Quantum theory of large amplitude collective motion and the Born-Oppenheimer method

We study the quantum foundations of a theory of large amplitude collective motion for a Hamiltonian expressed in terms of canonical variables. In previous work the separation into slow and fast (collective and non-collective) variables was carried out without the explicit intervention of the Born Oppenheimer approach. The addition of the Born Oppenheimer assumption not only provides support for the results found previously in leading approximation, but also facilitates an extension of the theory to include an approximate description of the fast variables and their interaction with the slow ones. Among other corrections, one encounters the Berry vector and scalar potential. The formalism is illustrated with the aid of some simple examples, where the potentials in question are actually evaluated and where the accuracy of the Born Oppenheimer approximation is tested. Variational formulations of both Hamiltonian and Lagrangian type are described for the equations of motion for the slow variables.Comment: 29 pages, 1 postscript figure, preprint no UPR-0085NT. Latex + epsf styl

A basis of cranking operators for the pairing-plus-quadrupole model

We investigate the RPA normal-mode coordinates in the pairing-plus-quadrupole model, with an eye on simplifying the application of large amplitude collective motion techniques. At the Hartree-Bogoliubov minimum, the RPA modes are exactly the cranking operators of the collective coordinate approach. We examine the possibility of representing the self-consistent cranking operator by linear combinations of a limited number of one-body operators. We study the Sm nuclei as an example, and find that such representations exist in terms of operators that are state-dependent in a characteristic manner.Comment: 6 pages, 1 figure, using IOP journal style files, to be published in J. Phys.

Towards a practical approach for self-consistent large amplitude collective motion

We investigate the use of an operatorial basis in a self-consistent theory of large amplitude collective motion. For the example of the pairing-plus-quadrupole model, which has been studied previously at equilibrium, we show that a small set of carefully chosen state-dependent basis operators is sufficient to approximate the exact solution of the problem accuratly. This approximation is used to study the interplay of quadrupole and pairing degrees of freedom along the collective path for realistic examples of nuclei. We show how this leads to a viable calculational scheme for studying nuclear structure, and discuss the surprising role of pairing collapse.Comment: 19 pages, 8 figures Revised version To be published in Phys. Rev.

Occupation probabilities of single particle levels using the microscopic interacting boson model: Application to some nuclei of interest in neutrinoless double- β

We have developed a new method to calculate the occupancies of single particle levels in atomic nuclei. This method has been developed in the context of the microscopic interacting boson model, in which neutron and proton degrees of freedom are treated explicitly. The energies of the single particle levels constitute a very important input for the calculation of the occupancies in this method. In principle these energies can be considered as input parameters that can be fitted to reproduce the experimental occupancies. Instead of fitting, in this study we have extracted the single particle energies from experimental data on nuclei with a particle more or one particle less than a shell closure. We provide the sets of these single particle energies suitable for several major shells and apply our method to calculate the occupancies of several nuclei of interest in neutrinoless double-β decay using these sets. Our results are compared with other theoretical calculations and experimental occupancies, when available.peerReviewe

Functional renormalisation group for few-nucleon systems: SU(4) symmetry and its breaking

We apply the functional renormalisation group to few-nucleon systems. Our starting point is a local effective action that includes three- and four-nucleon interactions, expressed in terms of nucleon and two-nucleon boson fields. The evolution of the coupling constants in this action is described by a renormalisation group flow. We derive these flow equations both in the limit of exact Wigner SU(4) symmetry and in the realistic case of broken symmetry. In the symmetric limit we find that the renormalisation flow equations decouple, and can be combined into two sets, one of which matches the known results for bosons, and the other result matches the one for fermions with spin degrees only. The equations show universal features in the unitary limit, which is obtained when the two-body scattering length tends to infinity. We calculate the spin-quartet neutron-deuteron scattering length and the deuteron-deuteron scattering lengths in the spin-singlet and quintet channels

