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We review the application of Migdal’s Theory of Finite Fermi Systems to the structure of deformed nuclei, approaches beyond the conventional linear response, and microscopic calculations of the Migdal-parameters.

A self-consistent version of the model based on the method of Green’s functions which takes into account conventional phonons of the random phase approximation, complex configurations like 2 quasiparticles⊗phonon ones, and exact single-particle continuum is used to describe many discrete natural-parity states and giant resonances in the 123Sn and 208Pb nuclei. The quasiparticle-phonon interaction is shown to be important not only for low-lying and high-lying collective states but also for low-lying noncollective states.

The properties of the low lying and high lying electric dipole strength in the stable 40Ca, 44Ca and 48Ca isotopes have been calculated within the Extended Theory of Finite Fermi Systems (ETFFS). This approach is based on the random phase approximation (RPA) and includes the single particle continuum as well as the coupling to low lying collective states which are considered in a consistent microscopic way. For 44Ca we also include pairing correlations. We obtain good agreement with the existing experimental data for the gross properties of the low lying and high lying strength. It is demonstrated that the recently measured A-dependence of the electric dipole strength below 10 MeV is well understood in our model: due to the phonon coupling some of the strength in 48Ca is simply shifted beyond 10 MeV. The predicted fragmentation of the strength can be investigated in ( e , e ′ ) and ( γ , γ ′ ) experiments. The isovector dipole strength below 10 MeV is small in all Ca isotopes. Surprisingly, the proton and neutron transition densities of these low lying electric dipole states are in phase, which indicate isoscalar structure. We conclude that for the detailed understanding of the structure of excited nuclei e.g. the low lying and high lying electric dipole strength an approach like the present one is absolutely necessary.

We present fully self-consistent calculations of isoscalar giant monopole and quadrupole as well as isovector giant dipole resonances in heavy and light nuclei. The description is based on Skyrme energy-density functionals determining the static Hartree–Fock ground state and the excitation spectra within random-phase approximation (RPA) and RPA extended by including the quasiparticle-phonon coupling at the level of the time-blocking approximation (TBA). All matrix elements were derived consistently from the given energy-density functional and calculated without any approximation. As a new feature in these calculations, the single-particle continuum was included thus avoiding the artificial discretization usually implied in RPA and TBA. The step to include phonon coupling in TBA leads to small, but systematic, down shifts of the centroid energies of the giant resonances. These shifts are similar in size for all Skyrme parametrizations investigated here. After all, we demonstrate that one can find Skyrme parametrizations which deliver a good simultaneous reproduction of all three giant resonances within TBA.

Effective field theory provides a systematic approach to hardon physics and few-nucleon systems. It allows one to determine the effective two-, three-, and more-nucleon interactions which are consistent with each other. We present a project to derive bulk properties of nuclei from the effective nucleonic interactions.

A hypothesis that the financial log-periodicity, cascading self-similarity through various time scales, carries signatures of a law is pursued. It is shown that the most significant historical financial events can be classified amazingly well using a single and unique value of the preferred scaling factor lambda=2, which indicates that its real value should be close to this number. This applies even to a declining decelerating log-periodic phase. Crucial in this connection is identification of a "super-bubble" (bubble on bubble) phenomenon. Identifying a potential "universal" preferred scaling factor, as undertaken here, may significantly improve the predictive power of the corresponding methodology. Several more specific related results include evidence that: (i) the real end of the high technology bubble on the stock market started (with a decelerating log-periodic draw down) in the begining of September 2000; (ii) a parallel 2000-2002 decline seen in the Standard & Poor's 500 from the log-periodic perspective is already of the same significance as the one of the early 1930s and of the late 1970s; (iii) all this points to a much more serious global crash in around 2025, of course from a level much higher (at least one order of magnitude) than in 2000., Talk given by S. Drozdz at International Econophysics Conference, Bali, August 28-31, 2002; typos corrected

The magnitude and density-dependence of the non-spin dependent Landau-Migdal parameters are derived from Skyrme energy functionals and compared with the phenomenological ones. We perform RPA calculations with various approximations for the Landau-Migdal particle-hole interaction and compare them with the results obtained with the full Skyrme interaction. For the first time the next to leading order in the Landau-Migdal approach is considered in nuclear structure calculations., Comment: Dedicated to the memory of G.E. Brown

