Doubly Charmed Baryon Mass and Wave Function through a Random Walks Method

The mass and the wave function of doubly charmed Ξ_cc⁺⁺ (ccu) baryon are evaluated using Green Function Monte Carlo method to solve the three-body problem with Cornell potential. The mass of Ξ_cc⁺⁺ with spin 1/2 is in a good agreement with the LHCb value. Simulation of the wave function by random walks resulted in a configuration of the quark–diquark type. The radius of Ξ_cc⁺⁺ is much larger than the size needed for a large isospin splitting. The prediction for the Ω_cc mass is presented.     

Shell-model calculations in the A = 5 system

The A = 5 structure problem is solved within the framework of the nuclear shell model. The model states are expanded on a basis of properly symmetrized translationally invariant harmonic oscillator eigenstates including states of up to 5(kh)gw of oscillator excitation. Ground and excited levels of the ⁵H, ⁵He, ⁵Li and ⁵Be systems are presented. The two-body interaction is based on the Sussex matrix elements. Model results are in good agreement with measured A = 5 level positions. The model $\text{T =}\text{3}\text{2}$ results lead to a quartet of levels, whose positions are given roughly by the isobaric multiplet mass equation.     

Majorons: A simultaneous solution to the large and small scale dark matter problems

It is shown that the existence of majorons, which enable a heavy neutrino, 500 eV ? m_νH ? 25 keV to decay into a light neutrino m_νL ? 8 eV and a majoron, with lifetime 10⁴ yr ? τ_νH ? 10⁸ yr can solve both the large and small scale dark matter problems. For a primordial “Zeldovich” spectrum of fluctuations the limits are $\text{m}{}_{\mathrm{<mtext>v</mtext><mtext>H</mtext>}}\text{?}\text{?}\text{550}\text{eV and}\text{τ}{}_{\mathrm{<mtext>v</mtext><mtext>H</mtext>}}$ > 10⁷ to 10⁸ yr (the ranges m_νH ? eV and τ_νH ? 10⁸ yr are allowed by the model but galaxy formation becomes problematic). The large scale dark matter problem is how to achieve the critical density as implied by inflation, the small scale problems deal with the halos of galaxies and galaxy formation and perturbation growth. The heavy neutrino could provide the solution to the small scale problem by initiating perturbation growth before decoupling. The decay products will be fast and thus not bound to the initial clumps, thus solving the large scale problem. The low mass relic neutrinos that were not decay products would remain bound in the gravitational potentials which grew from the initial perturbations. The resulting universe would be radiation dominated, which is consistent with present observations if H₀ ? 40 km/s/Mpc. An alternative solution can occur when m_νH ≈ 10 eV: the universe can again become matter dominated in the present epoch. This solution still allows H⁰ ～ 50 km/s/Mpc. The majoron model parameters which best fit the dark matter considerations are presented.     

Application of the HN method to the critical slab problem for reflecting boundary conditions

The recently developed H_N method is used to solve the critical slab problem for a slab which is surrounded by a reflector. In the special case for R=0 (the reflection coefficient) the problem reduces to the one under vacuum boundary conditions. It is shown that the method is concise and leads to fast converging numerical results. The presented numerical results are compared with the data available in literature.     

Precision Penning trap mass measurements of rare isotopes produced by projectile fragmentation

The low-energy beam and ion trap facility LEBIT at NSCL/MSU is at present the only facility where precision experiments are performed with stopped rare isotope beams produced by fast-beam fragmentation. LEBIT combines high-pressure-gas stopping with advanced ion manipulation techniques to provide brilliant low-energy beams. So far these beams have mainly been used for mass measurements on short-lived rare isotopes with a 9.4T Penning trap mass spectrometer. Recent examples include ^70m Br , located at the proton dripline, ³²Si and the iron isotopes ^63-65Fe . While the measurement of ³²Si helps to solve a long-standing dispute over the validity of the isobaric multiplet mass equation (IMME) for the A = 32 , T = 2 multiplet, the mass measurements of ^65m,g Fe marked the first time a nuclear isomeric state has been discovered by Penning trap mass spectrometry.     

Optimal mass transport for higher dimensional adaptive grid generation

In this work, we describe an approach for higher dimensional adaptive grid generation based on solving the L² Monge–Kantorovich problem (MKP) which is a special case of the classical optimal mass transportation problem. Two methods are developed for computing the coordinate transformation used to define the grid adaptation. For the first method, the transformation is determined by solving a parabolic Monge–Ampère equation for a steady state solution. For the second method, the grid movement is determined from the velocity field obtained by solving a fluid dynamics formulation of the L² MKP. Several numerical experiments are presented to demonstrate the performance of the MKP methods and to compare them with some related adaptive grid methods. The experimental results demonstrate that the MKP methods show promise as effective and reliable methods for higher dimensional adaptive grid generation.     

