Vibrational predissociation quasiclassical tunnelling and classical diffusion

For a positron with wave number $k$, the rate of annihilation when scattered by an atom or molecule is proportional to ${Z}_{\mathrm{eff}}(k)$, the effective number of electrons in the target that are available to the positron for annihilation. There is currently great interest in the very large positron annihilation rates, and hence values of ${Z}_{\mathrm{eff}}(k)$, that have been observed in low-energy positron scattering by some molecules. These are observed experimentally to occur at energies just below the energies of excited vibrational states of the molecule concerned. This has been explained by Gribakin [Phys. Rev. A 61, 022720 (2000)] and Gribakin and Lee [Phys. Rev. Lett. 97, 193201 (2006)] as being due to Feshbach resonances involving excited quasibound vibrational states. These treatments make skilful use of approximate methods. It is of interest to determine how the expression obtained for the resonant contribution to ${Z}_{\mathrm{eff}}(k)$ from a quasibound state using a very accurate method is related to the expressions obtained in the previously mentioned articles. In view of this, in this article I carry out a detailed ab initio theoretical treatment of positron scattering by ${\mathrm{H}}_{2}$ using the Kohn variational method. ${\mathrm{H}}_{2}$ is the simplest molecule, which makes it easier to take into account all the interactions involved. However, a positron does not form a bound state with ${\mathrm{H}}_{2}$. To investigate resonant behavior in ${Z}_{\mathrm{eff}}(k)$, I increase the mass ${m}_{p}$ of the positron so that it forms a weakly bound state with ${\mathrm{H}}_{2}$. This gives rise to excited quasibound vibrational states. The expression I obtain for the resonant contribution to ${Z}_{\mathrm{eff}}(k)$ has some similarity with the expressions obtained by Gribakin and Lee. This gives some support to their explanation of the very large values of ${Z}_{\mathrm{eff}}(k)$. However, they make no explicit mention of corrections to the Born-Oppenheimer (BO) approximation. These play a key role in my treatment as they couple the quasibound states to the continuum. I am able to show how the BO corrections are taken into account implicitly in calculating the expressions obtained by Gribakin and Lee. The most important difference between my treatment and their treatments is that in my treatment ${Z}_{\mathrm{eff}}(k)$ may be infinite at the resonant energy, whereas in the other treatments it is likely to be large, but can never be infinite. Further investigation is necessary to determine the origin of this infinity in my treatment. My treatment could be applied to positron scattering by molecules such as methyl halides in which very high ${Z}_{\mathrm{eff}}(k)$ values are observed, though using the Kohn variational method would be considerably more complicated than in the case of ${\mathrm{H}}_{2}$.

Comparison is made between the use of two different types of vibrational basis functions for the expansion of the total wave function in a vibrationally inelastic scattering problem. The calculations are performed within the framework of the sudden approximation for the rotational motion of the molecular fragments. The different basis functions that are compared are a vibrationally adiabatic set and the standardly used set of diabatic vibrational basis functions. The adiabatic vibrational basis functions are chosen so as to approximately diagonalize the matrix representation of the interaction potential at each value of the scattering coordinate. Nevertheless, they permit the formulation of analytic expressions for the nonadiabatic coupling terms of the kinetic energy operator that are present when an adiabatic basis is used. In order to provide a reference against which to judge the two different bases, the sets of coupled differential equations which arise in the rotational sudden approximation are solved for the He+H2 system, and fixed-angle S matrices are calculated at several scattering energies and different values of the total angular momenta. It is shown that if the customary diabatic basis is used in conjunction with first order distorted wave perturbation theory to calculate the fixed-angle S matrices, these do not agree well with the exactly computed S matrices to which they should correspond. In contrast, if an adiabatic vibrational basis is used, the distorted wave approximation yields fixed-angle S matrices which are in good agreement (within 15% or better) with the fully converged exact calculations.

