Feynman path integration in phase space

Bonasera, A.; Kondratyev, V. N.

doi:10.1016/0370-2693(94)90632-7

Cited by 27 publications

(44 citation statements)

References 18 publications

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“…1, where the colliding ions at a given beam energy E in the center of mass (CM) system must overcome the Coulomb barrier in order to fuse. In general, the cross section for the sub-barrier fusion at energy E and angular momentum l is given by [20]:…”

Section: Pacs Numbersmentioning

confidence: 99%

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Isospin effects on astrophysicalS-factors

Kimura

Bonasera

2007

Phys. Rev. C

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We estimate the ratios of bare astrophysical S-factors at zero incident energy for proton and deuteron induced reactions in a model which assumes a compound nucleus formation probability plus a statistical decay. The obtained ratios agree well with available experimental values, as far as the reactions which have dominant s-wave entrance channel components are investigated. Due to its simplicity the model could be used as a guidance for predictions on reactions which have not been investigated yet. PACS numbers:The nuclear fusion cross sections of proton and deuteron induced reactions at low energies are of particular interest from the points of view of the stellar nucleosynthesis and the nuclear energy production. These cross sections are measured at laboratory energies and extrapolated to thermal energies [1,2], because of their small values at such low energies. This extrapolation is done by introducing the astrophysical S-factor:where σ(E) is the reaction cross section at the incident center-of-mass energy E and η(E) = Z T Z P α µc 2 2E , Z T , Z P , µ denoting the atomic numbers and the reduced mass of the target and the projectile. α and c are the fine-structure constant and the speed of light, respectively. The exponential term in the equation represents the Coulomb barrier penetrability. Since one has factored out the strong energy dependence of σ(E) due to the barrier penetrability, the S-factor could be approximated by a smooth energy dependence in the absence of low-energy resonance. A lot of effort has been made to extract the S-factor in the low energy region in particular for transfer reactions experimentally [3,4,5,6]. Although to know the low energy S-factor for radiative capture reactions, still one needs the extrapolation with theoretical formulae [7]. Owing to this experimental effort one can, in principle, determine the S-factor in the energy region of astrophysical interest directly. However at such a low energy it is known that electrons around the target nucleus have an effect on the fusion cross section. In contrast, in the stellar nucleosynthesis, nuclei are almost fully ionized and are surrounded by the plasma electrons. The nuclear reactions in such a circumstance are affected by a different mechanism of the plasma electron screening [8,9]. Hence the screening effects of the bound electrons should be removed from the S-factor data, in order to asses the reaction rate in the stellar site correctly. The enhancement by the bound electrons is discussed in terms of a constant potential shift(screening potential U e ) [4,5,10,11,12,13]. * Also at Libera Università Kore di Enna, 94100 Enna, ItalyIn this paper we would like to investigate in detail the physical origins of the bare S-factor. We propose visualizing the fusion mechanism under the assumption of the compound nucleus (CN) formation as a two step process:STEP 1) The nuclear fusion under the Coulomb barrier occurs with a given probability which depends crucially on nuclear effects (the nuclear potential, nuclear sizes, an excitation o...

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Section: Pacs Numbersmentioning

confidence: 99%

“…We point out that T l (E) is not the pure Coulomb penetrability but the penetrability of the Coulomb + centrifugal + nuclear potentials. The tunneling probability T 0 (E) can be written in terms of the action A in the low incident energy limit [20,21]:…”

Section: Pacs Numbersmentioning

confidence: 99%

Isospin effects on astrophysicalS-factors

Kimura

Bonasera

2007

Phys. Rev. C

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“…To a minor extent, the "inverse process" of SF i.e. subbarrier fusion has also stimulated many workers [1,2]. It is the purpose of this letter to suggest a similar problem which involves the quantum N -body features as well as the possibility of critical phenomena.…”

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confidence: 90%

“…The dynamics has been formulated introducing a onedimensional collective degree of freedom which develops in real-and imaginary-time. The method has reproduced well the fusion cross sections, fission kinetic energies of the fission fragments and other observables [2]. The essential point is to introduce collective coordinates which enables us to treat the dynamics in imaginary time.…”

