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Neutron physics is one of the oldest brach of the experimental nuclear physics, but the investigation of the spontaneous neutron emission from the ground state along the neutron dripline is still at its beginning, in spite of the crucial importance for nuclear astrophysics. The proton dripline is much better investigated and a systematics of spontaneous proton half lives is available in terms of the Coulomb parameter, characterizing the outgoing irregular Coulomb wave. Our purpose is to propose a similar systematics of spontaneous neutron half lives, but in terms of the nuclear reduced radius, characterizing the "neutral" spherical irregular Neumann wave., Comment: 4 pages, 3 figures, 38 references

We show that the Hartree-Fock-Bogoliubov (HFB) method is able to describe experimental values of alpha decay widths by including a residual nucleon-nucleon Surface Gaussian Interaction (SGI) within the standard procedure used to calculate the nuclear mean field. We call this method the Cluster HFB (CHFB) approach. In this way we correct the deficient asymptotic behaviour of the corresponding single-particle (sp) wave functions generated by the standard mean field. The corrected mean field becomes a sum between the standard mean Woods-Saxon-like field and a cluster Gaussian component centered at the same radius as the SGI. Thus, we give a confirmation of the mean field plus cluster potential structure, which was assumed in our previous work on alpha-decay widths. Systematic calculations evidence the linear correlation between the SGI strength and fragmentation potential, allowing for reliable predictions concerning the half lives of superheavy emitters., Comment: 12 pages, 8 figures, 3 tables

We propose a semi-microscopic model for the simultaneous emission of two protons. This model has the advantage of avoiding certain technical aspects of a fully microscopic 3-body framework, while also allowing the investigation of the influence of proton pairing on the total lifetime of the decaying nucleus. Thus, we use the standard singlet two-proton wave function on the nuclear surface, provided by the Bardeen-Cooper-Schrieffer (BCS) approach, as a boundary condition for the propagator operator. Our model allows for the estimation of all quantities related to the $2p$ emission process, since it provides the 3-body wave function over most of the domain. We show that reasonable agreement with experimental values can be reached by varying the $pp$ pairing strength outside the nucleus in an interval close to the "bare" singlet value.

The simultaneous emission of two protons is an exotic and complex three-body process. It is very important for experimental groups investigating the nuclear stability on the proton drip line to have a simple rule predicting the two-proton decay widths with a reasonable accuracy for transitions between ground as well as excited states in terms of relevant physical variables. In spite of its complexity, we show that the two-proton emission process obeys similar rules as for binary emission processes like proton, alpha and heavy cluster decays. It turns out that the logarithm of the decay width, corrected by the centrifugal barrier, linearly depends upon the Coulomb parameter within one order of magnitude. On the other hand, the universal linear dependence with a negative slope between the logarithm of the reduced width and the fragmentation potential, valid for any kind of binary decay process, is also fulfilled for the two-proton emission with a relative good accuracy. As a consequence of pairing correlations the two protons are simultaneously emitted from a singlet paired state. We evidence that indeed one obtains a linear dependence between the logarithm of the reduced width and pairing gap within a factor of two, giving a good predictive power to this law. It turns out that the diproton and alpha-cluster formation probabilities have similar patterns versus the pairing gap, while in the one-proton case one has a quasi-constant behavior., Comment: 5 pages, 4 figures, 2 tables, 36 references

We compare the coupled channels procedure to the semiclassical approach to describe two-body emission processes, in particular $\alpha$-decay, from deformed nuclei within the propagator method. We express the scattering amplitudes in terms of a propagator matrix, describing the effect of the deformed field, multiplied by the ratio between internal wave function components and irregular Coulomb waves. In the spherical case the propagator becomes diagonal and scattering amplitudes acquire the well-known form. We describe a more rigorous formulation of the 3D semiclassical approach, corresponding to deformed potentials, which leads to the exact results and we also compare them with the much simpler expressions given by the Angular Wentzel-Krames-Brillouin (AWKB) and Linearized WKB (LWKB) with its approximation, known as Fr\"oman WKB (FWKB) method. We will show that LWKB approach is closer than AWKB to the exact coupled-channels formalism. An analysis of alpha-emission from ground states of even-even nuclei evidences the important role played by deformation upon the channel decay widths.

