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Background: Zr region is characterized by very rapid changes in the ground state structure of the nuclei. In particular, the onset of deformation when passing from $^{98}$Zr to $^{100}$Zr is one of the fastest ever observed in the nuclear chart. It has been probed both experimental and theoretically that certain low-lying excited states of Zr isotopes own different shapes than the ground state. Purpose: We intend to disentangle the interplay between the sudden changes in the ground state shape, i.e., the existence of a quantum phase transition, and the presence in the spectra of coexisting states with very different deformation, i.e., the presence of shape coexistence. Method: We rely on a previous calculation using the Interacting Boson Model with Configuration Mixing (IBM-CM) which reproduces in detail the spectroscopic properties of $^{96-110}$Zr. This IBM-CM calculation allows to compute mean-field energy surfaces, wave functions and any other observable related with the presence of shape coexistence or with a quantum phase transition. Results: We obtain energy surfaces and the equilibrium value of the deformation parameter $\beta$, the U(5) decomposition of the wave functions and the density of states. Conclusions: We confirm that Zr is a clear example of quantum phase transition that originates from the crossing of two configurations with a very different degree of deformation. Moreover, we observe how the intruder configuration exhibits its own evolution which resembles a quantum phase transition too., Comment: Accepted in Physical Review C

The mass region with A~100 and Z~40 is known to experience a sudden onset of deformation. The presence of the subshell closure $Z=40$ makes feasible to create particle-hole excitations at a moderate excitation energy and, therefore, likely intruder states could be present in the low-lying spectrum. In other words, shape coexistence is expected to be a key ingredient to understand this mass region. The aim of this work is to describe excitation energies, transition rates, radii, and two-neutron separation energies for the even-even 94-110Zr nuclei and, moreover, to obtain information about wave functions and deformation. The interacting boson model with configuration mixing will be the framework to study the even-even Zr nuclei, considering only two types of configurations: 0particle-0hole and 2p-2h excitations. On one hand, the parameters appearing in the Hamiltonian and in the E2 transition operator are fixed trough a least-squares fit to the whole available experimental information. On the other hand, once the parameters have been fixed, the calculations allow to obtain a complete set of observables for the whole even-even Zr chain of isotopes. Spectra, transition rates, radii, $\rho^2(E0)$, and two-neutron separation energies have been calculated and a good agreement with the experimental information has been obtained. Moreover, a detailed study of the wave function has been conducted and mean-field energy surfaces and deformation have been computed too. The importance of shape coexistence has been shown to correctly describe the A~100 mass area for even-even Zr nuclei. This work confirmed the rather spherical nature of the ground state of 94-98Zr and its deformed nature for 100-110Zr isotopes. The sudden onset of deformation in 100Zr is owing to the rapid lowering of a deformed (intruder) configuration which is high-lying in lighter isotopes., Comment: Submitted to PRC

The goal of this contribution is to analyze the connection between shape coexistence and quantum phase transition, two seemingly unrelated phenomena that share common aspects, namely, the rapid change in the ground state structure along an isotope chain or the presence of several minima at the mean-field level. To illustrate the similarities and differences between both phenomena, we will focus in the Pb region, in particular in Pt and Hg isotopes, as well as in Zr isotopes., Comment: To be published in the CGS16 (Shanghai, China) conference proceedings

Large-scale shell-model calculations for the even-even Cadmium isotopes 98 Cd - 108 Cd have been performed with the ANTOINE code in the {\pi}(2p 1/2 ; 1g 9/2 ) {\nu}(2d 5/2 ; 3s 1/2 ; 2d 3/2 ; 1g 7/2 ; 1h 11/2 ) model space without further truncation. Known experimental energy levels and B(E2) values could be well reproduced. Taking these calculations as a starting ground we analyze the deformation parameters predicted for the Cd isotopes as a function of neutron number N and spin J using the methods of model independent invariants introduced by K. Kumar and D. Cline.

