arXiv subjects
Publications and source records attributed to A. Frank.
Extensions of nuclear supersymmetry are discussed, together with a proposal for new, more stringent and precise tests that probe the susy classification and specific two-particle correlations among supersymmetric partners. The combination of these theoretical and experimental studies may play a unifying role in nuclear phenomena.
We present a design for high energy density laboratory experiments studying the interaction of hypersonic shocks with a large number of inhomogeneities. These ``clumpy'' flows are relevant to a wide variety of astrophysical environments including the evolution of molecular clouds, outflows from young stars, Planetary Nebulae and Active Galactic Nuclei. The experiment consists of a strong shock (driven by a pulsed power machine or a high intensity laser) impinging on a region of randomly placed plastic rods. We discuss the goals of the specific design and how they are met by specific choices of target components. An adaptive mesh refinement hydrodynamic code is used to analyze the design and establish a predictive baseline for the experiments. The simulations confirm the effectiveness of the design in terms of articulating the differences between shocks propagating through smooth and clumpy environments. In particular, we find significant differences between the shock propagation speeds in a clumpy medium compared to a smooth one with the same average density. The simulation results are of general interest for foams in both inertial confinement fusion and laboratory astrophysics studies. Our results highlight the danger of using average properties of inhomogeneous astrophysical environments when comparing timescales for critical processes such as shock crossing and gravitational collapse times.
New experimental tests of nuclear supersymmetry are suggested. They involve the measurement of one- and two-nucleon transfer reactions between nuclei that belong to the same supermultiplet. These reactions provide a direct test of the `fermionic' sector, i.e. of the operators that change a boson into a fermion or vice versa. We present some theoretical predictions for the supersymmetric quartet of nuclei: 194Pt, 195Pt, 195Au and 196Au.
A systematic study of isotope chains in the rare--earth region is presented. For the chains (144-154)Nd, (146-160)Sm, (148-162)Gd, and (150-166)Dy, energy levels, E2 transition rates, and two--neutron separation energies are described by using the most general (up to two--body terms) IBM Hamiltonian. For each isotope chain a general fit is performed in such a way that all parameters but one are kept fixed to describe the whole chain. In this region nuclei evolve from spherical to deformed shapes and a method based on catastrophe theory, in combination with a coherent state analysis to generate the IBM energy surfaces, is used to identify critical phase transition points.
It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one of randomly interacting fermions in a j=7/2 shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. Extensions to more general situations are discussed.
A variable combination of realistic and random two-body interactions allows the study of collective properties, such as the energy spectra and B(E2) transition strengths in 44Ti, 48Cr and 24Mg. It is found that the average energies of the yrast band states maintain the ordering for any degree of randomness, but the B(E2) values lose their quadrupole collectivity when randomness dominates the Hamiltonian. The high probability of the yrast band to be ordered in the presence of pure random forces exhibits the strong correlations between the different members of the band.
Low-lying collective states involving many nucleons interacting by a random ensemble of two-body interactions (TBRE) are investigated in a collective SD-pair subspace, with the collective pairs defined dynamically from the two-nucleon system. It is found that in this truncated pair subspace collective vibrations arise naturally for a general TBRE hamiltonian whereas collective rotations do not. A hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the hamiltonian is key to producing generic collective rotation.
We study the origin of the regular features obtained in numerical studies of the IBM with random interactions, in particular the dominance of L=0 ground states and the occurrence of vibrational and rotational band structures. It is shown that the geometric shapes associated with IBM Hamiltonians play a crucial role in understanding these regular properties. Different regions of the parameter space are associated with definite geometric shapes, such as spherical and deformed shapes and a condensate of quadrupole bosons.
We describe a new mechanism for pulsations in evolved stars: relaxation oscillations driven by a coupling between the luminosity-dependent mass-loss rate and the H fuel abundance in a nuclear-burning shell. When mass loss is included, the outward flow of matter can modulate the flow of fuel into the shell when the stellar luminosity is close to the Eddington luminosity $L_{\rm Edd}$. When the luminosity drops below $L_{\rm Edd}$, the mass outflow declines and the shell is re-supplied with fuel. This process can be repetitive. We demonstrate the existence of such oscillations and discuss the dependence of the results on the stellar parameters. In particular, we show that the oscillation period scales specifically with the mass of the H-burning relaxation shell (HBRS), defined as the part of the H-burning shell above the minimum radius at which the luminosity from below first exceeds the Eddington threshold at the onset of the mass loss phase. For a stellar mass $M_*\sim 0.7\Msun$, luminosity $L_*\sim 10^4\Lsun$, and mass loss rate $|\dot M|\sim 10^{-5}\Msun$ yr$^{-1}$, the oscillations have a recurrence time $\sim 1400$ years $\sim 57τ_{\rm fsm}$, where $τ_{\rm fsm}$ is the timescale for modulation of the fuel supply in the HBRS by the varying mass-loss rate. This period agrees with the $\sim$ 1400-year period inferred for the spacings between the shells surrounding some planetary nebulae, and the the predictied shell thickness, of order 0.4 times the spacing, also agrees reasonably well.
