Complementarity and Scientific Rationality

Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the acceptance of his approach to quantum mechanics over de Broglie's had no reasonable foundation. But Bohr's interpretation changed little from the time of its first appearance, and stood independent of any philosophical presuppositions. The principle of complementarity is itself best read as a conjecture of unusually wide scope, on the nature and future course of explanations in the sciences (and not only the physical sciences). If it must be judged a failure today, it is not because of any internal inconsistency.Comment: 29 page

The Higgs mass derived from the U(3) Lie group

The Higgs mass value is derived from a Hamiltonian on the Lie group U(3) where we relate strong and electroweak energy scales. The baryon states of nucleon and delta resonances originate in specific Bloch wave degrees of freedom coupled to a Higgs mechanism which also gives rise to the usual gauge boson masses. The derived Higgs mass is around 125 GeV. From the same Hamiltonian we derive the relative neutron to proton mass ratio and the N and Delta mass spectra. All compare rather well with the experimental values. We predict scarce neutral flavor baryon singlets that should be visible in scattering cross sections for negative pions on protons, in photoproduction on neutrons, in neutron diffraction dissociation experiments and in invariant mass spectra of protons and negative pions in B-decays. The fundamental predictions are based on just one length scale and the fine structure constant. More particular predictions rely also on the weak mixing angle and the up-down quark flavor mixing matrix element. With differential forms on the measure-scaled wavefunction, we could generate approximate parton distribution functions for the u and d valence quarks of the proton that compare well with established experimental analysis.Comment: 18 pages, 13 figures, 3 table

Geometric factors in the Bohr--Rosenfeld analysis of the measurability of the electromagnetic field

The Geometric factors in the field commutators and spring constants of the measurement devices in the famous analysis of the measurability of the electromagnetic field by Bohr and Rosenfeld are calculated using a Fourier--Bessel method for the evaluation of folding integrals, which enables one to obtain the general geometric factors as a Fourier--Bessel series. When the space region over which the factors are defined are spherical, the Fourier--Bessel series terms are given by elementary functions, and using the standard Fourier-integral method of calculating folding integrals, the geometric factors can be evaluated in terms of manageable closed-form expressions.Comment: 21 pages, REVTe

Electromagnetic transition strengths in soft deformed nuclei

Spectroscopic observables such as electromagnetic transitions strengths can be related to the properties of the intrinsic mean-field wave function when the latter are strongly deformed, but the standard rotational formulas break down when the deformation decreases. Nevertheless there is a well-defined, non-zero, spherical limit that can be evaluated in terms of overlaps of mean-field intrinsic deformed wave functions. We examine the transition between the spherical limit and strongly deformed one for a range of nuclei comparing the two limiting formulas with exact projection results. We find a simple criterion for the validity of the rotational formula depending on $$, the mean square fluctuation in the angular momentum of the intrinsic state. We also propose an interpolation formula which describes the transition strengths over the entire range of deformations, reducing to the two simple expressions in the appropriate limits.Comment: 16 pages, 5 figures, supplemental material include

DMRG evaluation of the Kubo formula -- Conductance of strongly interacting quantum systems

In this paper we present a novel approach combining linear response theory (Kubo) for the conductance and the Density Matrix Renormalization Group (DMRG). The system considered is one-dimensional and consists of non-interacting tight binding leads coupled to an interacting nanostructure via weak links. Electrons are treated as spinless fermions and two different correlation functions are used to evaluate the conductance. Exact diagonalization calculations in the non-interacting limit serve as a benchmark for our combined Kubo and DMRG approach in this limit. Including both weak and strong interaction we present DMRG results for an extended nanostructure consisting of seven sites. For the strongly interacting structure a simple explanation of the position of the resonances is given in terms of hard-core particles moving freely on a lattice of reduced size.Comment: 7 pages, 2 figures. Minor typos correcte

Structural evolution in Pt isotopes with the Interacting Boson Model Hamiltonian derived from the Gogny Energy Density Functional