Direct mass measurements of the low-spin $3/2^{(-)}$ and high-spin $13/2^{(+)}$ states in the neutron-deficient isotopes $^{195}$Po, $^{197}$Po, and high-spin $13/2^{(+)}$ state in $^{199}$Po were performed with the Penning-trap mass spectrometer ISOLTRAP at ISOLDE-CERN. These measurements allow the determination of the excitation energy of the isomeric state arising from the $\nu$i$_{13/2}$ orbital in $^{195,197}$Po. Additionally, the excitation energy of isomeric states of lead, radon, and radium isotopes in this region were obtained from $\alpha$-decay chains. The new excitation energies complete the knowledge of the energy systematics in the region and confirm for the first time that the $13/2^{(+)}$ states remain isomeric, independent of the number of valence neutrons.

We study the role of intruder states and shape coexistence in the even-even $^{190-206}$Po isotopes, through an interacting boson model with configuration mixing calculation. We analyzed the results in the light of known systematics on various observable in the Pb region, paying special attention to the unperturbed energy systematics and quadrupole deformation. We find that shape coexistence in the Po isotopes behaves in very much the same way as in the Pt isotopes, i.e., it is somehow hidden, contrary to the situation in the Pb and the Hg isotopes., Comment: Contribution to the Nuclear Structure and Dynamics 2015 (Portorose, Slovenia) proceedings

Background: The lead region, Po, Pb, Hg, and Pt, shows up the presence of coexisting structures having different deformation and corresponding to different particle-hole configurations in the Shell Model language. Purpose: We intend to study the importance of configuration mixing in the understanding of the nuclear structure of even-even Po isotopes, where the shape coexistence phenomena are not clear enough. Method: We study in detail a long chain of polonium isotopes, 190-208Po, using the interacting boson model with configuration mixing (IBM-CM). We fix the parameters of the Hamiltonians through a least-squares fit to the known energies and absolute B(E2) transition rates of states up to 3 MeV. Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, B(E2)'s, electric quadrupole moments, nuclear radii and isotopic shifts, quadrupole shape invariants, wave functions, and deformations. Conclusions: We obtain a good agreement with the experimental data for all the studied observables and we conclude that shape coexistence phenomenon is hidden in Po isotopes, very much as in the case of the Pt isotopes., Comment: To be published in Physical Review C. arXiv admin note: text overlap with arXiv:1312.4595

We intend to provide a consistent description of the even-even Hg isotopes, 172-200Hg, using the interacting boson model including configuration mixing. We pay special attention to the description of the shape of the nuclei and to its connection with the shape coexistence phenomenon., Comment: To appear in CGS15 conference proceedings (EPJ Web of Conferences)

The evolution of the total energy surface and the nuclear shape in the isotopic chain $^{172-194}$Pt are studied in the framework of the interacting boson model, including configuration mixing. The results are compared with a self-consistent Hartree-Fock-Bogoliubov calculation using the Gogny-D1S interaction and a good agreement between both approaches shows up. The evolution of the deformation parameters points towards the presence of two different coexisting configurations in the region 176 $\leq$ A $\leq$ 186., Comment: Submitted to PRC

In this paper a review is given of a class of sub-models of both approaches, characterized by the fact that they can be solved exactly, highlighting in the process a number of generic results related to both the nature of pair-correlated systems as well as collective modes of motion in the atomic nucleus., Comment: 34 pages, 8 figures accepted for publication in Scholarpedia

Background: The Po, Pb, Hg, and Pt region is known for the presence of coexisting structures that correspond to different particle-hole configurations in the Shell Model language or equivalently to nuclear shapes with different deformation. Purpose: We intend to study the configuration mixing phenomenon in the Hg isotopes and to understand how different observables are influenced by it. Method: We study in detail a long chain of mercury isotopes, $^{172-200}$Hg, using the interacting boson model with configuration mixing. The parameters of the Hamiltonians are fixed through a least square fit to the known energies and absolute B(E2) transition rates of states up to $3$ MeV. Results: We obtained the IBM-CM Hamiltonians and we calculate excitation energies, B(E2)'s, quadrupole shape invariants, wave functions, isotopic shifts, and mean field energy surfaces. Conclusions: We obtain a fairly good agreement with the experimental data for all the studied observables and we conclude that the Hamiltonian and the states we obtain constitute a good approximation to the Hg isotopes., Comment: Submitted to PRC

