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In this work, one-neutron transfer (pickup and stripping), complete and incomplete fusion cross sections for the $^{9}\mathrm{Be}+^{197}\mathrm{Au}$ system were measured over a wide range of energies around the Coulomb barrier by the offline $\ensuremath{\gamma}$-ray detection method. Coupled-channel calculations were used to determine the elastic, inelastic, and transfer cross sections. Coupled reaction channel calculations were performed to derive the one-neutron stripping and pickup cross sections. Three-body continuum discretized coupled-channel calculations were used to determine the effect of the breakup channel on the other reaction mechanisms. The reduced complete and total fusion were found to be hindered above and enhanced below the Coulomb barrier compared with the universal fusion function due to the breakup plus transfer effects.

The eastern region of the calcium isotope chain of the nuclei chart is, nowadays, of great activity. The experimental assessment of the limit of stability is of interest to confirm or improve microscopic theoretical models. The goal of this work is to provide the drip line of the calcium isotopes from the exact solution of the pairing Hamiltonian which incorporates explicitly the correlations with the continuum spectrum of energy. The modified Richardson equations, which include correlations with the continuum spectrum of energy modeled by the continuum single particle level density, is used to solve the many-body system. Three models are used, two isospin independent models with core 40Ca and 48Ca, and one isospin dependent model. One and two-neutron separation energies and occupation probabilities for bound and continuum states are calculated from the solution of the Richardson equations. The one particle drip line is found at the nucleus 57Ca, while the two neutron drip line is found at the nucleus 60Ca from the isospin independent model and at 66Ca from the isospin dependent one., 9 pages, 14 figures, 63 references

The structure of $^{26}$O is currently being investigated on both theoretical and experimental fronts. It is well established that it is unbound and the resonance parameters are fairly well-known. The theoretical analysis may involved two- and three-body interactions, as well as correlations with the continuum spectrum of energy. In order to properly assess the structure of the ground and excited states, it is imperative to include a large single particle representation with the right asymptotic behavior. The purpose of this work is to provide details of the single particle continuum configurations of the ground and excited $0^+$ states. We use a large complex energy single particle basis, formed by resonances and complex energy scattering states, the so called Berggren basis, and a separable interaction, which is convenient to solve in a large model space. Three $0^+$ states were found in the complex energy plane. Changes of the resonant parameters, i.e. energy and width, were analyzed as a function of strength of the residual interaction. It is shown how a subtle difference in the interaction could change the unbound character of $^{26}$O into a Borromean nucleus. Only one of the two excited states can be considered as a candidate for a physical meaningful resonance. The calculated occupation probabilities are in agreement with other theoretical approaches although the calculated half live is three-order of magnitude smaller than the experimental one., 7 pages, 5 figures, 5 tables, 47 references

In this work we measured elastic and inelastic angular distributions of the weakly bound 9Be projectile on the 197Au target at several bombarding energies from 84% up to 140% of the Coulomb barrier. The elastic angular distributions were analyzed using a phenomenological Woods-Saxon potential and a double folding Sao Paulo potential and the energy dependence was extracted. Angular distributions from two inelastic peaks were compared with coupled channel calculations using reduced transition probabilities available in the literature. The energy dependence of the two interaction potential models show a similar trend in the region of the Coulomb barrier. Dispersion relation calculation demonstrates the presence of the breakup threshold anomaly proposed for weakly bound systems., Comment: 12 pages, 6 figures, 55 references

We study a non-relativistic particle subject to a three-dimensional spherical potential consisting of a finite well and a radial $\delta$-$\delta'$ contact interaction at the well edge. This contact potential is defined by appropriate matching conditions for the radial functions, thereby fixing a self adjoint extension of the non-singular Hamiltonian. Since this model admits exact solutions for the wave function, we are able to characterize and calculate the number of bound states. We also extend some well-known properties of certain spherically symmetric potentials and describe the resonances, defined as unstable quantum states. Based on the Woods-Saxon potential, this configuration is implemented as a first approximation for a mean-field nuclear model. The results derived are tested with experimental and numerical data in the double magic nuclei $^{132}$Sn and $^{208}$Pb with an extra neutron., Comment: 19 pages, 9 figures, 4 tables

