Initial Momentum Distribution Research Articles

X‐Ray Activity in the Open Cluster IC 4665

We present the results of a joint ROSAT High Resolution Imager (HRI) and optical investigation of the open cluster IC 4665. The ROSAT data contains detections for 28 stellar sources in the field, including 22 cluster members and candidate members spanning the color range -0.18 less than or equal to (B - V(sub o)) less than or equal to +1.63 (approx. B3 - M3). Upper limits are given for the remaining members (or candidate members) in the HRI field. Keck HIRES spectra have been obtained that yield radial and rotational velocity measures, respectively, for faint, low mass candidate members located within the field of the ROSAT HRI observation. In addition, photometry of possible optical counterparts to previously uncatalogued X-ray sources in the HRI field is presented. The trends in X-ray properties with (B - V) color in IC 4665 are found to be quite similar to that for other, more nearby young clusters such as the Pleiades and alpha Persei. In particular, a maximum in normalized X-ray luminosity of log (L(sub x)/L(sub bol)) approx. equal 3 is observed, beginning in the color range of (B - V)(sub o) = 0.7 - 0.8. This is similar to the corresponding color range among Pleiades members, in agreement with the earlier estimate, that the age of IC 4665 is similar to the age of the Pleiades. The correlation of rotation and X-ray emission levels is consistent with that in other young clusters. Among the high mass stars in IC 4665, five B stars are detected as X-ray sources. Of these, one is a spectroscopic binary while the remaining objects are apparently single staxs. The level of intrinsic X-ray emission observed in the rapidly rotating (v sini greater than 200 km/ s), single B stars is consistent with an origin due to shock heating of the ambient medium by radiatively driven, rotationally enhanced winds. On the basis of these observations and the results for other clusters, we argue that observed levels of X-ray emission in high mass stars of log (L(sub x)/L(sub bol)) greater than -6.0 are likely due to intrinsic emission associated with the B stax itself rather than emission from a late-type secondary. Finally, our results suggest that the initial angular momentum distributions and the subsequent evolution of rotation, L(sub x), and (L(sub x)/L(sub bol)) occur in practically identical fashions in clusters with ages approx. less than 100 Myr.

Angular-momentum-driven chaos in small clusters

The effects of the rotational motion on the chaotic behavior of triatomic Lennard-Jones clusters are studied. A set of initial momentum distributions with tunable parameters is chosen to correspond to various rigid-body rotations around symmetry axes of the cluster. By smoothly varying the direction of the initial kicks given to the cluster, periodic transitions between regular and chaotic regimes are obtained. A study of initial conditions leading up to such transitions shows that the major factor that determines the extent of the chaotic behavior is the initial partitioning of the kinetic energy between the rotational and vibrational motion. From the analysis of the time evolution of various properties it is concluded that the basic role of this initial partitioning is to control the energy transfer between the kinetic and the potential energy.

Quantum theory of resonant scattering of atoms by a pulsed field under coherent population trapping conditions

We develop an entirely quantum mechanical analytical description of scattering of atoms with angular momenta j g →j→j e =j (j is an integer) by a pulsed σ+−σ− field. In the stationary-atom approximation with exact accounting for recoil effects, we solve the problem of the change in the distribution of atoms among the internal and translational degrees of freedom initiated by a single pulse for j g =1, 2. We find in analytical form recurrence formulas that make it possible to calculate the distribution of the atoms after an arbitrary sequence of pulses has acted on the system. We show that for discrete (resonant) values of the time interval between the pulses, the action of N pulses leads to effective formation and narrowing of peaks at discrete points in momentum space and to a broadening of the envelope of these peaks. In the case of a broad initial momentum distribution we derive explicit formulas for the peaks and the envelope and study their asymptotic behavior for N≫1. Finally, in the weak-field limit we study numerically the dependence of the contrast of the scattering diagram on pulse length.