A tunable X-ray microprobe using synchrotron radiation

The isovector giant dipole resonance (IVGDR) $\ensuremath{\gamma}$ decay was measured in the compound nuclei $^{80}\mathrm{Zr}$ and $^{81}\mathrm{Rb}$ at an excitation energy of ${E}^{*}=54$ MeV. The fusion reaction $^{40}\mathrm{Ca}+^{40}\mathrm{Ca}$ at ${E}_{\mathrm{beam}}=136$ MeV was used to form the compound nucleus $^{80}\mathrm{Zr}$, while the reaction $^{37}\mathrm{Cl}+^{44}\mathrm{Ca}$ at ${E}_{\mathrm{beam}}=95$ MeV was used to form the compound nucleus $^{81}\mathrm{Rb}$ at the same excitation energy. The IVGDR parameters extracted from the analysis were compared with the ones found at higher excitation energy (${E}^{*}=83$ MeV). The comparison allows one to observe two different nuclear mechanisms: (i) the IVGDR intrinsic width remains constant with the excitation energy in the nucleus $^{81}\mathrm{Rb}$; (ii) the isospin-violating spreading width (i.e., Coulomb spreading width) remains constant with the excitation energy in the nucleus $^{80}\mathrm{Zr}$. The experimental setup used for the $\ensuremath{\gamma}$-ray detection was composed by the AGATA demonstrator array coupled to the large-volume ${\mathrm{LaBr}}_{3}$:Ce detectors of the ${\mathrm{HECTOR}}^{+}$ array.

Excitation functions and angular distributions for the reaction $^{54}\mathrm{Cr}(p, \ensuremath{\alpha})^{51}\mathrm{V}$ have been measured between 6.5 and 20.0 MeV for the ground state and the first two excited states in $^{51}\mathrm{V}$ at 0.32 and 0.92 MeV, with spins ${\frac{7}{2}}^{\ensuremath{-}}$, ${\frac{5}{2}}^{\ensuremath{-}}$, and ${\frac{3}{2}}^{\ensuremath{-}}$, respectively. From the angular distributions and the excitation functions, a compound nuclear mechanism is supported for the population of the ${\frac{5}{2}}^{\ensuremath{-}}$ and ${\frac{3}{2}}^{\ensuremath{-}}$ levels. At higher bombarding energies there is evidence that a simple pickup mechanism dominates for producing the ${\frac{7}{2}}^{\ensuremath{-}}$ level. From the fluctuation analysis of the excitation functions for the ${\frac{5}{2}}^{\ensuremath{-}}$ and ${\frac{3}{2}}^{\ensuremath{-}}$ levels, the decay width of the compound nucleus $^{55}\mathrm{Mn}$ was obtained as a function of energy. From the differential cross sections and decay widths, the level density of $^{55}\mathrm{Mn}$ was deduced at excitation energies between 15 and 23 MeV. The results were combined with low-energy level-density data previously obtained with a magnetic spectrograph. These results, when compared with similar data for even-even $^{56}\mathrm{Fe}$, show that the energy shift required to match level densities for odd and even nuclei is the same at low and high excitation energies. The energy dependence of the level density cannot be reproduced over the whole energy range with level-density expressions employing conventional odd-even corrections. The same conclusion is supported by statistical-model calculations of the excitation functions.

We discuss how the large-basis shell-model wave functions can be used to understand the transition from order in the low-lying nuclear levels to disorder at high excitation energy. The level spacing at high excitation energy shows the usual Wigner (GOE) distribution. But other properties at both low and high excitation show deviations from the GOE. The strength distribution of basis states amplitudes in the eigenfunctions is not uniform but evolves from a Breit-Wigner shape at weak off-diagonal interaction strengths to a Gaussian shape for the normal off-diagonal interaction strength. We define an information entropy in the shell-model basis for each eigenstate which shows a smooth increase at low excitation energy to a value near the GOE limit at high excitation energy. This information entropy has a temperature associated with it which is nearly identical to the temperature obtained from the level density and from the Fermi distribution function for the single-particle occupancies. The interrelation between quantum chaos, Fermi liquid theory and thermalization is discussed.

