Scission-point Model Research Articles

Nuclear-charge distribution forA=121from thermal-neutron-induced fission ofU235

The fractional cumulative yield of $^{121}\mathrm{Ag}$ and the fractional independent yields of $^{121}\mathrm{Cd}$, $^{121}\mathrm{In}$, and $^{121}\mathrm{Sn}$ from thermal-neutron-induced fission of $^{235}\mathrm{U}$ were determined radiochemically to be 0.12\ifmmode\pm\else\textpm\fi{}0.05, 0.61\ifmmode\pm\else\textpm\fi{}0.09, 0.24\ifmmode\pm\else\textpm\fi{}0.08, and 0.03\ifmmode\pm\else\textpm\fi{}0.04, respectively. The yield values were used to determine the nuclear-charge-distribution parameters ${\ensuremath{\sigma}}_{Z}$=0.55\ifmmode\pm\else\textpm\fi{}0.10 and \ensuremath{\Delta}Z=0.50\ifmmode\pm\else\textpm\fi{}0.05 for A=121. The ${\ensuremath{\sigma}}_{Z}$ for A=121 is close to ${\ensuremath{\sigma}}_{Z}$\ifmmode\bar\else\textasciimacron\fi{}=0.52\ifmmode\pm\else\textpm\fi{}0.02 for high-yield fission products, and no evidence for an even-odd Z effect was found for A=121. The positive \ensuremath{\Delta}Z value, which corresponds to ${Z}_{P}$=48.15, is similar to those for several higher mass numbers reported previously, and it is considerably greater than the negative values predicted by the scission-point theoretical model. The use of a separation distance between nascent fragments greater than 1.4 fm, the value used in the theoretical calculations, could reduce the discrepancy and could also account for the observed enhanced independent yields of tin fission products with ${Z}_{P}$ near 50 (A=126--129).

Mass and kinetic energy distributions in near-barrier fission ofW182

Mass and kinetic energy distributions have been measured for the fission of /sup 182/W at an excitation energy above the fission barrier E(-E/sub f/roughly-equal20 MeV. A primary motivation for these studies was to search for evidence of asymmetric mass division and anomalously low total kinetic energy release, as predicted by scission-point model calculations which include deformed (Strutinsky) shell effects. Double kinetic energy measurements of coincident fission fragments were performed, from which fragment mass distributions were derived. From the data it is concluded that at this excitation energy, liquid-drop behavior dominates the fission of /sup 182/W and any shell strength, if present, is less than 20 percent of full strength.

Comparison of the energy and mass characteristics of thePu239(nth,f)and thePu240(sf) fragments

The energy and mass distributions and their correlations have been studied for the spontaneous fission of $^{240}\mathrm{Pu}$ and the thermal neutron induced fission of $^{239}\mathrm{Pu}$. A comparison of the $^{240}\mathrm{Pu}$(sf) and the $^{239}\mathrm{Pu}({\mathrm{n}}_{\mathrm{th}},f)$ results shows a narrower mass distribution, a much higher peak yield, a much lower symmetric fission yield, and a more pronounced fine structure for the spontaneous fission than for the neutron induced fission. The average total kinetic energy is 1.3 MeV higher for $^{240}\mathrm{Pu}$(sf) than for $^{239}\mathrm{Pu}({\mathrm{n}}_{\mathrm{th}},f)$, and also the energy-mass correlations behave differently in both cases. All these results are discussed and interpreted in the framework of the scission point model of Wilkins et al. Finally, the damping of the $^{240}\mathrm{Pu}$ fission mode below the barrier is demonstrated.

Fragment mass and kinetic energy distributions forPu242(sf),Pu241(nth,f), andPu242(γ,f)

Energy correlation measurements were performed for the spontaneous fission of /sup 242/Pu, the thermal-neutron-induced fission of /sup 241/Pu, and the photofission of /sup 242/Pu with 12-, 15-, 20-, and 30-MeV bremsstrahlung. The photofission cross section for /sup 242/Pu was determined up to 30 MeV. For /sup 242/Pu(sf) the overall kinetic energy distribution is strongly asymmetric and the overall mass distribution has a very high peak yield (9%). Important deviations of the average total kinetic energy release and the average light and heavy fragment masses and from the systematics of Unik et al. are also observed for this fissioning system. These effects can be explained in the framework of the static scission point model by the strong preferential formation of a shell-stabilized scission configuration with the neutron number of the heavy and light fragments in the vicinity of the spherical N = 82 neutron shell and the deformed N = 66 neutron shell, respectively. A decrease of with the average excitation energy , d/d = -0.30 +- 0.04, is observed in the photofission of /sup 242/Pu.

