Charge and transition densities of samarium isotopes in the interacting boson modei

The interacting boson approximation (IBA) model has been used to interpret the ground-state charge distributions and lowest 2⁺ transition charge densities of the even samarium isotopes for A = 144–154. Phenomenological boson transition densities associated with the nucleons comprising the s- and d-bosons of the IBA were determined via a least squares fit analysis of charge and transition densities in the Sm isotopes. The application of these boson transition densities to higher excited 0⁺ and 2⁺ states of Sm, and to 0⁺ and 2⁺ transitions in neighboring nuclei, such as Nd and Gd, is described. IBA predictions for the transition densities of the three lowest 2⁺ levels of ¹⁵⁴Gd are given and compared to theoretical transition densities based on Hartree-Fock calculations. The deduced quadrupole boson transition densities are in fair agreement with densities derived previously from ¹⁵⁰Nd data. It is also shown how certain moments of the best fit boson transition densities can simply and successfully describe rms radii, isomer shifts, B(E2) strengths, and transition radii for the Sm isotopes.     

Calculation of charge and transition charge densities in some even mass Ge isotopes from microscopic nuclear structure wave functions

Microscopic nuclear structure wave functions obtained within the EXCITED FED VAMPIR approach are used to calculate the charge densities for the ground states as well as the transition charge densities for the transitions from the ground to the first and second 2⁺ states in some doubly even Ge isotopes. The results are compared with the data extracted from elastic and inelastic electron scattering experiments. Except for the heavier isotopes, where the calculations fail to yield enough collectivity, rather nice agreement is obtained. This result strongly supports the theoretically predicted shape coexisting structures in the low spin states of the nuclei in this mass region.     

Electron scattering from transitional nuclei

An electron scattering experiment on ¹⁸⁸Os, ¹⁹⁰Os, ¹⁹²Os, ¹⁹⁴Pt and ¹⁹⁶Pt has been performed at momentum transfers q = 0.6 to 3.2 fm⁻¹. Transition charge densities have been determined for the low-lying 2⁺, 3⁻ and 4⁺ states. The 2⁺ densities are well reproduced within the framework of the interacting boson model 2, where we have determined the boson densities α_ν, α_π, β_νv and β_π. The 4⁺ transition densities could not be reproduced indicating the need for including a g-boson. The ground and transition charge densities of ¹⁸⁸Os, ¹⁹²Os and ¹⁹⁶Pt have been compared with a microscopic calculation. The total binding energies and the intrinsic wave functions have been calculated for different values of β and γ with the constrained triaxial Hartree-Fock-Bogoliubov method using the finite range interaction D1SA. These energies are interpreted as potential energy surfaces and used in the Bohr hamiltonian in order to obtain the total nuclear wave functions. We obtain very good agreement with experiment. The calculated potential energy surfaces show these nuclei to be γ-soft with a shallow minimum for triaxial deformations and rigid in the β direction.     

Transition densities between the 01+, 21+, 41+, 02+, 22+, 11− and 31− states in 12C derived from the three-alpha resonating-group wave functions

All the multipole transition densities between the seven T = 0 states in ¹²C are calculated with the use of the microscopic 3α resonating-group wave functions which are obtained by dynamically solving the 3α relative motion with the total antisymmetrization taken into account exactly. The observed elastic and inelastic electron scattering form factors for the transition to the 2₁⁺, 4₁⁺, 0₂⁺, 1₁^?and 3₁^? states are well reproduced with no additional effective charge. The existence of a deformed intrinsic state for the 0₁⁺, 2₁⁺and 4₁⁺states is deduced by the analysis of the transition densities between them which are derived by the weak-coupling-type 3α wave functions; the intrinsic density distribution is illustrated. The monopole density distribution of the 0₂⁺, 2₂⁺ and 1₁^?, states is found to be much longer ranged than that of the 0₁⁺, 2₁⁺ and 4₁⁺ states; the 3₁^? state case is intermediate. On the basis of the transition densities between the 0₁⁺, 2₁⁺, 0₂⁺ and 2₂⁺ states, analysis is made of the transition between the shell-like states and the molecule-like states with a large spatial-structure change. Specific, effective nucleon-nucleon interactions are folded into the transition densities here obtained. The evident dependence of the radial shape of the folded nucleon-¹²C form factors on the choice of the interactions and the multi-step form factors for the excitation of the 0₂⁺, 1₁^? and 3₁^? states are discussed.     

Calibration of the isomer shift of121Sb and119Sn by means of Mössbauer spectroscopy and molecular orbital calculation

The relationship between the isomer shifts in Mössbauer spectroscopy and the electron contact densities has been investigated for several antimony and tin compounds. Mössbauer spectra for¹²¹Sb in rapidly frozen solutions of antimony compounds were measured. The isomer shifts are compared with the valence electron densities at the antimony nucleus calculated with theab initio molecular orbital method. The relative difference of the nuclear charge radius ΔR/R could be obtained as ΔR/R =?(10.2±1.0)×10^?4 for the 37.15 keV M1 transition of¹²¹Sb. Further, some computations of the electron density at the tin nucleus for several tin compounds were performed. By comparing the valence electron contact densities with isomer shifts, which had been reported for several tin compounds in rare-gas matrix states, the value of ΔR/R for 23.87 keV M1 transition in¹¹⁹Sn was estimated to be (1.57±0.03)×10^?4.     

