Survival Mediated Heavy Element Capture Cross Sections

Abstract

Abstract. Formally, the cross section for producing a heavy evaporation residue, σ EVR , in a fusion reaction can be written aswhere E is the center of mass energy, and T is the probability of the colliding nuclei to overcome the potential barrier in the entrance channel and reach the contact point. P CN is the probability that the projectile-target system will evolve from the contact point to the compound nucleus. W sur is the probability that the compound nucleus will decay to produce an evaporation residue rather than fissioning. However, one must remember that the W sur term effectively sets the allowed values of the spin, which in turn, restricts the values of the capture and fusion cross sections. We point out the implications of this fact for capture cross sections for heavy element formation reactions.

Survival-mediated capture and fusion cross sections for heavy-element synthesis

“…As explained in [2], the formalism for calculating the survival, against fission, of a highly excited nucleus is relatively well understood [3]. One starts with a single particle model [4] of the level density in which one allows the level density parameter to be a function of the excitation energy.…”

“…Thus, in the product of terms in equation 1, only those terms with a high survival rate, i.e., low spin, are relevant. We show, in Figure 1, the calculated spin dependence of the capture cross section for the reaction of 3 He + 233 U and the calculated spin dependence of the evaporation residue cross section for the 5n channel [1,2]. The surviving spins are restricted due to angular momentum effects and thus the spin distributions in the capture cross sections are significantly different from those of the evaporation residues.…”

“…formation cross section for 3 He + 233 U. From [1,2] In this paper, we examine the impact of the restrictions on spin placed by the survival probabilities upon the effective capture and fusion cross sections for heavy element formation. By the term "effective " capture cross section, we mean the capture events resulting in non-zero survival probabilities.…”

“…By using a simple formulation of the spin dependence of the capture cross sections and modern calculations of the survival probability of heavy evaporation residues, we attempt to deduce the impact of this spin restriction upon the synthesis of heavy nuclei. A preliminary account of this work has been presented elsewhere [2]. In [2], we introduced the concept of survival mediated cross sections and showed some examples of these effects.…”

“…A preliminary account of this work has been presented elsewhere [2]. In [2], we introduced the concept of survival mediated cross sections and showed some examples of these effects. In this work, we show the full details of the calculations and draw some new conclusions, regarding P CN , from the calculations.…”