Zum Drei- und Vierkörperproblem der Kernphysik

The independent pair model has been applied to the nuclear three- and four-body problem. The equations of the model have been solved by a perturbation approach in the case of spin- and charge-independent central two-body forces with hard-core. In lowest order of perturbation theory the nuclear average potential has been approximated by an oscillator potential including an effective mass, the parameters of which were so chosen as to give as nearly a self-consistent potential as possible. For a sqare well two-body interaction the lowest order equations have been solved exactly, the corrections are shown to be small. Some tests for the internal consistency of the approach have been developped and are shown to be well fulfilled by our solutions. According to a proposal byLipkin we succeeded in separating off the energy of the center of mass motion. The results for the binding energy of He⁴(27,9 MeV), the binding energy of H³ (7,1 MeV), the energy difference between H³ and He³ (0,735 MeV) and the RMS-radius of He⁴ (1,75f) are in rather good agreement with experimental results.     

Investigation of α-nucleus interaction in the 27Al (α,α)27Al scattering and 27Al (α, d )29Si reaction

Full finite-range macroscopic calculations in the distorted-wave Born approximation have been performed using the molecular and Michel α-nucleus potentials to analyze the angular distributions of cross-sections of the ²⁷Al(α, d)²⁹Si reaction, at 26.5 and 27.2 MeV incident energies, leading to seven transitions up to the excitation energy E _X = 4.08 MeV of the final nucleus. The parameters of the two types of the α-nucleus potentials are determined from the elastic-scattering data. Both the molecular and Michel potentials, without any adjustment to the parameters needed to fit the elastic-scattering data, are able in most cases to reproduce, simultaneously, the absolute cross-sections particularly at large angles, where the previous calculations failed to reproduce by orders of magnitude, and the gross pattern of angular distributions of the reaction. The deuteron-cluster spectroscopic factors for most of the seven transitions, deduced using the two α-²⁷Al potentials, differ from those obtained in earlier works. The spectroscopic factor for the ground-state transition, deduced in the present work for the 25.8 MeV data, agrees well with the shell model prediction. Received: 15 July 2002 / Accepted: 8 August 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: akbasak2001@Yahoo.com Communicated by G. Orlandini     

The ηHe scattering length revisited

The possible existence of -mesic nuclei poses an interesting and still open issue of research. Since the occurence of such -nucleus bound states is reflected in the corresponding -nucleus scattering length, we critically review the present knowledge for the ³He system. Specifically, we scrutinize the available experimental information for the reaction p + d + ³He which is commonly used to extract the ³He scattering length. We point out several striking discrepancies between the various measurements. Subject to those inconsistencies, we deduce a value a = | 4.3±0.3| + i(0.5±0.5) fm.     

Charged cores in ionized $\mathsf{{^{4}He}}$ clusters III: A quantum modeling for the collisional relaxation dynamics

When a pure ⁴He droplet is ionized by electron impact, the most abundant fragment detected in mass spectra after ionization is He₂ ⁺ . All the models that have been proposed thus far to explain the experimental evidence therefore involve the formation of the He₂ ⁺ molecular ion. The understanding of the interactions between this ion and the surrounding He atoms in the cluster and of their dynamical behavior during cluster break-up is an important element for the modeling of the cluster evolution after the ionization event. In previous works [1,2] we have computed and described the Potential Energy Surface (PES) of the electronic ground state for the He₃ ⁺ system that provides the required forces between He₂ ⁺ and He. After ionization He₂ ⁺ is presumably formed by association of an He ⁺ and any of the neutral atoms in the cluster via a 3-body collision process. The ensuing vibrational quenching of the hot molecular ion may release the energy necessary to evaporate the entire droplet, or most of it, and give the fragmentation patterns detected by experiments. We present here a model quantum dynamics that generates vibrational deexcitation cross-sections and the corresponding rate coefficients for the collision of He₂ ⁺ with He. A timescale of the cluster evaporation due to vibrational relaxation is estimated and the present findings are compared with earlier studies on the same system.Received: 15 June 2004, Published online: 24 August 2004PACS: 31.15.Qg Molecular dynamics and other numerical methods - 34.50.Ez Rotational and vibrational energy transfer - 36.40.Wa Charged clusters     

