This loss is interpreted to be due to an excitation from below the Fermi level to the shifted K valence level Increasing the density further from 3.10¹⁴ to 6.10¹⁴ K atoms per cm² yields a loss peak that increases in energy from 1.5 to 2.3 eV. This loss peak merges into the surface-bulk plasmon complex for a thick K film and the energy vs density dependence is compatible with a plasmon excitation in the K layer.     

Inclusion of the Δ resonance in the optical potential between two nuclei and its application to medium energy12C-12C scattering

An energy dependent complex optical potential between two nuclei is calculated from the potential energy density for two colliding nuclear matters generated by solving the Bethe-Goldstone equation in whichNΔ and ΔΔ channels are explicitly coupled to theNN channel. By adding the contributions from the third and fourth order ring diagrams and the relativistic correction to the calculated potential energy density, the saturation property of a nuclear matter is reasonably well reproduced. This is used together with the kinetic energy density to calculate the optical potential for the¹²C+¹²C system in the energy density formalism with the local density approximation. The surface correction term and the symmetry energy term in the energy density functional are determined to reproduce the observed binding energy and the rms radius of¹²C. Using this potential, the differential cross sections for elastic¹²C-¹²C scattering atE _lab=1440 and 2400 MeV are calculated and compared with recent experimental data.     

IUPAC critical evaluation of the rotational-vibrational spectra of water vapor. Part II: Energy levels and transition wavenumbers for HDO, HDO, and HDO

This is the second of a series of articles reporting critically evaluated rotational-vibrational line positions, transition intensities, pressure dependences, and energy levels, with associated critically reviewed assignments and uncertainties, for all the main isotopologues of water. This article presents energy levels and line positions of the following singly deuterated isotopologues of water: HD¹⁶O, HD¹⁷O, and HD¹⁸O. The MARVEL (measured active rotational-vibrational energy levels) procedure is used to determine the levels, the lines, and their self-consistent uncertainties for the spectral regions 0-22 708, 0-1674, and 0-12 105 cm⁻¹ for HD¹⁶O, HD¹⁷O, and HD¹⁸O, respectively. For HD¹⁶O, 54 740 transitions were analyzed from 76 sources, the lines come from spectra recorded both at room temperature and from hot samples. These lines correspond to 36 690 distinct assignments and 8818 energy levels. For HD¹⁷O, only 485 transitions could be analyzed from three sources; the lines correspond to 162 MARVEL energy levels. For HD¹⁸O, 8729 transitions were analyzed from 11 sources and these lines correspond to 1864 energy levels. The energy levels are checked against ones determined from accurate variational nuclear motion computations employing exact kinetic energy operators. This comparison shows that the measured transitions account for about 86% of the anticipated absorbance of HD¹⁶O at 296 K and that the transitions predicted by the MARVEL energy levels account for essentially all the remaining absorbance. The extensive list of MARVEL lines and levels obtained are given in the Supplementary Material of this article, as well as in a distributed information system applied to water, W@DIS, where they can easily be retrieved. In addition, the transition and energy level information for H₂¹⁷O and H₂¹⁸O, given in the first paper of this series [Tennyson, et al. J Quant Spectr Rad Transfer 2009;110:573-96], has been updated.     

The thermal-neutron-induced alpha-accompanied fission of235U investigation of the low energy part of the alpha spectrum

The energy spectrum of the α-particles emitted in the thermal-neutron induced fission of²³⁵U was measured from 11.5 MeV down to 2 MeV using the parabola mass spectrometer Lohengrin at the I.L.L. high flux reactor. This low energy part of the energy spectrum presents a smooth connection with the energy spectra which have been recently reported above 7 MeV. The overall energy spectrum, which is known to be quasi-gaussian above 12 MeV, is slightly asymmetric at low energy, where the observed particles are 6% more than expected from a gaussian shape. As a consequence, all the values reported for²³⁵U for the rate of α-accompanied fission compared to binary fission have to be multiplied by 1.06. This asymmetry is about 2 times less important than the one reported for²⁵²Cf. No evidence was seen for any intense low energy component as reported before. The possible reasons for the existence of this asymmetry are discussed.     

