Gamow-teller strength function and the missing strength

The Gamow-Teller strength function including all 2p2h states with excitation energy up to 4 ?ω is calculated for the ⁴⁸Ca(p, n)⁴⁸ Sn reaction. A detailed discussion on the treatment of the self-energy term in connection with the non-energy-weighted sum rule is presented. The quenching of the Gamow-Teller strength in the low-lying region may chiefly be explained by the tensor correlation, and partly by some vertex corrections due to the Δ-hole and other exchange currents.     

Natural-parity excitations in light nuclei described with realistic two-body interactions

Using effective interactions derived from a nuclear-matter G-matrix in local-density approximation we calculate natural-parity vibrations in ¹⁶O and ⁴⁰Ca. The conventional RPA theory is extended to include 1p1h as well as 2p2h excitations in a consistent way. The extended theory introduces additional correlations which screen the long-range part of the effective interaction similar to Thomas-Fermi screening in the Coulomb gas. In this way the stability of the ground state against density fluctuations is enhanced. We find that the central part of the effective interaction plays the dominant role in coupling the isovector collective modes to high-energy 2p2h excitations.     

Contribution of particle-particle,hole-hole and particle-hole ring diagrams to the binding energies of finite nuclei

Two classes of diagrams, namely particle-particle, hole-hole (pp, hh) and particle-hole (ph) ring diagrams are summed for the nuclei ¹⁶O and ⁴⁰Ca, and their contributions to the ground-state energy shift ΔE of these nuclei is calculated. We find that hh and mixed diagrams (involving both pp and hh interactions) are not less important than the usual pp ladder diagrams which are summed in the standard Brueckner approach. We also study the convergence of these two classes of diagrams as the dimension of the model space involved is increased, and as a function of the residual interaction used. In evaluating these diagrams a transition-amplitude method is used. This is compared to the quasi-boson correlation expression for the ground-state energy due to particle-hole excitations and to an analogous correlation expression resulting from particle-particle and hole-hole excitations. Additionally we derive expressions for, and evaluate a subclass of these diagrams namely “TDA” ring diagrams, where unlike the usual pp, hh and ph diagrams, backward-folding graphs are excluded. We find that the backward-folding graphs are negligible for pp, hh ring diagrams and small for ph graphs. In the smallest model space considered for ⁴⁰Ca we also obtained the TDA ring diagram contributions via matrix inversion techniques which additionally allow us to study the relative importance of ph exchange graphs neglected in the ring-diagram formalism, and of cross TDA diagrams (i.e. TDA ring diagrams where both pp, hh, and ph interactions are allowed). Finally we study the uncertainties spurious effects introduce in ring-diagram calculations.     

Self-consistent medium polarization in RPA

The standard random-phase approximation for finite systems is extended by including the effect of the exchange of the RPA phonons in the residual interaction selfconsistently. It is shown that this particle-hole interaction is strongly energy dependent due to the presence of poles corresponding to 2p2h (and more complex) excitations. The RPA eigenvalue problem with this energy-dependent residual interaction also provides solutions for these predominantly 2p2h-like states. In addition a modified normalization condition is obtained.This new scheme is applied to ⁵⁶Ni (⁵⁶Co) in a large (up to 7ħω) configuration space using a residual interaction of G-matrix type. It is shown that the lowest 2⁺ eigenvalue, which in the standard RPA becomes imaginary, is stabilized when the selfconsistent screening is taken into account. Another feature observed is the splitting of the M1 strength as an example of 1p1h and 2p2h mixing.     

Influence of 2p-2h excitations in the41Sc-41Ca Coulomb energy shift

The influence of 2p-2h core excitations on the⁴¹Sc-⁴¹Ca Coulomb energy difference is studied. A simple parametrization of the main wave function components shows that the calculated energy shift could only agree with experiment for rather unrealistic values of the amplitudes. Using an effective interaction appropriate for this region, we find that when this kind of excitations is included, the calculated Coulomb energy shift is increased by 105keV.     

The effect of collective spin-1 excitations on electronic spectra in high- Tc superconductors

We review recent experimental and theoretical results on the interaction between single-particle excitations and collective spin excitations in the superconducting state of high-T_c cuprates. We concentrate on the traces that sharpen features in the magnetic-excitation spectrum (measured by inelastic neutron scattering) and imprint in the spectra of single-particle excitations (measured, e.g. by angle-resolved photoemission spectroscopy, tunnelling spectroscopy, and indirectly also by optical spectroscopy). The ideal object to obtain a quantitative picture for these interaction effects is a spin-1 excitation around 40?meV, termed ‘resonance mode’. Although the total weight of this spin-1 excitation is small, the confinement of its weight to a rather narrow momentum region around the antiferromagnetic wavevector makes it possible to observe strong self-energy effects in parts of the electronic Brillouin zone. Notably, the sharpness of the magnetic excitation in energy has allowed these self-energy effects to be traced in the single-particle spectrum rather precisely. Namely, the doping and temperature dependence together with the characteristic energy and momentum behaviour of the resonance mode has been used as a tool to examine the corresponding self-energy effects in the dispersion and in the spectral line-shape of the single-particle spectra, and to separate them from similar effects due to the electron–phonon interaction. This leads to the unique possibility to single out the self-energy effects due to the spin–fermion interaction and to directly determine the strength of this interaction in high-T_c cuprate superconductors. The knowledge of this interaction is important for the interpretation of other experimental results as well as for the quest for the still unknown pairing mechanism in these interesting superconducting materials.

