Vibrational Enhancement Factor Research Articles

Imaging the Mode-Specificity in Cl + CH3D(v1-I, v1-II, v4 = 1; |jK⟩ = |10⟩) → CH2D(41) + HCl(v).

We report a crossed-beam imaging experiment on the title reactions at two collisional energies (Ec) of 5.3 and 10 kcal mol-1. Both the integral cross sections relative to the ground-state reactivity and the differential cross sections were measured and compared. We found that one-quantum excitations of the CH3-stretching vibrations of the CH3D reagent exerted profound mode-specificity in forming the umbrella-mode-excited CH2D(41) products with the vibrational efficacy of v4 > v1-I > v1-II at both Ec values. The concomitantly formed HCl(v) coproducts were vibrationally cold. Interestingly, the branching ratios of (v = 1)/(v = 0) appeared invariant to the initial stretch-modes of excitation at Ec = 5.3 kcal mol-1, yet exhibited a pronounced mode-specific dependency in the order of v1-II > v1-I > v4 at Ec = 10.3 kcal mol-1. This large and Ec-dependent disparity between the two Fermi-coupled reagents, v1-I and v1-II, is particularly significant and could be another facet─in addition to that in the recently reported vibrational enhancement factors─of the Fermi-phase-induced interference effect manifested in the product vibrational branching ratio. The pair-correlated angular distributions (vCH2D, vHCl)s = (41, 0)s in the three stretch-excited reactions were globally alike and resembled that of the ground-state reaction pair (00, 0)g, suggestive of a direct abstraction mechanism of the peripheral type. This is in sharp contrast to all other vibrationally excited pairs of (11, 0)s, (31, 0)s, and (61, 0)s previously reported in the CH2D + HCl isotopic channel, for which both the direct abstraction and a time-delayed resonance pathway partake.

A fully microscopic model of total level density in spherical nuclei

A fully microscopic model for the description of nuclear level density (NLD) in spherical nuclei is proposed. The model is derived by combining the partition function of the exact pairing solution plus the independent-particle model at finite temperature (EP+IPM) with that obtained by using the collective vibrational states calculated from the self-consistent Hartree-Fock mean field with MSk3 interaction plus the exact pairing and random-phases approximation (SC-HFEPRPA). Two important factors are taken into account in a fully microscopic way, namely the spin cut-off and vibrational enhancement factors are, respectively, calculated using the statistical thermodynamics and partition function of the SC-HFEPRPA without any fitting parameters. The numerical test for two spherical 60Ni and 90Zr nuclei shows that the collective vibrational enhancement is mostly dominated by the quadrupole and octupole excitations. This is the first microscopic model confirming such an effect, which was phenomenologically predicted long time ago and widely employed in several NLD models. In addition, the influence of collective vibrational enhancement on nuclear thermodynamic quantities such as excitation energy, specific heat capacity and entropy is also studied by using the proposed model.

Nuclear Level Density within Extended Superfluid Model with Collective State Enhancement

For nuclear level densities, an enhanced generalized superfluid model with different vibrational enhancement factors is studied. The ready-to-use tables for the asymptotic value of a-parameter of level density as well as for additional shift to excitation energy for 291 atomic nuclei are prepared using the chi-square fit of the theoretical values of neutron resonance spacing and cumulative number of low-energy levels to the experimental values. The systematics of these parameters as a function of mass number and neutron excess are obtained. The vibrational enhancement descriptions are additionally tested for a wide range of excitation energies. Simple methods of the vibrational enhancements lead to increasing the level density due to vibrational states by factor ∼ 2 to 3 for the isotopes A ∼ 100 with the excitation energies near the neutron binding energies.

Vibrational Enhancement Factor of the Cl + CHD3(v1 = 1) Reaction: Rotational-Probe Effects.

The vibrational enhancement factor in the Cl + CHD3(v1 = 1) reaction is revisited over the collisional energy range of 2-5.9 kcal mol(-1). Contrary to the previous results obtained by probing the low-|N, K⟩ states of CD3(v = 0) products, CH stretching excitation becomes more efficacious than the same amount of translational energy in promoting the HCl(v) + CD3(v = 0) product pairs when all-|N, K⟩ states are probed. Whereas the new vibrational enhancement factors, which are three to four times larger than the previous report, agree reasonably well with a recent reduced-dimensionality quantum dynamics calculation, a cautious note is made on the different initial |J,K⟩ rotational selections of the CHD3 reactants in the present theory-experiment comparison.

