Fission Fragment Angular Correlations Research Articles

Systematics of angular momentum transfer in intermediate energy nuclear collisions

We have measured the fission fragment angular correlations, both in- and out-of-the-reaction-plane, in coincidence with projectile-like fragments, to infer the linear and angular momentum transfer and its alignment in the reaction of 16O with 197Au at 22 and 30 MeV/nucleon. A general correlation between transferred angular and linear momentum is observed for fissioning nuclei that is different from that observed in reactions where the intermediate complex survives fission.

Missing momentum vector in the 197Au(20Ne;F1,F2PLF) reaction at 15 MeV/u

Abstract Projectile-like fragments (PLF's) emitted in damped collisions of 15 MeV/u 20Ne ions with 197Au were observed in coincidence with two fission fragments. For given detection angles of the PLF's differential and energy-integrated fission probabilities were obtained and the average missing momentum vectors were deduced by using improved analysis methods of the fission fragment angular correlation. The average missing momentum vectors were found to point in the direction of the observed PLF, with a systematic deviation towards beam direction for larger mass transfers. The missing momentum thus appears to mainly originate from the sequential decay of the PLF's.

(e,e'f) Coincidence experiments on 235U and 238U

Coincidence experiments for (e, e'f) on the actinide nuclei 235U and 238U have been performed at the Mainz Microtron (MAMI A) concentrating on three subjects: multipole strength distributions and form factors for the lowest multipolarities, the mass split in the fission decay of various giant multipole resonances, and the separation of near barrier fission channels. Data were taken at four values of momentum transfer ( q eff ≈ 0.20, 0.28, 0.53, and 0.71 fm −1 for 238U, q eff ≈ 0.20, 0.44, 0.57, and 0.71 fm −1 for 235U) for excitation energies ω = 4–22 MeV. The fission fragments have been detected using the Giessen PPAC-Ball. A model-independent multipole analysis yields both form factors and strength distributions for E1, E2/E0, and E3 excitations. The extracted E1 strength distributions in the fission channel are in good agreement with recent photofission data. The extracted E2/E0 strength distributions in the fission channel show two distinct resonant structures centered at ω ≈= 10 and 14 MeV, attributed to concentrated collective E2 and E0 strength, respectively. Up to 12 MeV for 238U (19±2)% and for 235U (39±2)% of the isoscalar E2 energy-weighted sum rule is exhausted. The extracted form factors can be described within a hydrodynamical model by use of parameters c tr c 0 = 1.2 and 1.0 for E1 and E2, respectively. The mass split in the fission decay of giant multipole resonances has been studied via the measurement of time-of-flight difference spectra of both fission fragments. A model-independent multipole decomposition yields the fission width ratios Γ S/Γ A as functions of excitation energy for separated multipoles (E1, E2/E0, and E3). An increased symmetric contribution is evident for the isoscalar giant quadrupole resonance as compared to giant E1 and E3 resonances. Complete in- and out-of-plane fission fragment angular correlations for 238U have been measured for the two lowest values of momentum transfer. A combined analysis with the extracted E1 and E2/E0 multipole strength distributions yields strength distributions for 6 near-barrier fission channels ( J π , K)=(0 +,0), (1 −,0), (1 −, 1), (2 +,0), (2 +, 1), and (2 +, 2) up to 8 MeV. An estimation of the respective fission barriers deduced from the increase of the fission cross sections is given.

Fission: A filter for the study of nuclear reaction mechanisms

The use of nuclear fission as a reaction filter to study the dynamics of low-to-intermediate energy nucleus-nucleus collisions has been widely exploited over the past decade. In particular, the fission fragment angular correlation (folding-angle) technique has been utilized to derive an understanding of linear momentum and energy transfer in projectile-nucleus interactions. These results illustrate the systematic evolution in reaction mechanisms from relatively simple processes such as complete fusion and peripheral transfer reactions at near-barrier bombarding energies to highly complex interactions dominated by precompound processes at intermediate energies. Studies of light charged particles, neutrons and complex fragments in coincidence with fission-tagged events demonstrate the growing influence of nucleon-nucleon collision mechanisms relative to the dinuclear mean field in determining the reaction dynamics with increasing projectile energy. The application of these same techniques to the investigation of the inverse fission process--damped collisions--has also yielded important new insights into this class of reactions and recent results for nuclide distributions and excitation energy sharing are described.