A novel application of the correlation matrix formalism to study dynamics of the financial evolution is presented. This formalism allows to quantify the memory effects as well as some potential repeatable intraday structures in the financial time series. The present study is based on the high-frequency Deutsche Aktienindex (DAX) data over the time period between November 1997 and December 1999 and demonstrates a power of the method. In this way, two significant new aspects of the DAX evolution are identified: (i) the memory effects turn out to be sizably shorter than what the standard autocorrelation function analysis seems to indicate and (ii) there exist short term repeatable structures in fluctuations that are governed by a distinct dynamics. The former of these results may provide an argument in favour of the market efficiency while the latter one may indicate origin of the difficulty in reaching a Gaussian limit, expected from the central limit theorem, in the distribution of returns on longer time horizons.

The properties of proton-rich nuclei in the 2s1d shell are investigated using the relativistic mean-field theory with the new TM2 and NL-SH interactions, which have been fitted carefully to the asymmetry energy, and therefore are well suited for studies of nuclei far off stability. The results of the calculations predict that there are one-proton halos in (26,27,28)P and two-proton halos in (27,28,29)S.

Deformed Hartree-Fock-Bogoliubov calculations for finite nuclei are carried out. As residual interaction, a Brueckner G-matrix derived from a meson-exchange potential is taken. Phenomenological medium modifications of the meson masses are introduced. The binding energies, radii, and deformation parameters of the Carbon, Oxygen, Neon, and Magnesium isotope chains are found to be in good agreement with the experimental data., 10 pages, LaTeX2e, elsart, 4 eps-figures includes with graphicx

The ground state properties of proton and neutron rich nuclei in the vicinity of 100Sn are investigated by the relativistic mean field theory with the NL-SH interaction. The numerical results are compared with experimental data and those given by other models. It turns out that the relativistic mean field theory with a proper interaction describes the nuclei near the proton and the neutron drip line successfully.

While bulk properties of stable nuclei are successfully reproduced by mean-field theories employing effective interactions, the dependence of the centroid energy of the electric giant dipole resonance on the nucleon number A is not. This problem is cured by considering many-particle correlations beyond mean-field theory, which we do within the "Quasiparticle Time Blocking Approximation". The electric giant dipole resonances in $^{16}$O, $^{40}$Ca, and $^{208}$Pb are calculated using two new Skyrme interactions., Comment: 4 pages, 4 figures

We compare correlations and coherent structures in nuclei and financial markets. In the nuclear physics part we review giant resonances which can be interpreted as a coherent structure embedded in chaos. With similar methods we investigate the financial empirical correlation matrix of the DAX and Dow Jones. We will show, that if the time-zone delay is properly accounted for, the two distinct markets largely merge into one. This is reflected by the largest eigenvalue that develops a gap relative to the remaining, chaotic eigenvalues. By extending investigations of the specific character of financial collectivity we also discuss the criticality-analog phenomenon of the financial log-periodicity and show specific examples., Comment: 6 pages, 10 figures, elsarticle class

The recent investigations of the shape-coexistence phenomena dominating the structure of the even-even nuclei in the A ∼ 70 mass region are extended by introducing neutron-proton and unnatural-parity correlations in the mean field, while keeping the time-reversal invariance and the axial-symmetry restrictions. Selected low-lying states in 68Ge, 72Ge and 72Kr nuclei are investigated within the FED VAMPIR or EXCITED FED VAMPIR approaches. The results obtained using real and complex mean fields in a relatively large model space are compared with the experimental data. Similar qualitative features are obtained with both real and complex calculations concerning the evolution of the shape transition and shape coexistence with increasing spin and excitation energy. The results obtained indicate the importance of the new type of correlations introduced by the complex mean fields.

We consider a partially bosonized SU(2) Nambu-Jona-Lasinio model with classical scalar-isoscalar and pseudoscalar-isovector meson fields σ and π in the baryonic sector. The meson fields are not restricted to the chiral circle (σ 2 (r)+π 2 (r)≠ƒ π 2 ) . Taking a suitably chosen parameterization for σ(r) and π(r) in terms of their size R, depth U and topological winding number n, we show that in the limit R → 0, U → ∞ a system carrying baryon number B = n but with an arbitrarily small total energy can be obtained. Hereby the valence quarks get part of the negative continuum. In this way we show that independently of the constituent mass m and the UV-cutoff Λ no stable solitonic solutions of the linear model exist.