The reaction mechanism of heavy ion scattering at intermediate energies

The contribution to the real and imaginary nucleus-nucleus (N-N) optical potential from nucleon-nucleon scattering in the medium is calculated in a local density approximation from a two Fermi sphere nuclear matter picture for the N-N collision. This reaction mechanism is shown to be dominant for ¹²C + ¹²C scattering at all considered energies (160 MeV < E_lab < 2250 MeV) giving a weakly energy dependent reaction cross section of about 900 mb. Inclusion of the collective 2⁺, 3^? excitations in a coupled channel calculations gives good agreement for both the measured elastic and inelastic 2⁺ cross section at E_lab = 1016 MeV. This fully microscopic parameter free calculation indicates that the energy dependence of the reaction cross section for this system is mostly due to the decrease of the collective contribution with increasing energy contrary to current theoretical models.     

Fissionlike exit channel in the 5.8 MeV/u84Kr on24Mg reaction

Fissionlike (FL) phenomena for systems around mass 100 have been shown previously interpretable in terms of dynamical fission. This appears to be dependent on the entrance channel mass asymmetry. We have studied the fissionlike exit channel in the⁸⁴Kr+²⁴Mg reaction atE(Kr)=5.8 MeV/u. This energy is just above the threshold of fission, so that a clear separation between the Deep Inelastic Component (DIG) and the FL one can be achieved. The bombarding energy corresponds to the same excitation energy in the composite system¹⁰⁸Cd (E ^*=101 MeV) as in the³²S (158 MeV) on⁷⁶Ge reaction we studied earlier and for which fusion-evaporation along with fission-like contributions were measured. The width of the FL distribution confirms the previously observed dependence with the mass asymmetry in the entrance channel which is consistent with the extra push model.     

A fresh look at the electric-field dependence of surface-atom binding energy

This paper aims to clarify the theoretical concepts associated with the field dependence of surface-atom binding energy. The various coefficients involved are defined, and orbital-polarization and charge-transfer effects are distinguished. It is demonstrated that the latter, as well as the former, may have an F² form. A new empirical method of estimating the polarization-energy coefficient for a field-evaporating surface atom is described: this is based on the joint measurements of activation energy and onset appearance energy made by Ernst. His data for rhodium are reanalysed to give the value 1.05 ± 0.3 meV V^?2 nm². This value is then used to show that polarization-type effects will influence the interpretation of field-sensitivity data. Further experiments are called for.     

Vibrational and rotational energy transfer of CH+ in collisions with 4He and 3He

A quantum mechanical investigation of vibrational and rotational energy transfer in cold and ultra cold collisions of CH⁺ with ³He and ⁴He atoms is presented. Ab initio potential energy calculations are carried out at the BCCD(T) level and a global 3D potential energy surface is obtained using the Reproducing Kernel Hilbert Space (RKHS) method. Close coupling scattering calculations using this surface are performed at collision energy ranging from 10^-6 to 2000 cm^-1. In the very low collision energy limit, the vibrational and rotational quenching cross sections of CH⁺ in collisions with He are found to be of the same order of magnitude. This unusual result is attributed to the large angular anisotropy of the intermolecular potential and to the unusually small equilibrium value of the Jacobi R coordinate of the He–CH⁺ complex. As for the He–N₂ ⁺ collision, we also find a strong isotope effect in the very low collision energy range which is analyzed in terms of scattering length and the differences between these two collisions are also discussed.     

The measurement of energy spectra of neutral particles in low energy ion scattering

An apparatus is described for low energy (0.1–10 keV) ion scattering (LEIS) experiments. A time of flight (TOF) spectrometer is incorporated in the system to be able to measure the energy of particles in the neutral state after scattering. The energy resolution ΔE/E of the TOF spectrometer is discussed and found to be 0.5% (FWHM). This is sufficient for our scattering experiments. An electrostatic analyzer (ESA) is used to measure the energy of scattered ions [ΔE/E=0.5% (FWHM)]. Experiments show that in general the ion dose needed to obtain a TOF spectrum (2×10¹⁰ ions/cm²) is much smaller than the dose needed for an ESA-spectrum (6×10¹³ ions/cm²). The ion spectra measured with the TOF spectrometer, by subtracting the neutral yield from the total yield, as well as with the ESA are found to agree quite well. This provides a way to calibrate the TOF spectrometer. The determination of the ion fraction of scattered particles is discussed [10 keV⁴⁰Ar⁺ on Cu(100), scattering angle 30°]. It is shown that the TOF spectrometer is able to measure light recoil particles (e.g. hydrogen) from a heavy substrate. In the analysing system is, in addition to the TOF spectrometer, also incorporated a stripping cell to measure the energy of neutral scattered particles. An energy spectrum of neutral scattered particles measured with both methods is shown.     