Near barrier fission channels ( Jπ, K) in 238U for spins Jπ=0 +, 1 −, and 2 + from (e, e′f) angular correlation measurements

Complete in- and out-of-plane fission fragment angular correlations for 238U have been measured in (e, e′f) coincidence experiments for momentum transfers q eff=0.20 and 0.28 fm − and excitation energies ω=5.5–15 MeV. A combined analysis with previously extracted E1 and E2/E0 multipole strength distributions yields strength distributions for all 6 near barrier fission channels ( J π , K) = (0 +, 0), (1 −, 0), (1 −, 1), (2 +, 0), (2 +, 1), and (2 +, 2) up to ≈8 MeV. An estim ate of the respective fission barriers, deduced from the increase of the fission cross sections, is given.

Formation and decay of hot nuclei

Formation and decay properties of composite-like nuclei produced by 58Ni projectiles bombarding 232Th target nuclei are investigated at different energies by means of fission fragment angular correlation measurements. Experimental results are compared to the excition model and excitation energies in the fissioning nuclei are deduced. By comparing the present data with the results on other systems, the influences of entrance channel conditions and composite-like nuclei temperatures are discussed to explain the evolution of the high linear momentum transfer region. The coexistence of both massive transfer mmechanism and head-on collisions followed by preequilibrium is suggested.

Target mass dependence of the average linear momentum transfer

The average transferred linear momentum in nuclear reactions induced by 3He, 4He, 14N, and 20Ne projectiles on Co, Cu and Ag targets was determined by thick-target-thick-catcher recoil range techniques for bombarding energies between 10 AMeV and 90 AMeV. A comparison with results obtained from fission fragment angular correlations indicates a strong target mass dependence of the linear momentum transfer.

Reaction mechanisms in the 40Ar + 197Au collisions at 35 MeV/nucleon

The fission fragment angular correlation has been measured in the Ar + Au reaction at 35 MeV/nucleon. Two components are clearly separated: the sequential fission of the target ( σ = 320 ± 80 mb) and a fusion-like process ( σ = 480 ± 120 mb). The linear momentum transfer per nucleon for the fusion-like events reaches the limitation of 190 MeV/ c observed in earlier studies. This limitation does not reflect a limit to the excitation energy that a nucleus can contain. Heavy residues with energies larger than 0.13 MeV nucleon have been measured in the forward region. This observation of residues with high excitation energies implies the existence of a competition between fission and evaporation at excitation energies as high as ∼800 MeV. Particles and light nuclei have been detected in a forward multidetector in coincidence with two fission fragments or a heavy residue.

Neutron multiplicities in heavy-ion-induced fission: Timescale of fusion-fission

Neutron fission-fragment angular correlations have been measured for the compound nuclei 168Yb, 192,198,200Pb, 210Po, 213Fr and 251Es formed at excitation energies between 45 and 90 MeV by fusion reactions induced by beams of 16,18O, 19F and 28,30Si. Analysis allows the determination of the mean multiplicities of neutrons originating from the fused system ( v pre) and the fission fragments (2 v post). The total multiplicities ( v pre + 2 v post ) are in good agreement with calculated values. However, calculations of v pre using the statistical model code ALERT1 underestimate the multiplicities, the discrepancy increasing with excitation energy and fissility. This is interpreted in terms of the dynamics of the fission process, and can be resolved by including in the calculations the effects of a delayed onset of fission (delay time 70 × 10 −21s) or a slow saddle-to-scission transition (transit time 30 × 10 −21s). Simple theoretical estimates suggest that both effects are significant, and their characteristic times may be similar. With these constraints, the data are fitted when both effects are applied, each for 20 × 10 −21s. Such long times are not inconsistent with the results of pure one-body dissipation calculations, and are supported by recent results on the timescale of quasi-fission. The quoted results are for a level-density parameter a n = 1 10 A . Use of 1 12 A ( 1 8 A) results in shorter (longer) times; however, it is concluded that for all reasonable values, motion in the fission direction is overdamped.

