Search

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

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

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

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

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

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.

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