Effects of large angular momenta on the fission properties of Pt isotopes

The effects of large angular momenta on the fission properties of Pt isotopes are studied. Fissioning Pt systems were produced in fusion reactions of /sup 16/O+/sup 170/Yb and /sup 32/S+/sup 114,150,,152,154/Sm in the energy range of 0.8--2.0 times the fusion barrier. The sub-barrier fusion-fission cross sections show a strong dependence on the target deformation. A pronounced increase in a simple model calculation in the total kinetic energy release with bombarding energy is accounted for by the increasing contribution of centrifugal energy. The widths of the mass and kinetic energy distributions increase rapidly with the angular momentum of the fissioning system. This effect is not accounted for by simple scission point model calculations.

Nuclear temperature effects in the scission-point model of nuclear fission

According to the scission-point model, the probability for a particular fission event can be expressed in terms of the collective potential and the collective kinetic energy at the scission point. Two additional assumptions make the scission-point model an easily calculable model: the assumption of equal collective kinetic energies for constant distances $d$ between the tips of the fragments, and the assumption that one is able to characterize the excitation energy of the fragments with a nuclear temperature $T$, independent of both the mass ratio and the charge ratio, and of the deformations of the fragments. It is pointed out that the latter assumption violates energy conservation. A modified, recursive procedure is proposed, resulting in an "energy conservation consistent" scission-point method. Mass and charge distributions for the fission of $^{235}\mathrm{U}$ and $^{252}\mathrm{Cf}$ compound systems have been calculated and compared with distributions following the "standard" scission-point method of Wilkins, Steinberg, and Chasman.NUCLEAR REACTIONS Scission-point model. Collective potential and intrinsic excitation energy. Nuclear temperature $T$. Mass and charge distributions. Fission of $^{235}\mathrm{U}$ and $^{252}\mathrm{C}$.

Kinetic energy distributions around symmetric thermal fission of U234 and U236

The kinetic energy distributions have been measured at LOHENGRIN for symmetric fission of U234 and U236. The pre-neutron emission values for the average total kinetic energy and its rms width have been deduced using a Monte Carlo simulation for neutron evaporation. The total kinetic energy dip between symmetric and asymmetric divisions is 24 MeV for U234 and 29 MeV for U236. A strong peak in the initial rms width has been observed for masses 111–123 in U234 and for 111–125 in U236. A static scission point model is used to understand the origin of these features.

Energy and mass distributions for 241Pu(n th, f), 242Pu(s.f.) and 244Pu(s.f.) fragments

The energy and mass distributions and their correlations have been studied for the spontaneous fission of 242Pu and 244Pu and for the thermal-neutron induced fission of 241Pu. A comparison of the 242Pu(s.f.) and the 241Pu(n th, f) results shows a narrower mass distribution, a much higher peak yield and a more pronounced fine structure for the spontaneous fission than for the neutron induced fission. The average total kinetic energy is higher for 242Pu(s.f.) than for 241Pu(n th, f), and also the energy-mass correlations behave differently in both cases. The 244Pu(s.f.) data are very similar to these for 242Pu(s.f.). All these results are discussed and interpreted in the frame of the scission point model of Wilkins et al.

Kinetic energy and fragment mass distributions forPu240(s.f.),Pu239(nth,f), andPu240(γ,f)

Energy correlation measurements were performed for $^{240}\mathrm{Pu}$(s.f.), $^{239}\mathrm{Pu}({n}_{\mathrm{th}},f)$, and the photofission of $^{240}\mathrm{Pu}$ with 12-, 15-, 20-, and 30-MeV bremsstrahlung. The photofission cross section for $^{240}\mathrm{Pu}$ was determined up to 30 MeV, which permitted the calculation of the average excitation energy $〈{E}_{\mathrm{exc}}〉$ of the compound nucleus. The average total kinetic energy $〈{E}_{k}〉$ of the fragments for $^{240}\mathrm{Pu}$(s.f.) was found to be 1.2\ifmmode\pm\else\textpm\fi{}0.5 MeV higher than for $^{239}\mathrm{Pu}({n}_{\mathrm{th}},f)$. A decrease of $〈{E}_{k}〉$, with $〈{E}_{\mathrm{exc}}〉$, $\frac{d〈{E}_{k}〉}{d〈{E}_{\mathrm{exc}}〉}=\ensuremath{-}0.37\ifmmode\pm\else\textpm\fi{}0.08$, is observed in the photofission of $^{240}\mathrm{Pu}$. Fragment shell effects are present in the kinetic energy and mass distributions for $^{240}\mathrm{Pu}$(s.f.). Changes in the measured distributions with increasing excitation energy of the compound nucleus $^{240}\mathrm{Pu}$ are discussed in the framework of the scission point model of Wilkins et al.RADIOACTIVITY Fission $^{240}\mathrm{Pu}$(s.f.). NUCLEAR REACTIONS Fission $^{239}\mathrm{Pu}({n}_{\mathrm{th}},f)$, $^{240}\mathrm{Pu}(\ensuremath{\gamma},f)$, ${E}_{{\ensuremath{\gamma}}_{max}}=12, 15, 20, 30$ MeV; measured: photofission yields, fragment energies ${E}_{1}$, ${E}_{2}$; deduced: $\ensuremath{\sigma}(\ensuremath{\gamma},f)$, $\frac{N(\ensuremath{\mu},{E}_{k})}{〈{E}_{\mathrm{exc}}({E}_{e})〉}$.