Background: Weakly bound and unbound nuclei close to particle drip lines are laboratories of new nuclear structure physics at the extremes of neutron/proton excess. The comprehensive description of these systems requires an open quantum system framework that is capable of treating resonant and nonresonant many-body states on equal footing. Purpose: In this work, we construct the minimal complex-energy configuration interaction approach to describe binding energies and spectra of selected 5 $\leq$ A $\leq$ 11 nuclei. Method: We employ the complex-energy Gamow shell model (GSM) assuming a rigid $^4$He core. The effective Hamiltonian, consisting of a core-nucleon Woods-Saxon potential and a simplified version of the Furutani-Horiuchi-Tamagaki interaction with the mass-dependent scaling, is optimized in the sp space. To diagonalize the Hamiltonian matrix, we employ the Davidson method and the Density Matrix Renormalization Group technique. Results: Our optimized GSM Hamiltonian offers a good reproduction of binding energies and spectra with the root-mean-square (rms) deviation from experiment of 160 keV. Since the model performs well when used to predict known excitations that have not been included in the fit, it can serve as a reliable tool to describe poorly known states. A case in point is our prediction for the pair of unbound mirror nuclei $^{10}$Li-$^{10}$N in which a huge Thomas-Ehrman shift dramatically alters the pattern of low-energy excitations. Conclusion: The new model will enable comprehensive studies of structure and reactions aspects of light drip-line nuclei., Comment: 11 pages, 3 figures

We show the feasibility of calculating the decay energy spectrum of neutron emitting nuclei within the Gamow-state description of resonances by obtaining the decay energy spectrum of 25O. We model this nucleus as a valence neutron interacting with an 24O inert core, and we obtain the resulting resonant energies, widths and decay energy spectra for the ground and first excited states. We also discuss the similarities and differences between the decay energy spectrum of a Gamow state and the Breit–Wigner distribution with energy-dependent width. Fil: Id Betan, Rodolfo Mohamed. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario. Instituto de Física de Rosario. Universidad Nacional de Rosario. Instituto de Física de Rosario; Argentina Fil: de la Madrid, Rafael. Lamar University; Estados Unidos

An algebraic Quantum Field Theory formulation of separable pairing interaction for spherical finite systems is presented. The Lipkin formulation of the model Hamiltonian and model wave function is used. The Green function technique is applied to obtain the model energy through the spectral function. Closed equation for the many-body energy of the system is given and comparison with exact models are performed., Comment: 18 pages for the body document + 6 pages for two appendixes. 2 figures. 46 references

The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interactions approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow Shell Model (GSM) provides such a framework as it is capable of describing resonant and non-resonant many-body states on equal footing. To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the $psdf$ shell model space. The resulting interaction is expected to describe nuclei with $5 \leqslant A \leqslant 12$ at the $p-sd$-shell interface. The optimized one-body potential reproduces nucleon-$^4$He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the Helium, Lithium, and Beryllium isotopes up to $A=9$. A very good agreement with experiment was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the $psd$ region of the nuclear chart., 11 pages, 6 figures, 9 tables