The electronic structure of KMnO4 investigated by photoemission and electron-energy-loss spectroscopy

From photoemission and electron-energy-loss data the following picture of KMnO₄, with Mn^VII (with a formal charge state Mn⁷⁺ (3d ⁰)) tetrahedrally surrounded by four O^2–-ions, is deduced: strong covalent bonding between Mn^VII and O^2– leads to a considerable occupation of the Mn-3 d shell. The ground state of the (MnO₄)^–1 molecule is an orbital and spin singlet as seen by the absence of any multiplet splitting in the Mn core levels. The valence band shows a four peak structure extending form 4 eV to 8 eV below the Fermi energy. The first peak at 4.2 eV has mainly O-2p character. The remaining peaks are of strongly mixed Mn-3d/O-2p character due to the covalent bonding. This mixing decreases with increasing binding energy. The electron energy loss data show a variety of structures between 2 eV and 10 eV independent of the primary electron energy which defines them as dipole allowed charge-transfer transitions. An additional excitation at 1.8 eV decreases quickly in intensity with increasing electron energy which classifies it as a dipole or spin forbidden transition in the compound. This energy is close to the value of 1.6 eV reported for the activation energy observed in electrical transport data. The results are compared to quantum chemical molecular orbital calculations of the (MnO₄)^–1 molecule.Physics Department, Allahabad University Allahabad 211002, India     

Energy dependence of ion beam mixing at Fe-Al and Fe-Cu interface: A conversion electron Mössbauer spectroscopic study

The energy dependence of ion beam mixing in the Fe-Al and Fe-Cu bilayer configuration on the energy of bombarding Kr⁺ ions has been investigated by using the technique of conversion electron Mössbauer spectroscopy. The ion energy has been varied over a range between 30 keV and 120 keV by keeping the dose value fixed at 10¹⁶ ions/cm². In both the cases the extent of mixing shows an interesting variation with increase in the value of ion energy. This behaviour is discussed in the light of the calculated energy deposition distributions for the case of the given bilayer systems. The variations in the microstructural details of the mixed region with change in the incident ion energy have also been brought out via determination of hyperfine interaction parameters.     

Multifragmentation and incomplete fusion in central heavy ion collisions within a schematic phenomenological model

The projectile-energy thresholds for nuclear multifragmentation in the collisions of ¹²C, ²⁰Ne and ⁴⁰Ar with ¹⁹⁷Au have been calculated using a schematic model applicable to central collisions of intermediate energy heavy ions. The properties of the composite nucleus which remains following the incomplete fusion of the projectile and target nuclei are calculated using the master equation approach of Harp and Miller to determine the number of preequilibrium nucleons emitted and the energy and linear momentum removal by these nucleons. This nucleus is followed through an isentropic expansion phase and the probability distribution of clusters is determined using a percolation approach based on a 3-dimensional cubic lattice. The input parameters for the percolation calculation are derived from the results of the preequilibrium calculation. While the calculated thresholds in projectile energy per nucleon decrease rapidly as the projectile mass increases, the excitation energy at which multifragmentation is first predicted to occur is approximately the same for each system, i.e., 4.5 to 5 MeV/u. This result is consistent with the apparent disappearance of residual heavy products at such bombarding energies.     

The Condition of Invariance of the Energy of an Atomic-Molecular System with Respect to Rotations of the Jacobi Coordinates

An additional condition for the wave functions of the ground and excited states of atomic-molecular systems, which follows from the energy invariance with respect to rotations of the Jacobi coordinates, is studied. This condition makes a substantial contribution to the conventional criterion of the quality of wave functions, based on the variational principle for the average energy value. The explicit form of this condition is found for an arbitrary interaction potential dependent on the particle-particle distances and the requirements for realization of this condition are ascertained. Variational calculations of ³He²⁺ μ^? e ^? and ⁴He²⁺ μ^? e ^? mesoatoms in the basis of correlated exponential functions dependent on the particle-particle distances are performed with a detailed optimization of all nonlinear parameters for each individual energy level. A high sensitivity of the condition under study to the quality of approximate wave functions and the efficiency of the detailed optimization of the nonlinear variational parameters in calculation of each individual energy level are demonstrated.     

