Papers by Vladimir Zelevinsky
Physical Review C, 2001
A method is proposed to improve the treatment of the ground-state correlations in a finite Fermi ... more A method is proposed to improve the treatment of the ground-state correlations in a finite Fermi system compared with the standard random phase approximation ͑RPA͒ or earlier suggested renormalized RPA. The correlations lead to nonzero quasiparticle occupancies in the ground state. The method employs modified quasiparticles obtained by a canonical transformation of usual quasiparticles explicitly involving the quasiparticle occupation numbers. A set of equations is derived, which allows one to determine these occupation numbers along with the RPA modes. The formalism is illustrated with the Lipkin-Meshkov-Glick model, and a model for superconducting pairing at a finite temperature. With the new approach, the ground-state correlations are significantly reduced, the energy of the first excited state becomes closer to the exact solution around the region where the RPA collapses, and the superconducting gap monotonously decreases instead of the sharp phase transition. We discuss the effective equivalence of the interaction effects and variation of temperature for the ground-state correlations.
Physical Review C, 1999
We study the bremsstrahlung radiation of a tunneling charged particle in a time-dependent picture... more We study the bremsstrahlung radiation of a tunneling charged particle in a time-dependent picture. In particular, we treat the case of bremsstrahlung during alpha-decay, which has been suggested as a promissing tool to investigate the problem of tunneling times. We show deviations of the numerical results from the semiclassical estimates. A standard assumption of a preformed particle inside the well leads to sharp high-frequency lines in the bremsstrahlung emission. These lines correspond to "quantum beats" of the internal part of the wavefunction during tunneling arising from the interference of the neighboring resonances in the well. Recent experiments have triggered a great interest in the phenomena of bremsstrahlung during tunneling processes which was discussed from different theoretical viewpoints in . This can shed light on basic and still controversial quantum-mechanical problems of tunneling times [5], especially in a complex and nonstationary environment. It seems that α-decay offers a unique possibility to study these fundamental questions. In ref. [1] it was claimed that the bremsstrahlung spectrum in alpha-decay of 210 Po could provide information about the tunneling time. Their claim is based on the comparison of the experimental spectra with a semiclassical calculation of Dyakonov and Gornyi , which shows an interference pattern arising from the contributions to bremsstrahlung from the inner, under the barrier, and outer parts of the wave function. Papenbrock and Bertsch [3] performed a quantum-mechanical calculation for the bremsstrahlung in α-decay in perturbation theory. They have shown that the contribution from the tunneling wave function under the barrier is small, as well as the appearance of interference effects in the spectrum. The greater effect, as expected, arises from the Coulomb acceleration of the α-particle outside the nuclear well. Later, Takigawa et al. [4] compared the quantum-mechanical calculations with classical and semiclassical results. They conclude that subtle interferences of contributions from different parts of the wave function do indeed arise. However, in both cases, the authors infer that the experimental data are not conclusive. More exclusive experiments, with better statistics, are needed to give a clearer understanding of the phenomena. The theoretical approaches of refs. assume a standard stationary description of quantum tunneling which is very successful for α-decay lifetime and probabilities. However, a time dependent picture of a decay process may be essential in understanding physics of the bremsstrahlung and similar processes, in particular in obtaining the appropriate bremsstrahlung spectrum. This can be shown, for example, by looking into a case where there is no Coulomb acceleration after the tunneling. In this letter we model the time evolution of the wave function during the tunneling using again α-decay as an example. We do not attempt to compare our results with the experimental data. The reason is simple: the α-decay time, e.g., the lifetime of 210 Po, is many orders of magnitude larger than typical times for an α-particle to traverse across the nucleus. This implies that a stable numerical solution of the Schrödinger equation, keeping track simultaneously of fast oscillations in the well ("escape attempts") and extremely slow tunneling, is virtually impossible: for 210 Po it would require about 10 30 time steps in the iteration process. Instead, we study the bremsstrahlung in high energy α-decays, for which the decay time is treatable numerically. This allows us to pay attention to qualitatively new aspects of the bremsstrahlung in decay processes, and compare with traditional aproaches. For an α-particle being accelerated from the turning point to infinity, the classical bremsstrahlung can be calculated analytically. Using the well known equations, see for example , and integrating along the outward branch of the Rutherford trajectory in a head-on collision we get for the energy emitted by bremsstrahlung per frequency interval dω, in the long-wavelength approximation,
EPJ Web of Conferences, 2018
The knowledge of the level density as a function of excitation energy and nuclear spin is necessa... more The knowledge of the level density as a function of excitation energy and nuclear spin is necessary for the description of nuclear reactions and in many applied areas. We discuss the level density problem as a part of the general understanding of mesoscopic systems with strong interactions. The underlying physics is that of quantum chaos and thermalization which allows one to use statistical methods avoiding full diagonalization. The resulting level density is well described by the constant temperature model in agreement with experimental data. We discuss the effective temperature parameter and show that it is not related to the pairing phase transition being analogous to the limiting temperature in particle physics. Other aspects of underlying physics include the collective enhancement of the level density, random coupling of individual spins and the role of incoherent collision-like interactions.