The role of configuration mixing in the Pt region is investigated. For this chain of isotopes, the nature of the ground state changes smoothly, being spherical around mass $A\sim 174$ and $A\sim 192$ and deformed around the mid-shell N=104 region. This has a dramatic effect on the systematics of the energy spectra as compared to the systematics in the Pb and Hg nuclei. Interacting Boson Model with configuration mixing calculations are presented for gyromagnetic factors, $\alpha$-decay hindrance factors, and isotope shifts. The necessity of incorporating intruder configurations to obtain an accurate description of the latter properties becomes evident., Comment: Accepted in Physical Review C

A discussion on the nature of the 0+ states in 68Ni (Z=28, N=40) is presented and a comparison is made with its valence counterpart 90Zr (Z=40, N=50). Evidence is given for a 0+ proton intruder state at only ~2.2 MeV excitation energy in 68Ni, while the analogous neutron intruder states in 90Zr reside at 4126 keV and 5441 keV. The application of a shell-model description of 0+ intruder states reveals that many pair-scattered neutrons across N=40 have to be involved to explain the low excitation energy of the proton-intruder configuration in 68Ni., Comment: 10 pages, 2 figures, 1 table

We present a quantitative study of the role played by different components characterizing the nucleon-nucleon interaction in the evolution of the nuclear shell structure. It is based on the spin-tensor decomposition of an effective two-body shell-model interaction and the subsequent study of effective single-particle energy variations in a series of isotopes or isotones. The technique allows to separate unambiguously contributions of the central, vector and tensor components of the realistic effective interaction. We show that while the global variation of the single-particle energies is due to the central component of the effective interaction, the characteristic behavior of spin-orbit partners, noticed recently, is mainly due to its tensor part. Based on the analysis of a well-fitted realistic interaction in sdpf-shell model space, we analyze in detail the role played by the different terms in the formation and/or disappearance of N=16, N=20 and N=28 shell gaps in neutron-rich nuclei., Comment: 6 pages, 4 figures

The role of intruder configurations in the description of energy spectra and B(E2) values in the Pt region is analyzed. In particular, we study the differences between Interacting Boson Model calculations with or without the inclusion of intruder states in the even Pt nuclei $^{172-194}$Pt. As a result, it shows that for the description of a subset of the existing experimental data, i.e., energy spectra and absolute B(E2) values up to an excitation energy of about 1.5 MeV, both approaches seem to be equally valid. We explain these similarities between both model spaces through an appropriate mapping. We point out the need for a more extensive comparison, encompassing a data set as broad (and complete) as possible to confront with both theoretical approaches in order to test the detailed structure of the nuclear wave functions., Comment: To be published in NPA

The spectral properties of a tractable collective model Hamiltonian are studied. The potential energy is truncated up to quartic terms in the quadrupole deformation variables, incorporating vibrational, $\gamma$-independent rotational and axially deformed rotational structures. These physically significant limits are analysed in detail and confronted with well-established approximation schemes. Furthermore, transitional Hamiltonians in between the limits are presented and discussed. All results are obtained within a recently presented Cartan-Weyl based framework to calculate $SU(1,1)\times SO(5)$ embedded quadrupole collective observables., Comment: submitted to PRC

The 1789 keV level in 30Mg was identified as the first excited 0^+ state by measuring its E0 transition to the ground state. The measured small value of rho^2(E0,0^+_2 --> 0^+_1) = 5.7(14) x 10^-3 implies a very small mixing of competing configurations with largely different intrinsic quadrupole deformation near N=20. Axially symmetric Beyond-Mean-Field configuration mixing calculations identify the ground state of 30Mg to be based on neutron configurations below the N=20 shell closure, while the excited 0^+ state mainly consists of a two neutrons excitated into the nu1 f_{7/2} orbital. Using a two-level model, a mixing amplitude of 0.08(4) can be derived., Comment: 4 pages, 4 figures, submitted to Physical Review Letters