The formal implications of a quartet coherent state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many body correlation functions. The intrinsic structure of the quartet coherent state is detailed, as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations., Comment: 6 pages, 1 figure

The status of different extensions of the Random Phase Approximation (RPA) is reviewed. The general framework is given within the Equation of Motion Method and the equivalent Green's function approach for the so-called Self-Consistent RPA (SCRPA). The role of the Pauli principle is analyzed. A comparison among various approaches to include Pauli correlations, in particular, renormalized RPA (r-RPA), is performed. The thermodynamic properties of nuclear matter are studied with several cluster approximations for the self-energy of the single-particle Dyson equation. More particle RPA's are shortly discussed with a particular attention to the alpha-particle condensate. Results obtained concerning the Three-level Lipkin, Hubbard and Picket Fence Models, respectively, are outlined. Extended second RPA (ESRPA) is presented.

We introduce a BCS-like theory for the quartet correlations induced by the isovector pairing interaction. It is based on a coherent state of BCS type and, unlike usual mean field approaches, it displays a vanishing pair anomalous density $\langle c^\dagger c^\dagger\rangle =0$. We find good agreement between our theory and the exact results. We discuss how the pairing and quarteting correlations share some similar qualitative features within the BCS approach. However, there is no sharp quarteting phase transition. We also present various ways in which our theory may be further developed., Comment: 7 pages, 5 figures

We study the nontrivial interplay of the well known \emph{pairing} and the more complex \emph{quarteting} correlations in the particular case of $N>Z$ atomic nuclei. Within the new Analytical Disentangled Condensate model, by implementing the notion of \emph{fractional degeneracy} we obtain the clear physical picture of a rather weakly interacting mixture of quartet and neutron pair condensates which mainly feel each other's influence through Pauli blocking. The basic idea of our approach may be generalized in order to scrutinize the extent to which similar manifestations are present in various many-body systems., Comment: 5 pages, 2 figures

We study the description of single-species and isovector pairing correlations in the framework of the projected-BCS (PBCS) and the Quartet Condensation Model (QCM) from a particle-hole perspective and we introduce the representation of the QCM quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. We also present a new bosonic approximation for both PBCS and QCM. In each case, the starting point is the reformulation of the pair/quartet condensate state in terms of particle-hole excitations with respect to the Hartree-Fock state. The main simplification of our approach is the assumption that the pair operators corresponding to both particle and hole states obey bosonic commutation relations. This simplifies tremendously the computations and allows for an analytic derivation of the averaged Hamiltonian on the condenstate state as a function of the mixing amplitudes. We study both the pure bosonic approach and the renormalized version, and compare the particle-hole bosonic version to the naive prescription of applying the boson approximation directly to the original condensate state. We compare the fermionic and the renormalized particle-hole bosonic approach in the case of a picket fence model of doubly degenerate states and in a realistic shell model space with an effective interaction for the $N=Z$ nuclei above $^{100}$Sn., Comment: 17 pages, 8 figures

Within the Quartet Condensation Model (QCM), the isovector pairing correlations for $N = Z$ nuclei are described with a very high accuracy by a condensate of $\alpha$-like quartets. The usual approach involves cumbersome recurrence relations in order to compute numerically the relevant quantities of the model: the norm of the quartet states and the mean value of the isovector pairing Hamiltonian as functions of the pair mixing amplitudes. We present the final analytical expressions for the above mentioned quantities, for all cases up to four quartets in the valence shell. The analytical QCM expressions were obtained by a straightforward implementation of the SO(5) algebra in the symbolic computer algebra system Cadabra2. The norm of the quartet states and the mean value of the Hamiltonian are polynomial functions of the mixing amplitudes. The numerical implementation of the QCM model is thus made trivial as matter of copying and pasting the presented formulas. We introduce in this work the method of computer aided analytical calculus for a many body setting. In particular, we provide precise and easy to use tools for the description of isovector pairing correlations., Comment: 5 pages

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 double folding 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., Comment: 8 pages, 6 figures

The Self-Consistent RPA (SCRPA) approach is elaborated for cases with a continuously broken symmetry, this being the main focus of the present article. Correlations beyond standard RPA are summed up correcting for the quasi-boson approximation in standard RPA. Desirable properties of standard RPA such as fullfillment of energy weighted sum rule and appearance of Goldstone (zero) modes are kept. We show theoretically and, for a model case, numerically that, indeed, SCRPA maintains all properties of standard RPA for practically all situations of spontaneously broken symmetries. A simpler approximate form of SCRPA, the so-called renormalised RPA, also has these properties. The SCRPA equations are first outlined as an eigenvalue problem, but it is also shown how an equivalent many body Green's function approach can be formulated., Comment: 13 pages, 8 figures

