Fission-fragment kinetic-energy distributions from a two-dimensional Fokker-Planck equation

Scheuter, F.; Grégoire, C.; Hofmann, Helmut; Nix, J.R.

doi:10.1016/0370-2693(84)90411-8

Cited by 27 publications

(13 citation statements)

References 11 publications

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“…Consideration of the stochastic force in fission dynamics began as early as 1940, when Kramers considered the average delay in establishing a stationary flow rate over a one-dimensional barrier, thus inferring an increase of the fission lifetime due to dissipation [18]. Further approximate treatments of the Fokker-Planck equation in one or two dimensions began around 1980 [19][20][21][22][23]. These calculations often retained the assumption of constant inertia and dissipation, using very simplified potentials.…”

Section: Introductionmentioning

confidence: 99%

Calculated fission-fragment yield systematics in the region74≤Z≤94and90≤N≤150

Möller

Randrup

2015

Phys. Rev. C

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Background: In the seminal experiment by Schmidt et al. [Nucl. Phys. A 665, 221 (2000)] in which fissionfragment charge distributions were obtained for 70 nuclides, asymmetric distributions were seen above nucleon number A ≈ 226 and symmetric below. Because asymmetric fission had often loosely been explained as a preference for the nucleus to always exploit the extra binding of fragments near 132 Sn it was assumed that all systems below A ≈ 226 would fission symmetrically because available isotopes do not have a proton-to-neutron Z/N ratio that allows division into fragments near 132 Sn. But the finding by Andreyev et al. [Phys. Rev. Lett. 105, 252502 (2010)] did not conform to this expectation because the compound system 180 Hg was shown to fission asymmetrically. It was suggested that this was a new type of asymmetric fission, because no strong shell effects occur for any possible fragment division.Purpose: We calculate a reference data base for fission-fragment mass yields for a large region of the nuclear chart comprising 987 nuclides. A particular aim is to establish whether 180 Hg is part of a contiguous region of asymmetric fission and if so its extent, or if, in contrast to the actinides there are scattered smaller groups of nuclei that fission asymmetrically in this area of the nuclear chart. Methods:We use the by now well benchmarked Brownian shape-motion method and perform random walks on the previously calculated five-dimensional potential-energy surfaces. The calculated shell corrections are damped out with energy according to a prescription developed earlier. Results:We have obtained a theoretical reference data base of fission-fragment mass yields for 987 nuclides. These results show an extended region of asymmetric fission with approximate extension 74 ≤ Z ≤ 85 and 100 ≤ N ≤ 120. The calculated yields are highly variable. We show 20 representative plots of these variable features and summarize the main aspects of our results in terms of "nuclear-chart" plots showing calculated degrees of asymmetry versus N and Z.Conclusions: Experimental data in this region are rare: only ten or so yield distributions have been measured, some with very limited statistics. We agree with several measurements with higher statistics. Regions where there might be differences between our calculated results and measurements lie near the calculated transition line between symmetric and asymmetric fission. To draw more definite conclusions about the accuracy of the present implementation of the Brownian shape-motion approach in this region experimental data, with reliable statistics, for a fair number of suitably located additional nuclides are clearly needed. Because the nuclear potential-energy structure is so different in this region compared to the actinide region additional experimental data together with fission theory studies that incorporate additional, dynamical aspects should provide much new insight.

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Section: Introductionmentioning

confidence: 99%

Calculated fission-fragment yield systematics in the region74≤Z≤94and90≤N≤150

Möller

Randrup

2015

Phys. Rev. C

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“…For instance, manifestations of proton pair breaking are observed in 238 U and 239 U nuclei for an excitation energy of 2.3 MeV above the barrier: first the proton odd-even effect observed in the fragment mass distributions decreases exponentially for an excitation energy slightly higher than 2.3 MeV [16] and then the total kinetic energy drops suddenly [17,18]. Some theoretical calculations have studied the dissipation during the fission process, most of them are based on a semi-classical formalism such as Focker-Plank equations [19][20][21], or Hamiltonian equations with one body dissipation and two-body viscosity [22,23], or Langevin equations [24,25]. Here we aim at developing a microscopic non-adiabatic Schrödinger equation, in order to obtain a microscopic description of the coupling between collective and intrinsic excitations.…”

Section: Introductionmentioning

confidence: 99%

Microscopic and nonadiabatic Schrödinger equation derived from the generator coordinate method based on zero- and two-quasiparticle states

et al. 2011

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A new approach called the Schrödinger Collective Intrinsic Model (SCIM) has been developed to achieve a microscopic description of the coupling between collective and intrinsic excitations. The derivation of the SCIM proceeds in two steps. The first step is based on a generalization of the symmetric moment expansion of the equations derived in the framework of the Generator Coordinate Method (GCM), when both Hartree-Fock + BCS (HF+BCS) states and two-quasiparticle excitations are taken into account as basis states. The second step consists in reducing the generalized Hill and Wheeler equation to a simpler form to extract a Schrödinger-like equation. The validity of the approach is discussed by means of results obtained for the overlap kernel between HF+BCS states and two-quasi-particle excitations at different deformations.

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“…Some theoretical calculations have already studied nonadiabatic effects during the fission process, most of them being based on a semi-classical formalism such as FokkerPlank equations [5][6][7], or Hamilton equations with one body dissipation and two-body viscosity [8,9], or Langevin equations [10,11]. In addition, a microscopic approach based on transport theories has recently been proposed by K. Dietrich et al [12].…”

Section: Introductionmentioning

confidence: 99%

First step towards a non-adiabatic description of the fission process based on the Generator Coordinate Method

Bernard

Goutte

Gogny

et al. 2010

EPJ Web of Conferences

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Abstract. Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238 U [1]. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn't seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238 U and 239 U for an excitation energy of 2.3 MeV above the barrier [2][3][4]. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.

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Fission-fragment kinetic-energy distributions from a two-dimensional Fokker-Planck equation

Cited by 27 publications

References 11 publications

Calculated fission-fragment yield systematics in the region74≤Z≤94and90≤N≤150

Calculated fission-fragment yield systematics in the region74≤Z≤94and90≤N≤150

Microscopic and nonadiabatic Schrödinger equation derived from the generator coordinate method based on zero- and two-quasiparticle states

First step towards a non-adiabatic description of the fission process based on the Generator Coordinate Method

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