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In this review are summarized about 20 years of theoretical research with applications in the field of many-body physics for strongly correlated fermions with Rowe's equation of motion (R-EOM) method and extended RPA equations. One major goal is to set up, via EOM, RPA equations with a correlated ground state. Since the correlations depend on the RPA amplitudes, it follows that RPA becomes a selfconsistency problem which is called Self-Consistent RPA (SCRPA). This then also improves very much the Pauli principle violated with standard RPA. The method was successfully applied to several non trivial problems, like the nuclear pairing Hamiltonian in the particle–particle channel (pp-RPA) and the Hubbard model of condensed matter. The SCRPA has several nice properties, as for instance, it can be formulated in such a way that all very appreciated qualities of standard RPA as, e.g., appearance of zero (Goldstone) modes in the case of broken symmetries, conservation laws, Ward identities, etc. are maintained. For the Goldstone mode an explicit example of a model case is presented. The formalism has its sound theoretical basis in the fact that an extension of the usual RPA operator has been found which exactly annihilates the Coupled Cluster Doubles (CCD) ground state wave function. This has been a longstanding problem for all RPA practitioners from the beginning. There exists a rather simplified version of SCRPA which is the so-called renormalized RPA (r-RPA) where only the correlated occupation numbers are involved in the selfconsistent cycle. Because its numerical solution is rather similar to standard RPA, it has known quite a number of applications, like beta and double beta decays, which are reviewed in this article. In this review also an extended version of second RPA (ERPA)is described. This ERPA maintains all appreciable properties of standard RPA. Several realistic applications for, e.g., the damping of giant resonances are presented. Another important aspect of

We present a new approach to investigate the evolution of collectivity on the nuclear map based on the ratio R = B(E2; 2(1)(+) -> 0(1)(+))(exp)/B(E2;2(1)(+) -> 0(1)(-))(Q), where the quantity in the denominator is calculated using the quadrupole moment of the 2(1)(+) level when known. The systematics of such ratios in even-even nuclei reveals interesting features including signatures for particular collective excitations and sensitivity to shell- and subshell closures. A reproduction of these data by theoretical models is highly desirable with the potential to shed more light on the interplay between collective and single-particle motions. In particular, a new signature for shape coexistence was found: R < 1.

We present a new approach to investigate the evolution of collectivity on the nuclear map based on the ratio R = B(E2; 2(1)(+) -> 0(1)(+))(exp)/B(E2;2(1)(+) -> 0(1)(-))(Q), where the quantity in the denominator is calculated using the quadrupole moment of the 2(1)(+) level when known. The systematics of such ratios in even-even nuclei reveals interesting features including signatures for particular collective excitations and sensitivity to shell- and subshell closures. A reproduction of these data by theoretical models is highly desirable with the potential to shed more light on the interplay between collective and single-particle motions. In particular, a new signature for shape coexistence was found: R < 1.

We propose a simple method to evaluate alpha-transition rates to low-lying excited states in even-even nuclei. For this a realistic alpha-daughter doublefolding interaction is approximated by a parabola in the region where the decay process takes place. This allows us to evaluate the penetration probability analytically. The main experimental features of branching ratios to excited states are reproduced by this simple approach., QC 20161013

We compare the quantum mechanical procedures to estimate the total alpha-decay width from deformed nuclei in the laboratory and intrinsic systems of coordinates. Our analysis shows that the total half-life estimated in the intrinsic frame by neglecting the rotational motion of the core (adiabatic approach) is one order of magnitude smaller at beta(2) = 0.3 than the corresponding value in the spherical case. A similar calculation in the laboratory system of coordinates by considering the core motion (giving the correct theoretical estimate) predicts a reduction by only a factor of 2. The widely used "angular WKB" (Wentzel-Kramers-Brillouin) semiclassical procedure provides decay widths which are comparable to the adiabatic approach. We propose a new and very simple semiclassical "angular momentum WKB" procedure to evaluate the decay width in deformed nuclei. It provides decay widths very close to the ones obtained by the exact laboratory coupling channels procedure., QC 20151202

