F. Pérez-Bernal

Equivalent rotations associated with the permutation inversion group revisited: symmetry projection of the rovibrational functions of methane

In this work the analysis of the equivalent rotations from the permutation inversion group formalism is revisited. We emphasize that explicit knowledge of changes in the Euler angles are not required in order to determine the transformation that a given symmetry operation causes to the rotational functions when dealing with the permutation inversion group formalism. Indeed, matrix elements of the equivalent rotations are provided by a single Wigners D (j)(R) function. Taking advantage of this, we propose a symmetry projection approach to build the rovibrational functions of methane. This approach focuses on the relevance of the isomorphism between permutations and equivalent rotations. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigners D functions and vibrational matrix representations provided by a local scheme. The proposed approach is general and permits us to obtain in a systematic fashion an orthonormal set of symmetry-projected functions, with good total angular momentum, and carrying the irreducible representations of the molecular symmetry group.

α-particle production in the scattering of 6He by 208Pb at energies around the Coulomb barrier

New experimental data from the scattering of 6He + 208Pb at energies around and below the Coulomb barrier are presented. The yield of breakup products coming from projectile fragmentation is dominated by a strong group of α particles. The energy and angular distribution of this group have been analyzed and compared with theoretical calculations. This analysis indicates that the α particles emitted at backward angles in this reaction are mainly due to two-neutron transfer to weakly bound states of the final nucleus.

Simulation of the Raman spectra of CO2: Bridging the gap between algebraic models and experimental spectra

The carbon dioxide Raman spectrum is simulated within an algebraic approach based on curvilinear coordinates in a local representation. The two main advantages of the present algebraic approach are a possible connection with configuration space and the correct description of systems with either local or normal mode character. The system Hamiltonian and polarizability tensor are expanded in terms of curvilinear coordinates. The curvilinear coordinates are in turn expanded into normal coordinates, obtaining an algebraic representation in terms of normal bosonic operators. A canonical transformation maps the operators into a local algebraic representation. The final step is an anharmonization procedure to local operators. The Raman spectrum of CO2 has been simulated, obtaining results close to experimental accuracy, and polarizability transition moments for the Raman spectral lines between 1150 cm(-1) and 1500 cm(-1) are reported. The comparison between experimental and simulated spectra has provided six new CO2 experimental vibrational terms.

Bending vibrational modes of ABBA molecules: algebraic approach and its classical limit

A simple three-parameter model of coupled bending vibrations in ABBA molecules is proposed. The correlation diagram between linear, cis-bent, and trans-bent configurations is constructed. Potential energy surfaces are computed. The phase diagram for these configurations is derived and quantum shape phase transitions briefly discussed.

Structure of eigenstates and quench dynamics at an excited state quantum phase transition

L.F.S. thanks the ITAMP, where part of this work was done, for its hospitality. We thank Jose M. Arias, Jose E. Garcia-Ramos, Francesco Iachello, and Pedro Perez-Fernandez for useful discussions. L.F.S. was supported by the NSF Grant No. DMR-1147430. F.P.B. was funded by MINECO Grants No. FIS2011-28738-C02-02 and No. FIS2014-53448-C2-2-P and by the Spanish Consolider-Ingenio 2010 (CPANCSD2007-00042).

Excited-state quantum phase transitions in many-body systems with infinite-range interaction : localization, dynamics, and bifurcation

LFS and MT were supported by the NSF grant No. DMR- 1147430. FPB was funded by MINECO grant FIS2014- 53448-C2- 2-P and by Spanish Consolider-Ingenio 2010 (CPANCSD2007- 00042). LFS and FPB thank Pedro Perez- Fernandez and Jorge Dukelsky for discussions, as well as the hospitality of Alejandro Frank and the Centro de Ciencias de la Complejidad (C3) at the UNAM in Mexico, where part of this work was carried out.

Symmetry projection of the rovibrational functions of methane

In this work we propose a symmetry projection approach to build a rovibrational basis for methane. In our method, symmetry adapted functions are obtained by simultaneous diagonalization of a set of commuting operators, whose representation is given in terms of direct products of Wigner’s D functions and vibrational matrix representations provided by a local scheme. The proposed approach is general and permits to obtain in a systematic fashion an orthonormal set of symmetry‐projected functions, with good total angular momentum, and carrying the irreducible representations of the molecular symmetry group.

Coulomb breakup in a transformed harmonic oscillator basis

The problem of Coulomb breakup in the scattering of a two-body loosely bound projectile by a heavy target is addressed. A basis of transformed harmonic oscillator (THO) wave functions is used to discretize the projectile continuum and to diagonalize the Hamiltonian of the two-body system. Results for the reaction {sup 8}B+{sup 58}Ni at sub-Coulomb energies are presented. Comparison of different observables with those obtained with the standard continuum discretized coupled-channels (CDCC) method shows good agreement between both approaches.

Identifying the order of a quantum phase transition by means of Wehrl entropy in phase space.

We propose a method to identify the order of a quantum phase transition by using area measures of the ground state in phase space. We illustrate our proposal by analyzing the well known example of the quantum cusp and four different paradigmatic boson models: Dicke, Lipkin-Meshkov-Glick, interacting boson model, and vibron model.

Novel results from an algebraic approach to molecular bending dynamics

We present a brief review of research topics of current interest that depend on an algebraic approach to molecular bending dynamics. This approach is based on a u(3) spectrum generating algebra. In particular, we briefly present results on three topics: the calculation of finite-size analytical corrections to mean field results, the application of the model to the large-amplitude vibrational bending mode of the NCNCS molecule, and the analysis of the influence of quadratic Casimir operators on excited state quantum phase transitions.