Differential cross-sections of the 11B + α inelastic scattering at E(α) = 65 leading to the most of the known 11B states at the excitation energies up to 14 MeV were measured. The data analysis was done by DWBA and in some cases by the modified diffraction model allowing determining the radii of the excited states. The radii of the states with excitation energies less than ∼ 7 MeV with the accuracy not less than 0.1-0.15 fm coincide with the radius of the ground state. This result is consistent with the traditional view of the shell structure of the low-lying states in 11B. Most of the observed high-energy excited states are distributed among four rotational bands. The moments of inertia of band states are close to the moment of inertia of the Hoyle state of 12C. The calculated radii, related to these bands, are 0.7 - 1.0 fm larger than the radius of the ground state, and are close to the radius of the Hoyle state. These results are in agreement with existing predictions about various cluster structure of 11B at high excitation energies. The state with the excitation energy 12.56 MeV, Iπ = 1/2+, T = 1/2 and the root mean square radius R ∼ 6 fm predicted in the frame of the alpha condensate hypothesis was not found.

Background: Asymmetric fission is known to occur in two regions, the\nactinides and sub-lead, and is dependent on the fissioning system excitation\nenergy. Experimental evidence in the sub-lead region show that this mode is\nsurprisingly persistent with increasing energy and its origin is not fully\nunderstood.\n Purpose: To experimentally study the fusion-fission reaction of $^{215}$Fr at\nmoderate excitation energy and determine previously unknown independent fission\nyields and other properties.\n Method: The compound nucleus was formed in the reaction $^{18}$O +\n$^{197}$Au. The prompt gamma-rays emitted during the reaction were measured\nwith the high efficiency and high granularity $\\nu$-ball2 spectrometer.\nIndependent fission yields of even-even nuclei were determined by detecting\ntriple-gamma cascades in the fission fragments.\n Results: The observed yields, although dominated by a symmetric peak, show\nmaxima for heavy fragment of $Z \\approx 54-56$, which is consistent with the\nknown results in the actinide region but unexpected for the nuclide of\ninterest, and at the studied excitation energy.\n Conclusions: The mode of asymmetric fission is present even at relatively\nhigh excitation energies in the system studied. This observation matches\nexperimental findings in the sub-lead region, contrary to the actinides, and so\nfar there is no well-developed explanation of this phenomenon.\n

In the study of the fission of actinide nuclei at low excitation energies including the spontaneous fission, it was found that the fragment mass distribution and the total kinetic energy (TKE) distribution consist of more than one component, in contrast to the simple single peak structure that is found in the fission at high excitation energies. 1– 6 This phenomenon is attributed to the existence of more than one fission path and is called the multi-modal fission. The mass and TKE distributions depend sensitively on the excitation energy and the position of the peaks of the mass distribution suggests the influence of the closed shell structure of the fragments. Therefore, it is supposed that the microscopic energy plays an important role for the manifestation of this phenomenon. It is a great challenge for us to understand this phenomenon in terms of nuclear many-body dynamics. Several authors studied the potential energy surface (PES) including the microscopic energy in a multi-dimensional parameter space that describes various nuclear shapes; one can deduce the possible fission paths by studying the location of the saddle points and the fission valleys in multi-dimensional parameter space. 7 With this method, they could explain the general trend of the position of the peaks of the mass distribution. The dynamical point of view is necessary to progress the study of the fission mode. We have applied the Langevin approach to the study of the fission modes in uranium nuclei and in fermium nuclei. 8–10 We studied the mass and TKE distributions and demonstrated that we can decompose the fission events into several components by tracing the Langevin trajectories. We also studied the isotope dependence and the excitation energy dependence of the fission mode. 8–10 In the previous studies, we adopted the wall-and-window type one-body friction as the dissipation mechanism of the nuclear fission dynamics. The validity of this dissipation mechanism has been demonstrated by one of the authors (T.W.) who studied the dissipation tensor dependence of the pre-scission neutron multiplicity and the mean TKE. 11–14 From the comparison of the results of the dynamical calculation with experimental data, they excluded the possibility of the two-body type dissipation to be the dominant mechanism by showing that it cannot reproduce the pre-scission neutron data and the TKE data simultaneously. On the other hand, they showed that the wall-and-window type one-body friction can reproduce both data reasonably well and concluded that it is a reasonable model for the dissipation mechanism of nuclear fission. There are other models that are of one-body nature, e.g. surface-plus-window formula, modified wall-and-window formula and chaos weighted wall formula. 15–17 Though there were no free parameters in the original derivation of the one-body friction, 18, 19 the strength has been modified frequently in order to reproduce some experimental data. For example, in the study of the light particle evaporation and the mass distribution, Schmitt et al. used the strength as a free parameter. 17 The modification itself should be acceptable when we take account of the simplicity of the model; it is a macroscopic model without any microscopic effect and it has no dependence on the temperature. However, when one modifies the strength of the nuclear dissipation just to reproduce only one physical quantity, it might be inappropriate to conclude that the deduced strength has definite physical meanings. It may reflect the other effects completely different from the dissipation, like the insufficiency of the model space. It is very important to compare many (at least more than one) physical quantities at the same time. Among the physical quantities that are measured in nuclear fission, the TKE and mass distributions are well investigated experimentally in many cases. In this study, we use these quantities to discuss the dissipation dependence of the fission modes. It is shown that the TKE distribution is, as was expected, directly connected to the strength of the dissipation and we can put some constraints on the strength of the dissipation. Furthermore, it is shown that the mass distribution changes rather drastically when one uses different models for the dissipation mechanism. These results demonstrate the importance and the usefulness of the dynamical approach to the study of the fission mode. Section 2 gives a concise description of our framework. Results are shown in Sec. 3 concerning the fission of 264 Fm nucleus at Ex = 20 MeV. Summary is given in Sec. 4. 2. Methods