Momentum-Transfer Dependence of the Near Edge Structure of Li

The dynamic structure factor S ( q , ω) of the K -electrons in Li metal was measured in an inelastic X-ray scattering experiment with 0.8 eV resolution using synchrotron radiation. The near edge structure of S ( q , ω) over an energy range of 30 eV from the edge has been obtained for values of q a of 0.22, 0.38, 1.17 and 1.55, where \(\hbar q\) is the momentum-transfer and a is the K -electron orbital radius. The overall shape of the near edge region changes remarkably with q . On the other hand, the near edge fine structure varies hardly with q and is similar to the soft X-ray absorption near edge fine structure over a wide range of q . This weakly q -dependent fine structure can be attributed to the band structure effecting the final state electron symmetry, while the strongly q -dependent overall shape may be influenced mainly by the initial momentum distribution of the K -electrons.

Classical trajectory study of product state vector correlations: A model for the photodissociation of CF3NO

The photodissociation dynamics of CF3NO are modeled by three-dimensional classical trajectory calculations on the S0 and T1 electronic potential surfaces that include all vibrational and rotational degrees of freedom. The intramolecular potential energy surface for CF3NO was obtained by optimizing parameters in an analytical potential function to best fit spectroscopic data and the results of UMP2/6-31+G* level ab initio calculations. Initial parent molecule energy and angular momentum distributions are computed using a new method that simulates the conditions of molecular beam experiments. The calculations are directed at interpreting experimental measurements of correlated NO product state distributions in the photodissociation of the nitrosoalkanes. The results show that the v–j correlation of NO photofragment is primarily determined by the C–N–O bending force constant and exit channel barrier on the T1 surface.

Quantum theory of cooling of atoms below the one-photon recoil energy by a pulsed field

A completely quantum-analytical description of the cooling of atoms with angular momenta jg=1→je=1 by a pulsed σ1−σ− field is developed. The problem of the change produced in the distribution of the atoms over the internal and translational degrees of freedom by a single field pulse is solved exactly with respect to recoil effects. Recurrence formulas for the distribution after the action of an arbitrary sequence of pulses are found in analytical form. It is shown that N field pulses result in the formation and narrowing of peaks at discrete points in momentum space as well as broadening of the envelope of these peaks. Explicit formulas are obtained for the peaks and envelopes in the case of a wide initial momentum distribution, and their asymptotic behavior for N≫1 is investigated.

Motion-quantized Jaynes-Cummings models with an arbitrary intensity-dependent medium.

The exact time dependence of the density operator and various physical quantities for the motion-quantized Jaynes-Cummings models (MQJCMs) is given using the operator transformation under which it is shown that the MQJCMs have the same dynamics as the ordinary JCMs in the Kerr medium. The quantum collapses and revivals of the atomic motion due to the quantum properties of light fields and the quantization of atomic position and momentum, are predicted. The effects of the initial atomic momentum distribution and the arbitrary intensity-dependent medium on the collapse and revival phenomena of the population inversion, atomic momentum and radiation are formulated in detail. \textcopyright{} 1996 The American Physical Society.

Exact time evolution of the density of a classical many-body system: The open one-dimensional gravitational gas.

We introduce an exact equation for the time evolution of a classical many-body system, and apply it to the one-dimensional gravitational gas. An irreversible approach to a final density distribution is found for a large class of initial momentum distributions, allowing us to introduce the idea of ``semiergodicity.'' \textcopyright{} 1996 The American Physical Society.

Dynamical effects in the population of compound nuclei

Evidence for the influence of reaction dynamics on the population of compound nuclei will be presented. Large dissipation in certain heavy-ion reactions leads to long compound nucleus formation times which can change the initial angular momentum and excitation energy distribution of the compound nucleus. This effect can be observed by measuring high energy γ-rays from the giant dipole resonance. The overall neutron multiplicity, however, is not a sensitive observable. The long formation times might even influence the final spin distribution of evaporation residues, which could possibly explain the entrance channel dependent population of superdeformed bands.

Polarization-gradient-assisted subrecoil cooling: Quantum calculations in one dimension.