We analyze the alpha-decay fine structure to excited 0(2)(+) states in Hg and Rn isotopes. These states are described as minima in the potential energy surface (PES) provided by the standard deformed Woods-Saxon plus pairing approach. We also investigate alpha decay from the excited state P(0(2)(+)) in the parent nucleus by evaluating the corresponding hindrance factor (HF). By analyzing the experimental HF's we find the remarkable property that the ground and excited states D(0(1)(+)) and D(0(2)(+)) in the daughter nuclei are occupied with almost equal probabilities if there is no excited P(0(+)) states in the parent nucleus. Moreover, if there exists an excited state P(0(2)(+)) then the occupation probability of this state is 25%., QC 20150224

The two-proton decay process is studied by using a simple approach within the framework of scattering theory. We assume that the decaying nucleus is in a pairing state and, therefore, the two-particle wave function on the nuclear surface corresponds to the two protons moving in time-reversed states. This allows us to sustain a simplified version of the decay where the protons are simultaneously emitted with the same energies. We thus obtain a coupled system of radial equations with outgoing boundary conditions. We use similar proton-proton interactions to solve BCS equations and to describe external two-proton dynamics. A strong dependence of the pairing gap and decay width upon the proton-proton interaction strength is revealed. The experimental half-lives of Fe-45 and Ni-48 are reproduced by using a realistic proton-proton interaction., QC 20130502

The intraband electromagnetic transitions in Po-210 and Pb-210 are well described within the shell model approach. In contrast, similar transitions in Po-212 are one order ofmagnitude smaller than the experimental values, suggesting the existence of an alpha-cluster component in the structure of this nucleus. To probe this assumption we introduced Gaussian-like components in the single-particle orbitals. We thus obtained an enhancement of intraband transitions, as well as a proper description of the absolute alpha-decay width in Po-212. We analyzed the recently measured unnatural parity states I- in Po-212 in terms of the collective octupole excitation in Pb-208 coupled to positive parity states in Pb-210. They are connected by relatively large dipole transitions to yrast positive natural parity states. We described E1 transitions by using the same alpha-cluster component and an effective neutron dipole charge e(nu) = -eZ/A. B(E2) values and absolute alpha-decay width in Po-212 are simultaneously described within the shell model plus a cluster component depending upon one free strength parameter., QC 20120703

Proton-neutron correlations in nuclei above the Z = 50 shell closure are investigated with the aim of understanding the behavior of the 2(+) and 4(+) states in Te and Xe isotopes, which remain at a rather constant energy as one approaches the shell closure at N = 50. Our calculations reveal that standard quasiparticle random phase approximation calculations, involving a quadrupole-quadrupole (QQ) interaction with constant strengths, cannot explain this feature. It is found that to reproduce the experimental data within this model one has to include a variable proton-neutron interaction. It turns out that an increased proton-neutron QQ interaction increases the collectivity (i.e., B(E2) values) when approaching the N = 50 region, whereas an increased proton-neutron pairing interaction decreases the collectivity. We thus conclude that the ratio between the B(E2) value and 2(+) energy is a "fingerprint" of proton-neutron collectivity and it should be determined in future experiments concerning light Te isotopes. Based on this criterion, we conclude that the available experimental data indicate an enhanced proton-neutron pairing interaction by approaching doubly magic Z = N = 20 and Z = N = 28 regions., QC 20101201

Hindrance factors corresponding to alpha decay from two quasiparticle isomeric high K states are evaluated in superheavy nuclei. We found that the hindrance factors are very sensitive to the deformations and, therefore, they may constitute a powerful tool to extract spectroscopic information in these nuclei. The hindrance factors turn out to be very large, specially for nonaligned configurations. This indicates that if one of such states is reached the parent nucleus may become isomeric. It is also possible that alpha decay may not proceed through ground state to ground state chains but rather through excited states., QC 20100525