Imaging the nature of the mode-specific chemistry in the reaction of Cl atom with antisymmetric stretch-excited CH4

Following up our preliminary communication [Kawamata et al., Phys. Chem. Chem. Phys. 10, 4378 (2008)], the effects of the antisymmetric-stretching excitation of methane on the Cl((2)P(3/2))+CH(4) reaction are examined here over a wide range of initial collision energy in a crossed molecular beam imaging experiment. The antisymmetric stretch of CH(4) is prepared in a single rovibrational state of (v(3)=1, j=2) by direct infrared absorption, and the major product states of CH(3)(v=0) are probed by a time-sliced velocity-map imaging method. We find that at fixed collision energies, the stretching excitation promotes reaction rate. Compared to the ground-state reaction, this vibrational enhancement factor is, however, no more effective than the translational enhancement. The correlated HCl(v'=1) vibrational branching fraction shows a striking dependence on collision energies, varying from 0.7 at E(c)=2 kcal mol(-1) to about 0.2 at 13 kcal mol(-1). This behavior resembles the previously studied Cl+CH(2)D(2)(v(6)=1), but is in sharp contrast to the Cl+CHD(3)(v(1)=1) and CH(2)D(2)(v(1)=1) reactions. Dependences of experimental results on the probed rotational states of CH(3)(v=0) are also elucidated. We qualitatively interpret those experimental observations based on a conceptual framework proposed recently.

Unravelling the reactivity of antisymmetric stretch-excited CH4 with Cl by-product pair-correlation measurements

The vibrational branching ratio [CH(3)(v=0) + HCl(v'=1)]/[CH(3)(v=0) + HCl(v'=0)] of two correlated product pairs from the title reaction shows a dramatic E(c)-dependence, in sharp contrast to the previously observed behavior in Cl + CHD(3)(v(1)=1), while the vibrational enhancement factors in reactivity of the two reactions are remarkably similar.

Effect of vibrational states on nuclear level density

Simple methods to calculate a vibrational enhancement factor of a nuclear level density with allowance for damping of collective state are considered. The results of the phenomenological approach and the microscopic quasiparticle-phonon model are compared. The practical method of calculation of a vibrational enhancement factor and level density parameters is recommended.

VIBRATIONAL STATE CONTRIBUTION TO NUCLEAR LEVEL DENSITY

The different simple methods for evaluation of vibrational enhancement factor of nuclear level density with allowance for collective state damping are considered and compared. A practical method for calculation of nuclear level density is recommended taking into account quadrupole and octupole vibrational states.

Combinatorial level densities from a relativistic structure model

A new model for calculating nuclear level densities is investigated. The single-nucleon spectra are calculated in a relativistic mean-field model with energy-dependent effective mass, which yields a realistic density of single-particle states at the Fermi energy. These microscopic single-nucleon states are used in a fast combinatorial algorithm for calculating the non-collective excitations of nuclei. The method, when applied to magic and semi-magic nuclei, such as 60Ni, 114Sn and 208Pb, reproduces the cumulative number of experimental states at low excitation energy, as well as the s-wave neutron resonance spacing at the neutron binding energy. Experimental level densities above 10 MeV are reproduced by multiplying the non-collective level densities by a simple vibrational enhancement factor. Problems to be solved in the extension to open-shell nuclei are discussed.

Collective Degrees of Freedom in Nuclear Level Densities

A finite temperature extension of the interacting boson model is developed and applied to the calculation of the collective partition function of transitional even-even Sm isotopes. The effective boson number decreases with increasing temperature, leading to a natural damping of collectivity. Positive and negative parity contributions to the boson partition function are computed and compared to rotational and vibrational enhancement factors commonly used in the generalized superfluid model.

Level density and collective enhancement factor of a compound nucleus in non-adiabatic approach

In this paper a simple statistical formalism that takes into account the diabatic motion of a compound system to calculate total level density is given. The diabatic motion is introduced by coupling the adiabatic collective motion to an environment consisting of intrinsic degrees of freedom. The collective enhancement of level density is studied. It has anadiabatical coefficient that depends only on the excitation energy and adynamical one that depends on the excitation energy and the coupling between intrinsic and collective modes. Qualitatively, the coefficients of the vibrational enhancement factor forA=240 have been studied. The coupling is understood as the initial effect of the oscillatory motion of the mass asymmetry of fragments on the nucleonic motion. The damping effect of the vibrational motion is taken into account considering the collective motion of the fragments as a zero-sound wave propagating in the Fermiliquid. The intrinsic state in the framework of the Fermi Gas Model (FGM) is described. The Pashkevich’s parametrization is used to describe the binary decay of the compound nucleus.

Theory of Raman scattering by molecules adsorbed at electrode surfaces. Model calculations for resonance Raman scattering by an adsorbed diatomic

Model calculations of the resonant Raman cross section of a homonuclear diatomic adsorbate on a metallic electrode surface are performed. If the excited intermediate electronic state is weakly dipole coupled to the electronic ground state (relative to some other excited electronic states), electric field induced intensity borrowing is found to be very large for the adsorbate. The important excited state involved is that describing charge transfer from adsorbate to the metallic substrate. We have also carried out a simplified calculation of the vibrational Franck—Condon factors for the adsorbate. Combining electronic with vibrational enhancement factors, we find that there may be an overall intensity enhancement for the adsorbate of 10 4–10 8 depending on the electric field strength.