The authors consider the collective quantization of translational degrees of freedom of the hedgehog soliton in the Nambu-Jona-Lasinio model. They show explicitly that for an O(4)-invariant regularization scheme in Euclidean space-time the translational mass obtained in the perturbative pushing model coincides with the static mass. Zero-point energies for translation and rotation are evaluated numerically. The nucleon mass appears to be around 900 MeV.

The nucleon electric form factors are extracted from the semiclassically quantized solitonic solution of the Nambu-Jona-Lasinio model. To this end the model is solved self-consistently in the SU(2) sector with scalar coupling using the zero-boson and one-quark loop approximation on the chiral circle. Charge distributions, squared radii and the Coulomb energy splitting are calculated as well. For constituent masses around M =400 MeV one obtaine good agreement with the experimental data of the proton. The tail of the neutron charge distribution is made of polarized sea quarks.

We have calculated the strength distributions of the isoscalar giant monopole resonance (ISGMR) in the even-A tin isotopes (A=112-124) that were recently measured in inelastic {alpha} scattering. The calculations were performed within two microscopic models: the quasiparticle random phase approximation (QRPA) and the quasiparticle time blocking approximation (QTBA), which is an extension of the QRPA including quasiparticle-phonon coupling. We used a self-consistent calculational scheme based on the Hartree-Fock+Bardeen-Cooper-Schrieffer approximation. Within the RPA the self-consistency is full. The single-particle continuum is also exactly included at the RPA level. The self-consistent mean field and the effective interaction are derived from the Skyrme energy functional. In the calculations, two Skyrme force parametrizations were used: T5 with a comparatively low value of the incompressibility modulus of infinite nuclear matter (K{sub {infinity}}=202 MeV) and T6 with K{sub {infinity}}=236 MeV. The T5 parametrization gives theoretical results for tin isotopes in good agreement with the experimental data including the resonance widths. The results of the ISGMR calculations in {sup 90}Zr, {sup 144}Sm, and {sup 208}Pb performed with these Skyrme forces are discussed and compared with the experiment.

The self-consistent chiral soliton of the Nambu-Jona-Lasinio model is quantized by means of the collective coordinate method and the rotational moment of inertia is evaluated. For constituent masses around 400 MeV the nucleon-delta splitting agrees well with the experimental data. The contribution of the sea quarks to the moment of inertia is about 20%. In this region the isoscalar quadratic radius of the nucleon is reproduced as well and a clear valence quark picture prevails.

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.

Several nucleon form factors are computed within the framework of the linear chiral soliton model. To this end variational means and projection techniques applied to generalized hedgehog quark-boson Fock states are used. In this procedure the Goldberger-Treiman relation and a virial theorem for the pion-nucleon form factor are well fulfilled demonstrating the consistency of the treatment. Both proton and neutron charge form factors are correctly reproduced, as well as the proton magnetic one. The shapes of the neutron magnetic and of the axial form factors are good but their absolute values at the origin are too large. The slopes of all the form factors at zero momentum transfer are in good agreement with the experimental data. The pion-nucleon form factor exhibits to great extent a monopole shape with a cut-off mass ofΛ=690 MeV. Electromagnetic form factors for the vertexγNΔ and the nucleon spin distribution are also evaluated and discussed.

The shape coexistence phenomena dominating the structure of the nucleus 68 Ge are reinvestigated by taking the dominant correlations on top of the symmetry-projected quasiparticle mean-field solutions of the earlier EXCITED VAMPIR description into account. It turns out that in spite of some quantitative changes the main qualitative features of the older description like, e.g., the occurrence of multiple band structures, the coexistence of many differently deformed configurations, the high level density for medium and high spin values, and the corresponding complex feeding pattern do persist. Qualitatively these features are confirmed by recent experimental data. In addition an EXCITED VAMPIR description of the positive-parity states with even angular momenta in the nucleus 70 Se is reported. The results for this nucleus are besides a few peculiarities qualitatively rather similar to those of our earlier calculations for the nucleus 72 Se.