Structures in far-out asymmetric mass distributions in low energy fission

The far-out asymmetric mass distributions for 235U(n th, f), 239Pu(n th, f), 243Am(n th, f) and 252Cf(sf) have been determined. The structures in these data and those in the existing results on 238U, 234Np and 235Np have been analysed in a systematic way in terms of the static scission-point model of Wilkins et al. The model explains well all the structures seen in very asymmetric fission.

Excitation energy dependence of the total kinetic energy release in thePu241(He3,αf) reaction

Total fission kinetic energies E/sub K/ have been measured as a function of excitation energy in the /sup 240/Pu nucleus excited in the /sup 241/Pu(/sup 3/He,..cap alpha..) reaction. A small negative slope of dE/sub K//dE* approx. = -0.05 is observed in the excitation energy region E*=5--9 MeV. This is substantially smaller than the slope of dE/sub K//dE*=-1.1 observed in the /sup 240/Pu(..cap alpha..,..cap alpha..'f ) reaction and slightly smaller than the slope of dE/sub K//dE* approx. = -0.35 obtained from (d,pf ) and neutron capture reactions. It is concluded that the primary reaction mechanism plays a decisive role for the total kinetic energy release at near barrier energies but that the angular momentum transfer is not the important parameter. The data are discussed in terms of a simple scission-point model, and in particular the effect of the Z=50, N=82 spherical doubly magic shell in the nascent fragments.

Distribution of mass, kinetic energy, and neutron yield in the spontaneous fission ofFm254

The mass distribution for spontaneous fission of /sup 254/Fm was determined for both pre- and post-neutron-emission fragments. The post-neutron-emission (final) mass distribution was deduced from radiochemical measurements of 24 mass yields. Starting with an assumed distribution of neutron yield versus fragment mass, the pre-neutron-emission (initial) mass distribution and neutron-yield distribution were derived from the kinetic-energy measurements of the fragments and the final-mass distribution by an iterative method. These distributions together with distributions of fragment kinetic energy, total kinetic energy of both fragments, and average kinetic energy and average total kinetic energy as functions of fragment mass are presented. The results are discussed in terms of a scission-point model of fission.

Scission-point model of nuclear fission based on deformed-shell effects

A static model of nuclear fission is proposed based on the assumption of statistical equilibrium among collective degrees of freedom at the scission point. The relative probabilities of formation of complementary fission fragment pairs are determined from the relative potential energies of a system of two nearly touching. coaxial spheroids with quadrupole deformations. The total potential energy of the system at the scission point is calculated as the sum of liquid-drop and shell- and pairing-correction terms for each spheroid, and Coulomb and nuclear potential terms describing the interaction between them. The fissioning system at the scission point is characterized by three parameters---the distance between the tips of the spheroids ($d$), the intrinsic excitation energy of the fragments (${\ensuremath{\tau}}_{\mathrm{int}}$), and a collective temperature (${T}_{\mathrm{coll}}$). No attempt is made to adjust these parameters to give optimum fits to experimental data, but rather, a single choice of values for $d$, ${\ensuremath{\tau}}_{\mathrm{int}}$ and ${T}_{\mathrm{coll}}$ is used in the calculations for all fissioning systems. The general trends of the distributions of mass, nuclear charge, and kinetic energy in the fission of a wide range of nuclides from Po to Fm are well reproduced in the calculations. The major influence of the deformed-shell corrections for neutrons is indicated and provides a convenient framework for the interpretation of observed trends in the data and for the prediction of new results. The scission-point configurations derived from the model provide an interpretation of the saw-tooth neutron emission curve as well as previously unexplained observations on the variation of $\stackrel{-}{\mathrm{TKE}}$ for isotopes of U, Pu, Cm, and Cf; structure in the width of total kinetic energy release as a function of fragment mass ratio; and a difference in threshold energies for symmetric and asymmetric mass splits in the fission of Ra and Ac isotopes. In spite of a number of recognized simplifications in the model, quantitative fits to the data are generally within expected errors of the shell corrections determined by the Strutinski prescription.NUCLEAR REACTIONS, FISSION Po, Ra, U, Cm, Cf, Fm; calculated $A$, $Z$, and KE distribution of fragments. Liquid-drop model. Deformed-shell corrections. Strutinski prescription. Asymmetric and symmetric fission.