Self-consistent wave functions,center-of-mass motion and high-energy particle-nucleus scattering

Elastic electron and hadron scattering by ⁴He and ¹⁶O is calculated using for the latter nucleus Brueckner-Hartree-Fock (BHF) wave functions obtained in the harmonic oscillator representation. The effects of the center-of-mass motion spuriosity are estimated.     

Spherical Hartree-Fock calculations with linear-momentum projection before the variation

The hole spectral functions and from these the spectroscopic factors have been calculated in a Galilei-invariant way for the ground-state wave functions resulting from spherical Hartree-Fock calculations with projection onto zero total linear momentum before the variation for the nuclei ⁴He, ¹²C, ¹⁶O, ²⁸Si, ³²S and ⁴⁰Ca. The results are compared to those of the conventional approach which uses the ground states resulting from usual spherical Hartree-Fock calculations subtracting the kinetic energy of the center-of-mass motion before the variation and to the results obtained analytically with oscillator occupations.     

Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei (⁴He and ¹⁶O). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own “Tassie-Barker” factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of ⁴He and ¹⁶O evaluated by using the well-known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.     

单个二能级超冷原子在多个单模腔场间的共振隧穿和光子辐射

考虑单个二能级超冷原子穿过多个空间分离的单模腔场，研究原子质心运动的动能、腔长和腔间距对原子透射率和光子辐射率的影响.在腔间距等于原子质心运动de Broglie波的半波长整数倍时，结果表明，原子透射率和光子辐射率在多腔系统中出现多共振峰结构.这一结果说明，可以通过一系列腔的安排在宏观上实现对超冷原子质心运动波函数的调制. 关键词： 超冷原子 单模腔场 共振隧穿     

On the calculation of densities of light nuclei

For certain classes of wave functions one can calculate the exact expressions of the charge distribution and similar densities. One has to make use of the asymptotic behaviour of these wave functions (whose radial parts have to be of the form \(r^{2k} e^{ - \beta r^2 } \) , in order to obtain a closed form forp(r); the problem is then reduced to the computation of moments, which can be evaluated by a generating function technique. No complications due to a spurious center-of-mass motion do appear. The method is most appropriate for the calculation of densities of refined cluster model functions or translationally invariant shell model functions (both for a nucleon or an alpha-particle shell model) including short-range correlation factors that take care of a soft core in nuclear potentials.     

Diabatic aspects of single-particle motion within the time-dependent Hartree-Fock theory

Time-dependent Hartree-Fock (TDHF) calculations for central collisions of⁸⁶Kr on¹⁶⁶Er are investigated with respect to quasi-stationary properties for various energies in the center-of-mass system. A quasi-stationary potential as well as quasi-stationary single-particle levels are extracted as functions of the relative distance between the two nuclei. A quantitative comparison with the diabatic two-center shell-model yields surprising agreement with the results from TDHF-calculations for both the nucleus-nucleus potential and the single-particle levels. From this we conclude that the approach phase of a nucleus-nucleus collision can be well described within a diabatic approximation for the single-particle motion.     

Double S- and P-wave charmonium production in e+e? annihilation

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $ \sqrt s $ \sqrt s up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy $ \sqrt s $ \sqrt s = 10.6 GeV.     

Annihilation of positronium atoms in an oscillatory field

Annihilation parameters (the angular correlation curve and positronium lifetime) are calculated for annihilation of positronium atoms in a three-dimensional oscillatory well. This well can serve as a model of a positron trap in rigid bodies. The model lends itself to exact mathematical analysis, and it admits separation of variables of the center-of-mass motion and the relative motion of the particle. A calculation is given for the wave functions of a positronium, which oscillatory field. The wave function of the relative motion of the particles at small distances is similar to the wave function of free positronium, which gives us a basis to speak of the annihilation of an electron-positron pair as the annihilation of a positronium atom in an oscillatory field. With a decrease in the size of the trap, broadening of the correlation curve occurs, which has Gaussian form for the annihilation of positronium from the minimum condition for center-of-mass motion. The bound state of the electron and positron exists even in traps of the size of the Bohr radius. The model permits evaluation of the size of traps over an experimentally chosen narrow component of the correlation curve.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 82–87, March, 1989.     

