A folded diagram microscopic calculation of nuclear Coulomb displacement energies

We have performed a rather extensive microscopic calculation of the ¹⁷F-¹⁷O Coulomb energy differences ΔE_C. Our main purpose has been to study the effects of (i) folded diagrams, (ii) core polarization and (iii) the effects due to different nucleon-nucleon potentials, different single-particle spectra and different radial wave functions. Using a proton-neutron representation we have included higher-order Coulomb corrections like e.g. the coupling of valence particles to collective vibrations of the core.The inclusion of folded diagrams is very important; it is equivalent to a self-consistent treatment of the Q-box starting energies. It causes a significant suppression of the effect due to core polarization, its contribution to ΔE_C becoming small, about 0.03 MeV. As a consequence of this “self-correcting” behavior our results for ΔE_C are quite stable with respect to the choice of different single-particle spectra. Two rather different nucleon-nucleon potentials, the Reid soft-core potential and a meson exchange potential of the Bonn-Jülich group also lead to quite similar results for ΔE_C. In the case of $\text{J =}\text{5}\text{2}{}^{\mathrm{+}}$, for example, Δ_C calculated with the Reid potential ranges, depending on other assumptions, from 3.36 to 3.43 MeV and from 3.36 to 3.40 MeV with the Bonn-Jülich potential: Both are significantly smaller than the experimental value of 3.54 MeV. Optimizing the radial wave functions in the spirit of a Brueckner-Hartree-Fock theory improves the calculated values of ΔE_C for the $\text{J =}\text{1}\text{2}{}^{\mathrm{+}}$ state but not for $\text{J =}\text{5}\text{2}{}^{\mathrm{+}}\text{or}\text{3}\text{2}{}^{\mathrm{+}}$.We feel that other processes such as the explicit inclusion of core deformation or mesonic degrees of freedom or both are needed to explain the Coulomb displacement energies.     

Comparison of short-range correlation and distortion effects in quasielastic electron scattering

The cross section for the (e, e'p) reaction is calculated in a single-particle model, taking into account simultaneously both the effects of short-range correlations and of the distortion of the outgoing nucleon due to its interaction with the residual nucleus. It is shown that for large recoil momenta $\text{(q}{}_{\mathrm{<mtext>R</mtext>}}\text{≧ 300}\text{MeV}\text{/c)}$ the effects of distortions are dominated by the effects of correlations, provided the outgoing nucleon is described by a realistic optical potential.     

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.     

An energy-independent nonlocal potential model. II. The asymmetry term

We analyze the single-particle bound-state properties and the elastic scattering of protons and neutrons in various groups of isotopes, ranging from C up to Sn, by means of an energy-independent nonlocal optical model. The potential is obtained as an extension of the one used in the analysis of N = Z nuclei, the new term being a Lane-type potential with the same geometrical parameters as the isoscalar one. The radius of the potential is determined by the fit of single-particle energies and charge distribution in one nuclide of each group and it is given by $\text{R}{}_{\mathrm{N}}\text{= 1.16 (A?1)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{F}$. The well depths of the equivalent local potential are fitted to a large set of single-particle energies, measured in stripping and pick-up reactions, and show an energy dependence which is consistent with a unique nonlocal energy-independent potential having isoscalar nonlocality $\text{β ? 1F}$ and isovector nonlocality $\text{β}{}_{\mathrm{T}}\text{? 1.6F}$. In particular, the bound-state data can determine the isovector part of the potential with fair accuracy, provided that proton and neutron, T> and T<, particle and hole states are analyzed: its average value at zero energy shows an increasing behavior from C to Mo. The nucleon point distribution and r.m.s. radii corresponding to this model potential have been calculated in various nuclei.     

Angular momentum transfer in very heavy ion direct reactions

We demonstrate using simple calculations and empirically well-founded parameters that direct one- or two-particle transfer reactions are capable of probing nuclear structure in the $\text{I ? 20}\text{h}\text{?}$ region for rare earth nuclei and 30 ? for actinide nuclei.     

Studies of single neutron holes in the transitional nuclei N = 83–89:: The 150, 148Nd(d,t) and 150, 148, 146Nd(3He, α) pick-up reactions

The level structures of the ^{145, 147, 149}Nd nuclei up to about 5 MeV excitation energy have been investigated with the (³He, α) reaction at 24 MeV. Additional 17 MeV (d, t) data have been obtained for ^{147, 149}Nd. The angular distributions have been analyzed with standard DWBA calculations, and spectroscopic factors have been deduced. Two groups of states carrying h_{$\text{11}\text{2}$} single-particle strength may be associated with the $\text{9}\text{2}$^? [514] and $\text{11}\text{2}$^? [505] Nilsson orbitals. A considerable amount of high-l single-particle strength may be found in the continuum observed in the (³He, α) spectra above 3 MeV in all the nuclei.     

An anharmonic force field for SO3

An anharmonic force field for SO₃ based on the valence force model has been investigated. The results of extending the model to include some further estimated cubic interaction potential constants have also been investigated. The phenomenological parameters calculated from both model force fields agree with those few values which have been experimentally determined. A calculation of the inertia defect has been made, and thus the value of C₀ has been determined. The equilibrium structure has been determined to be: $\text{r}{}_{\mathrm{e}}\text{= 1.4184 ± 0.0010}\text{A}\text{?}$.     

