P. Fernández de Córdoba

Decay modes of sigma and lambda hypernuclei

Abstract A review is presented of the problem of Σ and Λ decay in nuclei. By means of handy, yet reliable approximations, an approach to Σ decay is developed which allows a clear insight into the different aspects of the problem. The role of nuclear polarization, due to the spin-isospin ΣN → ΛN interaction, in the reduction of the Σ widths is discussed. Many experimentally observable Σ hypernuclei are predicted by showing that their widths are narrower than the separation energies between levels. The mesonic and non-mesonic decays of Λ hypernuclei are analyzed. The non-mesonic width is fairly well reproduced by simplified models for the ΛN → NN weak transition, but quantities like the ratio of proton to neutron induced Λ decay are highly sensitive to the models used. On the other hand, the mesonic width is very sensitive to the pion-nucleus optical potential and can be used to discriminate between different potentials which are equally suited to describe low energy pion-nucleon scattering.

A heuristic algorithm based on Monte Carlo methods for the rural postman problem

Abstract In Routing Problems the aim is to determine a minimum cost traversal over a graph satisfying some specified constraints. Most of them are NP-hard problems and many different heuristic solution algorithms have been proposed. The name Monte Carlo, MC, applies to a set of heuristic procedures with the common feature of using random numbers to simulate a given process. MC approach has not been applied to the framework of Routing Problems in the literature. The purpose of this paper is to demonstrate that MC methods could be useful in implementing heuristic algorithms for Routing Problems. In particular, we design an efficient MC heuristic algorithm for the well known Rural Postman Problem (RPP), for which we have a set of instances with known optimal solution taken from the literature. The Rural Postman Problem (RPP) consists of finding a minimum cost traversal of a specified arc subset of a graph. Given that the RPP is a NP-hard problem, heuristic algorithms are interesting both to handle large size instances and to provide upper bounds that could be used in branch and cut procedures. In this paper we propose a heuristic algorithm for the RPP based on Monte Carlo methods. We simulate a vehicle travelling randomly over the graph, jumping from one node to another on the basis of certain probabilities. Monte Carlo methods provide a simple approach to many different Routing Problems and they are easily implemented in a computer code. The application of this algorithm to a set of RPP instances taken from the literature demonstrates that, using the appropriate probabilities, they are also efficient.

Muon capture revisited

Abstract The problem of inclusive muon capture in nuclei is studied by calculating the capture rate in asymmetric infinite nuclear matter and using the local density approximation to evaluate the capture rates in nuclei. It is shown that the method is rather reliable and allows one to improve on approximations used in the past. The need for a strong nuclear renormalization is shown, reducing the capture rates by about a factor two in medium and heavy nuclei. By using standard effective interactions in the spin-isospin channel one can account for this renormalization and one finds a remarkable overall agreement with the measured capture rates for a large list of nuclei through the periodic table.

Mesonic and binding contributions to the EMC effect in a relativistic many body approach

Abstract We revise the conventional nuclear effects of Fermi motion, binding and pionic effects in deep inelastic lepton scattering using a relativistic formalism for an interacting Fermi sea and the local density approximation to translate results from nuclear matter to finite nuclei. In addition we also consider effects from ϱ-meson renormalization in the nucleus. The use of nucleon Green functions in terms of their spectral functions offers a precise way to account for Fermi motion and binding. On the other hand the use of many-body Feynman diagrams in a relativistic framework allows one to avoid using prescriptions given in the past to introduce relativistic corrections in a nonrelativistic formalism. We show that with realistic nucleon spectral functions and meson nucleus self-energies one can get a reasonable description of the EMC effect for x > 0.15, outside the shadowing region.

Projectile delta excitation in alpha-proton scattering

Abstract The (α, α′) reaction in the Δ-region is a clear example of projectile delta excitation. We study the reaction theoretically and compare the results to a recent experiment. The agreement is rather good. On the other hand the reaction offers a test for models of coherent pion production. Finally, the use of the present model should provide the appropriate background to extract the excitation strength of the Roper resonance observed in the same reaction.

Coherent pion production in the (3He,t) reaction in nuclei

Abstract We have evaluated the cross section for coherent pion production in the 3 He + 12 C → t + 12 C + π + reaction. The Δ peak of the energy distribution is considerably shifted with respect to the peak in the p( 3 He ,t)Δ ++ reaction. The coherent pions represent a sizable fraction of all pions produced and are a major ingredient in the interpretation of the shift of the Δ peak in the inclusive ( 3 He,t ) reaction in nuclei. The coherent production process qualifies as production of virtual pions followed by elastic scattering of the virtual pions with the nucleus and the investigation of this channel will offer information about pion nucleus interaction complementary to the one obtained from scattering of real pions.

AN ENTROPIC PICTURE OF EMERGENT QUANTUM MECHANICS

Quantum mechanics emerges a la Verlinde from a foliation of ℝ3 by holographic screens, when regarding the latter as entropy reservoirs that a particle can exchange entropy with. This entropy is quantized in units of Boltzmanns constant kB. The holographic screens can be treated thermodynamically as stretched membranes. On that side of a holographic screen where spacetime has already emerged, the energy representation of thermodynamics gives rise to the usual quantum mechanics. A knowledge of the different surface densities of entropy flow across all screens is equivalent to a knowledge of the quantum-mechanical wavefunction on ℝ3. The entropy representation of thermodynamics, as applied to a screen, can be used to describe quantum mechanics in the absence of spacetime, that is, quantum mechanics beyond a holographic screen, where spacetime has not yet emerged. Our approach can be regarded as a formal derivation of Plancks constant ℏ from Boltzmanns constant kB.

Roper excitation in alpha - proton scattering

We study the Roper excitation in the ({alpha},{alpha}{sup {prime}}) reaction. We consider all processes which may be relevant in the Roper excitation region, namely, Roper excitation in the target, Roper excitation in the projectile, and double {Delta} excitation processes. The theoretical investigation shows that the Roper excitation in the proton target mediated by an isoscalar exchange is the dominant mechanism in the process. We determine an effective isoscalar interaction by means of which the experimental cross section is well reproduced. This should be useful to make predictions in related reactions and is a first step to construct eventually a microscopic {ital NN}{r_arrow}{ital NN{sup {asterisk}}} transition potential, for which the present reaction does not offer enough information. {copyright} {ital 1996 The American Physical Society.}

A code to evaluate modified bessel functions based on thecontinued fraction method

Abstract We present an algorithm to evaluate the modified Bessel functions I v and K v of integral and half-integral order based onthe calculation of the continued fraction for the I v I s , the Wronskian and the application of forward recurrence relations for the K v I s and backward recurrence for the I v I s . The main feature of the algorithm is that it does not require recalculations using normalization relations nor trial values to start the recurrences; the code evaluates in each step (already normalized) Bessel functions. The accuracy of the method (10 −16 for half-integral order and better than 2×10 −7 for integral order in our code) is limited only by the precision in the initial values for the recurrence and the maximum order available for a given value of the argument is restricted only by the maximum real number available in the computer.

Coherent pion production induced by protons and light ions

Abstract We study coherent pion production by means of the (p,n) and (He,t) reactions on different nuclei and at different energies of the projectile. Energy and angular distributions are calculated. The angular distributions are rather narrow along the direction of the momentum transfer, particularly in heavy nuclei. The reaction is sensitive to the longitudinal part of the elementary NN→NΔ interaction. It also provides a new tool to obtain information on the pion-nuclear interaction, complementary to that offered by reactions with real pions.