Effect of potential-energy-model inaccuracies on predictions of fission-fragment mass distributions based on the Brownian shape-motion method

: Most actinide nuclides fission asymmetrically. A common explanation was that this division benefited from leading to fragments in the vicinity of the doubly magic <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mmultiscripts><a:mi>Sn</a:mi><a:mprescripts/><a:none/><a:mn>132</a:mn></a:mmultiscripts></a:math>. It was tacitly assumed that lighter nuclides would all fission symmetrically because a similar situation could not occur there. However, a weakly asymmetric mass distribution was found for some preactinides at energies about 10 MeV above the fission saddle point by Itkis [Yad. Fiz. , 944 (1990)] and Mulgin []. A more recent experiment by Andreyev performed in June 2008 [Andreyev ] showed a strongly asymmetric mass distribution in fission of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mmultiscripts><b:mi>Hg</b:mi><b:mprescripts/><b:none/><b:mn>180</b:mn></b:mmultiscripts></b:math> at low excitation energies. This gave rise to a new focus on fission properties in the “below Pb” region. Möller and Randrup presented a comprehensive calculation, based on the Brownian shape-motion (BSM) method, of fission-fragment charge distributions [P. Möller and J. Randrup, ] which obtained that “a new region of asymmetry” appeared for approximately <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>95</c:mn><c:mo>≤</c:mo><c:mi>N</c:mi><c:mo>≤</c:mo><c:mn>115</c:mn></c:mrow></c:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>75</d:mn><d:mo>≤</d:mo><d:mi>Z</d:mi><d:mo>≤</d:mo><d:mn>94</d:mn></d:mrow></d:math>. Available experimental results at the time, except for the observation of symmetric fission of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mmultiscripts><e:mi>Ir</e:mi><e:mprescripts/><e:none/><e:mn>187</e:mn></e:mmultiscripts></e:math> by Itkis [Yad. Fiz. , 944 (1990)], agreed with these predictions apart for minor differences in the transition regions between predicted symmetric and asymmetric fission. It was argued [P. Möller and J. Randrup, ] that the inaccurate results for <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mmultiscripts><f:mi>Ir</f:mi><f:mprescripts/><f:none/><f:mn>187</f:mn></f:mmultiscripts></f:math> were related to inaccuracies in the calculated potential-energy surface and that such inaccuracies are related to the (in)accuracies of the calculated ground-state masses for the corresponding mass splits. : We expand on our previous discussion of a possible source of the difference between the experimental and theoretical fission-fragment mass distributions for <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mmultiscripts><g:mi>Ir</g:mi><g:mprescripts/><g:none/><g:mn>187</g:mn></g:mmultiscripts></g:math> and furthermore investigate if such differences may occur for other fissioning nuclides in the below Pb and actinide regions. : It has been shown that all structure in the mass distributions obtained by use of the BSM method is entirely due to the structure of the potential-energy surfaces on which the random walks are executed. Therefore, to understand the discrepancy between the previous theoretical results and the experimental observations for <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mmultiscripts><h:mi>Ir</h:mi><h:mprescripts/><h:none/><h:mn>187</h:mn></h:mmultiscripts></h:math> we focus on the accuracy of the calculated potential-energy surface. : We find that in symmetric fission of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mmultiscripts><i:mi>Ir</i:mi><i:mprescripts/><i:none/><i:mn>187</i:mn></i:mmultiscripts></i:math> the corresponding calculated fragment ground-state masses are too high compared to experiment by about 2.5 MeV each so the scission potential energy is calculated to be too high by 5 MeV. We also find that this is the largest error that can occur for any scission configuration in heavy-element fission. : As earlier we pose that the reason that symmetric fission is not favored in the calculated fission-fragment distribution of <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mmultiscripts><j:mi>Ir</j:mi><j:mprescripts/><j:none/><j:mn>187</j:mn></j:mmultiscripts></j:math> is that the potential-energy surface is overestimated by 5 MeV for symmetric splits. In the calculations a large error for symmetric splits extends only to nuclides a few nucleons beyond <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mmultiscripts><k:mi>Ir</k:mi><k:mprescripts/><k:none/><k:mn>187</k:mn></k:mmultiscripts></k:math> and does not occur elsewhere. Therefore, to test this hypothesis of the origin of the discrepancy, it is of interest to map out in experiments how far this region of symmetric fission “within the predicted region of asymmetry” extends and if substantial discrepancies occur elsewhere.