Core-polarization and open-shell effects in E6 transitions

The problem of isomeric E6 transitions recently measured in the fp shell is investigated. In the shell model these E6 decay rates require negative proton polarization charges and are quite anomalous in the context of usually enhanced E2 and E4 transitions. We demonstrate that usual core-polarization mechanisms cannot be invoked to explain the data and that the quadrupole deformations of the open shell that must be taken into account are instrumental in yielding negative P₆ moments.     

Electron scattering and charged pion photoproduction on12C and13C

Electron scattering and charged pion photoproduction at 200 MeV on¹²C and¹³C have been studied by the nuclear shell model to investigateM1 andE2 nuclear form factors of the isovector type. Starting with the Op-shell model of Hauge-Maripuu, the effects of core polarization by theM 3Y force and the one-pion-exchange current are taken into account. The effect of core polarization is found to be essential in both electron scattering and pion photoproduction, while the meson-exchange current, which also improves the calculated results, gives contributions of about 10%–15%.     

Effective coupling constants for beta and gamma transitions in medium and heavy nuclei

Effective coupling constants (g^eff) for favored (but hindered) beta and gamma transitions in medium and heavy nuclei are studied systematically. Experimental g^eff values for the β and γ transitions with parity change are presented, and are analyzed in terms of the susceptibility κ (polarization factor) defined as g^eff=g/(1 + κ). Most of the first forbidden β transitions and E1, M2, M4 gamma transitions are shown to have uniformly g^eff/g=0.2～0.4 and thus κ=3～2. Emphasis is placed upon the problem as to how large the value of susceptibility (or polarizability) due to nuclear spin-isospin core polarization is for the nuclear matter. Theories of the core polarization effects are reviewed, and are shown to predict well the observed susceptibilities κ for the various modes. Discussions are given on higher order effects, couplings with different modes, and mass and multipole dependence in the nuclear core polarization phenomena.     

Interplay of valence-shell clusters and the vibrational field in58Ni

The level scheme and electromagnetic properties of⁵⁸Ni are described in the two-particle cluster core coupling model without parameter fitting. The present results are compared to previous shell-model and quasi-particle calculations. To explain the enhancedE2 transitions a neutron effective charge ofe is needed, while the bare value for the vibrator charge has been used.     

Self-consistent core polarization near 16O

Self-consistent fully-screened core polarization is evaluated by use of the mutually consistent particle-hole, particle-phonon, hole-phonon, and core-to-2p2h vertices. The sensitivity of the results to changes in unperturbed single-particle energies and in reaction matrix elements is tested, and it is found that the usual effects of collective enhancements and screening reductions persist. The final results are remarkably stable, even though individual renormalization effects show strong pathologies. It is argued that the RPA is not a good method for treating vibrations of the nuclear core. The self-consistent vertices are applied to calculations of the hole-hole effective interaction, of shell breaking, and of E2 effective charges, and it is shown that all the renormalization effects found in the particle-particle effective interaction show up in these other quantities as well. The conclusion is that self-consistent core polarization is too weak to account for significant renormalizations of effective operators.     

Model-potential oscillator strengths for 4fn6s2–4fn6s6p transitions in Sm(I), Eu(I), Dy(I), Er(I) and Yb(I)

The 4fⁿ6s²?4fⁿ6s6p transitions are studied for neutral samarium, europium, dysprosium, erbium, and ytterbium. Four different couplings between the valence electrons and the 4fⁿ shell are considered, three are based on the LS and one on the J_IJ_II scheme. The radial integrals are computed with the model-potential method, which includes both exchange and core polarization. The results are compared with those obtained by employing the Coulomb approximation and the ab initio Hartree + Exchange (HX) approach, as well as with available experimental data. The core-polarization influence on oscillator strengths for these transitions is also investigated.     