Blurred images of complete fusion and incomplete fusion: Reaction simulation analysis of fission-fragment angular correlations

We use Monte Carlo reaction simulation calculations to reassess several studies of fissionfragment angular correlations. The reactions chosen are 15–30 MeV/nucleon14N +238U and 14.6 MeV/nucleon20Ne +197Au. Reanalysis by means of these stimulations leads to much lower limits than originally reported for the fraction of complete fusion. We infer that at these energies the probability is very large for the direct emission of at least one light particle prior to fission. This implies that the distinction between “complete fusion” and “incomplete fusion” has become blurred beyond meaningful distinction.

Studies of4He emission in both fusion-like and inelastic reactions of 340-MeV40Ar+238U

The fission-fragment angular correlation technique has been used in conjunction with a position-sensitive avalanche detector to identify the fusion-like and inelastic collisions of 340-MeV40Ar+238U. For each of these two reaction types, we have characterized the correlated4He emission by measuring three-fold coincidences between two fission fragments and the light charged particle. We find an abundance of both evaporation-like and direct4He emission, each of which is associated with both fusion-fission and sequential-fission processes. Several comparison tests of both the coincidence and singles data strongly indicate that very little4He emission is due to evaporation from accelerated fission fragments in this system. The evaporative4He emission appears instead to have a strong contribution originating from the composite system prior to fission. The forward angle4He emissions, characterized by prominent forward-peaking and relatively high energies, suggest an origin associated with the very early stages of the collision.

Linear momentum transfer in nonrelativistic nucleus-nucleus collisions

The systematic behavior of linear momentum transfer from projectile to target in nonrelativistic nucleus-nucleus collisions has been studied using the results of fission-fragment angular-correlation measurements on uranium target nuclei. Data for $^{4}\mathrm{He}$, $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, and $^{20}\mathrm{Ne}$ projectiles have been analyzed over an energy range which extends well above the interaction barrier. The data illustrate the division of the total reaction cross section into two primary components: one associated with \ensuremath{\sim} 90 percent or greater linear momentum transfer and the other involving much smaller amounts of linear momentum transfer. The former is attributed to fusionlike collisions and the latter to peripheral collisions. The minimum between these two components corresponds to a linear momentum transfer of about 50 percent. It is observed that the ratio of fusionlike collisions to the total reaction cross section decreases regularly as a function of both increasing bombarding energy and projectile mass. From comparison of the experimental fission-fragment angular correlation functions with the predictions of complete fusion kinematics, it is shown that above 10 MeV/nucleon, the experimental definition of complete fusion is complicated by the increasing probability for large, but incomplete, linear momentum transfer collisions. Estimates of critical angular momenta derived from these data do not show any major disagreement with rotating-liquid-drop predictions.NUCLEAR REACTIONS, FISSION Studied systematics of fission-fragment angular correlation measurements from uranium target nuclei. Deduced linear momentum transfer distributions, fusionlike collision and complete fusion probabilities, and critical angular momenta.

Reaction mechanism studies with 7-35 MeV/nucleonHe4ions incident on heavy target nuclei

