arXiv subjects

D. S. Delion

Publications and source records attributed to D. S. Delion.

At least 19 recordsLinked to original sources

arXiv2026

Self-consistent description of emission processes in axially-symmetric nuclei

We present a theory of cluster emission processes in terms of proton ($π$) and neutron ($ν$) single--particle (sp) degrees of freedom within a self--consistent mean--field (SCMF) constructed from a two--particle interaction having relative (rel) and center of mass (com) terms centered on the nucler surface, the latter describing the interaction between the com of a pair of particles and the surface of an axially--symmetric nucleus. In this way the $α$-clustering phenomenon becomes enhanced on the nuclear surface. We present applications for unstable nuclei that decay through the emission of $α$--particles above $^{100}\textrm{Sn}$, $^{208}\textrm{Pb}$ and within the actinidies series.

nucl-th↗

arXiv2026

Quartet Structure Above $^{100}$Sn and $^{132}$Sn Doubly Magic Isotopes

We calculate energy levels and B(E2) values for the $α$-like nuclei $^{104}$Te and $^{136}$Te. Their energy structure is described within a Multi Step Shell Model (MSM) type approach by coupling proton-proton (pp), neutron-neutron (nn) and proton-neutron(pn) phonon states over the doubly magic nuclei $^{100}$Sn and $^{132}$Sn, respectively. We also compute the electric transitions for A = 102 and A = 134 Sn, Sb and Te nuclei, described within the Tamm-Dankoff Approach (TDA) with multipole-multipole residual interaction. The encountered similarities concerning the B(E2) values and wavefunctions of the coupled states corresponding to $^{104}$Te and $^{136}$Te are analyzed.

nucl-th↗

arXiv2025

Proton emission systematics along proton drip line

We analyze the chart containing both spontaneous and beta-delayed proton emission processes in terms of the Coulomb parameter, reduced radius and angular momentum ($χ$, $ρ$, $l$). We then compare the methods to estimate decay width $Γ$ of a resonant state in a proton mean field, namely the continuity equation for outgoing Gamow states, phase shift analysis of real scattering states and numerical integration of the Schrödinger equation in the complex plane. We show that they provide similar results in the region where it is possible to evaluate the imaginary part of the energy for a resonant (Gamow) state. We then investigate the role of the centrifugal barrier induced by Coulomb interaction and also by proton single particle orbitals. We show that the so-called universal decay law, connecting the logarithm of the monopole reduced width to the fragmentation potential, remains also valid for beta-delayed proton emission processes. This fact allows us to describe experimental data for all proton emission processes in terms of a linear dependence connecting the logarithm of the monopole Coulomb-reduced decay width to the logarithm of the monopole Coulomb penetrability and fragmentation potential within a factor of three for absolute values.

nucl-th↗

arXiv2025

Systematics of neutron emission

Neutron physics is one of the oldest branches 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 corected by the centrifugal barrier (monopole transitions) is given by the Geiger-Nuttall law $\log_{10}T\simχ$, where $χ\sim ZQ^{-1/2}$ is the Coulomb parameter characterizing the outgoing Coulomb-Hankel wave in terms of the daughter charge $Z$ and Q-value. Our purpose is to propose a similar simple systematics of spontaneous neutron half lives, but in terms of the nuclear reduced radius $ρ=κR\sim A^{1/3}Q^{1/2}$, characterizing the "neutral" outgoing spherical Hankel wave. It turns out that the half life in emission of neutral particles is governed by the scaling law $T\simρ^{-2}\sim A^{-2/3}Q^{-1}$ for monopole transitions. We evidence the important role of the angular momentum carried by the emitted neutron. The influence of the neutron wave function generated by a Woods-Saxon nuclear mean field is also analyzed.

nucl-th↗

arXiv2025

Emission processes in a self-consistent field

We present a microscopic description of cluster emission processes within the Cluster--Hartree--Fock (CHF) self--consistent field (SCF) theory. The starting point is a Woods--Saxon (WS) mean field (MF) with spin--orbit and Coulomb terms. Pairing is treated through standard Bardeen--Cooper--Schrieffer (BCS) quasiparticles. The residual two--body interaction is given by a density--dependent Wigner force having a Gaussian shape with a center of mass (com) correction located in a region of low nuclear density slightly beyond the geometrical contact radius of a system comprised from a nucleus and a surface cluster. We show that such a description adequately reproduces the ground state (gs) shape of a spherical nucleus while the surface correction enhances the radial tail of single particle orbitals, thus allowing for an adequate description of the $α$-decay width for unstable systems.

nucl-th↗

arXiv2022

Cluster mean field description of alpha emission

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.

nucl-th↗

arXiv2022

Semi-microscopic theory of two proton emission

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.

nucl-th↗

arXiv2022

Two-proton emission systematics

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.

nucl-th↗

arXiv2021

Semiclassical propagator approach for emission processes. I. Two body non-relativistic case

We compare the coupled channels procedure to the semiclassical approach to describe two-body emission processes, in particular $α$-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 Fröman 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.

nucl-th↗

arXiv2020

Equation of Motion Method to strongly correlated Fermi systems and Extended RPA approaches

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.

nucl-th↗

arXiv2020

Bridging the quartet and pair pictures of isovector proton-neutron pairing

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.

nucl-th↗

arXiv2019

A quartet BCS-like theory

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.

nucl-th↗

arXiv2019

Disentangling the pair and quartet condensates

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.

nucl-th↗

arXiv2019

Unified description of pairing and quarteting correlations within the particle-hole-boson approach

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.

nucl-th↗

arXiv2019

Analytical approach for the Quartet Condensation Model

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 $α$-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.

nucl-th↗

arXiv2016

A simple approach to $α$-decay fine structure

We propose a simple method to evaluate $α$-transition rates to low-lying excited states in even-even nuclei. For this a realistic $α$-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.

nucl-th↗

arXiv2016

Sum-rules and Goldstone modes from extended RPA theories in Fermi systems with spontaneously broken symmetries

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.

cond-mat.str-el↗

arXiv2016

Description of electromagnetic and favored $α$-transitions in heavy odd-mass nuclei

We describe electromagnetic and favored α-transitions to rotational bands in odd-mass nuclei built upon a single particle state with angular momentum projection $Ω=\frac{1}{2}$ 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 $α$-decay widths. We reproduce the energy levels of the rotational band where favored $α$-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 $α$- 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 $α$-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 $α$-transitions for known heavy odd-mass $α$-emitters.

nucl-th↗