Core polarization and the Coulomb energy difference of mirror nuclei

The effect of the core polarization on the Coulomb displacement energies of mirror nuclei with a LS doubly closed shell plus or minus one nucleon is studied. Using the Kallio-Kolltveit interaction it is found that the first-order configuration mixing including 2p-2h core excitations is too small and sometimes of the wrong sign to explain the Nolen-Schiffer anomaly.     

Quartet structure and collective effects in the scandium isotopes

The systematics of the excitation energies of the non-normal parity states of the scandium isotopes are interpreted in terms of the formation of a quartet of 1f7/2 nucleons. Calculation of theB(E2) value for a typical radiative transition between non-normal parity states in⁴³Sc, using this model, shows that the transition must involve more than the single quartet formed in the 1f7/2 shell; that is, that core polarization is an important factor in determining theB(E2) value.     

Natural optical dichroism of A2MnX4 type crystals and mechanisms for producing intensity of the spin-forbidden d-d transitions

It has been found in a number of experiments that d-d transitions to A_1g and E_g states (in cubic notation) in tetragonal crystals Rb₂MnCl₄ and K₂MnF₄ have pronounced σ(α) polarization and the transitions to T_1g from liquid helium to room temperature. In this work the analysis of polarizable properties of different mechanisms for producing intensity of the spin-forbidden d-d transitions in A₂MnX₄ structure is carried out. It is shown that only cooperative absorption with the participation of odd vibrations can account for the observed transition polarization.     

Core polarization effects on the Coulomb form factor

Coulomb form factors for the transitions between single-particle (or -hole) states with LS closed shells are investigated. Core polarization effects are calculated by using microscopic models. Information on the effective interaction which cannot be provided by γ-transition data alone is obtained from the momentum transfer dependence of the form factor. An effective interaction is required not to be repulsive in triplet-odd two-particle states in order to explain the experimental data on ¹⁵N. The bare G-matrix gives a reasonable fit to the data while the phenomenological interaction with Rosenfeld mixture does not. It is also shown that the core polarization effect for the Coulomb form factors with high multipolarity is sensitive to the mixing character of the effective interaction.     

A shell-model study onM1 andE2 properties of Zn,Ga, and Ge

Electromagnetic properties of Zn, Ga, and Ge are studied by using the nuclear shell model. Empirically determinedM1 operators are found to be very successful to explainM1 transitions, moments, and mixing ratios. ManyE2 properties are also understood by the present shell-model calculations with effective charges.     

Anisotropy of the repulsive intermolecular potential from rotationally inelastic scattering

Structure is observed in recoil velocity distributions of potassium atoms scattered inelastically from N₂ and CO molecules at CMS angles?>π/2 and collision energies 0.34≦E≦1.24 eV. It is caused by rotational excitation mainly. Individual rotational transitions are not resolved. The quasi-continuous recoil velocity distributions extend between well defined bounds, the upper corresponding to elastic scattering, the lower marking a largest amount of energy transferred into molecular rotation at given? andE. This maximal transfer increases with angle and — forE?0.64 eV — in near proportion toE. At all? andE it is larger for CO than forN ₂, amounting to about 0.42E forN ₂ and 0.64E for CO at?=150°. At or very close to each of their bounds the distributions exhibit pronounced maxima. A third intermediate maximum is present for CO, but missing for N₂. The scattering in these experiments is dominated by the repulsive core of the interaction potential. On the basis of classical scattering from a rigid, ellipsoidal, initially nonrotating potential shell, the observations can be qualitatively understood as follows: The recoil velocity dependence of the orientation averaged cross section at fixed observation angle will exhibit classical, integrable singularities at extremal amounts of rotational energy transfer. If the center of symmetry of the shell coincides with the center of mass of the molecule, there will be two such extremal transfers,ΔE=0 and a largest transfer possible at the chosen angle. If the centers do not coincide, the singularity at the largest transfer will split into two, one corresponding to the short, the other to the long “lever arm” of the shell. K + N₂ is an example of the centrical, K+CO of the excentrical case. The finite energy losses, at which the singularities occur, are — at each angle — strongly dependent on the anisotropy and excentricity of the shell.     