Journal of physics, Jul 3, 2020
We consider time-dependent relaxation of observables in quantum systems of chaotic and regular ty... more We consider time-dependent relaxation of observables in quantum systems of chaotic and regular type. We show that the spread of the wave function in the Hilbert space is determined by the survival probability which is known to have pre-exponential, exponential, and long-term powerlaw limiting behaviors. This result relies on complexity of the wave functions and thus is generic to many systems. In the chaotic limit modeled by the Gaussian Orthogonal Ensemble we show that the survival probability obtained analytically also fully defines the relaxation timescale of observables. This is not the case in general, using realistic nuclear shell model and the quadrupole moment as an observable we demonstrate that the relaxation time is significantly longer than defined by the survival probability of the initial state. An example of the non-chaotic limit of coherent and squeezed states provides an additional illustration.
arXiv (Cornell University), May 30, 1994
The energies and wave functions of stationary many-body states are analyzed to look for the signa... more The energies and wave functions of stationary many-body states are analyzed to look for the signatures of quantum chaos. Shell model calculations with the Wildenthal interaction are performed in the J -T scheme for 12 particles in the sd-shell. The local level statistics are in perfect agreement with the GOE predictions. The analysis of the amplitudes of the eigenvectors in the shell model basis with the aid of the informational entropy and moments of the distribution function shows evidence for local chaos with a localization length reaching 90% of the total dimension in the middle of the spectrum. The degree of chaoticity is sensitive to the the strength of the residual interaction as compared to the single particle energy spacing.
Journal of Physics G: Nuclear and Particle Physics, 2020
This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Al... more This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program ‘From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory’. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to cur...
Nuclear Physics A, 2007
A mechanism is considered for generating doorway states and intermediate structure in low-energy ... more A mechanism is considered for generating doorway states and intermediate structure in low-energy nuclear reactions as a result of collectivization of widths of unstable intrinsic states coupled to common decay channels. At the limit of strong continuum coupling, the segregation of broad ("super-radiating") and narrow ("trapped") states occurs revealing the separation of direct and compound processes. We discuss the conditions for the appearance of intermediate structure in this process and doorways related to certain decay channels.
Moments Method for Shell-Model Level Density
Journal of Physics: Conference Series, 2016
Physics Letters B, 1997
We study the dependence of the total Gamow-Teller strength in an N = 2 nucleus (24Mg> as a functi... more We study the dependence of the total Gamow-Teller strength in an N = 2 nucleus (24Mg> as a function of excitation energy within a complete Ofiw shell-model space (the Odls shell). We find an essentially monotonic increase in strength with increasing excitation energy. We are able to relate this behavior to a decrease in spatial symmetry (increase in SU(4) symmetry) as a function of excitation energy.
Physical Review Letters, 2015
Experimental evidence has recently put the validity of the Porter-Thomas distribution (PTD) for p... more Experimental evidence has recently put the validity of the Porter-Thomas distribution (PTD) for partial neutron widths into question. We identify two terms in the effective Hamiltonian that violate orthogonal invariance (the basis for the PTD). Both are due to the coupling to the decay channels. We show that realistic estimates for the coupling to the neutron channel and for non-statistical gamma decays yield significant modifications of the PTD, similar to the observed ones.
Challenges of Nuclear Structure, 2002
We show and interpret three examples of nontrivial results obtained in numerical simulations of m... more We show and interpret three examples of nontrivial results obtained in numerical simulations of many-body systems: exponential convergence of low-lying energy eigenvalues in the process of progressive truncation of huge shell-model matrices, apparently ordered spectra generated by random interactions, and regular behavior of complex many-body energies in a system with single-particle orbitals in continuum. The possible practical applications and new approaches are suggested.
