Heavy Compound Nuclei Research Articles

Fusion-fission dynamics and perspectives of future experiments

The paper is focused on reaction dynamics of superheavy-nucleus formation and decay at beam energies near the Coulomb barrier. The aim is to review the things we have learned from recent experiments on fusion-fission reactions leading to the formation of compound nuclei with Z≥102 and from their extensive theoretical analysis. Major attention is paid to the dynamics of formation of very heavy compound nuclei taking place in strong competition with the process of fast fission (quasifission). The choice of collective degrees of freedom playing a fundamental role and finding the multidimensional driving potential and the corresponding dynamic equation regulating the whole process are discussed. A possibility of deriving the fission barriers of superheavy nuclei directly from performed experiments is of particular interest here. In conclusion, the results of a detailed theoretical analysis of available experimental data on the “cold” and “hot” fusion-fission reactions are presented. Perspectives of future experiments are discussed along with additional theoretical studies in this field needed for deeper understanding of the fusion-fission processes of very heavy nuclear systems.

Reaction dynamics and hot nuclei formation in the36Ar+98Moreaction at37AMeVstudied through light charged particle andγ-ray emission

Central and mid-central collisions which lead to the formation of a heavy residue in the 37A MeV ${}^{36}\mathrm{Ar}{+}^{98}$Mo reaction have been studied with the MEDEA multidetector array coupled to a Parallel Plate Avalanche Counter. The dependence of the high energy gamma ray and light charged particle production as a function of the linear momentum transferred to the fused system has been studied. The unique potentialities of the MEDEA detector have made it possible to follow the evolution of the reaction dynamics from the pre-equilibrium stage to the formation of a heavy compound nucleus. The analysis of the correlation between the most energetic photons and protons shows how both of them are mainly produced in the most energetic primary nucleon-nucleon collisions. The multiplicity of high energy ${(E}_{\ensuremath{\gamma}}>30\mathrm{MeV})$ $\ensuremath{\gamma}$ rays has been found to increase with the linear momentum transfer, showing the dominance of two-body dissipation in the transfer mechanism and giving a tool to correlate the momentum transfer with the centrality of the collision. Light charged particle kinetic energy spectra show how in these collisions, compound systems with excitation energies of more than $3A\mathrm{MeV}$ and temperature up to 7 MeV are formed. The experimental findings are compared with Boltzmann-Nordheim-Vlasov calculations. A scenario is found where the nucleus-nucleus interaction starts with two-body nucleon-nucleon collisions in the overlap region of nuclear densities. These collisions give rise to the production of high energy nucleons and $\ensuremath{\gamma}$ rays, and play a fundamental role in the energy transfer from the relative motion to internal excitation of the quasiprojectile and the target.

Systematics of fission-channel probabilities

Fissioning nuclei produce with increasing excitation varying yields of fragments. For compound nuclei ranging from ${}^{232}\mathrm{Th}$ to ${}^{242}\mathrm{Pu}$ endowed with excitation energies typically between 0 and 10 MeV, we analyze these variations in terms of a fission-channel model. Most of the variations can be attributed to changing channel probabilities. We present a systematics of channel probabilities with respect to compound nuclei and their excitation energies, and we relate the systematics to potential energy which the nuclei experience when they float to scission. The trend, which is most difficult to explain, is a shift in the energy sensitivity of the standard channels, as one compares light with heavy compound nuclei. According to their behavior, we divide nuclei into standard I increasers and decreasers and attribute the difference to the standard secondary barriers. As a basic concept, bifurcation ratios are introduced, and a novel expression for transmission coefficients is proposed.

Distribution of fusion barriers

Heavy ion fusion cross sections and compound nucleus average spin values obtained from distribution of fusion barriers are discussed. Various shapes of distribution functions are studied using a truncated Gaussian distribution function (TGD). It is shown that fusion cross section and average spin values are less sensitive to different parametrization of TGD function, whereas the second derivative of the product of energy and fusion cross sections (w.r.t. energy), obtained from the corresponding TGD functions are significantly different depending on the shape of the barrier distribution function. It is also shown byχ 2 analysis of fusion cross section data that some systems favour a narrow Gaussian distribution function whereas others, for which the vibrational and rotational collective states are less important, favour a flat barrier distribution. A physical interpretation of the dynamical process that gives rise to different barrier distribution is given in the framework of microscopic coupled channel calculations.

A viable route to the production of superheavy elements: Low-energy fusion of very neutron-rich nuclei

It is suggested that the inclusion of the virtual excitation of the soft giant dipole (pygmy) resonance in the calculation of the cross section for very neutron-rich radioactive beam-induced fusion reactions may enhance the formation probability of the heavy compound nucleus produced at low excitation energy. Both spherical and deformed target nuclei are considered.

Role of the pygmy resonance in the synthesis of heavy elements with radioactive beams.

It is suggested that the inclusion of the virtual excitation of the soft giant dipole (pygmy) resonance in the calculation of the cross section for very neutron-rich radioactive beam-induced fusion reactions may enhance the formation probability of the heavy compound nucleus produced at low excitation energy.