In this article we report the results of detailed interacting boson model calculations with configuration mixing for the neutron-deficient Pb isotopes. Calculated energy levels and $B(E2)$ values for $^{188-196}$Pb are discussed and some care is suggested concerning the current classification on the basis of level systematics of the $4_1^+$ and $6_1^+$ states in $^{190-194}$Pb. Furthermore, quadrupole deformations are extracted for $^{186-196}$Pb and the mixing between the different families (0p-0h, 2p-2h, and 4p-4h) is discussed in detail. Finally, the experimental and the theoretical level systematics are compared., Comment: to be published in Phys. Rev. C

The case of U(5)--$\hat{Q}(\chi)\cdot\hat{Q}(\chi)$ mixing in the configuration-mixed Interacting Boson Model is studied in its mean-field approximation. Phase diagrams with analytical and numerical solutions are constructed and discussed. Indications for first-order and second-order shape phase transitions can be obtained from binding energies and from critical exponents, respectively.

We present a quantum Monte Carlo method with exact projection on parity and angular momentum that is free of sign-problems for seniority-conserving nuclear interactions. This technique allows a microscopic calculation of angular momentum and parity projected nuclear level densities. We present results for the $^{55}$Fe, $^{56}$Fe and $^{57}$Fe isotopes. Signatures of the pairing phase transition are observed in the angular momentum distribution of the nuclear level density., Comment: 4 pages, 4 figures

The matrix elements of the quadrupole collective variables, emerging from collective nuclear models, are calculated in the natural Cartan-Weyl basis of O(5) which is a subgroup of a covering $SU(1,1)\times O(5)$ structure. Making use of an intermediate set method, explicit expressions of the matrix elements are obtained in a pure algebraic way, fixing the $\gamma$-rotational structure of collective quadrupole models., Comment: submitted to Journal of Physics A

The Bohr-Mottelson model is solved for a generic soft triaxial nucleus, separating the Bohr hamiltonian exactly and using a number of different model-potentials: a displaced harmonic oscillator in $\gamma$, which is solved with an approximated algebraic technique, and Coulomb/Kratzer, harmonic/Davidson and infinite square well potentials in $\beta$, which are solved exactly. In each case we derive analytic expressions for the eigenenergies which are then used to calculate energy spectra. Here we study the chain of osmium isotopes and we compare our results with experimental information and previous calculations., Comment: 13 pages, 9 figures

We study neutrino-induced nucleon knockout off atomic nuclei and examine the polarization properties of the ejectile. A detailed study of the spin dependence of the outgoing nucleon is presented. The numerical results are derived within a non-relativistic plane-wave impulse-approximation approach. Our calculations reveal large polarization asymmetries, and clear dissimilarities between neutrino- and antineutrino-induced reactions. They reflect the fact that neutrino-induced nucleon knockout is dominated by the transverse axial current and gains its major contributions from forward nucleon emission and backward lepton scattering., Comment: 9 pages, 7 figures, accepted for publication in Phys. Rev. C

The collective Bohr hamiltonian is solved for the soft triaxial rotor around $\gamma_0=\pi/6$ with a displaced harmonic oscillator potential in $\gamma$ and a Kratzer-like potential in $\beta$. The properties of the spectrum are outlined and a generalization for the more general triaxial case with $0<\gamma<\pi/6$ is proposed., Comment: Contribution to ENAM '04 conference. 2 pages, 2 figure

In the present paper, we carry out a detailed analysis of the presence and mixing of various families of collective bands in $^{188}$Pb. Making use of the interacting boson model, we construct a particular intermediate basis that can be associated with the unperturbed bands used in more phenomenological studies. We use the E2 decay to construct a set of collective bands and discuss in detail the B(E2)-values. We also perform an analysis of these theoretical results (Q, B(E2)) to deduce an intrinsic quadrupole moment and the associated quadrupole deformation parameter, using an axially deformed rotor model., Comment: submitted to prc