The effect of collective spin-1 excitations on electronic spectra in high- T_c superconductors

All authors

Matthias Eschrig

https://doi.org/10.1080/00018730600645636

Published online:

01 February 2007

Table     

M1 resonances in unstable magic nuclei

Within a microscopic approach which takes into account RPA configurations, the single-particle continuum and more complex 1p 1 h?phonon configurations isoscalar and isovector M1 excitations for the unstable nuclei^56,78Ni and^100,132Sn are calculated. For comparison, the experimentally known Ml excitations in⁴⁰Ca and²⁰⁸Pb have also been calculated. In the latter nuclei good agreement in the centroid energy, the total transition strength and the resonance width is obtained. With the same parameters we predict the magnetic excitations for the unstable nuclei. The strength is sufficiently concentrated to be measurable in radioactive beam experiments. New features are found for the very neutron rich nucleus⁷⁸Ni and the neutron deficient nucleus¹⁰⁰Sn.     

Ab initio calculations of the electron-phonon interaction and characteristics of large polarons in rutile and anatase

The calculations of the electron-phonon interaction and some characteristics of excited electrons near the bottom of the conduction band of titanium dioxide in the structure of anatase and rutile have been performed. The Eliashberg function, the imaginary and real parts of the self-energy potential, as well as the band and polaron masses and width of the photoemission line, have been calculated. It has been shown that the electron-phonon interaction is primarily determined by the interaction with optical photons. Moderate values of the polaron mass (<2m _e ) correspond to large polarons. The calculated values of the spectral line width are significantly less than those observed in the experiment. Arguments have been presented in support of the assumption that the main contribution to the spectral line width corresponds to the interaction of electrons with the potential of randomly arranged oxygen vacancies.     

Particle-hole excitations in the208Pb mass region

Spectra, magnetic dipole moments and spectroscopic factors of a number ofA=205–209 nuclei as well asM1 transitions in²⁰⁸Pb are investigated in terms of large-scale shell-model calculations which include 1p ?1h excitations and for some nuclei 2p ?2h excitations. The calculated spectra agree well with the data. The calculatedg-factors are in fair agreement with the data in most cases. The predicted strength forM1 transitions to low-lying states in²⁰⁸Pb is less than that obtained from previous calculations. Spectroscopic factors forl=0 proton pick-up from²⁰⁸Pb and²⁰⁶Pb agree very well with recent experimental data from (e, e′p) reactions.     

Structure of odd Ge isotopes with 40 < N < 50

We have interpreted recentlymeasured experimental data of ⁷⁷Ge, and also for ^73,75,79,81Ge isotopes in terms of state-of-the-art shell-model calculations. Excitation energies, B(2) values, quadrupole moments and magnetic moments are compared with experimental data when available. The calculations have been performed with the recently derived interactions, namely with JUN45 and jj44b for f _5/2pg9/2 space. We have also performed calculation for fpg _9/2 valence space using an fpg effective interaction with ⁴⁸Ca core and imposing a truncation to study the importance of the proton excitations across the Z = 28 shell in this region. The predicted results of jj44b interaction are in good agreement with experimental data.     

Shell-model study on magnetic dipole excitation of N = 28 isotones

Magnetic dipole excitation of N = 28 isotones — ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr, ⁵⁴Fe and ⁵¹V — is studied in terms of the shell model by assuming $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}{}^{\mathrm{n?m}}\text{(}\text{p}\text{3}\text{2}\text{p}\text{1}\text{2}\text{f}\text{5}\text{2}\text{)}{}^{\mathrm{m}}$ configurations with m = 0, 1 and 2 on an inert ⁴⁰Ca core. Strength distributions observed in (e,e′) and (p,p′) experiments are fairly well reproduced. Interference of proton and neutron excitations enhances B(M1) values around E_x = 10 MeV and reduces those of low-lying states. The strength for T = T₀ + 1 states substantially increases when orbital magnetization is not taken into account, whereas no appreciable consequences can be seen for T = T₀ states. In comparison with single-particle model predictions with m = 0, about 20–30% reduction of the total strength is obtained due to ground-state configuration mixing. It is shown that the isoscalar spin component is reduced as well as the isovector one. However, the theoretical total strength is still much larger than experimental values, and coupling with high-lying configurations and possible delta-hole excitation might be required in order to account for the discrepancy. In an odd-mass nucleus ⁵¹V, the ground-state transition strength is distributed continuously over a wide energy range, being very strongly fragmented.     