Using proper-time regularization the Nambu-Jona-Lasinio model in the chiral invariant SU (2)-sector with scalar and pseudoscalar couplings is solved in the zero-boson-loop approximation for baryon number B = 1. The cut-off Λ is fixed to reproduce the pion decay constant. The B = 1 solution is obtained by means of a chemical potential in the generating functional and by separating the valence contribution from the quark one-loop contribution. For a given chiral profile the behavior of the solutions in dependence on the quark meson coupling is discussed and the role of the destabilizing fourth order terms of the heat kernel expansion is clarified. It is shown that for physically relevant coupling constants the present Nambu-Jona-Lasinio model is intimately related to the valence quark approximation of the linear chiral soliton model. The renormalized one-quark-loop approach to the linear chiral soliton model turns out to be different. It is demonstrated that in the SU (2)-sector with scalar and pseudoscalar couplings the Skyrme model is not an approximation to the Nambu-Jona-Lasinio model and vice versa.

An expression is derived for the translationally invariant (transition-) charge density in the center of mass rest frame of the nucleus in between arbitrary wave functions. An explicit formulation is given for the charge density of spherically symmetric Hartree-Fock type ground states. The method is applied to the nuclei4He,16O,40Ca and90Zr using Woods-Saxon single nucleon orbits for the construction of the ground state wave functions. For the two lighter nuclei in addition realistic Hartree-Fock wave functions are investigated. The results are compared to those obtained with various approximate treatments of the center of mass motion. It turns out that at least in the lighter nuclei the usual center of mass correction, which is based on the assumption of pure non-spurious oscillator configurations and commonly used in the analysis of, e.g., electron scattering data, does not produce reliable (or even predictable) results. Thus here indeed the full translationally invariant treatment seems to be required. For the heavy nucleus90Zr on the other hand, as expected, the center of mass effects become negligibly small.

It is shown how the spurious components due to the center of mass motion can be eliminated from general Hartree-Fock-Bogoliubov quasi-particle configurations with the help of projection techniques. The problem how to restore the additional symmetries being broken by such configurations is discussed. An explicit formulation is given for the spherical Hartree-Fock problem with center of mass momentum projection before the variation. As an example for the application of this method the ground state of4He is studied using two different interactions, a microscopic two-body one as well as a phenomenological one including a Skyrme-type three-body force. The results are compared to those of the usual approximate treatment of the center of mass motion in Hartree-Fock calculations. It turns out that, at least for the chosen example, the latter yields a rather reasonable approximation to the correct total energy, single particle energy and even the mass density provided that it is calculated from a translationally invariant density operator.

A conceptional and numerical comparison of one parameter generator coordinate method (GCM) and quantised adiabatic time-dependent Hartree-Fock (ATDHF) theory is performed by applying both theories to the "C + "Ne and l60 + l60 system. Different parametrisations of the Skyrme interaction are used. The single-particle wavefunctions and the operators are represented on a three-dimensional grid in coordinate and momentum space. The collective path is evaluated in the gradient method, corresponding to GCM, and by solving the numerically more involved ATDHF equations. The potential, translational and rotational moments of inertia are calculated along these collective paths as well as the mass parameters corresponding to relative motion. As the next step, the quantised collective Hamiltonian is extracted from the collective path and subbarrier fusion cross sections, as well as astrophysical S factors, are calculated by means of generalised WKB techniques. This allows discussion of the differences between the various methods at a significant and sensitive physical quantity. Whereas for the doubly closed system l6O + l60 the GCM turns out to be a rather good approximation to quantised ATDHF, there are significant differences in the doubly open '*C + *'Ne system.

The Extended Theory of Finite Fermi Systems is based on the conventional Landau-Migdal theory and includes the coupling to the low-lying phonons in a consistent way. The phonons give rise to a fragmentation of the single-particle strength and to a compression of the single-particle spectrum. Both effects are crucial for a quantitative understanding of nuclear structure properties. We demonstrate the effects on the electric dipole states in {sup 208}Pb (which possesses 50% more neutrons then protons) where we calculated the low-lying noncollective spectrum as well as the high-lying collective resonances. Below 8 MeV, where one expects the so-called isovector pygmy resonances, we also find a strong admixture of isoscalar strength that comes from the coupling to the high-lying isoscalar electric dipole resonance, which we obtain at about 22 MeV. The transition density of this resonance is very similar to the breathing mode, which we also calculated. We shall show that the extended theory is the correct approach for self-consistent calculations, where one starts with effective Lagrangians and effective Hamiltonians, respectively, if one wishes to describe simultaneously collective and noncollective properties of the nuclear spectrum. In all cases for which experimental data exist the agreement with the present theory results ismore » good.« less