Angle and speed distributions of hydrogen desorbing thermally from metal surfaces

A quantum theoretical treatment of the angle and speed distributions of recombinatively desorbing hydrogen from metal surfaces is proposed. The desorption rate is discussed in the framework of the transition state theory. The recombinative reaction process of hydrogen due to thermal activation leads to the formation of an activated complex in the transition state. In the vicinity of a saddle point on a three-dimensional potential energy surface, the translational motion of the activated complex in the direction perpendicular to the metal surface is accompanied by its center-of-mass vibrational motion parallel to the metal surface. In order to carry out the quantum mechanical calculation, the potential surface is replaced by a simplified model potential, which provides a square potential barrier along the surface normal. It is shown that, on leaving the potential barrier, the activated complex is reflected by the boundary of the potential barrier with a certain probability and, at the same time, the center-of-mass modes of vibration with frequencies v ₁ and v ₂ are coupled with the translational motion along the surface normal. Vibrational wave functions in the momentum representation are used to calculate the transmission coefficient, which is incorporated into the conventional rate formula. The angle-dependent speed distributions of desorbing molecules are derived from the rate formula.     

Construction of one-gluon and one-pion exchange forces in the chiral bag

In the framework of a spherical chiral bag model we use the one-gluon exchange mechanism (inside) and the one-pion exchange (on the surface) to derive an interaction between quarks. In order to apply the force together with two-component (Pauli-spinor) wave functions, which considerably facilitates the elimination of center-of-mass motion, two approximately unitary transformations are performed. The salient features of the derived force are that the relativistic nature is maintained and that quark and gluon confinement is made explicit by force terms originating from the bag boundary conditions.     

A non-relativistic quark model for baryons with pion cloud

We incorporate chiral invariance into a non-relativistic scheme for baryon structure in an approximate way, by introducing additional mesonic degrees of freedom. We proceed to calculate static properties for the nucleon and isobar. Using standard few-body techniques we are able to eliminate center-of-mass spurious motion from the wave functions. In our scheme a D-state admixture arises in the nucleon and isobar wave functions. There are parametrizations compatible with sphericity leading to a strong quenching of the effective quark axial coupling constant. Others lead to deformed ground-state baryons with almost no quenching of the weak-coupling constant.     

Double P-wave charmonium production in e + e − annihilation

On the basis of perturbative QCD and relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of \(\mathcal{P}\) -wave charmonium states. Relativistic factors in the production amplitude are taken into account connected with the relative motion of heavy quarks and the transformation law of the bound-state wave function to the reference frame of the moving \(\mathcal{P}\) -wave mesons. Relativistic corrections to the quark bound-state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially nonrelativistic results of the cross section for the reaction e ⁺ + e ^? → h _c + χ _c J at the center-of-mass energy √s = 10.6 GeV.     

Symmetry violations in nuclear Hamiltonians and their consequences for electroweak decays

We discuss the results of the treatment of nuclear Hamiltonians in terms of collective and intrinsic variables. The BRST method is adapted to identify spurious and physical sectors of the wave functions and operators. Counterterms are added to the Hamiltonian to enforce the symmetries broken by the single-particle field and/or by the residual two-body interactions. We focus on the study of Fermi and Gamow-Teller transitions, with reference to the nuclear double-beta-decay processes, and on the study of vector operators (λ^π = 1^?) with reference to (μ, e^?) conversion processes. We address the following aspects of the problem: (a) Isospin symmetry and the calculation of 0₊ and 1⁺ states; sensitivity of the Fermi and Gamow-Teller response in double-beta-decay processes; (b) Restoration of the translational and Galilean invariance of the nuclear Hamiltonians and the calculation of I^π = 1^? states; sensitivity of the nuclear response to the spurious center-of-mass motion and μ-electron lepton-flavor-violation processes.     