Calculated pressure effects on spectral lines for long-range interatomic potentials: Rb and Cs with heavy rare gases

We have calculated the impact broadening and shift of the first and second doublets of Rb and Cs. The interaction potential of the collision pair is assumed to be a long-range van der Waals potential. The van der Waals constants involved are provided by recent theoretical calculations. We obtain good agreement between the calculated and experimental values for both the P_{$\text{1}\text{2}$} and P_{$\text{3}\text{2}$} component. Comparison of our calculated values is also made with those of Granier, Granier and Schuller.     

Self-consistent cranking calculations for 20Ne

The rotational spectrum of ²⁰Ne has been calculated in the self-consistent cranking model using the Skyrme interaction. The qualitative features of the spectrum, e.g., the band cutoff at $\text{J = 8}\text{h}\text{?}$, are reproduced. The inclusion of states of the oscillator f-shell in the expansion of the single-particle states leads to a transition to an excited band for $\text{J > 8}\text{h}\text{?}$. Special emphasis is put on an investigation of the structural properties near and beyond this band cutoff at $\text{J = 8}\text{h}\text{?}$. The calculated rotational spacings are found to be considerably too small with all conventional variants of the Skyrme interaction. The difficulty is attributed to the p-state part of the Skyrme interaction.     

Band structural properties of MoS2 (molybdenite)

Semiconductivity and superconductivity in MoS₂ (molybdenite) can be understood in terms of the band structure of MoS₂. We present here the band structural properties of MoS₂. The energy dependence of n_eff and ε_xeff is investigated. Using calculated values of n_eff and ε_xeff, the Penn gap has been determined. The value thus obtained is shown to be in good agreement with the reflectivity data and also with the value obtained from the band structure. The Ravindra and Srivastava formula has been shown to give values for the isobaric temperature gradient of $\text{E}{}_{\mathrm{G}}\text{[}\text{(?E}{}_{\mathrm{G}}\text{?T)}{}_{\mathrm{P}}\text{]}$, which are in agreement with the experimental data, and the contribution to $\text{(}\text{?E}{}_{\mathrm{G}}\text{?T)}{}_{\mathrm{P}}$ due to the electron lattice interaction has been evaluated. In addition, the electronic polarizability has been calculated using a modified Lorentz-Lorenz relation.     

An asymptotic form of the smooth part of the total single-particle energy

A method of separating the smooth part from the sum of the single-particle energies is discussed. The method consists of an expansion of this smooth part in the asymptotic series, i.e. in a series in powers of $\text{A}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$. The series is studied numerically in the case of a finite (Woods-Saxon) potential with realistic depth and surface thickness parameters. The Strutinsky smooth part of the energy is also extensively studied and compared with the asymptotic one.     

On the rotational contributions to the dipole-moment derivatives

In order to get dipole-moment derivatives, $\text{?}\text{u}\text{?}\text{?S}{}_{\mathrm{j}}$ that are free from rotational contributions, we used Crawford's method applied to a new type of reference molecule. The agreement with earlier calculated rotational correction terms is good, the applicability of the new reference molecule is wider. The rotational contributions to the $\text{?}\text{u}\text{?}\text{?S}{}_{\mathrm{j}}$-quantities are presented for a number of C_2v- and C_3v-type molecules.     

Folded diagrams and 1s-Od effective interactions derived from Reid and Paris nucleon-nucleon potentials

The sd-shell effective-interaction matrix elements are derived from the Paris and Reid potentials using a microscopic folded-diagram effective-interaction theory. A comparison of these matrix elements is carried out by calculating spectra and energy centroids for nuclei of mass 18 to 24. The folded diagrams were included by both solving for the energy-dependent effective interaction self-consistently and by including the folded diagrams explicitly. In the latter case the folded diagrams were grouped either according to the number of folds or as prescribed by the Lee and Suzuki iteration technique; the Lee-Suzuki method was found to converge better and yield the more reliable results. Special attention was given to the proper treatment of one-body connected diagrams in the calculation of the two-body effective interaction.We first calculate the (energy-dependent) G-matrix appropriate for the sd-shell for both potentials using a momentum-space matrix-inversion method which treats the Pauli exclusion operator essentially exactly. This G-matrix interaction is then used to calculate the irreducible and non- folded diagrams contained in the $\text{Q}\text{?}\text{-}\text{box}$. The effective-interaction matrix elements are obtained by evaluating a $\text{Q}\text{?}\text{-}\text{box}$ folded diagram series. We considered four approximations for the basic $\text{Q}\text{?}\text{-}\text{box}$. These were (C1) the inclusion of diagrams up to 2nd order in G, (C2) 2nd order plus hole-hole phonons, (C3) 2nd order plus (bare TDA) particle-hole phonons, and (C4) 2nd order plus both hole-hole and particle-hole phonons.The contribution of the folded diagrams was found to be quite large, typically about 30%, and to weaken the interaction. Also, due to the greater energy dependence of higher-order diagrams, the effect of folded diagrams was much greater in higher orders. That is, the contribution from higher-order diagrams for most cases was greatly reduced by the folded diagrams. The convergence of the folded-diagram series deteriorates with the inclusion of higher-order $\text{Q}\text{?}\text{-}\text{box}$ processes in the method which groups diagrams by the number of folds, but remains excellent in the Lee-Suzuki method.Whereas the inclusion of the particle-hole phonon was essential to obtain agreement with experiment in earlier work, when the folded diagrams are included the effect of the particle-hole phonon is to reduce the amount of binding. All four approximations to both potentials produce interactions which badly underbind nuclei. The excitation spectra given by these interactions are, however, all rather similar to each other. The Paris interaction produces more binding than does the Reid, but differences between results obtained with the two interactions were often less than differences obtained in the four approximations. Essentially no difference was found between the effective non-central interactions from the Reid and Paris potentials after including the folded diagrams, although these two potentials themselves are quite different, especially in the strength of the tensor force.Comparisons between.calculated spectra and experiment were done for ¹⁸O, ¹⁸F, ¹⁹F, ²⁰O, ²⁰Ne, ²²Ne, ²²Na and ²⁴Mg.     