A Borromean nucleus is a bound three-body system which is pairwise unbound because none of the two-body subsystem interactions are strong enough to bind them in pairs. As a consequence, the single-particle spectrum of a neutron in the core of a Borromean nucleus is purely continuum, similarly to the spectrum of a free neutron, but two valence neutrons are bound up in such a core. Most of the usual approaches do not use the true continuum to solve the three-body problem but use a discrete basis, like for example, wave functions in a finite box. In this paper the proper continuum is used to solve the pairing Hamiltonian in the continuum spectrum of energy by using the single particle level density devoid of the free gas. It is shown that the density defined in this way modulates the pairing in the continuum. The partial-wave occupation probabilities for the Borromean nuclei $^6$He and $^{11}$Li are calculated as a function of the pairing strength. While at the threshold strength the $(s_{1/2})^2$ and $(p_{3/2})^2$ configurations are equally important in $^6$He, the $(s_{1/2})^2$ configuration is the main one in $^{11}$Li. For very small strength the $(s_{1/2})^2$ configuration becomes the dominant in both Borromean nuclei. At the physical strength, the calculated wave function amplitudes show a good agreement with other methods and experimental data which indicates that this simple model grasps the essence of the pairing in the continuum., 19 pages, 5 tables, 4 figures, 1 appendix with 3 pages, 47 references

The goal of this Letter is to calculate bound, resonant and scattering states in the coupled-channel formalism without relying on the boundary conditions at large distances. The coupled-channel solution is expanded in eigenchannel bases i.e. in eigenfunctions of diagonal Hamiltonians. Each eigenchannel basis may include discrete and discretized continuum (real or complex energy) single particle states. The coupled-channel solutions are computed through diagonalization in these bases. The method is applied to a few two-channel problems. The exact bound spectrum of the Poeschl–Teller potential is well described by using a basis of real energy continuum states. For deuteron described by Reid potential, the experimental energy and the S and D contents of the wave function are reproduced in the asymptotic limit of the cutoff energy. For the Noro–Taylor potential resonant state energy is well reproduced by using the complex energy Berggren basis. It is found that the expansion of the coupled-channel wave function in these eigenchannel bases requires less computational efforts than the use of any other basis. The solutions are stable and converge as the cutoff energy increases.

One- and two-quasi particle states are studied in the complex energy plane. It is found that the pairing interaction does not change the character of the complex state. If a normal state is a physi ...

We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross sections in mirror reactions Be7(p,γ)B8 and Li7(n,γ)8Li. The GSM-CC formalism is applied to a translationally invariant Hamiltonian with an effective finite-range two-body interaction. Reactions channels are built by GSM wave functions for the ground state 3/2− and the first excited state 1/2− of Be7/Li7 and the proton/neutron wave function expanded in different partial waves. Fil: Fossez, K.. Grand Accélérateur National d’Ions Lourds; Francia Fil: Michel, N.. Grand Accélérateur National d’Ions Lourds; Francia Fil: Ploszajczak, M.. Grand Accélérateur National d’Ions Lourds; Francia Fil: Jaganathen, Y.. University Of Tennessee; Estados Unidos. Michigan State University; Estados Unidos Fil: Id Betan, Rodolfo Mohamed. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Rosario. Instituto de Física de Rosario (i); Argentina. Universidad Nacional de Rosario; Argentina

Processes occurring in the continuum part of the spectrum are described by using a basis consisting of bound and antibound states plus Gamow resonances and the continuum background. The calculations, performed in the complex energy plane, are applied to the study of weakly bound nuclei. The influence of antibound states upon physical quantities in halo nuclei is assessed.

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two-particle states are calculated by using a single-particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long-lived resonances are mostly determined by either bound states or by narrow Gamow resonances. However, they are significantly affected by wide resonances and the continuum background itself.

By extending the notion of mixed states to functionals acting on the space of observables with diagonal singularity we obtain a well-defined complex spectral decomposition of the time evolution for a quantum decaying system. In this formalism, generalized Gamow states are obtained with well-defined physical properties.

By extending the notion of states to functionals acting on the space of observables we obtain a well-defined complex spectral decomposition for the time evolution of quantum-decaying systems, where Gamov states play a fundamental role. It is shown that Gamov vectors are well-defined state functionals and, therefore, they stand on the same footing as plane waves.