Diffraction in the semiclassical approximation to Feynman's path integral representation of the Green function

We derive the semiclassical approximation to Feynman's path integral representation of the energy Green function of a massless particle in the shadow region of an ideal obstacle in a medium. The wavelength of the particle is assumed to be comparable to or smaller than any relevant length of the problem. Classical paths with extremal length partially creep along the obstacle and their fluctuations are subject to non-holonomic constraints. If the medium is a vacuum, the asymptotic contribution from a single classical path of overall length L to the energy Green function at energy E is that of a non-relativistic particle of mass E/c² moving in the two-dimensional space orthogonal to the classical path for a time τ=L/c. Dirichlet boundary conditions at the surface of the obstacle constrain the motion of the particle to the exterior half-space and result in an effective time-dependent but spatially constant force that is inversely proportional to the radius of curvature of the classical path. We relate the diffractive, classically forbidden motion in the “creeping” case to the classically allowed motion in the “whispering gallery” case by analytic continuation in the curvature of the classical path. The non-holonomic constraint implies that the surface of the obstacle becomes a zero-dimensional caustic of the particle's motion. We solve this problem for extremal rays with piecewise constant curvature and provide uniform asymptotic expressions that are approximately valid in the penumbra as well as in the deep shadow of a sphere.     

Monte Carlo simulation of finite mass nucleons interacting via a neutral,scalar boson field

A recently proposed Monte Carlo method to solve the Schrödinger equation when expressed in Fock space is applied to the hamiltonian which describes the interaction of nucleons via a neutral, scalar boson field. The fact that a nucleon has finite mass is taken into account and a gaussian cut-off for the nucleon form factor is adopted. The problem is solved for systems with A = 1 and 2 sources (nucleons) in the three-dimensional continuous space. From the results for A = 1 a bare nucleon mass, m_Bc² = 962.58 ± 0.06 MeV, is obtained. This value is used to determine the binding energy for an A = 2 system by means of this new algorithm. The result, B(2) = 2.14 ± 0.50 MeV, is consistent with the value corresponding to the static potential approximation.     

Investigation of double-beta decay at the Institute of Theoretical and Experimental Physics (ITEP, Moscow)

Investigation of neutrinoless double-beta (2β0ν) decay is presently being considered as one of the most important problems in particle physics and cosmology Interest in the problem was quickened by the observation of neutrino oscillations. The results of oscillation experiments determine the mass differences between different neutrino flavors, and the observation of neutrinoless decay may fix the absolute scale and the hierarchy of the neutrino masses. Investigation of 2β0ν decay is the most efficient method for solving the problem of whether the neutrino is a Dirae or a Majorana particle, Physicists from the Institute of Theoretical and Experimental Physics (ITEP, Moscow) have been participating actively in solving this problem. They initiated and pioneered the application of semiconductor detectors manufactured from enriched germanium to searches for the double-beta decay of ⁷⁶Ge. Investigations with ⁷⁶Ge provided the most important results. At present, ITEP physicists are taking active part in four very large projects, GERDA. Majorana, EXO, and NEMO, which are capable of recording 2β0ν decay at a Majorana neutrino mass of 〈m _ν〉 ≈ 10^?2 eV.     

Formation and decay of the compound nucleus studied in the reaction20Ne+27Al

Energy and velocity spectra, angular and mass distributions have been measured for evaporation residue products of the^{20, 22}Ne+²⁷Al system in the energy range ofE _L (²⁰Ne)=51 to 395 MeV and in the angular rangeθ=2° and 30°. Calculations with simple assumptions of the velocity and angular distributions of the evaporation residues are presented and compared to the data. The structure seen in the mass distributions, a competition between α-particle and nucleon evaporation in the deexcitation of the compound nucleus, is described well by calculations with the computer code CASCADE. The evaporation residues exhibit mass distributions varying systematically as a function of the excitation energy. The excitation function of the evaporation residue cross section is compared with theoretical models. At higher incident energies contributions of incomplete momentum transfer (incomplete fusion) are observed. A limitation for complete compound nucleus formation with following light particle evaporation is found.     