We describe electromagnetic and favored \alpha-transitions to rotational bands in odd-mass nuclei built upon a single particle state with angular momentum projection $\Omega=\frac{1}{2}$ in the region $88 \le Z \le 98$. We use the particle coupled to an even-even core approach described by the Coherent State Model (CSM) and the coupled channels method to estimate partial $\alpha$-decay widths. We reproduce the energy levels of the rotational band where favored $\alpha$-transitions occur for 26 nuclei and predict B (E2) values for electromagnetic transitions to the bandhead using a deformation parameter and a Hamiltonian strength parameter for each nucleus, together with an effective collective charge depending linearly on the deformation parameter. Where experimental data is available, the contribution of the single particle effective charge to the total B (E2) value is calculated. The Hamiltonian describing the $\alpha$- nucleus interaction contains two terms, a spherically symmetric potential given by the double-folding of the M3Y nucleon-nucleon interaction plus a repulsive core simulating the Pauli principle and a quadrupole-quadrupole (QQ) interaction. The $\alpha$-decaying state is identified as a narrow outgoing resonance in this potential. The intensity of the transition to the first excited state is reproduced by the QQ coupling strength. It depends linearly both on the nuclear deformation and the square of the reduced width for the decay to the bandhead, respectively. Predicted intensities for transitions to higher excited states are in a reasonable agreement with experimental data. This formalism offers a unified description of energy levels, electromagnetic and favored $\alpha$-transitions for known heavy odd-mass $\alpha$-emitters., Comment: 13 pages, 10 figures

Self-Consistent RPA is rederived in a consistent way with the help of the Coupled Cluster ground state wave function truncated at the two body level. An exact killing operator for this wave function is introduced allowing for a detailed discussion of the approximation scheme. Several exactly solvable models are reanalyzed under this new perspective giving raise to a quantitative evaluation of the performances of this many body method., Comment: 18 pages, 14 figures

We propose a simple systematics of low lying 2+ energy levels and electromagnetic transitions in semi-magic isotopic chains Z=28,50,82 and isotonic chains N=28,50,82,126. To this purpose we use a two-level pairing plus quadrupole Hamiltonian, within the spherical Quasiparticle Random Phase Approximation (QRPA). We derive a simple relation connecting the 2+ energy with the pairing gap and quadrupole-quadupole (QQ) interaction strength. It turns out that the systematics of energy levels and B(E2) values predicted by this simple model is fulfilled with a reasonable accuracy by all available experimental data. Both systematics suggest that not only active nucleons but also those filling closed shells play an important role.

Excited states in 212Po have been populated by alpha transfer using the 208Pb(18O,14C) reaction at 85MeV beam energy and studied with the EUROBALL IV gamma multidetector array. The level scheme has been extended up to ~ 3.2 MeV excitation energy from the triple gamma coincidence data. Spin and parity values of most of the observed states have been assigned from the gamma angular distributions and gamma -gamma angular correlations. Several gamma lines with E(gamma) < 1 MeV have been found to be shifted by the Doppler effect, allowing for the measurements of the associated lifetimes by the DSAM method. The values, found in the range [0.1-0.6] ps, lead to very enhanced E1 transitions. All the emitting states, which have non-natural parity values, are discussed in terms of alpha-208Pb structure. They are in the same excitation-energy range as the states issued from shell-model configurations., Comment: 21 pages, 19 figures, corrected typos, revised arguments in Sect. IIIC

We show that the sharp maximum corresponding to 107Mo in the fragment distribution of the 252Cf cold fission is actually a Sn-like radioactivity, similar to other decay processes in which magic nuclei are involved, namely alpha-decay and heavy cluster emission, also called Pb-like radioactivity. It turns out that the mass asymmetry degree of freedom has a key role in connecting initial Sn with the final Mo isotopes along the fission path. We suppose the cold rearrangement of nucleons within the framework of the two center shell model, in order to compute the cold valleys in the charge equilibrated fragmentation potential. The fission yields are estimated by using the semiclassical penetration approach. We consider five degrees of freedom, namely the inter-fragment distance, the shapes of fragments, the neck parameter and mass asymmetry. We found an isomeric minimum between the internal and external barriers. It turns out that the inner cold valley of the total potential energy is connected to the double magic isotope 132Sn, Comment: 5 pages 5 figs