Spectroscopic calculations are carried out, for the description of the shape/phase transition in Pt nuclei in terms of the Interacting Boson Model (IBM) Hamiltonian derived from (constrained) Hartree-Fock-Bogoliubov (HFB) calculations with the finite range and density dependent Gogny-D1S Energy Density Functional. Assuming that the many-nucleon driven dynamics of nuclear surface deformation can be simulated by effective bosonic degrees of freedom, the Gogny-D1S potential energy surface (PES) with quadrupole degrees of freedom is mapped onto the corresponding PES of the IBM. Using this mapping procedure, the parameters of the IBM Hamiltonian, relevant to the low-lying quadrupole collective states, are derived as functions of the number of valence nucleons. Merits of both Gogny-HFB and IBM approaches are utilized so that the spectra and the wave functions in the laboratory system are calculated precisely. The experimental low-lying spectra of both ground-state and side-band levels are well reproduced. From the systematics of the calculated spectra and the reduced E2 transition probabilities $B$(E2), the prolate-to-oblate shape/phase transition is shown to take place quite smoothly as a function of neutron number $N$ in the considered Pt isotopic chain, for which the $\gamma$-softness plays an essential role. All these spectroscopic observables behave consistently with the relevant PESs and the derived parameters of the IBM Hamiltonian as functions of $N$. Spectroscopic predictions are also made for those nuclei which do not have enough experimental E2 data.Comment: 11 pages, 5 figure

Symmetry energy and neutron-proton radii studies with a Wigner-Heisenberg monopole-monopole interaction

The symmetry energy in nuclei is studied using a monopole-monopole two boby interaction which has an isospin dependent term. A Hartree theory is developed for this interaction which has an oscillator shell model basis with corresponding shell structure. The role of shell structure on the symmetry energy is then studied. We also find that the strength of the Heisenberg interaction is very important for understanding the difference between proton and neutron radii and features associated with halo nuclei. PACS numbers: 21.10.Sf, 21.65Cd, 21.65EfComment: 1 table, i figur

Phase transitions in the Interacting Boson Fermion Model: the gamma-unstable case

The phase transition around the critical point in the evolution from spherical to deformed gamma-unstable shapes is investigated in odd nuclei within the Interacting Boson Fermion Model. We consider the particular case of an odd j=3/2 particle coupled to an even-even boson core that undergoes a transition from spherical U(5) to gamma-unstable O(6) situation. The particular choice of the j=3/2 orbital preserves in the odd case the condition of gamma-instability of the system. As a consequence, energy spectrum and electromagnetic transitions, in correspondence of the critical point, display behaviours qualitatively similar to those of the even core. The results are also in qualitative agreement with the recently proposed E(5/4) model, although few differences are present, due to the different nature of the two schemes.Comment: In press in PRC as rapid communication. 7 pages, 4 figure

Breaking of N=8 magicity in 13Be

Structure of $^{13}$Be was investigated with antisymmetrized molecular dynamics. The variation after spin and parity projections was performed. An unnatural parity $1/2^-$ state was suggested to be lower than $5/2^+$ state indicating that vanishing of the N=8 magic number occurs in $^{13}$Be. A low-lying $3/2^+$ state with a $2\hbar\omega$ configuration was also suggested. Developed cluster structures were found in the intruder states. Lowering mechanism of the intruder states was discussed in terms of molecular orbitals around a $2\alpha$ core.Comment: 9 pages, 8 figures, submitted to PR

Cooper pair sizes in superfluid nuclei in a simplified model

Cooper pair sizes are evaluated in a simple harmonic oscillator model reproducing the values of sophisticated HFB calculations. Underlying reasons for the very small sizes of 2.0-2.5 fm of Cooper pairs in the surface of nuclei are analysed. It is shown that the confining properties of the nuclear volume is the dominating effect. It is argued that for Cooper pair sizes LDA is particularly inadapted.Comment: 8 pages, 6 figure