The Extended Theory of Finite Fermi Systems(ETFFS) describes nuclear excitations considering phonons and pairing degrees of freedom, using experimental single particle energies and the effective Landau-Migdal interaction. Here we use the Skyrme interactions in order to extend the range of applicability of the ETFFS to experimentally not yet investigated short-lived isotopes. We find that Skyrme interactions which reproduce at the mean field level both ground state properties and nuclear excitations are able to describe the spreading widths of the giant resonances in the new approach, but produce shifts of the centroid energies. A renormalization of the Skyrme interactions is required for approaches going beyond the mean field level., 7 pages, 5 figures, corrected typos

Density dependent relativistic Hartree-Fock theory has been extended to describe properties of exotic nuclei. The contribution of Fock exchange terms is emphasized in this letter. It turns out that the influence of Fock terms on properties of neutron rich nuclei is very different from those for nuclei near stability line.

A phenomenon of the financial log-periodicity is discussed and the characteristics that amplify its predictive potential are elaborated. The principal one is self-similarity that obeys across all the time scales. Furthermore the same preferred scaling factor appears to provide the most consistent description of the market dynamics on all these scales both in the bull as well as in the bear market phases and is common to all the major markets. These ingredients set very desirable and useful constraints for understanding the past market behavior as well as in designing forecasting scenarios. One novel speculative example of a more detailed S&P500 development until 2010 is presented.

Financial empirical correlation matrices of all the companies which both, the Deutsche Aktienindex (DAX) and the Dow Jones comprised during the time period 1990–1999 are studied using a time window of a limited, either 30 or 60, number of trading days. This allows a clear identification of the resulting correlations. On both these markets the decreases turn out to be always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix, while increases are more competitive and thus less collective. Generically, however, the remaining eigenstates of the correlation matrix are, on average, consistent with predictions of the random matrix theory. Effects connected with the world globalization are also discussed and a leading role of the Dow Jones is quantified. This effect is particularly spectacular during the last few years, and it turns out to be crucial to properly account for the time-zone delays in order to identify it.

We show that a scale invariant chiral action proposed not long ago prevents the recently discovered collapse of the hedgehog soliton off the chiral circle calculated with a proper time regularized Nambu-Jona-Lasinio action. The soliton calculated with the scale invariant action turns out to be close to the chiral circle and hence has properties which are very similar to those of the chiral quark loop. Its mass obeys the Ioffe formula.

Detailed study of the financial empirical correlation matrix of the 30 companies comprised by DAX within the period of the last 11 years, using the time-window of 30 trading days, is presented. This allows to clearly identify a nontrivial time-dependence of the resulting correlations. In addition, as a rule, the draw downs are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which, at the same time, reduces the variance of the noise states. The opposite applies to draw ups. In this case the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy., Comment: 10 pages, 4 figures, LaTeX2e + graphicx

In the present paper a number conserving random phase approximation is derived as a special case of the recently developed random phase approximation in general symmetry projected quasiparticle mean fields. All the occurring integrals induced by the number projection are performed analytically after writing the various overlap and energy matrices in the random phase approximation equation as polynomials in the gauge angle. In the limit of a large number of particles the well-known pairing vibration matrix elements are recovered. We also present a new analytically number projected variational equation for the number conserving pairing problem.

The angular momentum fluctuations of cranked Hartree-Fock-Bogoliubov wave functions are shown to be quite large and strongly varying in the regions of band crossing. The distribution of angular momenta is explicitly calculated using angular momentum projection. The peculiar behaviour of those distributions around the band crossing is discussed.

An attempt is made to take into account single particle degrees of freedom in angular momentum projected HFB-calculations via the explicit inclusion of two quasiparticle states. For this purpose a formalism is used which, though being rather general, nevertheless is rather suitable for numerical applications even in realistic model spaces. As a first test the method is applied in thei13/2-shell, where exact shell model solutions are available. Though using only a rather truncated quasiparticle space we obtain almost perfect agreement with these exact solutions.