Reaction mechanism studies have been performed on the $^{4}\mathrm{He}$ + $^{233}\mathrm{U}$ system at energies of 7-35 MeV/nucleon and on the $^{4}\mathrm{He}$ + $^{209}\mathrm{Bi}$ system at 12-35 MeV/nucleon. Measurements included (1) forward-angle elastic scattering, (2) angular distributions and total cross sections for fission, (3) fission-fragment angular correlations, and (4) fragment charge, mass, and energy distributions for $^{233}\mathrm{U}$($\ensuremath{\alpha}$,$f$) at 140 MeV. Total inelastic cross sections and interaction radii were derived from the elastic scattering data. These values were found to be in good agreement with the total cross section for fission for the $^{233}\mathrm{U}$ + $^{4}\mathrm{He}$ system, confirming the assumption that ${\ensuremath{\sigma}}_{R}\ensuremath{\simeq}{\ensuremath{\sigma}}_{f}$. Fission-fragment angular-correlation measurements were performed in order to deduce the distribution of linear momenta which characterize the residual heavy nuclei formed in these collisions. Complete linear momentum transfer probabilities (complete fusion) were also derived for both target-projectile systems as a function of energy. The data are compared with predictions of the proximity potential with one-body energy dissipation and with the intranuclear cascade code. The results of these comparisons are consistent with a picture in which complete fusion dominates the reaction mechanism below 10 MeV/nucleon, but pre-equilibrium processes assume increasing importance above this energy at the expense of fusion. In addition, evidence for a possible reduction in the interaction radius above 20 MeV/nucleon is reported.NUCLEAR REACTIONS $^{209}\mathrm{Bi}$($\ensuremath{\alpha}$,$\ensuremath{\alpha}$), $^{233}\mathrm{U}$($\ensuremath{\alpha}$,$\ensuremath{\alpha}$), $E=69.2, 140$ MeV, ${\ensuremath{\sigma}}_{R}(E)$; $^{209}\mathrm{Bi}$($\ensuremath{\alpha}$,$f$), $E=69.2, 140$ MeV, $^{233}\mathrm{U}$($\ensuremath{\alpha}$,$f$), $E=28\ensuremath{-}140$ MeV, $\ensuremath{\sigma}(\ensuremath{\theta})$, $\ensuremath{\sigma}(E)$, fission-fragment angular correlations, $Z$ and $A$ distributions at 140 MeV; linear momentum transfer to residual nucleus deduced; results compared with ion-ion potential models and intranuclear cascade code.

Complete fusion studies of the 20Ne+ 235U system

The probability for complete fusion has been measured for the 20Ne+ 235U system at bombarding energies of 175 and 252 MeV. The fission fragment angular correlation technique was used to obtain both the absolute cross section for complete fusion and relative cross sections for the ratio of complete fusion to incomplete fusion processes. Total reaction cross sections were also determined from elastic scattering measurements. Values of σ R = 1900±40 and 2810 ± 140 mb were obtained at 175 and 252 MeV, respectively. These measurements yield if σ CF σ R = 0.74±0.05 at 175 MeV and 0.48 ±0.06 at 252 MeV . The corresponding values of the critical angular momentum are compared with the predictions of several heavy-ion interaction models. It is observed that the l c values obtained from these data agree well with the current models, although the energy dependence is not as strong as predicted. In addition, it is observed that these values of l c exceed the limiting value for a charged rotating drop.

Intermediate structure in the 239Pu(d, pf) reaction

Sub-barrier resonances in the 239Pu(d, pf) reaction have been investigated with a resolution of 3 keV. Many class II resonance groups with an average spacing of 11 keV have been observed in the region of the 5.0 MeV transmission resonance. The coincident fission fragment angular correlations indicate a spin 2 + for all lines resolved. The data are analyzed on the basis of a simple model of intermediate structure which also explains the observed broadening of the class II groups.

Linear momentum transfer in reactions between 140-MeVHe4ions and heavy nuclei

The fission of $^{238}\mathrm{U}$, $^{209}\mathrm{Bi}$, and $^{197}\mathrm{Au}$ induced by 140-MeV $^{4}\mathrm{He}$ ions has been studied in order to investigate the target-projectile reaction mechanism. The fission-fragment angular correlation technique was used to measure the linear momentum transfer in these reactions. It is found that an upper limit of (49.3\ensuremath{\ge}4.4)% of the fission in $^{238}\mathrm{U}$ results from the complete fusion of target and projectile. The incomplete fusion component of the $^{238}\mathrm{U}$ fission cross section includes a large fraction of high linear momentum transfer events, presumably produced in reactions where preequilibrium decay and/or deep knockout reactions are highly probable. The fission of $^{197}\mathrm{Au}$ and $^{209}\mathrm{Bi}$ is found to proceed almost completely via a complete fusion mechanism at this energy. The complete fusion cross section for $^{238}\mathrm{U}$ reactions with 140-MeV $^{4}\mathrm{He}$ ions is compared with that predicted from semiclassical collision models derived for heavy ion reactions.NUCLEAR REACTIONS, FISSION $^{238}\mathrm{U}(\ensuremath{\alpha},f)$, $^{209}\mathrm{Bi}(\ensuremath{\alpha},f)$, $^{197}\mathrm{Au}(\ensuremath{\alpha},f)$, $E=140$ MeV; measured ${\ensuremath{\sigma}}_{f}$, fragment-fragment angular correlation; deduced linear momentum transfer distribution, ${l}_{\mathrm{crit}}$.