A three-body model of the <Superscript>11</Superscript>B nucleus

The binding energy and the rms charge and mass radii have been calculated in terms of the single-channel three-body ⁴He⁴He³H model of the ¹¹B nucleus with an expansion of the three-body wave function in a nonorthogonal Gaussian basis. Parameters of the wave function are presented and convergence of the three-body energy depending on the number of expansion terms is demonstrated.     

A macroscopic theory of He3-He4 mixtures

A macroscopic theory of liquid He³-He⁴ mixtures is developed, analogous to the smoothed potential theory ofHeer andDaunt, when the energy spectrum has the generalized formE=Ap ^1/r. Takingr to be a function of atomic volumes of the two isotopes in the mixture, the observed data on the shift of lambda temperature, vapour pressure, heat of mixing etc. is accounted for satisfactorily. A quantitative agreement between the theory and measurements of specific heat, normal fluid density and second sound velocity in mixtures is reached by taking a temperature dependent effective mass of He⁴ particles below the lambda temperature, for which a physical picture is provided. Calculations on second sound velocity show that He³ moves with the same velocity as the normal component of He⁴, which is in agreement with the heat flush experiments.     

Momentum distribution and excitation spectrum of liquid helium

The consistency of recent experimental and theoretical analyses of liquid He⁴ is investigated. Further evidence is found for a strong depletion of the zero momentum state. The modifications of a Brueckner-Sawada type approximation implied by this depletion as well as by the existence of a net attraction of the helium atoms are discussed. It is found that a single particle model which does not allow for a sufficient width in the single particle spectral function is incapable of giving the observed excitation spectrum as well as the binding energy of liquid He. Better results are obtained with a single particle model which usesFeynman's energiesk ²/2ms(k) instead of the peak energy in neutron scattering.     

Calculated rates for the reactionμ −+He3→H3+ν

The effective Hamiltonian ofMorita andFujii is used to calculate the muon capture rate\(\mathfrak{W}_\mu \) in He³. The calculation is done including and omitting the “weak magnetic interaction” and for positive and negative sign of pseudoscalar coupling. The results are related to the known value offt for the beta decay of the triton. The r.m.s. radius of the charge distribution in He³ is taken to be 1·55 fm rsp. 1·85fm. (The first value follows from the results of the variational calculation ofKikuta, Morita, andYamada, the last value is based on a variational calculation for a potential with a long tailed attractive part.) The capture rates differ by 10% for the two r.m.s. radii. Our result forv _r.m.s.= 1·55 fm deviates slightly from the corresponding result ofWerntz.     

Mesonless decay of hypernucleiΛH4 andΛHe4 in a model of the direct conversion of Λ to a neutron

The decay probabilities of the hypernuclei H⁴ and He⁴ are calculated within the framework of the mesonless decay model of hypernuclei with direct conversion of to a neutron. All possible channels are considered: H⁴ tn, d2n, p3n and He⁴ He³n, tp, dd, dpn, 2p2n. Interaction in the final state between the decay products was neglected, but Pauli's principle for the final identical particles was taken into account completely. The predominant decay channels are three- and four-particle paths. The results are compared with experimental data.Translated from Izvestiya VUZ. Fizika, No. 1, pp. 86–94, January, 1972.     

Symmetry transformations in Batalin-Vilkovisky formalism

Let us suppose that the functionalS on an odd symplectic manifold satisfies the quantum master equation e ^s = 0. We prove that in some sense every quantum observable (i.e. every functionH obeying _p (He ^s) = 0) determines a symmetry of the theory with the action functionalS. Research supported in part by NSF grant No. DMS-9201366.     