We present a fully quantum-mechanical analysis of laser cooling of an angular momentum ${\mathit{J}}_{\mathit{g}}$=1 to ${\mathit{J}}_{\mathit{e}}$=1 transition in a laser configuration consisting of two counterpropagating linearly polarized laser beams. The essential feature of this configuration is the coexistence of velocity-selective coherent population trapping (VSCPT) and polarization-gradient cooling. The role of polarization-gradient cooling is to provide (i) for short interaction times ``precooling'' of the initial momentum distribution and (ii) in the long-time limit ``confinement of velocities.'' This eventually leads to a larger number of atoms being captured in the dark state when compared with the schme of Aspect et al. [Phys. Rev. Lett. 61, 826 (1988)]. We find that the optimum parameter values for polarization-gradient cooling and VSCPT are in a completely different parameter regime: polarization-gradient cooling works best off resonance and for low intensities, while VSCPT works best on resonance. We can combine the advantages of polarization-gradient cooling and VSCPT in a scheme where we cycle in time between the optimum cooling parameters for both cooling mechanisms.

Pionic X-ray intensities per captured negative pion in various elements

Pionic X-ray intensities were measured with Ge spectrometers for various atomic transitions in 30 elements (atomic numbers Z = 3 to 83). The Z-dependence of the pionic X-ray yield in the same transition showed sharp yield maxima in the neighborhood of the Z values of closed atomic shells in addition to the broad maximum expected from competition of radiative transitions with the Auger effect and absorption by strong interaction with the nucleus, respectively. The variation in the X-ray yields with Z could be made plausible in terms of a simple model, in which the initial angular momentum distribution of a captured pion is restricted by the maximum angular momentum deduced from the product of the atomic distance and the maximum linear momentum of the captured pion.

Distortions of the spectra of cumulative mesons by multiscattering in nuclei

The quantitative estimates of multiscattering distortions of momentum spectra for cumulative pions and kaons in p + A → π(K±) + X reaction at angles close to 180° are reported. The calculations for C, Al, Mo, W nuclei were made by using Monte Carlo simulation on the basis of the intranuclear cascade model. The fluctuon model of cumulative particles generation was used to give initial momentum and angular distributions of mesons. Multiscattering on the intranuclear nucleons causes the difference between the initial and observed (distorted by FSI-final state interactions in nuclei) meson spectra, which increases with increasing of atomic number. Due to the rescattering and absorption of pions and kaons by intranuclear nucleons their absolute yields decrease by about 2-5 times in the momentum range p = 0.3-1 GeV/c for medium and heavy nuclei. The relative distortions of the slope parameters of the momentum spectra are 3-10%. The correction of cross sections with account of FSI leads to the amplification of A-dependences for π, K± and to their bringing together. Taking into account FSI is also important when the ratios of particles yield of different types are considered. The K+ /K− -ratio corrections can reach a factor of about 3. Obtained values of distortions effects for cumulative reactions demonstrate evidently the necessity to account of FSI for data obtained in experiments with nuclei at momenta of reaction products <1-2 GeV/c.

Probing of alignment and orientation using electric-dipole-forbidden transitions

The probing of aligned and oriented molecules or atoms by electric quadrupole and magnetic dipole transitions is described using the spherical tensor formalism. The case of cylindrical symmetry is treated explicitly. It is shown how moments of the initial angular momentum distribution up to rank 4 are obtainable using electric quadrupole radiation. The interference between electric quadrupole and magnetic dipole transitions is also treated.

Quantum dynamical calculations for the vibrational predissociation of the He–ICl complex: Product rotational distribution

Three-dimensional quantum close-coupling calculations are presented for the vibrational predissociation of He–ICl B state complexes containing two quanta of ICl vibrational excitation. The dynamics are evaluated for the lowest quasibound van der Waals levels of He–ICl with total angular momentum J=0 and 1. The vibrational predissociation lifetime and final ICl B(v=1, j ) rotational distribution are calculated using the golden rule approximation. The calculated ICl product rotational distributions are broadly bimodal with maxima at j=7 and 15, as experimentally observed. The computed rotational distributions exhibit pronounced oscillations, which are expected to be suppressed when averaged over the initial angular momentum distribution sampled in the experiment. The theoretical analysis points to the dominant role of final-state interactions in determining the rotational distribution of the ICl fragments. The zero-point bending motion of the He–ICl complex and the coupling between the initial and final vibrational states make only small contributions to the final ICl rotational-state distributions. The extensive rotational excitation of the ICl product is primarily due to the anisotropic intermolecular interaction between the separating ICl and He fragments.