The quantized adiabatic time-dependent Hartree-Fock theory is numerically applied to the low energy large amplitude collective dynamics of heavy ion systems ranging from α + α to 16O + 16O. The problem is reduced to three successive steps. First, for the lowest mode the optimal, i.e., maximally decoupled, collective path {∥φq〉} is evaluated by solving a coupled set of nonlinear differential equations for the single-particle wave functions ϕq(a)(r) of ∥φq〉, depending on the collective coordinate q and three spatial coordinates. A density-dependent interaction with a direct finite range Yukawa-term is employed and three-dimensional coordinate- and momentum-grid techniques are used, including fast Fourier methods. In a second step the quantized collective Hamiltonian Hc(q, ddq) is extracted from {∥φq〉} by means of generator coordinate techniques involving, besides q, a conjugate variable p. Starting from {∥φ〉} this procedure includes the numerical evaluation of the classical potential, V(q), of the intertia parameter, M(q), of the quantum corrections with regard to rotation, translation and collective q-motion, L(q), and of the centrifugal potential. The third step consists of actually calculating the subbarrier fusion cross section by means of WKB methods applied to the collective Hamiltonian Hc(q, ddq). The theoretical numbers are compared with results from Hartree-Fock calculations with quadrupole constraint, and with experimental data. The microscopic aspects of the dynamics, the relation to other theories, and the practical and conceptual problems arising from the quantized ATDHF theory are discussed in detail.

Recent theoretical investigations revealed two different mechanisms for the backbending in 130Ce and 128Ba. While in 130Ce the well-known alignment of two nucleons at the beginning of the π h 11 2 shell is found, in 128Ba the effect is produced by the particles in the more than half-filled ν h 11 2 orbit and hence is preceded by the scattering of a nucleon pair in the nearby ν g 7 2 shell in order to increase the available alignment energy. The present paper is devoted to the possible experimental fingerprints of these different mechanisms. Using the wave functions already obtained, the total spin of each state is decomposed into the individual contributions from the different shells. Furthermore g-factors, static and dynamic quadrupole and also static hexadecapole moments are calculated. It turns out that the only decisive measurable quantities are the occupations of the relevant shells before and after the backbend, which are hardly accessible experimentally, at least at present.

The Hartree-Fock-Bogoliubov approach with spin and number projection before the variation extended to the description of nonyrast states (EXCITED VAMPIR) is used to describe simultaneously many properties of the 68,70,72,74Ge and 72,74Se nuclei. Low-lying spectra, neutron and proton occupation numbers for the spherical-basis orbitals, E0 and E2 transitions, and quadrupole moments are calculated and a fairly good agreement is obtained with experiment. The analysis of the EXCITED VAMPIR mean fields reveals that a strong mixing of prolate and oblate intrinsic quasiparticle determinants is responsible for the complex behaviour of the nuclei in A=70 region.

The solution of the Hartree-Fock-Bogoliubov problem with restoration of the broken symmetries before the variation, as it has been formulated within the VAMPIR and EXCITED VAMPIR approaches yields a description of each state of the nucleus by essentially one single symmetry-projected quasi-particle determinant. In the present paper we propose a procedure which allows to go beyond this mean-field approximation and to include the most important additional correlations in a systematic way. In this new approach each state is approximated by a linear combination of several symmetry-projected quasi-particle determinants, and the corresponding quasi-particle transformations are determined successively together with the configuration mixing via a chain of variational calculations. In this way the selection of the relevant configurations for each state is entirely left to the dynamics of the considered system. The method is applied to some selected examples within the 1sOd shell (the lowest three I π = 1 + states in 20 Ne and the 0 + , 2 + , 4 + members of the 28 Si ground-state band). The results are compared to the exact as well as to the VAMPIR and EXCITED VAMPIR results. Considerable improvements with respect to the latter approaches are obtained.

We have calculated the neutrinoless double beta decay rate of 76Ge. We take into account for the first time a relativistic correction to the nuclear current including weak magnetism. Its effect is to cancel a considerable part of the decay amplitude and we obtain less stringent upper limits on the neutrino Majorana mass and the right-handed weak leptonic current compared with previous calculations.

