Exact Calculation of the Penetrability Through Two-Peaked Fission Barriers

Cramer, J.D.; Nix, J.R.

doi:10.1103/physrevc.2.1048

Cited by 73 publications

(33 citation statements)

References 18 publications

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“…In this circumstances, it is necessary to use a phenomenological barrier. A phenomenological barrier is conventionally simulated as a function of a dimensionless parameter β, that characterizes a deformation, within three smoothed joined parabolas [28]. In our work, an imaginary component of the potential is added between the turning points of the second well, in order to simulate the damping due to gamma and neutron emission.…”

Section: Cross-sectionmentioning

confidence: 99%

Landau-Zener effect in fission

et al. 2007

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Abstract. The structures observed in the sub-threshold neutron-induced fission of 232 Th were investigated employing a recent developed model. Theoretical singleparticle excitations of a phenomenological two-humped barrier are determined by solving a system of coupled differential equations for the motion along the optimal fission path. A rather good agreement with experimental data was obtained using a small number of independent parameters. It is predicted that the structure at 1.4 and 1.6 MeV is mainly dominated by spin 3/2 partial cross-section with small admixture of spin 1/2, while the structure at 1.7 MeV is given by a large partial cross section of spin 5/2.

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Section: Cross-sectionmentioning

confidence: 99%

Landau-Zener effect in fission

et al. 2007

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“…Hence the isomer shelf cannot be due to an isomer in the 2nd minimum as recently suggested [15]. Here the single and double barrier penetrabilities were calculated with the relations proposed by Hill and Wheeler [16], and Cramer and Nix [17] respectively. If now we suppose that the isomer shelf is due to an isomer in the 3rd minimum, then with (1) and (2) and the barrier parameters given above, we can again reproduce reasonably the experimental isomeric shelf, with E~h ~ 4.6 MeV and the cross section value which is ~1~ compared to that for 23sU, for R~IO -s.…”

Section: 21mentioning

confidence: 99%

The sub-barrier photo-fission and the232Th fission barrier profile

Asghar

1978

Z Physik A

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The 232Th sub-barrier photo-fission data have been analysed in terms of the predicted triple-humped barrier. It is shown that these results and particularly the isomeric shelf seen in these data cannot be explained as being due to the 2nd minimum. However, one can explain these results in terms of the 3rd minimum on the assumptions that Eln (the energy of the 3rd minimum relative to the ground state energy) ~3 MeV instead of Em~4.5 MeV as generally thought and the isomeric state in this well is fed and decays like the heavier actinides with double-humped barriers.The static potential calculations [-1, 2] show that for the light actinides such as Th, the outer barrier of the usual double-humped barrier splits into two barriers of comparable heights separated by a shallow minimum. Gavron et al. [3] have recently reviewed the particle induced sub-barrier fission of 227Ac, 228Ra, 228'231'232'233'234Th and concluded that the observation of narrow sub-barrier resonances in these nuclei indicates the presence of the third shallow minimum (Em~4.5 MeV), (see also Ref. 18). We have analysed the photo-fission data for 2aZTh [4] to see whether or not they are consistent with the triple humped barrier picture. Let us start with a double-humped barrier. The compound nucleus excited by a y-ray of energy E~ to a class-II state in the 2nd minimum will decay partly by direct fission through the outer barrier (prompt fission) and partly by y-decay to the isomeric state in the 2nd well, which will then fission with a certain probability (isomeric fission) determined by the characteristics of two barriers. Bowman [5] showed that the prompt fission cross section (~p,,y) goes down much faster with the decrease of the y-ray energy than the isomeric fission cross section (%,f), and at a certain E~ = Esh (shelf energy) we have %,, z = ai,,, z and below this E~, the az~,: starts to dominate the total photo-fission cross section a~,y. As az~,z varies rather slowly with E~,a~,y(E~) shows a plateau (isomeric shelf) below E~=E~h up to E~.=E n (the minimum of the 2nd well). The experimental photo-fission data on 232Th, 23sU and 237Np show the existence of this isomeric shelf [4,6]. Bowman [5] has given the relations to calculate o-pr ' y and ~i,, r as a function of E 7 in terms of barrier parameters as 8p~, y = 5.92 x 10 3 E~, exp( -1.6 Ey)PA PB(1) and ffi~,.r= 5-04 x (2) where PA and PB are the penetrabilities of the inner and the outer barriers for a given El,; R, the ratio of the fission width of the isomer compared to its decay width. The value of R can be considerably less than one due to 7-decay of the isomeric state towards the first minimum, if the inner barrier is more penetrable than the outer one. Furthermore, it can be shown [5] that for Ppr, f~-ffis, f at E~=E~h, one gets where FYbn and D a 1 are respectively the total 7-decay width and the level spacing for the class-II states in the 2nd well. Now with the experimental barrier parameters [7,8] for 238U (E A ~--5.68 MeV, h o) A = 1.0 MeV, E B = 5.68 MeV PB=R[2g F~blt]

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“…[5][6] numerically by the Adams Moulton predictor-corrector method. The trajectories are computed as time goes on, keeping track of all three particles (the third one is easily done from conservation of momentum), and checking after a long time for the percentage of change in the ct-particle velocity.…”

Section: Dynamics Of the Modelmentioning

confidence: 99%

Monte Carlo studies of alpha-accompanied fission

et al. 1982

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Abstract:To compare with the wealth of new data on alpha-accompanied fission of 236U* we have made new trajectory calculations. Initial conditions for several parameters were selected from Gaussian distributions by the Monte Carlo method and about 15,000 trajectories were run for alpha source at the electrostatic saddle point. Momentum and energy are fully conserved in the three-body problem, though the usual point charge approximation without nuclear forces was used. The main calculations center the alpha source at the electrostatic saddle. General agreement with experiment is remarkable including even the appearance of low-energy secondary peaks at large angles. Effects of shiftingthe source from the saddle point toward either fragment are studied, running an additional 15,000 trajectories for each of two shifts. Both the satellite peak phenomena and the angular distribution indicate the need for a small shift of source toward the light fragment.--Keyword abstract: NUCLEAR REACTIONS. Alpha accompanied thermal neutron ternary fission 235 U(n,f). Monte Carlo theory; trajectory calculations; ct-particle angular --and energy distributions.-2-

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Exact Calculation of the Penetrability Through Two-Peaked Fission Barriers

Cited by 73 publications

References 18 publications

Landau-Zener effect in fission

Landau-Zener effect in fission

The sub-barrier photo-fission and the232Th fission barrier profile

Monte Carlo studies of alpha-accompanied fission

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