An algebraic model based on Lie-algebraic and discrete symmetry techniques is applied to the analysis of thermodynamic vibrational properties of molecules. The local anharmonic effects are described by a Morse-like potential and the corresponding anharmonic bosons are associated with the SU(2) algebra. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation with the specific heat. A physical interpretation of a quantum deformation associated with the model is given.
Powerful, highly collimated jets, surrounded by bipolar molecular outflows, are commonly observed near Young Stellar Objects (YSOs). In the usual theoretical picture of star formation, a jet is ejected from a magnetized accretion disk, with a molecular outflow being driven either by the jet or by a wider wind coming from the disk. Here, we propose an alternative global model for the flows surrounding YSOs. In addition to a central accretion-ejection engine driving the jet, the molecular outflow is powered by the infalling matter and follows a circulation pattern around the central object without necessarily being entrained by a jet. It is shown that the model produces a heated pressure-driven outflow with magneto-centrifugal acceleration and collimation. We report solutions for the three different parts of this self-similar model, i.e. the jet, the infalling envelope and the circulating matter that eventually forms the molecular outflow. This new picture of the accretion/outflow phase provides a possible explanation for several observed properties of YSO outflows. The most relevant ones are the presence of high mass molecular outflows around massive protostars, and a realistic fraction (typically 0.1) of the accretion flow that goes into the jet.
We present two-dimensional, cylindrically symmetric simulations of hydrodynamic and magnetohydrodynamic (MHD) wide-angle winds interacting with a collapsing environment. These simulations have direct relevance to young stellar objects (YSOs). The results may also be of use in the study of collimated outflows from proto-planetary and planetary nebulae. We study a range of wind configurations consistent with asymptotic MHD wind collimation. The degree of collimation is parameterized by the ratio of the wind density at the pole to that of the equator. We find that a toroidal magnetic field can have a significant influence on the resulting outflow, giving rise to a very dense, jet-like flow in the post-shock region. The properties of the flow in this region are similar to the asymptotic state of a collimated MHD wind. We conclude that wide-angle MHD winds are quite likely capable of driving molecular outflows. Due to difficulty in treating MHD winds ab-initio in simulations we choose magnetic field strengths in the wind consistent slow magnetic rotators. While MHD launched winds will be in the fast rotator regime we discuss how our results, which rely on toroidal pinch effects, will hold for stronger field strengths.
The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results that are, to a large extent, obtained in closed analytic form, provide a clear and transparent interpretation of the high degree of order that has been observed in numerical studies.
We consider the stability of an accretion disk wind to cloud formation when subject to a central radiation force. For a vertical launch velocity profile that is Keplerian or flatter and the presence of a significant radiation pressure, the wind flow streamlines cross in a conical layer. We argue that such regions are highly unstable, and are natural sites for supersonic turbulence and, consequently, density compressions. We suggest that combined with thermal instability these will all conspire to produce clouds. Such clouds can exist in dynamical equilibrium, constantly dissipating and reforming. As long as there is an inner truncation radius to the wind, our model emerges with a biconical structure similar to that inferred by Elvis (2000) for the broad line region (BLR) of active galactic nuclei (AGN). Our results may also apply to other disk-wind systems.
We investigate the phenomenom of emerging regular spectral features from random interactions. In particular, we address the dominance of L=0 ground states in the context of the vibron model and the interacting boson model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results that are, partly, obtained in closed analytic form, provide a clear and transparent interpretation of the distribution of ground state angular momenta as observed before in numerical studies.
We review recent results obtained in numerical studies of the nuclear shell model and the interacting boson model with random interactions, in particular the dominance of ground states with L=0 and the occurrence of vibrational and rotational bands. We discuss some possible explanations of the origin of these regular features.
We investigate the origin of the regular features observed in numerical studies of the interacting boson model with random interactions, in particular the dominance of L=0 ground states and the occurrence of vibrational and rotational band structures. It is shown that all of these properties can be interpreted and explained in terms of a Hartree-Bose mean-field analysis, in which different regions of the parameter space are associated with geometric shapes. The same conclusions hold for the vibron model.
A deformation of the harmonic oscillator algebra associated with the Morse potential and the SU(2) algebra is derived using the quantum analogue of the anharmonic oscillator. We use the quantum oscillator algebra or $q$-boson algebra which is a generalisation of the Heisenberg-Weyl algebra obtained by introducing a deformation parameter $q$. Further, we present a new algebraic realization of the $q$-bosons, for the case of $q$ being a root of unity, which corresponds to a periodic structure described by a finite-dimensional representation. We show that this structure represents the symmetry of a linear lattice with periodic boundary conditions.