For many types of vertical excitation energies, linear-response time-dependent density functional theory (LR-TDDFT) offers a useful degree of accuracy combined with unrivaled computational efficiency, although charge-transfer excitation energies are often systematically and dramatically underestimated, especially for large systems and those that contain explicit solvent. As a result, low-energy electronic spectra of solution-phase chromophores often contain tens to hundreds of spurious charge-transfer states, making LR-TDDFT needlessly expensive in bulk solution. Intensity borrowing by these spurious states can affect intensities of the valence excitations, altering electronic bandshapes. At higher excitation energies, it is difficult to distinguish spurious charge-transfer states from genuine charge-transfer-to-solvent (CTTS) excitations. In this work, we introduce an automated diabatization that enables fast and effective screening of the CTTS acceptor space in bulk solution. Our procedure introduces ``natural charge-transfer orbitals'' that provide a means to isolate orbitals that are most likely to participate in a CTTS excitation. Projection of these orbitals onto solvent-centered virtual orbitals provides a criterion for defining the most important solvent molecules in a given excitation and be used as an automated subspace selection algorithm for projection-based embedding of a high-level description of the CTTS state in a lower-level description of its environment. We apply this method to an ab initio molecular dynamics trajectory of I-(aq) and report the lowest-energy CTTS band in the absorption spectrum. Our results are in excellent agreement with experiment and only one-third of the water molecules in the I-(H2O)96 simulation cell need to be described with LR-TDDFT in order to obtain excitation energies that are converged to <0.1 eV. The tools introduced herein will improve the accuracy, efficiency, and usability of LR-TDDFT in solution-phase environments.

Information has been obtained on the mass distribution and kinetic energy release for fission of $^{226}\mathrm{Ra}$ induced by protons and deuterons at moderate bombarding energies (20 MeV). The mass distribution, which is triple peaked, has previously been interpreted in terms of two separate fission modes: a single symmetric peak, characteristic of symmetric fission, associated with higher excitation energies; and a double-peaked distribution, characteristic of asymmetric fission, associated with lower excitation energies. It is shown that by a proper choice of proton and deuteron bombarding energies, and by a proper weighting of their respective mass-yield curves, the mass distribution for the fission of a single species, $^{228}\mathrm{Ac}$, can be determined for a single excitation energy. At excitation energies near 25 MeV this mass distribution for $^{228}\mathrm{Ac}$ is shown to be a single symmetric peak, in agreement with the hypothesis of two fission components. It is shown further that the measured kinetic energy distributions can also be interpreted in terms of the two-component hypothesis.