Colour superconductivity in finite systems

In this paper we study the effect of finite size on the two-flavour colour superconducting state. As well as restricting the quarks to a box, we project onto states of good baryon number and onto colour singlets, these being necessary restrictions on any observable ``quark nuggets''. We find that whereas finite size alone has a significant effect for very small boxes, with the superconducting state often being destroyed, the effect of projection is to restore it again. The infinite-volume limit is a good approximation even for quite small systems.Comment: 14 pages RevTeX4, 12 eps figure

Application of a semi-microscopic core-particle coupling method to the backbending in odd deformed nuclei

In two previous papers, the Kerman-Klein-Donau-Frauendorf (KKDF) model was used to study rotational bands of odd deformed nuclei. Here we describe backbending for odd nuclei using the same model. The backbending in the neighboring even nuclei is described by a phenomenological two band model, and this core is then coupled to a large single-particle space, as in our previous work. The results obtained for energies and M1 transition rates are compared with experimental data for 165Lu and for energies alone to the experimental data for 179W. For the case of 165Lu comparison is also made with previous theoretical work.Comment: 16 pages including 8 figure(postscript), submitted to Phys.Rev.

Skyrmions and the Nuclear Force

The derivation of the nucleon-nucleon force from the Skyrme model is reexamined. Starting from previous results for the potential energy of quasistatic solutions, we show that a calculation using the Born-Oppenheimer approximation properly taking into account the mixing of nucleon resonances, leads to substantial central attraction. We obtain a potential that is in qualitative agreement with phenomenological potentials. We also study the non-adiabatic corrections, such as the velocity dependent transition potentials, and discuss their importance.Comment: 24 pages, UPR-0124M

A 12-week lifestyle intervention: effects on fatigue, fear, and nutritional status in children with a Fontan circulation

INTRODUCTION: Children and adolescents with a Fontan circulation are less physically active compared to healthy peers. In the current study, effects of a 12-week lifestyle intervention on fatigue, fears regarding exercise, caloric intake, rest energy expenditure (REE), and body composition were measured in children with a Fontan circulation.METHODS: This study was a semi-cross-over randomized controlled trial. The lifestyle intervention consisted of a 12-week high-weight resistance training (three supervised training sessions a week) supported by high-protein diet (&gt;2 g/kg) and tailored recommended caloric intake. Fatigue (measured by the validated PedsQol Multidimensional Fatigue Scale), fears regarding exercise (measured on a fear thermometer), REE (measured using indirect calorimetry), caloric intake and body composition using air displacement plethysmography, and four-skinfold method were measured before and after the intervention and control period.RESULTS: Twenty-seven pediatric Fontan patients, median age 12.9 years (IQR: 10.5-16.2), of the included 28 patients successfully completed the program. Before training, both child- and parent-reported levels of fatigue were significantly worse on all domains (general, sleep/rest, and cognitive fatigue) compared to healthy peers. After training, parent-reported fatigue significantly improved on the general and cognitive fatigue domains [effect size +16 points (7-25), p  &lt; 0.001, and +10 points (2-17), p  = 0.015, compared to the control period]. Before training, fear regarding exercise scored on the fear thermometer was low for both children and parents (median score 1 and 2, respectively, on a scale of 0-8). After training, child-reported fear decreased further compared to the control period [effect size -1.4 points (-2.3 to -0.6), p  = 0.001]. At baseline, children had increased REE +12% compared to reference values, which did not change after exercise. Children ate an average of 637 calories below recommended intake based on REE, caloric deficit became smaller after the intervention, and protein intake increased compared to the control period [-388 calories (-674 to -102), p  = 0.008, and +15 g (0.4-30), p  = 0.044]. Body fat percentage did not change significantly. CONCLUSION: A 12-week lifestyle intervention improved parent-reported fatigue symptoms in the children, further decreased child-reported fears, and increased caloric and protein intake.</p