Vibratile Coherence and Squeezing in Two Trapped Ions

It is shown that two trapped ions interacting with laser beams resonant to the first red side-band of center-of-mass mode,in Lamb-Dicke regime and under rotating wave approximation,is described by a Jaynes-Cummings model.For the initial condition that the motional state of center-of-mass mode is in vacuum state and the internal state is prepared in a coherent superposition of states,coherence and squeezing for the vibratile motion of center-of-mass mode are discussed,particularly,a“weak” coherent state and a “weak” squeezed vacuum state are obtained.Collapse and revival are also observed in this type of initial condition.     

Compact and loosely bound structures in light nuclei

The role of various components in the wave function of loosely bound light nuclei is considered in terms of the cluster model by taking into account orbital polarization. We show that several structures corresponding to particular modes of nucleon motion can be concurrently important for such structures. Specific examples of simple and fairly flexible trial wave functions are given for the ⁸Be and ⁶He nuclei. Explicit expressions are derived for the microscopic wave functions of these nuclei and employed to calculate basic nuclear parameters for commonly used central exchange NN potentials.     

Translationally invariant treatment of the charge density in nuclei

An expression is derived for the translationally invariant (transition-) charge density in the center of mass rest frame of the nucleus in between arbitrary wave functions. An explicit formulation is given for the charge density of spherically symmetric Hartree-Fock type ground states. The method is applied to the nuclei⁴He,¹⁶O,⁴⁰Ca and⁹⁰Zr using Woods-Saxon single nucleon orbits for the construction of the ground state wave functions. For the two lighter nuclei in addition realistic Hartree-Fock wave functions are investigated. The results are compared to those obtained with various approximate treatments of the center of mass motion. It turns out that at least in the lighter nuclei the usual center of mass correction, which is based on the assumption of pure non-spurious oscillator configurations and commonly used in the analysis of, e.g., electron scattering data, does not produce reliable (or even predictable) results. Thus here indeed the full translationally invariant treatment seems to be required. For the heavy nucleus⁹⁰Zr on the other hand, as expected, the center of mass effects become negligibly small.     

Measurements of the center-of-mass energies at BESIII via the di-muon process

From 2011 to 2014, the BESIII experiment collected about 5 fb^-1 data at center-of-mass energies around 4 GeV for the studies of the charmonium-like and higher excited charmonium states. By analyzing the di-muon process e⁺e^-→γ_ISR/FSRμ⁺μ^-, the center-of-mass energies of the data samples are measured with a precision of 0.8 MeV. The center-of-mass energy is found to be stable for most of the time during data taking.     

Are quantum wave packets observable? Sokolov effect: puzzling generation of 2p states in the 2s hydrogen beam passing trough a wide metal slit

The observation of excitation of 2p states in a collimated 2s hydrogen beam passing through a wide metal slit with no direct contacts or electric field applied (Sokolov effect) up to now has had no reasonable explanation. A solution presented in this paper is formulated within the standard quantum-mechanical framework with a consecutive wave packet treatment of the atomic center-of-mass wave function. It is found that a very weak interaction of the beam diffraction halo with the slit, though negligible for center-of-mass motion, coherently affects the intrinsic state of an atom in the beam and efficiently induces transitions. High sensitivity of this interference phenomena may be used to measure transverse coherence length of the beam.Received: 25 March 2003, Published online: 15 July 2003PACS: 03.65.-w Quantum mechanics     

Dark soliton in the Bose-Einstein condensates with nonlinearity and harmonic potential managements

The dynamics of dark solitons in one-dimensional Bose-Einstein condensates under the nonlinearity and harmonic potential managements is investigated. It is found that at the large particle limit the macroscopic wave function could evolve self-similarly, which provides a time-varying background for the propagation of dark solitons. The approximate dark soliton solution is derived and its center-of-mass motion is predicted analytically.     

The spreading of the proton of a hydrogen atom in strong magnetic fields

In the problem of a hydrogen atom in a strong magnetic field, the center-of-mass motion and the relative motion of the particles cannot be separated. At very high fields, the transversal wave function both of the electron and of the proton is determined dominantly by the interaction with the magnetic field. The proton spread leads to a substantial reduction of the binding energy.