Analytical aspects of different adjustment of parameters of an inductively coupled plasma atomic emission spectrometer (ICP‐AES) were investigated. The ICP‐AES was a LABTAM 8440M (now called GBC) spectrometer. Since at many times, the elemental concentration of the analyte is near to the detection limit, the lowest possible detection limit has to be reached. When the signal‐to‐background ratio (SBR) is maximized, the detection limit is the smallest. This is the reason why the effects of each adjustable parameters on the signal‐to‐background ratios were investigated. Seven adjustable parameters can be analyzed in this equipment: (i) viewing height, (ii) forward power, (iii) sample gas, (iv) coolant gas, (v) auxiliary gas, (vi) flushing gas, and (vii) sample uptake flow rates. Furthermore aerosol distribution by droplet size and nebulization efficiency were also examined applying three different sample gas flow rates and four elements [iron (Fe), magnesium (Mg), manganese (Mn), and nickel (Ni)]. The alkali metals with low excitation energy [potassium (K), lithium (Li), and sodium (Na)] were detectable in higher regions of the plasma, some alkali‐earth and transition metals with medium excitation energy [calcium (Ca), srontium (Sr), and copper (Cu)] were well detectable in medium height, whereas the maximum signal‐to‐background ratios of the other elements with relatively high excitation energy [e.g. cadmium (Cd), Ni, and phosphorus (P)] reached in lower regions of the plasma. On the basis of results the compromised viewing height for all the elements is found 5 mm, the optimum sample gas flow rate 1.14 dm3 min‐1 and the forward power 1200 W. Change of coolant and auxiliary gas flow rates has not changed the signal‐to‐background ratios significantly. Consequently the optimum argon flow rates in aspect of consumption of argon are the possible lowest flow rates, where plasma remains stable. For coolant and auxiliary gas flow rates these values are 10 dm3 min‐1 and 0.1 dm3 min‐1, respectively. Changing the rate of peristaltic pump (i.e. sample uptake rate) the signal‐to‐background ratios increase to 4‐ or 5‐fold of the original values, therefore the optimum sample uptake rate is considered 4 cm3min‐1. Increase of flushing gas flow rate has not changed the signal‐to‐background ratios significantly, except in case of sulfur (S) and P, because of oxygen (O2) absorption from the air. When analysis of S and P content is necessary, 0.13 dm3min‐1 and 0.2 dm3 min‐1, respectively, of flushing gas flow rate is recommended to use.

In the independent-particle model, the nuclear level density is determined from the neutron and proton single-particle level densities. The single-particle level density for the positive-energy continuum levels is important at high excitation energies for stable nuclei and at all excitation energies for nuclei near the drip lines. This single-particle level density is subdivided into compound-nucleus and gas components. Two methods are considered for this subdivision: In the subtraction method, the single-particle level density is determined from the scattering phase shifts. In the Gamov method, only the narrow Gamov states or resonances are included. The level densities calculated with these two methods are similar; both can be approximated by the backshifted Fermi-gas expression with level-density parameters that are dependent on A, but with very little dependence on the neutron or proton richness of the nucleus. However, a small decrease in the level-density parameter is predicted for some nuclei very close to the drip lines. The largest difference between the calculations using the two methods is the deformation dependence of the level density. The Gamov method predicts a very strong peaking of the level density at sphericity for high excitation energies. This leads to a suppression of deformed configurations and, consequently, the fission rate predicted by the statistical model is reduced in the Gamov method.

High energy $\gamma$-ray spectra measured by our group involving the compound nuclei (CN) $^{63}$Cu at excitation energy ($E^*$) $\sim$ 36 MeV with average angular momentum ($J$) = 12 - 17 $\hbar$, $^{97}$Tc at $E^* \sim$ 29 - 50 MeV with $J$ = 12 - 14 $\hbar$, $^{113}$Sb at $E^*$ = 109 MeV and 121 MeV with $J$ = 49 - 59 $\hbar$ and $^{201}$Tl at $E^*$ = 39.5, 47.5 MeV with $J$ = 18 - 24 $\hbar$ have been analyzed utilizing the level density prescriptions of (i)Ignatyuk, Smirenkin and Tishin (IST), (ii)Budtz-Jorgensen and Knitter (BJK), and (iii) Kataria, Ramamurthy and Kapoor (KRK). These three prescriptions have been tested for correct statistical model description of high energy $\gamma$-rays in the light of extracting the giant dipole resonance (GDR) parameters at low excitation energy and spin where shell effects might play an important role as well as at high excitation energy where shell effects have melted. Interestingly, only the IST level density prescription could explain the high energy $\gamma$-ray spectra with reasonable GDR parameters for all the four nuclei.

Employing the improved scission-point model, the isotopic and excitation energy trends of the charge distribution of fission fragments are studied in fission of even-even Th isotopes at low and high excitation energies.