Effect of large neutron excess on the dipole response in the region of the giant dipole resonance

The evolution of the dipole response in nuclei with strong neutron excess is studied in the Hartree-Fock plus random phase approximation with Skyrme forces. We find that the neutron excess increases the fragmentation of the isovector giant dipole resonance, while pushing the centroid of the distribution to lower energies beyond the mass dependence predicted by the collective models. The radial separation of proton and neutron densities associated with a large neutron excess leads to non-vanishing isoscalar transition densities to the GDR states, which are therefore predicted to be excited also by isoscalar nuclear probes. The evolution of the isoscalar compression dipole mode as a function of the neutron excess is finally studied. We find that the large neutron excess leads to a strong concentration of the strength associated with the isoscalar dipole operator ∑_ir_i³Y₁₀, that mainly originates from uncorrelated excitations of the neutrons of the skin.     

Isotope shift of182Hg and an update of nuclear moments and charge radii in the isotope range181Hg-206Hg

The technique of collinear fast-beam laser spectroscopy has been used to measure the isotope shifts of the even-even isotopes of Hg (Z=80) in the mass range 182≤A≤198 at the on-line mass separator ISOLDE at CERN. The atomic transition studied (6s 6p ³ P ₂- 6s7s ³ S ₁,λ=546.1 nm) starts from a metastable state, which is populated in a quasi resonant charge transfer process. The resulting changes in nuclear mean square charge radii show clearly that¹⁸²Hg follows the trend of the heavier, even, weakly oblate isotopes. Correspondingly the huge odd-even shape staggering in the light Hg isotopes continues and the nuclear shape staggering and shape coexistence persists down to the last isotope investigated,¹⁸¹Hg. An update of isotope shift and hyperfine structure data for^181–206Hg is given, with a revised evaluation of the differences in nuclear mean square charge radii and of spectroscopic quadrupole moments.     

Electric quadrupole and hexadecupole nuclear excitations from the perspectives of electron scattering and modern shell-model theory

Shell-model wave functions obtained from a complete, unified treatment of the structure of the positive parity states in nuclei between ¹⁶O and ⁴⁰Ca are used to calculate the features of inelastic electron scattering to 2+ and 4+ states in this region. These predictions of E2 and E4 form factors, and the corresponding elastic scattering predictions, are compared with the collected experimental data which are available on this topic. The dependence of the calculated results upon alternate models for single-nucleon wave functions and core-polarization transition densities is investigated, as is the consistency between the (e,e′) measurements and the analogous B(E2) measurements.     

Transition charge densities of low-lying collective states in even Zn isotopes

The inelastic electron scattering cross sections for the quadrupole transitions to the 2₁⁺ and 2₂⁺ states in the even Zn isotopes ⁶⁴Zn, ⁶⁶Zn and ⁶⁸Zn and for the hexadecapole transition to the 4⁺₁ state in ⁶⁴Zn have been measured in a momentum transfer range up to q = 2.2 fm^?1. In the frame-work of the vibrational model these states are considered as one- and two-quadrupole-phonon states. The measurements are characterized by high statistical accuracy and by an overall resolution of δE/E₀ = 10^?3 which permitted separation of almost all members of the two-phonon triplet. The measured cross sections are analyzed with phenomenological models as well as with a Fourier-Bessel expansion of the transition charge density. The latter analysis yields realistic error bands for the transition charge densities and model-independent values for the reduced transition probabilities and transition radii.     

Analyses of electron and proton scattering to low-excitation isoscalar states in 20Ne, 24Mg and 28Si

The excitation of low-lying isoscalar 2⁺ and 4⁺ states in ²⁰Ne, ²⁴Mg and ²⁸Si by electron and proton scattering is studied. Large basis models of nuclear structure are used to determine both the electromagnetic and hadronic transition densities. The analyses of the longitudinal form factors obtained from electron scattering show that little or no effective charges are required with these nuclear structure models. Proton inelastic scattering to these states then is analysed to test effective forces based upon the Paris and Hamada-Johnston interactions. At intermediate energies (155 MeV) density-dependent t-matrices from both potentials were used with fits to data giving a clear preference for that based upon the Paris interaction. For lower energies only the Hamada-Johnston t-matrix is available and comparison of analyses of 24 and 49 MeV data made using this (complex) t-matrix with those in which the (real) Paris G-matrix is used as the effective force show a clear preference for the t-matrix. This is particularly the case with analyses of polarization data and suggests that the use of the G-matrix as an effective force in nuclear reaction calculations is inadequate even at low energies.     