A brief overview is given of the Continuum Shell Model, a novel approach that extends the traditi... more A brief overview is given of the Continuum Shell Model, a novel approach that extends the traditional nuclear shell model into the domain of unstable nuclei and nuclear reactions. While some of the theoretical aspects, such as role and treatment of one-and two-nucleon continuum states, are discussed more in detail, a special emphasis is made on relation to observed nuclear properties, including definitions of the decay widths and their relation to the cross sections, especially in the cases of non-exponential decay. For the chain of He isotopes we demonstrate the agreement of theoretical results with recent experimental data. We show how the interplay of internal collectivity and coherent coupling to continuum gives rise to the universal mechanism of creating pigmy giant resonances.
Physical Review C, 2014
The decay of a very long-lived state, such as the famous J = 9 -isomeric state in 180 Ta, when ir... more The decay of a very long-lived state, such as the famous J = 9 -isomeric state in 180 Ta, when irradiated by γ rays or subjected to Coulomb excitation, can be accelerated by the existence of a doorway state for mixing an excited state of the isomeric band with the states of other bands decaying to the ground state. We describe the mechanism of such a decay similar to the chaos-assisted tunneling.
Physics of Atomic Nuclei, 2003
Nuclear pairing correlations are known to play an important role in various single-particle and c... more Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson and D. Pines on similarity of nuclear pairing to electron superconductivity, S.T. Belyaev gave a thorough analysis of the manifestations of pairing in complex nuclei. The current revival of interest in nuclear pairing is connected to the shift of modern nuclear physics towards nuclei far from stability; many loosely bound nuclei are particle-stable only due to the pairing. The theoretical methods borrowed from macroscopic superconductivity turn out to be insufficient for finite systems as nuclei, in particular for the cases of weak pairing and proximity of continuum states. We suggest a simple numerical procedure of exact solution of the nuclear pairing problem and discuss the physical features of this complete solution. We show also how the continuum states can be naturally included in the consideration bridging the gap between the structure and reactions. The path from coherent pairing to chaos and thermalization and perspectives of new theoretical approaches based on the full solution of pairing are discussed.
Physics Letters B, 2004
It is suggested that the narrow width of the recently observed resonance Θ + (1540) with strangen... more It is suggested that the narrow width of the recently observed resonance Θ + (1540) with strangeness S = +1 could be a result of the super-radiance mechanism of the redistribution of the widths of overlapping resonances due to their coupling through common decay channels.
Geometric Chaoticity Leads to Ordered Spectra for Randomly Interacting Fermions
Physical Review Letters, 2000
Physical Review Letters, 2005
A new version of the nuclear shell model unifies the consideration of the discrete spectrum, wher... more A new version of the nuclear shell model unifies the consideration of the discrete spectrum, where the results agree with the standard shell model, and continuum. The ingredients of the method are the non-Hermitian effective Hamiltonian, energy-dependent one-body and two-body decay amplitudes, and self-consistent treatment of thresholds. The results for helium and oxygen isotope chains well reproduce the data.
Physical Review Letters, 1995
Generic signatures of quantum chaos found in realistic shell model calculations are compared with... more Generic signatures of quantum chaos found in realistic shell model calculations are compared with thermal statistical equilibrium. We show the similarity of the informational entropy of individual eigenfunctions in the mean field basis to the thermodynamical entropy found from the level density. Mean occupation numbers of single-particle orbitals agree with the Fermi-Dirac distribution despite the strong nucleon interaction.
Physical Review C, 2008
The atomic electric dipole moment (EDM) currently searched by a number of experimental groups req... more The atomic electric dipole moment (EDM) currently searched by a number of experimental groups requires that both parity and time-reversal invariance be violated. According to current theoretical understanding, the EDM is induced by the nuclear Schiff moment. The enhancement of the Schiff moment by the combination of static quadrupole and octupole deformation was predicted earlier. Here we study a further idea of the possible enhancement in the absence of static deformation but in a nuclear system with soft collective vibrations of two types. Both analytical approximation and numerical solution of the simplified problem confirm the presence of the enhancement. We discuss related aspects of nuclear structure which should be studied beyond mean-field and random phase approximations.
Physical Review C, 2002
The properties of the pairing interaction in the shell model framework are considered with the ai... more The properties of the pairing interaction in the shell model framework are considered with the aid of the exact numerical solution utilizing the quasispin symmetry. We emphasize the features which are out of reach for the usual approximate techniques based on the BCS approach supplemented by the random phase approximation treatment of pair vibrations, especially in the region of weak pairing where the BCS+RPA theory fails. For the first time chaotic aspects of the mixing generated by the pairing interaction are studied. The level repulsion and large information entropy of the eigenstates coexist with the absence of thermalization of single-particle motion. The full spectrum of pair vibration in average displays the spin dependence similar to that for a rigid rotor.
Uploads
Papers by Vladimir Zelevinsky