The use of position-sensitive semiconductor detectors in the study of heavy element nuclear reactions

The application of position-sensitive semiconductor detectors to the study of heavy element nuclear reactions at intermediate energies is described. Experimental procedures and results are presented for the use of these devices in the following types of measurements: (1) binary fission fragment angular correlations; (2) fission fragment angular distributions; (3) kinetic energy release in fission, and (4) spallation recoil product angular distributions. The position-sensitive detectors are found to provide much improved experimental efficiency over normal semiconductor detectors in experiments where the angular dependence of the products is quite strong; e.g. fission fragment angular correlations and spallation recoil angular distributions. For experiments in which the product counting rates vary slowly with angle, such as fission fragment angular distributions, the position detector is much less useful. Although the energy resolution of these devices is poorer than normal detectors, they are advantageous in experiments designed to study fission energetics as a function of reaction kinematics.

Fission of Odd-AUranium and Plutonium Isotopes Excited by (d,p), (t,d), and (t,p) Reactions

Fission-fragment angular correlations and fission probabilities have been measured for a series of odd-$A$ uranium and plutonium isotopes excited by ($d,p$), ($t,d$), and ($t,p$) reactions. The following fissioning nuclei have been studied: (1) $^{235}\mathrm{U}$ from ($d,pf$), ($t,pf$); (2) $^{237}\mathrm{U}$ from ($d,pf$), ($t,df$), ($t,pf$); (3) $^{239}\mathrm{U}$ from ($d,pf$); (4) $^{241}\mathrm{Pu}$ from ($d,pf$), ($t,df$), ($t,pf$); and (5) $^{243}\mathrm{Pu}$ from ($d,pf$), ($t,df$). Fission probabilities and angular-correlation coefficients for each case are compared with previously reported ($n,f$) results. The direct-reaction experiments show fission thresholds at excitation energies equal to or less than threshold energies observed in ($n,f$) experiments. Some qualitative characteristics of the transition-state spectrum for the nuclei studied are determined from comparisons of the direct-reaction and ($n,f$) results.

Characteristics of the Transition-State Spectra for U234, U236, and Pu240 from (d,pf) and (t,pf) Angular-Correlation Experiments

Fission-fragment angular correlations have been measured as a function of the excitation energy of the fissioning nucleus for the reactions $^{233}\mathrm{U}(d,pf)$, $^{235}\mathrm{U}(d,pf)$, $^{239}\mathrm{Pu}(d,pf)$, and $^{234}\mathrm{U}(t,pf)$. A simplified microscopic model is developed and used to fit the experimental results in the energy range up to the neutron binding energy. From these fits, the positions of vibrational bands with $K={0}^{+},{2}^{+},{0}^{\ensuremath{-}},{1}^{\ensuremath{-}}, \mathrm{and} {2}^{\ensuremath{-}}$ are determined for the transition-state spectrum of $^{234}\mathrm{U}$, $^{236}\mathrm{U}$, and $^{240}\mathrm{Pu}$. Above the neutron binding energy, the angular correlations are analyzed with a statistical model, and the pairing energy for a highly deformed transition nucleus is determined. Values obtained for the pairing gap are $2{\ensuremath{\Delta}}_{0}=2.10\ifmmode\pm\else\textpm\fi{}0.15$ MeV for $^{236}\mathrm{U}$ and $2{\ensuremath{\Delta}}_{0}=1.98\ifmmode\pm\else\textpm\fi{}0.15$ MeV for $^{240}\mathrm{Pu}$.