Average Λ-nucleus potentials

A few model Λ-nucleus potentials are proposed which explain the ground state binding energy data of⁵He and thep-shell hypernuclei satisfactorily. Potential-II is capable of distinguishing the hypernuclei of the same mass number but of differentN andZ values. The dependence of this potential on (N ? Z) term indicates that there is a charge symmetry breaking component in ΛN force. Alongwith the earlier density dependent effective Λ-nucleus interaction, these potentials may be used to determine approximately the density distributions of light nuclei. From these potentials an estimate ofD _Λ is also made. It is found to be in conformity with the earlier estimates.     

Metastable helium cluster He<Stack><Subscript>4</Subscript><Superscript>*</Superscript></Stack>

The existence of a metastable cluster He ₄ ^* with total spin S = 2 is predicted. The cluster consists of two covalently bound excited spin-polarized triplet He ₂ ^* molecules and is rectangular in shape. The electron wavefunctions, the dependence of the energy He ₄ ^* system on the distance between the He ₂ ^* triplet molecules, the atomic spacing, the frequency spectrum of natural oscillations of the cluster, and other characteristics are calculated from first principles. It is shown that the metastable state is formed if one of the excited He ₂ ^* molecules is in the ³Σ _u ⁺ state, while the other is in the ³Π_g state. The radiation lifetime τ of the metastable cluster He ₄ ^* is calculated; it is found to range from 100 to 200 s, which is much longer than the lifetime τ ≈ 20 s of the triplet molecule He ₂ ^* (³Σ _u ⁺ ). The height U ≈ 0.5 eV of the potential barrier preventing the departure from the local energy minimum is determined. The energy E_acc ≈ 9 eV/atom accumulated in the He ₄ ^* cluster is calculated; this energy considerably exceeds the energy of known chemical energy carriers. It is shown that the accumulated energy is released virtually completely during decomposition of the He ₄ ^* cluster into individual helium atoms. This means that helium clusters are a promising material with a high accumulated energy density (HEDM).     

Excited states of the molecular ion (H2μ)+

The rotation-vibration spectrum of (H₂ )⁺ is computed. Radiative lifetimes of the excited states are of order 10^–4 s or more. These times can be considered infinite compared to the lifetime of ⁺. For the ion in a crystal the lifetimes are significantly decreased by interaction with polarized molecules of the lattice. Transition rates to the ground state are calculated for (H₂ )⁺ in a hydrogen crystal. The results make it possible to interpret the experimental data from SR investigations of hydrogen, deuterium and hydrogen-deuterium mixtures.     

Theory of Isotope Effects on He+ Trapping in Solid Hydrogen

We are currently investigating the influence of vibrational effects on the strength of trapping of He⁺ in solid hydrogen. Such effects can lead to an isotope dependence of the trapping energy associated with the hydrogen molecules and He⁺ ion. At the present time, our focus is on the isotope effect for ³He⁺ and ⁴He⁺, which we are studying through the vibrational motions of the trapped He⁺ ions in the potential they experience as they move about their equilibrium positions. The potential governing the vibrations has been obtained from Hartree–Fock cluster calculations of the total energy of the cluster composed of the He⁺ ion and up to the third nearest neighbor hydrogen molecules as a function of the displacement of the He⁺ ion from its trapped position. The energy eigenvalues for the ground vibrational states of ³He⁺ and ⁴He⁺ in this potential come out as 1.29 and 0.96 meV, respectively, leading to corresponding reductions by these amounts in the binding energy of 8.6 eV for both ions without vibrational effects. The difference of these reductions can be considered as an isotope shift, its value for this case being 0.33 meV. From the analysis for these results, it is suggested that isotope shift effects for deuteron and triton in solid D–T would have the same order of magnitude. A procedure for more accurate investigations of the isotope shifts is discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Harmonic maps with defects