We show that proton emission is a valuable tool to investigate mean field properties of exotic proton rich nuclei. We give a formula that relates the logarithm of the half-life, corrected by the centrifugal barrier, with the Somerfeld parameter in proton decay processes. The corresponding experimental data lie on two straigth lines which appear as a result of a sudden change in the nuclear shape, marking two regions of deformation. This feature provides a powerfull tool to assign experimentally quantum numbers and deformations in proton emitters., QC 20110811

We give a simple relation, connecting the logarithm of the half-life, corrected by the centrifugal barrier, with the Coulomb parameter in proton decay processes. The reduced experimental data lie on two straight lines as a result of a sudden change in the nuclear shape, marking two regions of deformation, divided by the charge number Z = 68. This feature provides a powerful tool to assign experimentally quantum numbers in proton emitters., QC 20141117

A very simple formula is presented that relates the logarithm of the half-life, corrected by the centrifugal barrier, with the Coulomb parameter in proton decay processes. The corresponding experimental data lie on two straight lines which appear as a result of a sudden change in the nuclear shape marking two regions of deformation independently of the angular momentum of the outgoing proton. This feature provides a powerful tool to assign experimentally quantum numbers in proton emitters., QC 20100525

Proton emission studies are presently the focal point of nuclear structure as well as nuclear reaction investigations in rare nuclei. Theoretical approaches to investigate the properties of such nuclei by using proton emission are reviewed. We analyse time-dependent and stationary formalisms within adiabatic and non-adiabatic methods. We investigate and compare the use of resonant Gamow states within coupled channels, R-matrix and distorded wave approaches. We give a description of odd-even as well as odd-odd proton emitters using axially symmetric or triaxial potentials. The emission to excited states of the daughter nucleus and angular distribution of the emitted proton is discussed. The status of numerical applications for both spherical and deformed approaches is reviewed. The importance of proton emission in analysing the properties of nuclear matter under exotic conditions is emphasized. in the appendices we give all technical details necessary to compute the observables connected with proton emission., QC 20100525

Proton decay from triaxially deformed nuclei is investigated. The deformation parameters corresponding to the mother nucleus are determined microscopically and the calculated decay widths are used to probe the mean-field wave function. The proton wave function in the mother nucleus is described as a resonant state in a coupled-channel formalism. The decay width, as well as the angular distribution of the decaying particle, are evaluated and their dependence upon the triaxial deformation parameters is studied in the decay of Re-161 and Bi-185. It is found that the decay width is very sensitive to the parameters defining the triaxial deformation while the angular distribution is a universal function which does not depend upon details of the nuclear structure., QC 20100525

We present a formalism to describe proton emission from odd-odd nuclei based on a scatteringlike approach. Special emphasis is given to the case of transitions between states with different deformations. As an example we estimate the proton half-life of the odd-odd nucleus Cu-58 . Our calculations show that the change of deformation in the decay process has a significant influence on the half life. In addition, the angular momentum coupling of proton and neutron orbitals can result in an additional K hindrance of the decay. To fully account for the observed half life in Cu-58 , we propose shape mixing of the final state., QC 20100525

The self-consistent quasiparticle random phase approximation (SCQRPA) within the O(5) model in the coupled proton-neutron representation is analyzed. The exact vacuum wave function is used to compute all involved matrix elements. A stability analysis of the stationary points is performed. A phase transition from the uncoupled to the coupled stable proton-neutron regime beyond the QRPA breakdown value of the particle-particle strength is evidenced. The excitation energies are close to the lowest stable exact eigenvalues given by the diagonalization procedure for all cases. The conditions for which the Ikeda sum rule is fulfilled for all values of the particle-particle strength are pointed out. ©2000 American Physical Society