On the use of Skyrme forces in self-consistent RPA calculations

Self-consistent random-phase (RPA) calculations including the continuum are presented using Skyrme forces. The density-dependent interpretation of the interaction is favoured as it does not violate the spin stability. A possible density dependence of the momentum-dependent S- and P-interaction is taken into account, which allows one to vary the incompressibility K and the effective mass $\text{m}{}^1\text{/m}$ independently. It is shown by analytic relations that these two quantities are the only degrees of freedom left in the parameterization of this Skyrme force,if the ground-state properties shall be reproduced, except for a still open degree of freedom in the spin exchange parameterization. The Landau parameters are discussed as a function of these degrees of freedom in order to find the best possible particle-hole interaction. Continuum calculations of the 1^?, 2 ⁺ and 3^? states in ¹⁶O are presented and compared with-discretized continuum calculations. It is found that the existing Skyrme forces do not show enough attraction and in addition cause relatively large isospin impurities, in ¹⁶O as well as in ²⁰⁸Pb. The influence of large configuration spaces is discussed. A systematic search for an interaction with a stronger particle-hole interaction is presented which seems to favour interactions with a high effective mass, but a low compression modulus.     

Study of the R meson produced in 13 GeV/cπ+p interactions

The missing mass spectrum opposite the proton in a 750 000 picture exposure, 13 GeV/cπ⁺p bubble chamber experiment, is investigated in two and four pion channels for structures observed or denied by boson spectrometers at the same energy in the reaction π^?p→X^?p.In the four pion final state the R⁺ enhancement is observed clearly and the possibility of multi-component mass structure is considered. Treating the phenomenon as one object, cross sections and branching ratios are derived for intermediate quasi two and three body decay modes (ωπ, ??, A₂π, ?ππ). The signals in the two pion state and for the neutral state produced opposite Δ⁺⁺(1231) are also presented and an elasticity is calculated.     

A study of e+e− pairs in the mass range 11 to 25 GeV/c2 at the CERN intersecting storage rings

A sample of 58e⁺e^? events with an invariant mass greater than 11 GeV/c² produced in pp collisions at a centre-of-mass energy of 62.3 GeV is discussed. The cross sections are presented as a function of the mass and transverse momentum. The electron pairs produced with a mean transverse momentum of 2.50 ± 0.25 GeV/c.     

Cosmology and the large-mass problem of the five-dimensional Kaluza-Klein theory

It is shown that in five-dimensional Kaluza-Klein theories the large-mass problem leads to circulus vitiosus: the huge recent e²/G value produces the large mass problem, which restricts the ratio e²/Gm² to the order of unity, in contradiction with the present 10⁴⁰ value for elementary particles.     

Differential cross sections for the charge exchange process π+p → π0 (π+p) at 8, 16 and 23 GeV/c

The differential cross section $\text{d}\text{σ}\text{d}\text{t′}$ for the charge-exchange process π⁺p → π⁰ (π⁺p) at 8, 16 and 23 GeV/c is presented for several regions of the π⁺p effective mass. It is found that the dip at t′ ≈ 0.6 (GeV/c)² which is observed in the Δ(1236) mass band becomes a less pronounced structure in the higher mass regions. However, while the slope of the $\text{d}\text{σ}\text{d}\text{t′}$ distributions in the near-forward direction decreases strongly with increasing π⁺p mass, there is no evidence that the observed structure moves to higher values of t′ as the π⁺p mass increases. These results are consistent with a Regge-exchange picture where the position of the dip is determined by the exchanged trajectory, but are inconsistent with a simple geometrical picture.     

Potential splitting approach to the three-body coulomb scattering problem

The potential splitting approach is extended to a three-body Coulomb scattering problem. The distorted incident wave is constructed and the driven Schrödinger equation is derived. The full angular momentum representation is used to reduce the dimensionality of the problem. The phase shifts for e⁺?H and e⁺?He⁺ collisions are calculated to illustrate the efficiency of the presented method.     

A Cartesian grid embedded boundary method for hyperbolic conservation laws

We present a second-order Godunov algorithm to solve time-dependent hyperbolic systems of conservation laws on irregular domains. Our approach is based on a formally consistent discretization of the conservation laws on a finite-volume grid obtained from intersecting the domain with a Cartesian grid. We address the small-cell stability problem associated with such methods by hybridizing our conservative discretization with a stable, nonconservative discretization at irregular control volumes, and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation. The resulting method is second-order accurate in L¹ for smooth problems, and is robust in the presence of large-amplitude discontinuities intersecting the irregular boundary.