A variational principle is used to determine the optimal angular momentum projected one determinant approach to theN-nucleon yrast-wave function for a given total spin value. The solution is given in terms of a set of coupled nonlinear equations. Besides an orthonormality constraint for the occupied orbits and a normalization condition for the total wave function, this set consists out of a matrix equation taking care of the fact that the spin-projected wave function does not depend on the orientation of the intrinsic determinant it is based on, and a second subset of equations, which can be considered as a Thouless theorem for the spin-projectedN-nucleon state, and describes the diagonalization of the total Hamiltonian in the subspace of linear independentN-nucleon shell model configurations contained in the test-determinant. Furthermore, a numerical method for the solution of these equations is proposed and an extension of the theory for the description of excited bands is given. Finally, the consistency of the equations is checked by solving them for a simple example analytically.

Two main shortcomings of the cranking model in band crossing regions, namely the possible occurrence of discontinuities and the strongly varying angular momentum fluctuations, are investigated. It is found that because of these drawbacks the reliability of the cranking approximation in regions of band crossing is more than doubtful, and that even the suggestions to overcome the difficulties by including the so-called physical parts of the 2qp trajectory do not improve the situation, at least as far as the wave functions are considered.

The ground state rotational band of 22 Ne has been investigated with the angular momentum and particle number projected Hartree-Bogoliubov theory. Variation before projections was performed in the framework of the constrained Hartree-Bogoliubov theory with the quadrupole moment and the degree of pairing as constraints. It is shown that there is a clear decrease of the pairing correlations (antipairing) and a decrease of the quadrupole deformation (antistretching) with increasing angular momentum. The antipairing effect appears to be essential to reproduce the experimentally known deviation of the spectrum from the J ( J + 1) rule. The antistretching indicated by the B (E2) values is much stronger than that indicated by the calculated static quadrupole moments. This amounts to a breakdown of the rotational picture which is possibly connected with the low band cut-off values in the sd shell. The antipairing effect decreases the antistretching only slightly. The interaction between the pairing and quadrupole degrees of freedom is found to be too weak to change the earlier conclusions concerning antipairing and antistretching in the whole sd shell. No inert core was assumed in the calculations. The effective G -matrix elements of the Hamada-Johnston potential were used as an interaction.

The linear chiral soliton model is solved for nucleon and delta by constructing Fock states in the coherent pair approximation with correct spin and isospin properties. The quark configurations are those arising from theSU(2)×SU(2) coupling of three quarks in 1s-orbits. The overall Fock state is formed by the vector coupling of the quark configurations with the pion coherent state and thus avoids the use of the hedgehog ansatz. The sigma field is treated in the mean field approximation. Equations of motion for the quark, sigma and pion fields are solved in the static approximation. Soliton solutions are found with properties that are in reasonable agreement with those observed for the nucleon and delta including the axial vector coupling constant. With only components having zero and one unpaired pion in the coherent pair approximation the nucleon mass is found to be larger than that using the projected hedgehog approach.

In the first part of the present series of two papers we discussed several nuclear structure models all working in configuration spaces consisting of spin- and number-projected quasiparticle determinants. In the present paper a particular version of the numerically simplest of these models is presented. This model approximates the nuclear wave functions by linear combinations of the angular momentum- and particle number-projected Hartree-Fock-Bogoliubov vacuum and the equally spin- and number-projected two quasiparticle excitations with respect to it. The model allows the use of realistic two body interactions and rather large model spaces. It can hence be applied to a large number of nuclear structure problems in various mass regions. First applications have been performed for the nuclei /sup 20/Ne, /sup 22/Ne, /sup 46/Ti, and /sup 164/Er. In all these cases the results are very encouraging.

In this first of two successive papers we present a microscopic model for nuclear reactions. It allows the description of elastic and inelastic nucleon scattering as well as photonuclear reactions with real and virtual photons. The model is based on a particular classification scheme of the many-body Hilbert space according to the number of continuum nucleons. By its very definition it is restricted to processes with at most one continuum particle in the entrance and/or exit channel. In a large model space, containing all single-particle resonances as bound states, nuclear wave functions are calculated by means of the structure model MONSTER(VAMPIR). Arbitrary general effective two-body forces may be used for the structure calculations as well as for the coupling of the resulting highly correlated wave functions to the continuum. It is the coupling to a modified resonance free continuum in the framework of a general coupled-channel calculation which allows the description of the intermediate structure of the nuclear continuum. In the second paper results obtained from an application to the reaction /sup 29/Si(e,e'x/sub i/)/sup 27/Al will be presented, while in a forthcoming paper the particular role of a fifth response function arising from polarized electron scattering will be discussed. copyrightmore » 1988 Academic Press, Inc.« less