Approximate solution of then-fermion problem,application to the16O nucleus

Recently published data on mass and charge distributions in interactions of⁵⁶Fe with²⁰⁹Bi are reexamined. Both the average mass-to-charge ratio and the relationship between the variances of the mass and charge distributions were found to depend on the degree of energy damping. This was reported to present evidence for long interaction times required for charge equilibration and for the evolution of correlations in the exchange of neutrons and protons. We show that the dependence of the equilibrated mass-to-charge ratios on energy loss is the combined result of i) the mass drift in the⁵⁶Fe+²⁰⁹Bi reaction and ii) the steep gradients of the potential energy surface which lead to a strong dependence of the mass-to-charge ratios on mass asymmetry. Also, the ratios of the variances of mass and charge distributions are shown to reflect the varying slope of the potential energy valley. It is concluded that the⁵⁶Fe+²⁰⁹Bi data are consistent with fast charge equilibration and fully correlated nucleon exchange in agreement with the behaviour of other systems.     

The total cross section for the reaction 24Mg(α, n)27Si up to 13.1 MeV

The total cross section for the ²⁴Mg(α, n)²⁷Si reaction was determined in 10 keV energy steps from threshold to 13.1 MeV incident energy using the activation method. Variations observed in the cross section were interpreted using fluctuation theory with two notable results; firstly, that Γ, the average width of the observed fluctuations, does not vary at the rate expected over the energy range measured, and secondly that the majority of this reaction goes by a direct mechanism. This latter result was also found for the ²⁷Al(p, n)²⁷Si reaction after a reanalysis of published data.     

Intra-center energy transfer dynamics in Cd1−xMnxTe semi magnetic semiconductors

Intra-center luminescence of Cd_1?xMn_xTe semi magnetic semiconductors under low excitation density was investigated both experimentally and by Monte-Carlo simulation. Experimental time-resolved spectra of 2 eV-band under different photon energy for excitation were used. The approach revealed that Mn²⁺–Mn²⁺excitation energy transfers take place by means of resonant dipole–dipole interaction. Besides energy transfer dynamics is strongly influenced by hopping-assisted quenching. Having been intra-center excitation selective-, mixed- and non-selective types of excitation are proved to occur if photon energy for excitation is increased. This is originated from overlapping of ⁴T₁- and ⁴T₂-states. Under inter-band excitation it was established that Mn²⁺-ion excitation takes place with the aid of excitonic energy transfer, with excitation energy being centered at exciton energy. Under temperature rise the transfer rate vigorously enhances due to great increase of overlap integral of Mn²⁺- ions' side-bands. The quenching is proved to be limited in accordance with existing theory. Inhomogeneous broadening diminishes as a result of fast fluctuation rate of excited ions' energy.     

Theoretical line list of D2 O up to 16,000 cm with an accuracy close to experimental

A line list for D₂ ¹⁶O isotopologue of water molecule was calculated in the region 0-16,000 cm⁻¹ with energy levels up to J=30. Variational calculations are based on the semi-theoretical potential energy surface obtained by morphing ab initio potential using the experimental energy levels of D₂ ¹⁶O. For energy levels with J=0, 2, 5 and 10, the standard deviation of the fit is 0.023 cm⁻¹. This line list should make an excellent starting point for spectroscopic modeling and analysis of D₂O rovibrational spectra.     

Partition of excitation energy between reaction products in heavy ion collisions

In the single-particle approach a partition of the excitation energy between the reaction products in deep inelastic collisions of heavy ions are investigated. The role of the particle-hole excitations and the nucleon exchange is considered. The ratio of the projectile excitation energy to the total excitation energy for the reactions²³⁸U(1468 MeV)+¹²⁴Sn,²³⁸U(1398 MeV)+¹¹⁰Pd,⁵⁶Fe(505MeV)+¹⁶⁵Ho,⁷⁴Ge (629 MeV)+¹⁶⁵Ho and⁶⁸Ni(880 MeV)+¹⁹⁷Au is calculated. The results of calculations are in good agreement with the experimental data.We are grateful to Dr. N.V. Antonenko for valuable discussions. This work was supported partly by the Russian Minister for Education and Research under the Grant N2-61-13-28.