scholarly journals Structure of double pionic atoms

2021 ◽  
Author(s):  
Akari Tani ◽  
Natsumi Ikeno ◽  
Daisuke Jido ◽  
Hideko Nagahiro ◽  
Hiroyuki Fujioka ◽  
...  
Keyword(s):  
Strong Interaction ◽  
Binding Energies ◽  
Point Of View ◽  
Heavy Nuclei ◽  
Electromagnetic Interactions ◽  
Pionic Atom ◽  
Charged Pions ◽  
Order Of Magnitude ◽  
Pionic Atoms ◽  
Interesting System

Abstract We study theoretically the structure of double pionic atoms, in which two negatively charged pions (π-) are bound in the atomic orbits. The double pionic atom is considered to be an interesting system from the point of view of the multi bosonic systems. In addition, it could be possible to deduce valuable information on the isospin I = 2 π π interaction and the pion-nucleus strong interaction. In this paper, we take into account the π π strong and electromagnetic interactions, and evaluate the effects on the binding energies by perturbation theory for the double pionic atoms in heavy nuclei. We investigate several combinations of two pionic states and find that the order of magnitude of the energy shifts due to the π π interaction is around 10 keV for the strong interaction and around 100 keV for the electromagnetic interaction for the ground states.

RELATIVISTIC NUCLEAR ENERGY DENSITY FUNCTIONALS

2010 ◽  
Vol 19 (04) ◽  
pp. 548-557 ◽  
Author(s):  
D. VRETENAR ◽  
T. NIKŠIĆ ◽  
P. RING
Keyword(s):  
Energy Density ◽  
Degrees Of Freedom ◽  
Nuclear Energy ◽  
Effective Interaction ◽  
Binding Energies ◽  
Large Set ◽  
Density Functionals ◽  
Heavy Nuclei ◽  
Interaction Terms ◽  
Range Dynamics

A class of relativistic nuclear energy density functionals is explored, in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance correlations, as well as intermediate and long-range dynamics, are encoded in the nucleon-density dependence of the strength functionals of an effective interaction Lagrangian. The resulting phenomenological effective interaction, adjusted to experimental binding energies of a large set of axially deformed nuclei, together with a new separable pairing interaction adjusted to reproduce the pairing gap in nuclear matter calculated with the Gogny force, is applied in triaxial relativistic Hartree-Bogoliubov calculations of sequences of heavy nuclei: Th , U , Pu , Cm , Cf , Fm , and No .

Microwave Activation of Homogeneous and Heterogeneous Catalytic Reactions

1997 ◽  
Vol 62 (2) ◽  
pp. 347-354 ◽  
Author(s):  
Milan Hájek
Keyword(s):  
Active Sites ◽  
Specific Effect ◽  
Point Of View ◽  
Heterogeneous Reactions ◽  
Microwave Activation ◽  
Rate Enhancement ◽  
Heterogeneous Catalytic ◽  
Order Of Magnitude ◽  
And Performance ◽  
Alkylation Reactions

Microwave heating was applied in homogeneous and in heterogeneous reactions and the results were compared from the point of view of activation of chemical reactions. Reactions including the addition of halo compounds to alkenes catalyzed by copper and ruthenium complexes in different solvents and NaY zeolite catalyzed alkylation of secondary amine in the absence of solvent were studied as model reactions to compare possibilities of microwave activation of reactants and catalysts. Rate enhancement of over one order of magnitude in homogeneous reactions was caused mainly by thermal dielectric heating effect which resulted from the effective coupling of microwaves to polar solvents. Activation of reactants and catalysts was very low if any. In heterogeneously catalyzed alkylation reactions highly efficient activation of zeolite catalyst was recorded. The results indicated that the best reaction conditions were in experiments when both activation of catalyst and performance of reaction were carried out under microwave conditions. Rate enhancement was most probably caused by "hot spots" or by "selective heating" of active sites. In both homogeneous and heterogeneous reactions non-thermal activation (specific effect) was excluded.

scholarly journals Numerical Simulations of Encounters of Hard Binaries

1985 ◽  
Vol 113 ◽  
pp. 335-338
Author(s):  
Seppo Mikkola
Keyword(s):  
Cross Sections ◽  
Transfer Rate ◽  
Binding Energies ◽  
Body System ◽  
Energy Transfer Rate ◽  
Orbital Elements ◽  
Numerical Integrations ◽  
Order Of Magnitude ◽  
Three Body ◽  
Theory And Experiments