Very recently the atomic masses of neutron-rich Zr isotopes, from $^{96}$Zr to $^{104}$Zr, have been measured with high precision. Using a schematic Interacting Boson Model (IBM) Hamiltonian, the evolution from spherical to deformed shapes along the chain of Zr isotopes, describing at the same time the excitation energies as well as the two-neutron separation energies, can be rather well reproduced. The interplay between phase transitions and configuration mixing of intruder excitations in this mass region is succinctly addressed., Comment: Accepted in European Journal of Physics A

We study neutrino-induced nucleon knockout from nuclei. Expressions for the induced polarization are derived within the framework of the independent-nucleon model and the non-relativistic plane-wave approximation. Large dissimilarities in the nucleon polarization asymmetries are observed between neutrino- and antineutrino-induced processes. These asymmetries represent a potential way to distinguish between neutrinos and antineutrinos in neutral-current neutrino-scattering on nuclei. We discuss astrophysical applications of these polarization asymmetries. Our findings are illustrated for neutrino scattering on $^{16}$O and $^{208}$Pb., Comment: 5 pages, 5 figures, accepted for publication in Phys. Rev. Lett

Based on Peskun's theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an application in classical physics. As an application in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework., Comment: 6 pages, 5 figures, replaced with published version

Variations in the nuclear mean-field, in neutron-rich nuclei, are investigated within the framework of the nuclear shell model. The change is identified to originate mainly from the monopole part of the effective two-body proton-neutron interaction. Applications for the low-lying states in odd-$A$ Cu nuclei are presented. We compare the results using both schematic and realistic forces. We also compare the monopole shifts with the results obtained from large-scale shell-model calculations, using the same realistic interaction, in order to study two-body correlations beyond the proton mean-field variations., Comment: Phys. Rev. C (in press)

A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a Numerical Renormalization Group (NRG) procedure in order to improve on both. Results are presented for one, two and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using Stochastich Series Expansion., Comment: 10 pages, 15 figures

A three-configuration mixing calculation is performed in the context of the interacting boson model with the aim to describe recently observed collective bands built on low-lying $0^+$ states in neutron-deficient lead isotopes. The configurations that are included correspond to the regular, spherical states as well as two-particle two-hole and four-particle four-hole excitations across the Z=82 shell gap., Comment: 20 pages, 4 figures, accepted by PRC, reference added for section 1 in this revised version

Motivated by the proposed experiment $^{14}N(d,{^2He})^{14}C$, we study the final states which can be reached via the allowed Gamow-Teller mechanism. Much emphasis has been given in the past to the fact that the transition matrix element from the $J^{\pi}=1^+ T=0$ ground state of $^{14}N$ to the $J^{\pi}=0^+ T=1$ ground state of $^{14}C$ is very close to zero, despite the fact that all the quantum numbers are right for an allowed transition. We discuss this problem, but, in particular, focus on the excitations to final states with angular momenta $1^+$ and $2^+$. We note that the summed strength to the $J^{\pi}=2^+ T=1$ states, calculated with a wide variety of interactions, is significantly larger than that to the $J^{\pi}=1^+ T=1$ final states., Comment: Submitted to Phys. Rev. C

We point out that the proton-neutron energy contribution, for low multipoles (in particular for the quadrupole component), effectively renormalizes the strength of the pairing interaction acting amongst identical nucleons filling up a single-j or a set of degenerate many-j shells. We carry out the calculation in lowest-order perturbation theory. We perform a study of this correction in various mass regions. These results may have implications for the use of pairing theory in medium-heavy nuclei and for the study of pairing energy corrections to the liquid drop model when studying nuclear masses., Comment: 19 pages, TeX, 3 tables, 2 figures. Accepted in PRC

Nuclear binding energies and two-neutron separation energies are analyzed starting from the liquid-drop model and the nuclear shell model in order to describe the global trends of the above observables. We subsequently concentrate on the Interacting Boson Model (IBM) and discuss a new method in order to provide a consistent description of both, ground-state and excited-state properties. We address the artefacts that appear when crossing mid-shell using the IBM formulation and perform detailed numerical calculations for nuclei situated in the 50-82 shell. We also concentrate on local deviations from the above global trends in binding energy and two-neutron separation energies that appear in the neutron-deficient Pb region. We address possible effects on the binding energy, caused by mixing of low-lying $0^{+}$ intruder states into the ground state, using configuration mixing in the IBM framework. We also study ground-state properties using a deformed mean-field approach. Detailed comparisons with recent experimental data in the Pb region are amply discussed., Comment: 69 pages, TeX (ReVTeX). 23 eps figures. 1 table. Modified version. Accepted in Nucl. Phys. A