Strictly finite-range (SFR) potentials are exactly zero beyond their finite range. Single-particle energies and densities as well as S-matrix pole trajectories are studied in a few SFR potentials suited for the description of neutrons interacting with light and heavy nuclei. The SFR potentials considered are the standard cut-off Woods--Saxon (CWS) potentials and two potentials approaching zero smoothly: the SV potential introduced by Salamon and Vertse and the SS potential of Sahu and Sahu. The parameters of these latter were set so that the potentials may be similar to the CWS shape. The range of the SV and SS potentials scales with the cube root of the mass number of the core like the nuclear radius itself. For light nuclei a single term of the SV potential (with a single parameter) is enough for a good description of the neutron-nucleus interaction. The trajectories are compared with a bench-mark for which the starting points (belonging to potential depth zero) can be determined independently. Even the CWS potential is found to conform to this bench-mark if the range is identified with the cutoff radius. For the CWS potentials some trajectories show irregular shapes, while for the SV and SS potentials all trajectories behave regularly., 14 figs

Background: Alpha emission from a nucleus is a fundamental decay process in which the alpha particle formed inside the nucleus tunnels out through the potential barrier.Purpose: We describe alpha decay of ${}^{212}$Po and ${}^{104}$Te by means of the configuration interaction approach.Method: To compute the preformation factor and penetrability, we use the complex-energy shell model with a separable $T=1$ interaction. The single-particle space is expanded in a Woods-Saxon basis that consists of bound and unbound resonant states. Special attention is paid to the treatment of the norm kernel appearing in the definition of the formation amplitude that guarantees the normalization of the channel function.Results: Without explicitly considering the alpha-cluster component in the wave function of the parent nucleus, we reproduce the experimental alpha-decay width of ${}^{212}$Po and predict an upper limit of ${T}_{1/2}=5.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}$ sec for the half-life of ${}^{104}$Te.Conclusions: The complex-energy shell model in a large valence configuration space is capable of providing a microscopic description of the alpha decay of heavy nuclei having two valence protons and two valence neutrons outside the doubly magic core. The inclusion of proton-neutron interaction between the valence nucleons is likely to shorten the predicted half-live of ${}^{104}$Te.

Department of Physics and Chemistry (FCEIA-UNR) - Physics Institute of Rosario (CONICET),Av. Pellegrini 250, S2000BTP Rosario, Argentina(Dated: February 20, 2012)The pairing Hamiltonian constitutes an important approximation in many-body systems, it isexactly soluble and quantum integrable. On the other hand, the continuum single particle leveldensity (CSPLD) contains information about the continuum spectrum of energy of the system. Thequestion if one could use the constant pairing strength for particles correlations in the continuumis still unanswered. In this paper we generalized the Richardson exact solution for the pairingHamiltonian in order to include correlation with the continuum spectrum of energy. The resonantand non-resonant continuum is included through the CSPLD relative to the free particles energy.The resonant correlations is made explicit by using the Cauchy theorem. Low lying states withseniority zero and two were calculated for the even Carbon isotopes. We concluded that energylevels can be calculated with the constant pairing in the continuum using the CSPLD. It was foundthat the nucleus

In his pioneering work of alpha decay, Gamow assumed that the alpha particle formed inside the nucleus tunnels through the barrier of the alpha-daughter potential. The corresponding metastable state can be viewed as a complex-energy solution of the time-independent Schrodinger equation with the outgoing boundary condition. The formation of the alpha cluster, missing in the original Gamow formulation, can be described within the R-matrix theory in terms of the formation amplitude. In this work, the alpha decay process is described by computing the formation amplitude and barrier penetrability in a large complex-energy configuration space spanned by the complexenergy eigenstates of the finite Woods-Saxon (WS) potential. The proper normalization of the decay channel is essential as it strongly modifies the alpha-decay spectroscopic factor. The test calculations are carried out for the 212Po alpha decay.

