Mass dispersion through particle emission from a vibrating nucleus

Troudet, T.; Vautherin, D.

doi:10.1103/physrevc.31.278

Cited by 16 publications

(17 citation statements)

References 4 publications

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“…[252]. The BV approach has been used in the past to study mass dispersion from giant resonance decay [253][254][255] as well as to compute the fluctuation of the particle number in fragments produced in deep-inelastic collisions [11,229,251,252,255,256]. This approach was also used to study hot Fermi gas [257], φ 4 theory [258], and Boson systems [259][260][261].…”

Section: Time-dependent Random Phase Approximationmentioning

confidence: 99%

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions

Simenel

Umar

2018

Progress in Particle and Nuclear Physics

168

103

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Microscopic methods and tools to describe nuclear dynamics have considerably been improved in the past few years. They are based on the time-dependent Hartree-Fock (TDHF) theory and its extensions to include pairing correlations and quantum fluctuations. The TDHF theory is the lowest level of approximation of a range of methods to solve the quantum many-body problem, showing its universality to describe manyfermion dynamics at the mean-field level. The range of applications of TDHF to describe realistic systems allowing for detailed comparisons with experiment has considerably increased. For instance, TDHF is now commonly used to investigate fusion, multi-nucleon transfer and quasi-fission reactions. Thanks to the inclusion of pairing correlations, it has also recently led to breakthroughs in our description of the saddle to scission evolution, and, in particular, the non-adiabatic effects near scission. Beyond mean-field approaches such as the time-dependent random-phase approximation (TDRPA) and stochastic meanfield methods have reached the point where they can be used for realistic applications. We review recent progresses in both techniques and applications to heavy-ion collision and fission. Introduction: nuclear quantum many-body dynamicsThe quantum many-body problem is vital to many areas of physics. Indeed, the description of complex quantum objects of interacting particles is of interests for many physical systems, from quarks and gluons in a nucleon to macromolecules, such as fullerenes, to Bose-Einstein condensates. Consequently, major developments in the description of quantum many-body systems are often of interest to many different fields. For instance, the BCS theory introduced to describe superconductivity [1] is also widely used in nuclear physics to incorporate the effect of pairing correlations. Similarly, the tools used to study low-energy fusion with multi-channel tunneling [2] are also used to describe dissociative adsorption of molecules on a surface [3].The similarity between dynamical processes in quantum many-body systems, whether their constituents are nucleons, electrons, or atoms, is quite striking. It is possible to make such systems vibrate, rotate, fuse, transfer particles, fission and break up. This is of course true for nuclear systems, where each of these processes can be used to learn about specific aspects of quantum many-body dynamics. For instance, the study of nuclear vibrations tells us how single-particles can produce collective motion, what is its interplay with the underlying shell structure, what are the source of non-linearities leading to anharmonicities, and how collective modes get damped and decay. These concepts and many others can also be studied via heavy-ion collisions:1 In the case of a time-independent Hamiltonian, we haveF H (t) = e iĤt/ F e −iĤt/ . 2 Of course, nucleons are indistinguishable fermions and there is no guarantee that the nucleon which is annihilated is the same as the one which is created. In fact, the question of "which one" is created or a...

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Section: Time-dependent Random Phase Approximationmentioning

confidence: 99%

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions

Simenel

Umar

2018

Progress in Particle and Nuclear Physics

168

103

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“…However, it can be solved exactly for simple cases only. The Balian-Vénéroni (BV) variational principle [2] offers an elegant starting point to build approximations of the many-body dynamics and has been applied to different problems in nuclear physics [3][4][5][6][7][8], hot Fermi gas [9], φ 4 theory [10], and Boson systems [11,12]. In particular, applications to deep-inelastic collisions (DIC) of atomic nuclei should be of interests to the upcoming exotic beam facilities.…”

mentioning

confidence: 99%

Particle-Number Fluctuations and Correlations in Transfer Reactions Obtained Using the Balian-Vénéroni Variational Principle