A microscopic theory of giant electric isovector resonances

The electric multipole isovector (τ = 1) giant resonances for Δτ_z = 0, ± 1 are studied using the self-consistent HF-RPA theory.The distributions of strength, energies, the isospin compositions and other properties of the J = 0⁺, 1^?, 2⁺ resonances in the ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn and ²⁰⁸Pb regions are calculated. Sum rules for the charge-exchange Δτ_z = ±1 excitations are derived.     

Scattering of polarized 7Li by 120Sn and projectile-target spin-dependent interactions

Scattering of ⁷Li by ¹²⁰Sn targets at E_lab = 44 MeV is investigated in the coupled-channel frame by taking account of the projectile virtual excitations to the lowest three excited states. Calculations are performed by the cluster-folding (CF) interactions and the double-folding (DF) one. Both interactions reproduce very well the experimental data on the cross section, the vector analyzing power, the second-rank tensor ones and the third-rank tensor one in elastic and projectile inelastic scattering, although some differences are found between the CF results and the DF ones. In the calculation, the virtual excitations of the projectile are important for most of the analyzing powers and the spin-orbit interaction is indispensable for the vector analyzing power. These features are in contrast to those in ⁷Li-⁵⁸Ni scattering at 20 MeV and are interpreted as over-Coulomb-barrier effects. The scattering amplitudes and the analyzing powers are investigated by the invariant amplitude method, which provides a key connecting the spin-dependent interactions to the analyzing powers. The method proposes an important relationship between the tensor analyzing powers, which is useful in analyses of both theoretical and experimental results. Finally, it is found that in the elastic scattering the second-rank tensor analyzing powers are proportional to the strength of the second-rank tensor interaction and the vector and third-rank tensor analyzing powers to the square or cube of the strength of this interaction, while in the inelastic scattering the cross section is proportional to the square of the strength of the tensor interaction, other quantities being weakly dependent on the strength.     

Missing Gamow-Teller strength in mass 42

The reaction ⁴²Ca(p,n)⁴²Sc at E_p = 160 MeV is used to measure the Gamow-Teller (GT) strength function. Normalization of the dominant peak in the (p,n) spectrum to B(GT) determined from the analogous transition in the beta decay of ⁴²Ti renders the strength function absolute, and the total measured stregth is about half of the minimum value required for a T = 1 nucleus. Shell model calculations are presented which reproduce the shape of the strength function, but overpredict the absolute measured strength by about a factor of two. Evidently the missing strength has been moved out of the region of nucleon particle-hole excitations, and quenching, due possibly to Δ₃₃ coupling, is indicated. Symmetry implications of an observed strong suppression of the T_> component of the GT strength are discussed.     

Search for M1 strength in 51V and the difference in 51V(e,e′) and 51V(p,p′) spectra

Following the studies of the distribution of M1 strength in the even-even N = 28 isotones ⁴⁸Ca, ⁵⁰Ti, ⁵²Cr and ⁵⁴Fe by inelastic electron scattering, the result of a search for M1 transitions in the odd-even N = 28 nucleus ⁵¹V is reported. No strong M1 excitation has been detected, in contrast to a recent (p, p') experiment. There is no immediate explanation for this discrepancy. Shell-model calculations indicate that a part of it might be accounted for by an interference between the spin and orbital term of the electromagnetic transition operator in the (e, e') experiment.     

Gamma-ray decay from the analogue state of the Ca g.s.

The γ-decay from three fine-structure components of the ⁴⁹Ca ground state analogue has been investigated. Angular distributions have been measured for the decay from the strongest component. Absolute γ-widths are found from the γ-spectra, and the proton and neutron widths from fits to the ⁴⁸Ca(p, p) and (p, n) excitation functions. A group of eight states with E_x around 7 MeV is found to carry a significant part of the M1 strength. A comparison with the β-decay from ⁴⁹Ca has been made.     

The photonuclear cross sections of 48Ca

The sum of the photoneutron and photoproton cross sections of ⁴⁸Ca (⁴⁸Ca(γ, n + p)), has been deduced from an activation yield curve measurement using bremsstrahlung. In a separate experiment the ⁴⁸Ca(γ, p) and partial photoproton cross sections to the ground and first excited states of ⁴⁷K have been deduced from measured photoproton spectra recorded from the electro-disintegration of ⁴⁸Ca. The ⁴⁸Ca(γ, n) cross section is estimated from these data. A statistical decay model is used to estimate the ⁴⁸Ca(γ, 2n) cross section. These reported cross sections are used to determine the relative strengths and energy distributions of the isospin components of the GDR states, and to compare these with theoretical predictions.