Two problems concerning maps with point singularities from a domain C ³ toS ² are solved. The first is to determine the minimum energy of when the location and topological degree of the singularities are prescribed. In the second problem is the unit ball and =g is given on ; we show that the only cases in whichg(x/|x|) minimizes the energy isg=const org(x)=±Rx withR a rotation. Extensions of these problems are also solved, e.g. points are replaced by holes, ³,S ² is replaced by ^N ,S ^N–1 or by ^N , P ^N–1, the latter being appropriate for the theory of liquid crystals.Work partially supported by U.S. National Science Foundation grant PHY 85-15288-A02     

Bag-model inspired nucleon-nucleon potentials and the three-nucleon system

Several examples of short-range energy-dependentN-N potentials derived in the quark-compound-bag (QCB) model are presented. They all satisfy the classical causality condition. We show that for radii of theN-N interactions ofb1.4 fm thes-wave QCB potentials reproduce fairly well the trinucleon binding energy and other three-nucleon observables.     

Generating fields from data onH − ⋃H +andH − ⋃I +

There are series solutions for characteristic boundary value problems for fields on black hole backgrounds that converge when the data are given on =^{– +}, or on =^{– +}, but may not converge when the data are given on ^{– –}, or on ^{+ +}. We specialize to oscillatory data of frequency and calculate approximate reflection and transmission coefficientsR() andT(), using a field generated by data on =^{– +}, and again, using a field generated by data on ^{– –}. The first calculation gives qualitatively good results at all frequencies at each order of approximation, and quantitatively better results at higher orders of approximation; the second calculation, using the series which may not converge, gives bad results except at very high frequencies. Thus for the physically unnatural case of a field that vanishes on ^– and goes toe ^iv on ⁺ we have a series that is convergent, and uniformly so with respect to frequency, while for the natural case of a field that vanishes on ^– and goes toe ^iv on ^– we are limited to high frequencies. It is argued that a frequency-dependent renormalization of a series of the first type provides an approximation scheme that is convergent, and uniformly so with respect to frequency, for the physically important problems of the second type. The difficulties posed by the -dependent renormalization for the study of incident pulses are discussed.     

Solutions to the Boltzmann Equation in the Boussinesq Regime

We consider a gas in a horizontal slab in which the top and bottom walls are kept at different temperatures. The system is described by the Boltzmann equation (BE) with Maxwellian boundary conditions specifying the wall temperatures. We study the behavior of the system when the Knudsen number is small and the temperature difference between the walls as well as the velocity field is of order , while the gravitational force is of order ². We prove that there exists a solution to the BE for which is near a global Maxwellian, and whose moments are close, up to order ², to the density, velocity and temperature obtained from the smooth solution of the Oberbeck–Boussinesq equations assumed to exist for .     

Image-potential surface states on Ag(100): A reinvestigation

Employing inverse photoemission we have remeasured the energy dispersionE(k) of the lowest-lying image state on Ag(100) with improved energy resolution (electrons and photons, E=0.35 eV) andk-resolution (k<0.1 Å^–1). In a least-square fit with the binding energyE _B atk=0 and the effective massm ^* as parameters we obtainE _B =E _vac –0.67 eV andm ^*=1.5 m in agreement with our earlier findings but differing from the two-photon photoemission values (0.53 eV and 1.15 m).     

双力程核子力的讨论

The binding energies of nuclei H³. He³, He⁴, the low energy n-p scattering length and effective range are calculated by using the standard variational methods. A two-range central Yukawa potential is considered in the first two sections. The longer range corresponds to the π meson mass. The smaller range corresponds either to the heavier meson or to the higher order field interactions. No repulsive core appears, when the force parameters are chosen to fit the low energy scattering and deuteron data. The calculated binding energies of nuclei H³, He³ and He⁴ are too high. This result is in agreement with most of the previous calculations. Tensor force of the Schwinger mixed type is considered in the third and fourth sections. The force parameters are chosen to fit the low energy two body data. They are not uniquely determined and are given for a set of possible D-percentage values. The adding of the tensor force reduces considerably the calculated binding energies of nuclei H³, He³, He⁴. But still, the calculated values increase too fast with the mass number. It does not fit the triton and helium binding energies simultaneously. The possibility of adding many body forces is discussed at the end of the paper.