A rare nuclear decay process: The internal conversion between bound atomic states

We shall report on the recently observed dependence of the lifetime of the first excited state in ¹²⁵Te on the ionic charge state. Then we shall give an interpretation of the dependence of the half-life in terms of a new type of nuclear internal conversion without emission of the electron into the continuum of electron energies. We have named this process internal conversion between bound atomic states or BIC. The resonant character of the BIC will be established and the main parameters governing the decay process will be discussed [1–3]. Finally the results of a recent experiment performed at the GANIL accelerator attempting to measure directly the value of the internal conversion coefficient associated with BIC in ¹²⁵Te ions with charge states ranging between 44+ and 48+ will be given. In conclusion we shall discuss the relation between the BIC and nuclear excitation by electron transition, NEET, in the excitation of some nuclear isomeric states.     

Der Einfluß der Nullpunktschwingungen der Kernoberfläche auf die Formfaktoren der inelastischen Elektronenstreuung

The transition densities from the ground state to exited states of atomic nuclei are calculated from the drop model, taking the zero-point oscillations of the nuclear surface into account. The calculation yields transition densities smeared out over a distance of 2–3 fm near the nuclear surface. In the case ofn-surfon transitions the radial dependence of these densities is proportional to then-th derivative of the ground-state density. The numerical evaluation yields inelastic form factors quite similar to those ofCrannell et al. Compared with the form factors ofWalecka, the higher maxima are less distinct.     

Matrix elements in appearance potential spectroscopy of Al and its alloys

The Al K appearance potential spectrum (APS) of Al and some Al alloys, measured with an X-ray monochromator tuned to the photon energy of the AI K ← L_2,3 transition, are presented.Theoretical arguments and APS spectral simulations using convolutions of total densities of states (DOS), partial densities of states, and BIS data give evidence for the importance of the angular parts of the transition matrix elements, as well as the radial parts. It is found that theoretical estimates of plasmon effects in APS are not in accord with experimental observations.     

The vertex constant for the virtual decay of a nucleus into two charged particles within the effective range theory

Explicit expressions for the virtual a → b + c decay vertex constant (or the asymptotic normalization factor) for charged particles b and c are obtained for the first time using the effective range function K(k ²) for the standard effective range expansion and for the case where K(k ²) has a pole. The bound and resonant states of the ²He nucleus and the resonant states of the ²He and ⁸Be nuclei are considered as physical examples. A trajectory in the complex momentum plane is constructed for the transition from the resonant state to the virtual state while the Coulomb interaction gradually decreases.     

Model independent evaluation of the inelastic e− scattering cross sections from the 3− (2.615 MeV) level in 208Pb

The radial transition charge density and the reduced transition probability of the 3^? level in ²⁰⁸Pb are determined model independently from inelastic e^? scattering cross sections. The results are compared with (α, α') experiments and theoretical calculations.     

Quenched disorder effects in electron transport in Si inversion layers in the dilute regime

In order to reveal the effects of disorder in the vicinity of the apparent metal-insulator transition in 2D, we studied electron transport in the same Si device after cooling it down to 4 K at different fixed values of the gate voltage V^cool. Different V^cool did not significantly modify either the momentum relaxation rate or the strength of electron-electron interactions. However, temperature dependences of the resistance and the magnetoresistance in parallel magnetic fields in the vicinity of the 2D metal-insulator transition carry a strong imprint of the quenched disorder determined by V^cool. This demonstrates that the observed transition between the metallic and insulating regimes, besides the universal effects of electron-electron interaction, depends on the sample-specific localized states (disorder). We report on evidence for a weak exchange of electrons between the reservoirs of extended and resonant localized states that occur at low densities. The strong cool-down dependent variations of ρ(T), we believe, are evidence for a developing spatially inhomogeneous state in the critical regime.     

Meson-exchange corrections to the nuclear weak axial charge density in the hard pion model and 0+ 3 0− transitions in A = 16 nuclei

Starting with the hard-pion model based on a minimal chiral invariant phenomenological lagrangian, the two-body part of the time component of the weak axial-vector current is constructed in the tree approximation. Pion, rho- and A₁-meson exchanges are considered. The mesonic exchange operator obtained is applied to describe the purely weak axial 0⁺?0^?, ΔT = 1 transition in the nuclear A = 16 system. In order to treat nuclear structure correlation effects, explicit use of shell-model wave functions with configuration mixing is made. We confirm the large enhancement of the nuclear weak axial charge density with respect to impulse approximation.     

A note on the transition probability over C*-algebras

The algebraic structure of Uhlmann's transition probability between mixed states on unital C ^*-algebras (see [2]) is analyzed. Several improvements of methods to calculate the transition probability are fixed examples are given (e.g., the case of quasi-local C ^*-algebras is dealt with) and two more functional characterizations are proved in general (see Theorems 1 and 3).