2011

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The Balian-Vénéroni (BV) variational principle, which optimizes the evolution of the state according to the relevant observable in a given variational space, is used at the mean-field level to determine the particle number fluctuations in fragments of many-body systems. For fermions, the numerical evaluation of such fluctuations requires the use of a time-dependent Hartree-Fock (TDHF) code. Proton, neutron and total nucleon number fluctuations in fragments produced in collisions of two 40 Ca are computed for a large range of angular momenta at a center of mass energy Ec.m. = 128 MeV, well above the fusion barrier. For deep-inelastic collisions, the fluctuations calculated from the BV variational principle are much larger than standard TDHF results, and closer to mass and charge experimental fluctuations. For the first time, correlations between proton and neutron numbers are determined within a quantum microscopic approach. These correlations are shown to be larger with exotic systems where charge equilibration occurs.The quantum many-body problem is the root of many theoretical fields aiming at describing interacting particles such as electrons in metals, molecules, atomic clusters, Bose-Einstein condensates, or atomic nuclei [1]. However, it can be solved exactly for simple cases only. The Balian-Vénéroni (BV) variational principle [2] offers an elegant starting point to build approximations of the many-body dynamics and has been applied to different problems in nuclear physics [3][4][5][6][7][8], hot Fermi gas [9], φ 4 theory [10], and Boson systems [11,12]. In particular, applications to deep-inelastic collisions (DIC) of atomic nuclei should be of interests to the upcoming exotic beam facilities. DIC will be used to investigate the role of the isospin degree of freedom in reactions and to extract the density dependence of the symmetry energy. Such reactions will produce nuclei in extreme, sometimes unknown, states (e.g., rotating nuclei with a neutron skin, or nuclei at or beyond the drip-lines).Assuming an initial density matrixD 0 at t 0 , The BV variational principle optimizes the expectation value of an observable Q = Tr(DQ) at a later time t 1 . In this approach, both the stateD(t) and the observableQ(t) vary between t 0 and t 1 within their respective variational spaces. In most practical applications, mean-field models are considered in a first approximation, and, eventually, serve as a basis for beyond-mean-field approaches [13,14]. For instance, restricting the variational space ofD(t) to pure independent particle states, and the one ofQ(t) to one-body operators, leads to the TDHF equation [15] ih ∂ρwhere ρ is the one-body density-matrix and h[ρ] is the Hartree-Fock (HF) single-particle Hamiltonian. According to this variational approach, TDHF is, then, the best mean-field theory to describe expectation values of onebody observables. However, it should not be used, in principle, to determine their fluctuations and correlations σ XY = XŶ − X Ŷ , (X andŶ are one-body operators, and fluctuations corre...

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“…(4.29) has been applied to heavy ion collisions in the special case when t = t and ρ 2 0 = ρ 0 . These computations [13][14][15], which led to a better agreement with experiment, have revealed the importance of the corrections introduced by the present method.…”

Section: Resultsmentioning

confidence: 81%

Variational approach to multi-time correlation functions

Balian¹,

Vénéroni²

1993

Nuclear Physics B

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URL: http://www-spht.cea.fr/articles/T93/030International audienceA variational method is proposed to evaluate the generating functional $ \varphi $ which gives the multi-time correlation functions in equilibrium and non-equilibrium statistical mechanics or field theories. Its definition, $ \varphi = {\rm ln\ Tr} \ D\ A, $ involves the density operator $ D $ describing the initial state and an operator $ A $ depending on the observables of interest (in the Heisenberg picture), on the associated time-dependent sources and on the initial time. Regarded as function of this time, $ A $ is specified by a simple differential equation with the time running backward. Lagrangian multipliers are introduced to account both for this equation and for the one which characterizes $ D. $ Through this procedure $ \varphi $ is obtained as the stationary value of a functional depending on state-like and observable-like trial operators, with a complex time. Within a trial subspace, the resulting approximation optimizes both the initial state and the dynamics. The example of interacting fermions in many-body physics is worked out by restricting the trial objects to exponentials of single-particle operators. This leads to an extended mean-field approximation for the generating functional associated with any set of observables. Expansion in powers of the sources provides a variational approximation for the two-time causal or response functions. The result incorporates both the static and dynamic Hartree-Fock equations as well as the associated RPA equations. It is free of several inconsistencies occurring in the conventional mean-field approximations. ----- Les auteurs proposent une méthode variationnelle très souple pour évaluer la fonction génératrice des fonctions de corrélations d'observables arbitraires dans un système de mécanique quantique général, où l'état initial est une matrice densité arbitraire. L'un des aspects originaux est d'envisager la dépendance des quantités dans la variable temporelle où sont identifiées les représentations de Schrödinger et de Heisenberg. Les données et les équations du mouvement sont traitées comme des contraintes dans ce formalisme en introduisant des multiplicateurs de Lagrange appropriés. Les auteurs présentent à titre d'application l'exemple d'un système de fermions en interaction et trouvent des généralisations des diverses méthodes de champ moyen, statique ou dynamique (approximation de Hartree-Fock stationnaire ou dépendant du temps, méthode des phases aléatoires...). Ils montrent que leur nouvelle théorie est plus cohérente que celles envisagées jusqu'ici. \vskip 20mm \hfill{C. Itzykson

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Mass dispersion through particle emission from a vibrating nucleus

Cited by 16 publications

References 4 publications

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions

Heavy-ion collisions and fission dynamics with the time-dependent Hartree–Fock theory and its extensions

Particle-Number Fluctuations and Correlations in Transfer Reactions Obtained Using the Balian-Vénéroni Variational Principle

Variational approach to multi-time correlation functions

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