Results from numerical integrations of random binary-binary encounters have been used to obtain various cross-sections and outcome distributions for the four-body scattering. The initial orbital elements were chosen randomly except the Kepler-energies for which various selected values were used. Rough estimates for mass effects were obtained by simulating encounters of binaries with unequal component masses.We developed a semi-analytical theory for obtaining the types and energies of the outcome configurations. The theory contains some adjustable parameters, the values of which we deduced by comparing the theory and experiments.The energy transfer rate by collisions (=outcome is not two binaries) dominates over that due to fly-by's by an order of magnitude, provided that the binaries are hard. The formation of a hierarchical three-body system is fairly common. In a collision of energetically similar very hard binaries the probability is about 20 percent, while it is greater than 50 percent if the binding energies differ by a factor of more than four.

scholarly journals Magnetic HexadecapoleγTransitions and Neutrino-Nuclear Responses in Medium-Heavy Nuclei

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lotta Jokiniemi ◽  
Jouni Suhonen ◽  
Hiroyasu Ejiri
Keyword(s):  
Nuclear Matrix ◽  
Wave Functions ◽  
Matrix Elements ◽  
Heavy Nuclei ◽  
Magnetic Quadrupole ◽  
Order Of Magnitude ◽  
Nuclear Responses ◽  
Beta Decays ◽  
Gamow Teller ◽  
Phonon Model

Neutrino-nuclear responses in the form of squares of nuclear matrix elements, NMEs, are crucial for studies of neutrino-induced processes in nuclei. In this work we investigate magnetic hexadecapole (M4) NMEs in medium-heavy nuclei. The experimentally derived NMEs,MEXP(M4), deduced from observed M4γtransition half-lives are compared with the single-quasiparticle (QP) NMEs,MQP(M4), and the microscopic quasiparticle-phonon model (MQPM) NMEsMMQPM(M4). The experimentally derived M4 NMEs are found to be reduced by a coefficientk≈0.29with respect toMQP(M4) and byk≈0.33with respect toMMQPM(M4). The M4 NMEs are reduced a little by the quasiparticle-phonon correlations of the MQPM wave functions but mainly by other nucleonic and nonnucleonic correlations which are not explicitly included in the MQPM. The found reduction rates are of the same order of magnitude as those for magnetic quadrupoleγtransitions and Gamow-Teller (GT) and spin-dipole (SD)βtransitions. The impacts of the found reduction coefficients on the magnitudes of the NMEs involved in astroneutrino interactions and neutrinoless double beta decays are discussed.

Methode der massenspektroskopischen Dispersionsbestimmung

1953 ◽  
Vol 8 (5) ◽  
pp. 293-305
Author(s):  
Josef Mattauch ◽  
Ludwig Waldmann
Keyword(s):  
Field Strength ◽  
Photographic Plate ◽  
Mass Scale ◽  
Binding Energies ◽  
Mass Spectrometers ◽  
Methods Of Evaluation ◽  
Special Cases ◽  
Order Of Magnitude ◽  
Actual Mass ◽  
The Ideal

Even in the most carefully built mass-spectrograph, one cannot rely on the ideal massscale when measuring isotopic weights with highest precision, as is necessary for the calculation of nuclear binding energies. Instead, the actual mass-scale in the neighbourhood of a “line” of unknown mass (line on a photographic plate or peak of a curve recording voltage, etc.) has to be ascertained with the help of neighbouring lines of known masses simultaneously recorded and measured (dispersion lines). The approximation of the mass-scale and the evaluation of the unknown line can be done in a clear and general way by the use of Lagrange′s method of interpolation (§ 1 and 2). — However, Lagrange′s approximation without any further assumption would not be sufficient if one has at one′s disposal only a few dispersion lines widely separated, as is the case especially in the range of light masses. Here one has to make partial use of the knowledge of the ideal mass-scale; this is outlined in detail for the special cases of one and of two dispersion lines. In certain cases one will have to use up to three dispersion lines (§ 3). — Furthermore, it is not sufficient to ascertain the mass-scale with the help of a set of dispersion lines in a certain range of the plate (or of the voltage, etc.) at a particular value of the field strength of the deflecting magnet (or of a similar parameter) in order to evaluate an unknown line which subsequently has been brought into this range by varying the field strength; because the dispersion of an apparatus depends always slightly on the field strength (f. i. on account of the unavoidable saturation phenomena of the iron). The order of magnitude of this effect has been estimated from experiments (§ 4). — Finally, there is given an account of the ideal mass-scales of all existing mass-spectrographs, including recent precision mass-spectrometers and a discussion of the methods of evaluation used up to the present time (§ 5 and 6).