A monte-carlo/molecular dynamics study of the diffusional recombination kinetics of C(a) + O(a) → CO(g) on Pt(111)

The diffusion constants for C and O adsorbates on Pt(111) surfaces have been calculated with Monte-Carlo/Molecular Dynamics techniques. The diffusion constants are determined to be D_C(T)=(3.4 × 10^?3e^{$\text{?13156}\text{T}$})cm²s^?1 for carbon and D_O(T) = (1.5×10^?3 e^{$\text{?9089}\text{T}$}) cm² s^?1 for oxygen. Using a recently developed diffusion model for surface recombination kinetics an approximate upper bound to the recombination rate constant of C and O on Pt(111) to produce CO_(g) is found to be (9.4×10^?3 e^{$\text{?9089}\text{T}$}) cm² s^?1.     

Internal rotation and molecular structure of ethaneselenol by microwave spectroscopy

The microwave spectra of ethaneselenol and its deuterated and ¹³C-substituted species were measured and assigned for the gauche and trans isomers. The double minimum splittings in the gauche isomers were directly observed for the species having a symmetry plane in the frame part. The rotational constants and the torsional splitting of the gauche isomer of the parent species were determined to be A = 27 148.86 ± 0.05, B = 3 623.68 ± 0.01, C = 3 399.21 ± 0.03, and Δν = 1 083.33 ± 0.04 MHz. From the torsional splittings of the parent and SeD species together with the vibrational frequencies already reported by Durig and Bucy, the Fourier coefficients of the selenol internal rotation potential function were determined to be V₁ = ?44 ± 17, V₂ = ?260 ± 3, V₃ = 1202 ± 16, and V₆ = ?43 ± 9 cal/mole. From the rotational constants obtained, the r_s structural parameters of the gauche and trans isomers were determined. The structural parameters in the skeletal part for the gauche isomer are $\text{r}\text{(CC) = 1.524}\text{A}\text{?}$, $\text{r}\text{(CSe) = 1.957}\text{A}\text{?}$, $\text{r}\text{(SeH) = 1.467}\text{A}\text{?}$, α(CCSe) = 113°31′, α(CSeH) = 93°05′, and the dihedral angle τ(CCSeH) = 61°39′. Those for the trans isomer are $\text{r}\text{(CC) = 1.525}\text{A}\text{?}$, $\text{r}\text{(CSe) = 1.962}\text{A}\text{?}$, $\text{r}\text{(SeH) = 1.440}\text{A}\text{?}$, α(CCSe) = 108°43′, and α(CSeH) = 93°30′. These parameters were compared with the corresponding ones of ethanethiol.     

Magnetovolume effect in transition metal-metalloid amorphous alloys

The thermal expansion, spontaneous volume magnetostriction ω_s, forced volume magnetostriction $\text{(}\text{?ω}\text{?H}\text{)}$ and Young's modulus of amorphous Fe-B, Fe-P, Co-B and (Fe-M)₇₇Si₁₀B₁₃ (M = Cr, Mn, Co, Ni) alloys have been measured to make clear the magnetovolume effect in transition metal-metalloid amorphous alloys. The thermal expansion coefficient α, ω_s and $\text{(}\text{?ω}\text{?H}\text{)}$ are dependent on the number of d-electrons per transition metal atom n_eff calculated based on the charge transfer model. The n_eff vs. α, ω_s and $\text{(}\text{?ω}\text{?H}\text{)}$ curves are quite similar to the corresponding curves in fcc alloys. The maxima in those curves are, however, found at n_eff ≈ 8.2 for the amorphous alloys in contrast with n_eff ≈ 8.7 for the fcc Fe-Ni alloys. On the other hand, Young's modulus measured under the saturation of magnetization is governed by the molar volume, irrespective of n_eff. The magnetovolume effect in transition metal-metalloid amorphous alloys is discussed in connection with the instability of ferromagnetism of amorphous Fe.