Excited states in $^{212}$Po were populated by $\alpha$ transfer using the $^{208}$Pb($^{18}$O, $^{14}$C) reaction and their deexcitation $\gamma$-rays were studied with the Euroball array. Several levels were found to decay by a unique E1 transition (E$_\gamma <$ 1 MeV) populating the yrast state with the same spin value. Their lifetimes were measured by the DSAM method. The values, found in the range [0.1-1.4] ps, lead to very enhanced transitions, B(E1) = 2$\times10^{-2}$ - 1$\times10^{-3}$ W.u.. These results are discussed in terms of an $\alpha$-cluster structure which gives rise to states with non-natural parity values, provided that the composite system cannot rotate collectively, as expected in the '$\alpha$ + $^{208}$Pb' case. Such states due to the oscillatory motion of the $\alpha$-core distance are observed for the first time., Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev. Lett

We investigate the cold fission of 252Cf within the two center shell model to compute the potential energy surface. The fission yields are estimated by using the semiclassical penetration approach. It turns out that the inner cold valley of the total potential energy is strongly connected with Z=50 magic number. The agreement with experimental values is very much improved only by considering mass and charge asymmetry degrees of freedom. Thus, indeed cold fission of 252Cf is a Sn-like radioactivity, related the other two "magic radioactivities", namely alpha-decay and heavy-cluster decay, called also Pb-like radioactivity. This calculation provides the necessary theoretical confidence to estimate the penetration cross section in producing superheavy nuclei, by using the inverse fusion process., Comment: 15 pages, 10 figures

Emission processes including $\alpha$-decay, heavy cluster decays, proton and di-proton emission are analyzed in terms of the well known factorisation between the penetrability and reduced width. By using a shifted harmonic oscilator plus Coulomb cluster-daughter interaction it is possible to derive a linear relation between the logarithm of the reduced width squared and the fragmentation potential, defined as the difference between the Coulomb barrier and Q-value. This relation is fulfilled with a good accuracy for transitions between ground states, as well as for most $\alpha$-decays to low lying $2^+$ excited states. The well known Viola-Seaborg rule, connecting half lives with the Coulomb parameter and the product between fragment charge numbers, as well as the Blendowke scalling rule connecting the spectroscopic factor with the mass number of the emitted cluster, can be easily understood in terms of the fragmentation potential. It is shown that the recently evidenced two regions in the dependence of reduced proton half-lives versus the Coulomb parameter are directly connected with the corresponding regions of the fragmentation potential., Comment: 8 pages, 10 figures

We investigate the cold fission/fusion paths of superheavy nuclei within the two center shell model, in order to find the best projectile-target combinations of their production. The fission/fusion yields are estimated by using the semiclassical approach. We predict several asymmetric combinations of relative long living fragments, which can be used in fusion experiments of superheavy nuclei with Z>118., Comment: 5 pages, 3 figures

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., Comment: 4 pages, 3 figures

We show that it is possible to restore the symmetry associated with the Goldstone mode within the Self Consistent Random Phase Approximation (SCRPA) applied to the three-level Lipkin model. We determine one and two-body densities as very convergent expansions in terms of the generators of the RPA basis. We show that SCRPA excitations correspond to the heads of some rotational bands in the exact spectrum. It turns out that the SCRPA eigenmodes for N=2 coincide with exact solutions, given by the diagonalisation procedure.

We present a formalism to describe proton emission from odd-odd nuclei based on a scattering like 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 $^{58}$Cu. 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 important $K$-hindrance of the decay. To fully account for the observed half-life in $^{58}$Cu, one has to consider a shape mixing in the final state., Comment: 8 pages, 1 fugre

Self Consistent Quasiparticle Random Phase Approximation (SCQRPA) is considered in application to the Fermi transitions within the O(5) model. It is demonstrated that SCQRPA improves on renormalized QRPA (RQRPA), a method that has recently become rather popular in this context. The analytical form of the SCQRPA vacuum is used to evaluate all the matrix elements. The SCQRPA results show a general trend similar to the exact solutions. The necessity to change the single particle basis beyond the transition point, and to include the proton-proton and neutron-neutron channels in the QRPA operator, in addition to the proton-neutron one, is pointed out., Comment: 28 pages, latex, 9 postSript figures, to be published in Nucl. Phys. A