scholarly journals The nature of the interaction between neutron and proton from scattering experiments

1937 ◽  
Vol 163 (913) ◽  
pp. 281-297 ◽  
Keyword(s):  
Binding Energies ◽  
Energy Curve ◽  
Simple Explanation ◽  
Heavy Nuclei ◽  
Atomic Nuclei ◽  
Nuclear Disintegration ◽  
Wide Range ◽  
Decisive Test ◽  
Spherical Potential ◽  
Positive Results

Although our knowledge of atomic nuclei has expanded greatly in the last few years we are still in the lamentable position of having no certain information concerning the nature of the interaction between neutron and proton. Heisenberg’s suggestion (1932), in the form as modified by Majorana (1933), that this interaction is of an exchange nature has been much used for the discussion of the binding energies of the heavy nuclei. It has the great advantage of providing a simple explanation of the proportionality of nuclear binding energies to the number of nuclear particles, but there is no direct experimental evidence that it is correct. The simplest way in which one can hope to test any assumed form of interaction is from observation of the collisions between neutrons and protons. Unfortunately the relative velocities of the colliding particles which would give the most decisive test are not easily realized in practice, but the recent advances in the technique of nuclear disintegration have provided a source of neutrons of homogeneous velocity which may be used to give results of a higher precision and definiteness than hitherto. It is our purpose in this paper to describe the results to be expected in such experiments on the assumption of either exchange or ordinary forces, for a variety of forms of interaction. The known binding energies of the nuclei H 2 , H 3 , He 3 , He 4 enable us to restrict considerably the magnitude and range of the forces assumed, and we take account of this in all cases. It is found that there is a fair expectation of positive results from accurate experiments on the angular distribution of protons projected by neutrons of 2½ mV energy provided that the form of the interaction does not approach too closely that of the spherical potential “well”, i. e. provided there is an appreciable “tail” to the potential energy curve at large distances of separation. The calculations have not been restricted to neutrons of this particular energy but have been carried out for energies up to 20 mV. This is important in order to examine what conclusions, if any, can be derived from the experiments already carried out with neutrons, having a wide range of velocities.

Monopole and quadrupole strong interaction effects in pionic atoms of 175Lu and 165Ho

1978 ◽  
Vol 296 (3) ◽  
pp. 493-518 ◽  
Author(s):  
P. Ebersold ◽  
B. Aas ◽  
W. Dey ◽  
R. Eichler ◽  
H.J. Leisi ◽  
...  
Keyword(s):  
Strong Interaction ◽  
Interaction Effects ◽  
Pionic Atoms

scholarly journals GENERIC q-MARKOV SEMIGROUPS AND SPEED OF CONVERGENCE OF q-ALGORITHMS

2006 ◽  
Vol 09 (04) ◽  
pp. 567-594 ◽  
Author(s):  
LUIGI ACCARDI ◽  
FRANCO FAGNOLA ◽  
SKANDER HACHICHA
Keyword(s):  
Pure State ◽  
Point Of View ◽  
Convergence To Equilibrium ◽  
Speed Of Convergence ◽  
Markov Semigroups ◽  
Bounded Operators ◽  
Initial State ◽  
Order Of Magnitude ◽  
The Given ◽  
Generic System

We study a special class of generic quantum Markov semigroups, on the algebra of all bounded operators on a Hilbert space [Formula: see text], arising in the stochastic limit of a generic system interacting with a boson–Fock reservoir. This class depends on an orthonormal basis of [Formula: see text]. We obtain a new estimate for the trace distance of a state from a pure state and use this estimate to prove that, under the action of a semigroup of this class, states with finite support with respect to the given basis converge to equilibrium with a speed which is exponential, but with a polynomial correction which makes the convergence increasingly worse as the dimension of the support increases (Theorem 5.1). We interpret the semigroup as an algorithm, its initial state as input and, following Belavkin and Ohya,10 the dimension of the support of a state as a measure of complexity of the input. With this interpretation, the above results mean that the complexity of the input "slows down" the convergence of the algorithm. Even if the convergence is exponential and the slow down the polynomial, the constants involved may be such that the convergence times become unacceptable from a computational standpoint. This suggests that, in the absence of estimates of the constants involved, distinctions such as "exponentially fast" and "polynomially slow" may become meaningless from a constructive point of view. We also show that, for arbitray states, the speed of convergence to equilibrium is controlled by the rate of decoherence and the rate of purification (i.e. of concentration of the probability on a single pure state). We construct examples showing that the order of magnitude of these two decays can be quite different.

Sign in / Sign up

Export Citation Format

Share Document