Pairing plays a central role in nuclear systems. The simplest model for the pairing is the constant-pairing Hamiltonian. The aim of the present paper is to include the continuum single particle level density in the constant pairing Hamiltonian and to make a comparison between the approximate BCS and the exact Richardson solutions. The continuum is introduced by using the continuum single particle level density. It is shown that the continuum makes an important contribution to the pairing parameter even in those case when the continuum is weakly populated. It is shown that while the approximate BCS solution depends on the model space the exact Richardson solution does not., Comment: 15 pages, 5 figures, accepted in Nucl. Phys. A

Pairing (particle-particle) giant resonances are analyzed within a shell-model formalism in the complex energy plane with the aim of understanding why they have not been observed so far. A comparison is made with the equivalent particle-hole mode by applying the formalism to the analysis of the well-understood particle-hole giant resonance. It is found that because of the proper treatment of the continuum intrinsic to the formalism, giant pairing resonances lie much higher than previously predicted and that some of them may be too wide to be observed, whereas others are meaningful excitations. For these, new experimental searches are proposed.

An unified shell model scheme to evaluate simultaneously the contributions of bound single-particle states, Gamow resonances, antibound (virtual) states and continuum complex scattering states is presented. The formalism could be very suitable to study processes occurring in the continuum part of the nuclear spectra.

We show how calculate the energies and the widths of quasiparticle resonant states without solving the complex bcs equations. The method is based on BCS equations solved in the real representation including the continuum. In this representation the quasiparticle resonances are associated to the Gamow states of the mean field.

We present a simple method for calculating the energies and the widths of quasiparticle resonant states. The method is based on BCS equations solved in the Berggren representation. In this representation the quasiparticle resonances are associated to the Gamow states of the mean field. The method is illustrated for the case of neutron-rich nuclei $^{20-22}$O and $^{84}$Ni. It is shown that the contribution of the continuum coupling to the pairing correlations is small and largely dominated by a few resonant states close to the continuum threshold., Comment: 14 pages, 2 figures

A generalization of the complex shell model formalism is presented that includes antibound states in the basis. These states, together with bound states, Gamow states, and the continuum background, represented by properly chosen scattering waves, form a representation in which all states are treated on the same footing. Two-particle states are evaluated within this formalism, and observable two-particle resonances are defined. The formalism is illustrated in the well-known case of $^{11}\mathrm{Li}$ in its bound ground state and in $^{70}\mathrm{Ca}$(g.s.), which is also bound. Both cases are found to have a halo structure. These halo structures are described within the generalized complex shell model. We investigated the formation of two-particle resonances in these nuclei, but no evidence of such resonances was found.

A new unified shell model scheme is introduced in which the single particle basis is a generalization of the Berggren representation. This repesentation includes virtual i.e. antibound basis states as well. We apply the new scheme to the ground state of the exotic nucleus 11Li. Here the antibound pole and the complex continuum both have large contributions and neither of them can be neglected.

An evaluation of two-particle resonances in the complex energy plane is presented. The representation used in the method consists of bound and antibound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Within this representation the structure of halo nuclei is studied.

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum., Comment: 11 pages, 4 figures

In this work we discuss possible definitions of the mean value of the energy for a resonant (Gamow) state. The mathematical and physical aspects of the formalism are reviewed. The concept of rigged Hilbert space is used as a supportive tool in dealing with Gamow-resonances., Comment: 9 pages

An unified shell model scheme is introduced that evaluates simultaneously the contributions of bound single-particle states, Gamow resonances and antibound states to processes occurring in the continuum part of nuclear spectra. This new scheme allows us to study the effect of the antibound pole and the remaining part of the complex continuum separately. The calculations, performed in the complex energy plane, are applied to the study of weakly bound nuclei. The influence of antibound states upon physical quantities in light as well as in heavy nuclei is assessed.

An implementation of the shell-model to the complex energy plane is presented. The representation used in the method consists of bound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Two-particle resonances are evaluated and their structure in terms of the single-particle degreees of freedom are analysed. It is found that two-particle resonances are mainly built upon bound states and Gamow resonances, but the contribution of the scattering states is also important., 20 pages, 9 figures, submitted to Phys.Rev.C