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confidence: 91%

Nuclear fragmentation by tunneling

2001

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Fragmentation of nuclear system by tunneling is discussed in a molecular dynamics simulation coupled with imaginary time method. In this way we obtain informations on the fragmenting systems at low densities and temperatures. These conditions cannot be reached normally (i.e. above the barrier) in nucleus-nucleus or nucleon-nucleus collisions. The price to pay is the small probability of fragmentation by tunneling but we obtain observables which can be a clear signature of such phenomena.For a long time the problem of spontaneous fission has been of large interest for both experimentalists and theorists [1]. In fact spontaneous fission is a nice example of a quantum many body problem. Both the N -particle nature of the system, the atomic nucleus, and the quantum aspect, penetration of a barrier, has stimulated a huge literature production and still the problem is largely unsolved from a quantum mechanical point of view. To a minor extent, the "inverse process" of SF i.e. subbarrier fusion has also stimulated many workers [1,2]. It is the purpose of this letter to suggest a similar problem which involves the quantum N -body features as well as the possibility of critical phenomena.Finite systems might show signatures which are typical of a phase transition. Experiments on fragmentation of atomic nuclei display typical features of a second order, power laws, critical exponents, etc..or a first order phase transition (caloric curve). More recently similar features have been observed in metallic clusters and fullerens [3]. These are systems that in the infinite size limit have an equation of state that resembles a Van Der Waals. Finite size effects smooth divergences which become maxima for some function. Nevertheless careful analysis are able to extract to a good accuracy the values of critical exponents which are very close to the liquid-gas values. The problem of these experiments is that the role of dynamics is dominant [4]. As a consequence it is not possible to prepare the system at all desired excitation energies, densities or temperatures as for a macroscopic system. For instance in heavy ion collisions if the energy of the particle is too low we observe fusion-fission of the two nuclei, while, if too large, fragmentation occurs. Imagine that in some way we have been able to prepare the system at density ρ and temperature T . Because of the compression and/or thermal pressure, the system will expand. If the excitation energy is too low the expansion will come to an halt and the system will shrink back. This is some kind of monopole oscillation. On the other hand if the excitation is very large it will quickly expand and reach a region where the system is unstable and many fragments are formed. It is clear that in the expansion process the initial temperature will also decrease. We could roughly describe this process with a collective coordinate R(t), the radius of the system at time t and its conjugate coordinate. Here we are simply assuming that the expansion is spherical. These coordinates are somewhat the ...

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“…≡ −Ṗ coll , to enter into imaginary time [17]. We follow the time evolution in the tunneling region using the equations…”

Section: Constrained Molecular Dynamicsmentioning

confidence: 99%

Influence of chaos on the fusion enhancement by electron screening

2006

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Abstract. We study the effect of screening by bound electrons in low energy nuclear reactions. We use molecular dynamics to simulate the reactions involving many electrons: D+d, D+D, 3 He+d, 3 He+D, 6 Li+d, 6 Li+D, 7 Li+p, 7 Li+H. Quantum effects corresponding to the Pauli and Heisenberg principles are enforced by constraints in terms of the phase space occupancy. In addition to the well-known adiabatic and sudden limits, we propose a new "dissipative limit" which is expected to be important not only at high energies but in the extremely low energy region. The dissipative limit is associated with the chaotic behavior of the electronic motion. It affects also the magnitude of the enhancement factor. We discuss also numerical experiments using polarized targets. The derived enhancement factors in our simulation are in agreement with those extracted within the R-matrix approach. PACS. 25.45.-z2 H-induced reactions -34.10.+x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.)

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Feynman path integration in phase space

Cited by 27 publications

References 18 publications

Isospin effects on astrophysicalS-factors

Isospin effects on astrophysicalS-factors

Nuclear fragmentation by tunneling

Influence of chaos on the fusion enhancement by electron screening

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