Elastic effects on deformation of impulsively loaded elastoplastic beams

Velocity trajectories for simple lumped mass models of an impulsively loaded elastoplastic beam and a cantilever are used to compare rigid-plastic and elastoplastic solutions. Accuracy of a rigid-plastic approximation depends on both the energy ratio R and similarity of the initial momentum distribution to the shape of a stable dynamic plastic mode. For the discrete model of a beam, the region of initial velocities where early elastic effects result in errors of 20% for the rigid-plastic approximation extends to R = 77 for an initial momentum distribution that is close to a plastic mode; this occurs because the beam has multiple stable plastic modes. These modes are “attractors” for the elastoplastic motion and elastic effects can switch convergence from one to another.

Muon capture through bonding electrons in pure silicon.

The muonic x-ray intensities of the Lyman series in pure silicon are investigated. The fitted data are compatible with a statistical initial angular momentum distribution of the captured muons. From a comparison with data measured in diamond, cubic boron nitride and in the two isoelectronic series ${\mathrm{F}}^{\mathrm{\ensuremath{-}}}$,Ne,${\mathrm{Na}}^{+}$ and ${\mathrm{Cl}}^{\mathrm{\ensuremath{-}}}$,Ar,${\mathrm{K}}^{+}$, we conclude that the calculated muon distribution reflects the symmetry of the electrons through which muon capture proceeds.

Yrast feeding and multiplicity of gamma transitions in the reaction 124Sn(28Si, 5n) 147Gd at 139, 146 and 152 MeV

The population of high-spin yrast and near yrast states of 1347 Gd and the associated multiplicity of feeding transitions have been studied in the 124 Sn ( 28 Si, 5n) reaction at 139, 146 and 152 MeV. The yrast feeding is found to be independent of the initial angular momentum distribution and very weak for states of spin greater than 30 ħ. The average multiplicity of γ-transitions is found to increase with increasing beam energy. The experimental results are interpreted in terms of collective excitations within rotational bands that channel the γ- decay towards the known oblate single-particle yrast states below ~30 ħ.

Thermalization of quarks and gluons in heavy-ion collisions.

The thermalization problem in relativistic heavy-ion collisions is considered. The initial momentum distribution of the quarks and gluons in a nucleus-nucleus collision before thermalization takes place is first determined. It is then argued that the relativistic Fokker-Planck equation is the appropriate transport equation to describe the time evolution of the quark-gluon system. In terms of a scaled time variable, the thermalization time is determined without fully solving the Fokker-Planck equation. The actual proper time of local thermalization is then estimated on the basis of some reasonable inputs on the soft interactions among quarks and gluons; the resultant value is of order 0.1 fm/c. The time for global (in rapidity) thermalization is longer.

Wave packet scattering model with quantum friction for heavy-ion collisions

The model reaction 11B + 159Tb at 51 MeV is treated in a quantum mechanical wave packet scattering model and the results are compared with classical trajectory calculations. In the course of evolution of the wave packet, it splits up into well-separated elastic (or quasielastic), deep-inelastic (or direct), and fusion components. Probabilities for these events are deconvoluted with the initial angular momentum distribution and critical and maximum angular momenta as well as fusion, deep-inelastic and reaction cross sections are calculated. The quantum effects tend to soften the sharp l cr, l max values of the classical trajectory model, thus spreading the cross sections over a wider range of l-values, thereby enhancing the deep-inelastic cross section and reducing the fusion cross section.

Corrections to measurements of pion capture ratios

The authors have recently reported measurements of pionic X-rays from some organic molecules (Jackson et al., Phys. Rev. A, vol.25, p.326, 1982), tissues and tissue-equivalent materials (Lewis et al., ibid., vol.27, p.683, 1982). The intensities of the X-ray lines in the Balmer series in carbon and in oxygen were summed to give the C/O pion capture ratios, which showed marked departures from the Fermi-Teller Z-law. The dependence of the capture ratios on molecular structure has raised serious questions about the effect on dose calculations for pion radiotherapy (Lewis et al., 1982, G. Buche private communication) and on the definition of tissue equivalence for pions (Jackson, 1982). It is concluded that the electromagnetic corrections to the C/O pion capture ratios deduced from the summed intensities of pionic Balmer series are small, and much less than the authors experimental errors. The magnitude of the correction due to nuclear absorption depends on the initial angular momentum distribution which in turn depends on molecular structure.