Microscopic calculations of fission barriers and critical angular momenta for excited heavy nuclear systems

Abstract An extended version of Strutinsky's macro-microscopic method is used to calculate effective potential energies for rotating, excited heavy compound nuclei undergoing fission. Nuclear deformation is parameterized in terms of Lawrence's family of shapes. A two-center single-particle potential corresponding to these shapes is employed, with BCS pairing added. Statistical excitation is introduced by temperature-dependent occupation of (quasi-) particle energy levels. We calculate shell corrections to the energy, the free energy and the entropy as functions of deformation and temperature. The associated average quantities are derived from a temperature-dependent liquid drop model. The resulting static deformation energy is augmented by the rotational energy to yield the isothermal effective potential energy as a function of deformation, temperature and angular momentum. Moments of inertia are obtained from the adiabatic cranking model with temperature-dependent pairing included. We have also calculated the effective potential for constant entropy rather than constant temperature. Although this isentropic process physically is more appropriate than the isothermal process, it has not been treated before. For the same amount of excitation energy in the spherical state of the compound nucleus, the isentropic barriers turn out higher than the isothermal ones. For both processes we have extracted the critical angular momentum (defined as the one for which the barrier approximately vanishes) as a function of excitation. Our model is applied to the super-heavy nuclei 270 110, 278 110, 298 114, 292 118 and 322 128, which have been tried to form in krypton and argon induced heavy ion reactions.

Coincidence studies of heavy fragments in deeply inelastic collisions between heavy ions: Sequential fission probability in reactions of 730-MeVKr86with Au

Angular correlations have been measured between heavy fragments in $^{86}\mathrm{K}$R + $^{197}\mathrm{Au}$ reactions using two gas telescopes. The data have been analyzed to yield a separation of two-body from multibody events. The assumption that sequential fission accounts for all multibody breakup allows the determination of sequential fission probability as a function of inelastic energy transfer. Comparison to fission excitation functions for similar heavy compound nuclei provides insight into the deposition of energy and angular momentum. For $\ensuremath{-}Q$ of \ensuremath{\approx} 200 MeV or E* \ensuremath{\approx} 140 MeV typical spin values of $30\ensuremath{-}40\ensuremath{\hbar}$ can be estimated for the heavy (Aulike) fragments.

Macroscopic potential-energy surfaces for symmetric fission and heavy-ion reactions

We calculate the macroscopic potential energy of deformation for symmetric configurations of interest in fission and heavy-ion reactions. The shape of the system is characterized in terms of two moments of the matter distribution. These moments correspond to the distance between the centers of mass of the two halves of the system and to the elongation of each half about its center of mass. The configurations studied include a continuous sequence of shapes from the sphere to two-, three-, and four-fragment scission lines. Beyond the scission lines and prior to the line of first contact in heavy-ion reactions we represent the system in terms of separated oblate and prolate spheroids. The macroscopic energy is calculated as the sum of a Coulomb energy and a nuclear macroscopic energy that takes into account the finite range of the nuclear force. For systems throughout the periodic table we display the calculated energy as a function of the two moments in the form of contour maps. Some important features of the contour maps are the binary, ternary, and quaternary saddle points, the fission and fusion (or two-fragment) valleys, and the three- and four-fragment valleys. The maps illustrate how the topography of the potential energy changes as a function of the nuclear system considered. For example, as we move from lighter to heavier nuclear systems the binary saddle point moves from outside the point of first contact in heavy-ion reactions to inside the contact point. Because of this, the formation of a heavy compound nucleus requires additional energy relative to the maximum in a one-dimensional interaction barrier. The maps also illustrate for moderately heavy systems the presence of separate valleys for binary fission and fusion. For still heavier systems the ternary and quaternary saddle points are no longer present. This means that the ternary and quaternary valleys are accessible by paths that decrease monotonically in energy beyond the binary saddle point. Finally, for nuclear systems heavier than about 300120, the binary saddle point itself disappears, which in the absence of single-particle effects precludes altogether the formation of a compound system.

A velocity separator for heavy ions using radiofrequency deflection

A new type of particle separator is proposed. It is intended primarily to separate heavy compound nuclei produced in fusion reactions from the intense background of heavy projectiles, but it should also be useful for separation of any rare reaction product from the beam background. Separation with respect to velocity as well as time of travel is accomplished by using two radiofrequency deflectors operated synchronously with the heavy ion accelerator Unilac. A practical system is investigated in some detail, and a new type of resonator providing a maximum deflection voltage of 600 kV over 6 cm at 27 MHz is described.

Ternary Fission of Heavy Compound Nuclei in Thorite Track Detectors

Ternary Fission of Heavy Compound Nuclei in Thorite Track Detectors

The distorted wave theory of heavy particle stripping

The nuclear reaction known as heavy particle stripping is treated as a general type of nuclear reaction using the distorted wave Born approximation. General expressions for angular distributions and polarizations and polarizations are obtained and simple cases discussed,. The dynamical part of the amplitude is evaluated by the method of Fourier transforms which allows the centre-of-mass motion of the “heavy particle” or “core” to be included without any approximations being made. The decay of the residual nucleus by γ-radiation following a heavy particles stripping reaction is examined with particular reference to the B 11( d, n) C 12∗(γ) C 12 reaction. A close semilarity between heavy particle stripping and compound nucleus theory is found when the centre-of-mass motion of the core is neglected. The assumed relationship between heavy particle stripping and backward peaked angular distributions becomes questionable when distored waves are used. It is concluded that more refined experiments are required to establish the tru importance particle stripping in nuclear reactions.