In the framework of the interacting boson model the three transitional regions (rotational-vibrational, rotational-$\gamma$-unstable and, vibrational-$\gamma$-unstable transitions) are reanalyzed. A new kind of plot is presented for studying phase transitions in finite systems such as atomic nuclei. The importance of analyzing binding energies and not only energy spectra and electromagnetic transitions, describing transitional regions is emphasized. We finally discuss a number of realistic examples., Comment: 34 pages, TeX (ReVTeX). 12 ps figures. 3 tables. Submitted to Nucl. Phys. A

In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model., Comment: 5 pages, 4 figures, submitted to Phys. Rev. Lett

An algorithm is presented for the efficient and accurate computation of the coefficients of the characteristic polynomial of a general square matrix. The algorithm is especially suited for the evaluation of canonical traces in determinant quantum Monte-Carlo methods., Comment: 8 pages, no figures, to appear in J. Comp. phys

A mean-field plus pairing model for atomic nuclei in the Fe region was studied using a finite-temperature quantum Monte-Carlo method. We present results for thermodynamical quantities such as the internal energy and the specific heat. These results give indications of a phase transition related to the pairing amongst nucleons, around temperatures of 0.7 MeV. The influence of the residual interaction and of the size of the model space on the nuclear level densities is discussed too., Comment: 23 pages, including 17 eps figures

A scheme is presented to decompose the exponential of a two-body operator in a discrete sum over exponentials of one-body operators. This discrete decomposition can be used instead of the Hubbard-Stratonovich transformation in auxiliary-field quantum Monte-Carlo methods. As an illustration, the decomposition is applied to the Hubbard model, where it is equivalent to the discrete Hubbard-Stratonovich transformation introduced by Hirsch, and to the nuclear pairing Hamiltonian., Comment: 8 pages, includes 2 eps figures, to appear in Phys. Lett. A

We present a model to calculate cross sections for electroinduced two-nucleon emission from finite nuclei. Short-range correlations in the wave functions and meson-exchange contributions to the photoabsorption process are implemented. Effects of the short-range correlations are studied with the aid of a perturbation expansion method with various choices of the Jastrow correlation function. The model is used to investigate the relative importance of the different reaction mechanisms contributing to the A(e,e$'$pn) and A(e,e$'$pp) process. Representative examples for the target nuclei $^{12}$C and $^{16}$O and for kinematical conditions accessible with contemporary high-duty cycle electron accelerators are presented. A procedure is outlined to calculate the two-nucleon knockout contribution to the semi-exclusive (e,e$'$p) cross section. Using this technique we investigate in how far semi-exclusive (e,e$'$p) reactions can be used to detect high-momentum components in the nuclear spectral function., Comment: 51 pages, Latex, uses epsf.sty and elsart.sty, 17 figures (in eps format)

A technique to deal with Coulomb electron distortions in the analysis of (e,e'p) reactions is presented. Thereby, no approximations are made. The suggested technique relies on a partial-wave expansion of the electron wave functions and a multipole decomposition of the electron and nuclear current in momentum space. In that way, we succeed in keeping the computational times within reasonable limits. This theoretical framework is used to calculate the quasielastic (e,e'p) reduced cross sections for proton knockout from the valence shells in $^{16}$O, $^{40}$Ca, $^{90}$Zr and $^{208}$Pb. The final-state interaction of the ejected proton with the residual nucleus is treated within an optical potential model. The role of electron distortion on the extracted spectroscopic factors is discussed., Comment: 45 pages, 10 encapsulated postscript figures, Revtex, uses epsfig.sty and fancybox.sty, to be published in Physical Review C