Exciton transitions from spin-orbit split off valence bands in layer compound InSe

The absorption spectrum of E′₁ and E₁ exciton transitions in 3R(γ)-InSe has been measured at 1.8 K. Their photon energies, oscillator strengths and polarization dependences are fully explained in terms of Hopfield's quasicubic model. The analysis shows that the valence band structure reflects the crystalline field anisotropy characteristics of its layer structure.     

Core polarization effects in effective Hamiltonians far from stability

We investigate the neutron rich nuclei which can be described by shell model calculations in the p–sd and sd–pf model spaces. We quantify the effects of the core polarization on the multipole part (pairing and quadrupole) of the effective Hamiltonians. We show that proton core polarization contributions are responsible for the reduction of the neutron–neutron nuclear matrix elements which, in the recent shell model studies, appeared necessary between p–sd carbon and oxygen and sd–pf silicon and calcium nuclei.     

Core polarization effects in the unified analysis of weak,electromagnetic, and strong processes in 6Li

The contribution of core polarization to the ⁶Li wave function is evaluated in lowest order (single bubble) and in the Tamm-Dancoff and random-phase approximations. The effects of core polarization on various electromagnetic transitions, β-decay rates, and threshold pion-photo-production in the A = 6 system are then determined.     

Shell-model analysis of helion and triton inelastic scattering from90Zr including core polarization effects

A microscopic analysis of the inelastic scattering of helions and tritons from⁹⁰Zr is performed using the shell-model wavefunctions and phenomenological effective interactions. Effects of the core polarization are studied assuming a collective model for the core of closed shells. Core coupling parametersA _L , are obtained from the measured electromagnetic transition rate,B(EL). For those transitions for which no meauredB(EL) values are available,A _L values which fit the data have been extracted. The radial forms of both the Gaussian and Yukawa interactions were studied. Effects of the non-locality of the bound states on the predicted cross sections are found to be small. As in the case of proton inelastic scattering, it is found that the valence (direct) contributions are small and the transitions are dominated by core polarization. The strength of the effective interaction required to fit the data is reduced by a factor of two or more when the core polarization contributions are included.     

Optical transitions on GaAs [110] surface

Modulation techniques have been employed in optical reflection measurements on GaAs [110] cleaved surface. Spectral bands at 2.62 and 2.83 eV observed for the light polarization $\text{E6[}\text{1}\text{10]}$ have been assigned to the surface state transitions. The E₁ and E₁ + Δ₁ bulk transitions were found to be sensitive to the surface conditions.     

Core polarization effects on transition densities in medium-heavy nuclei

We propose a microscopic model to study the core-polarization effects of giant resonances on the transition densities of open-shell nuclei. We use the Hartree-Fock-RPA method for the calculation of the single-particle wave functions and the response function of the giant resonances. Particle-vibration coupling is applied to take into account the core polarization effect on the valence many-body wave functions. We apply our model to the quadrupole transitions in the several medium-heavy nuclei. Valence many-body wave functions are calculated with the generalized seniority scheme and with the shell model. Results for the proton and neutron effective charges and the Coulomb form factors for the N = 82 isotones and for ¹¹⁶Sn and ¹¹⁰Pd are presented and discussed. The effective coupling hamiltonian is determined by the Skyrme interaction SGII which is used also in the HF and RPA calculations. The calculated core polarization charges show some state dependences. The average theoretical values are δe_p = 0.4–0.5 and δe_n = 0.6–0.7 compared to typical empirical values of δe_p = 0.6 and δe_n = 1.2.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

Transitions between E and T states each coupled to e vibrational modes: The GR1 band in diamond

Transition between two electronic states are strongly affected because of Jahn—Teller coupling. The strengths of transitions from a T state to an E state, both states interacting with e vibrational modes, are investigated. Results are used to explain the origin of the GR1 band in diamond.