Deeply inelastic transfer reactions induced by heavy ions in rare-earth targets

Recoil techniques have been used for a systematic study of deeply inelastic transfer reactions induced in rare earth targets by⁴⁰Ar,⁵²Cr,⁵⁶Fe and⁶³Cu projectiles. The targets were separated isotopes of Eu, Sm, Nd and Pr. The residual nuclei^149gTb,¹⁵⁰Dy and¹⁵¹Dy were identified by their radioactive properties. The reactions studied involved the transfer of 3 to 7 charges from projectile to target. The c.m. angular and energy distributions were measured over the whole angular range from 0 to 180° (c.m.). A special device was used to measure accurately the c.m. energy of products emitted in the angular range 170–180° in the c.m.s. The c.m. angular distributions depend strongly on the ratio of the incident energy to the strong interaction barrier, and slightly on the number of transferred charges. The c.m. energy distributions are typical of completely damped collisions for 6-charge transfer reactions, and include a contribution of partially damped collisions for 4-charge transfer reactions. A kinematic analysis was used to determine the most probable number of neutrons transferred in the first reaction step with a given number of protons. The numbers found correspond to equilibration of the neutron to proton ratio in the composite system.     

Model Experiments on Study of the First Wall Erosion Under the Action of Vacuum Arcs

With d. c. vacuum arc discharges the dependence of cathode erosion rate on the transverse magnetic field induction is non-linear. At first erosion rate rises with the magnetic induction and then drops. The maximum erosion rate value corresponds to the magnetic induction interval (50 – 115) · 10^?4 T. The range of the vacuum arc discharge maximum stability also corresponds to the same interval. When the magnetic induction rises from 2 · 10^?3 up to 1.1 · 10^?2 T (I = 50 A), the erosion products angular distribution monotoneously narrows and with further magnetic ficld enhancement it abruptly widens. Current rise results in increasing extension of erosion products angular distribution. Asymmetry of erosion products angular distribution does not depend on the direction of the magnetic induction vector and gradually vanishes when the magnetic induction rises up to 1 · 10^?2 T and higher.     

The reaction mechanism in the system132Xe+56Fe at 5.73 MeV/u: Evidence for a new type of strongly damped collisions

We present data for the¹³²Xe+⁵⁶Fe-system at 5.73 MeV/u laboratory energy. Due to inverted kinematics, where Xe is the projectile, we were able to measure energy spectra as well as angular distributions for reaction products with 20≦Z≦60 with unitZ-resolution; i.e. target- and projectile-like fragments have been investigated. The reaction shows a well focussed quasielastic component, where charge transfer from the light to the heavy collision partner dominates. This apparent tendency towards more asymmetric fragmentation is explained by a potential energy surface which favours such charge transfer in order to minimize the asymmetry energy of the liquid drop. The strongly damped component which constitutes the major part of the reaction cross section exhibits characteristics of a fusion-fission reaction with typical fission fragment kinetic energies and 1/sinΘ _c.m. angular distributions. The maximum cross section is found for the symmetric fragmentation, no clear indication is observed for a diffusion process leading to target- and projectile-like fragments. Our data are difficult to reconcile either with the standard diffusion models or with an equilibrated compound nucleus fission picture. We tentatively conclude that an essential part of the fully damped cross section originates from partial waves for which the compound nucleus has no fission barrier.     

The rotational quasi-continuum in specific configurations: high-K states and superdeformation

The analysis of the fluctuations of the counts of unresolved γ-γ energy spectra can extend our knowledge of the rotational motion at high angular momentum and excitation energy above the yrast band. Detailed studies of the rotational quasi-continuum built on specific intrinsic nuclear configurations are here discussed. First, the validity of the K-selection rules in the quasi-continuum region is investigated in the case of the normal deformed nucleus ¹⁶³Er. The γ cascades feeding into low-K and high-K bands are analyzed studying variance and covariance of the spectrum fluctuations. Low-K bands are found to be fed by a much larger effective number of cascades than high-K bands, while the covariance between pairs of gated spectra shows that the cascades feeding into low-K bands are different from those feeding into high-K bands. These findings suggest a persistence of K-selection rules in the region of excitation energy and angular momentum probed by the rotational decay of ¹⁶³Er. As a second case, the existence of a rotational quasi-continuum in the super deformed well of ¹⁴³Eu is discussed. An intense bump of rotationally correlated transitions is observed to develop as function of fold in the high spin region of gated spectra. Fold distribution, angular anisotropies, moment of inertia and life time show that the bump consists of fully damped super deformed transitions. This gives experimental evidence of damped rotational motion up to several MeV excitation energy above the super deformed yrast line.     

The effect of nuclear structure in the emission of reaction products in heavy-ion reactions

Study of intermediate mass fragments (IMFs) and light charged particles (LCPs) emission has been carried out for a few reactions involving α-cluster and non- α-cluster systems to see how the emission processes are affected by nuclear clustering. Li, Be, B and α-particles have been studied from α-clustered system ¹⁶O + ¹²C for 117, 125, 145 and 160 MeV bombarding energies respectively. The enhanced yields of near-entrance channel fragment B and large quadrupole deformation of the produced composite ²⁸Si^? extracted from LCP spectra indicate the survival of orbiting-like process in ¹⁶O + ¹²C system at these energies. The same IMFs emitted from the α-cluster system ¹²C (77 MeV) + ²⁸Si and nearby non- α cluster ¹¹B (64 MeV) + ²⁸Si and ¹²C (73 MeV) + ²⁷Al (all having the same excitation energy of ～67 MeV) have also been studied. The fully energy damped (fusion–fission) and the partially energy damped (deep inelastic) components of the fragment energy spectra have been extracted. It has been found that the yields of the fully energy damped fragments for all the above reactions are in conformity with the respective statistical model predictions. The time-scales of various deep inelastic fragment emissions have been extracted from the angular distribution data. The angular momentum dissipation in deep inelastic collisions has been estimated from the data and it has been found to be close to the corresponding sticking limit value.     

Study of angular asymmetries in the 2H(α, 3He)3H reaction

The Barshay-Temmer theorem predicts that the angular distribution of the products of the reaction ²H(α, ³He)³H will be symmetric about 90° in the c.m. system. Recently, asymmetries have been reported in the angular distribution in excess of 10 % at some angles. These asymmetries clearly violate the theorem. In an effort to explain the asymmetry as well as describe the angular distribution an exact finite-range multi-interaction DWBA calculation, which includes all appropriate one-particle transfer reaction mechanisms, was employed. Semi-realistic three-nucleon wave functions were utilized in one case in deriving the form factors appropriate for two-particle clustering of the tri-nucleon systems and various Coulomb effects associated with the interactions were included. It was found that both the asymmetry and angular distribution are well described within the present formalism.     

Mass resolved angular distribution in helium ion induced fission of233U

Mass resolved fission fragment angular distribution was measured in the 28.5 MeV alpha induced fission of²³³U using recoil catcher technique and direct gamma spectrometry. The angular distribution of 8 fission products were obtained. The angular anisotropies of asymmetric fission products were found to be higher than those of symmetric products indicating a correlation between the fragment angular distribution and the mass distribution.The authors are grateful to Dr. S.K. Kataria and Dr. T. Datta for fruitful discussions. We thank the operation crew of the variable energy cyclotron, Calcutta for their help in carrying out the irradiations. Thanks are due to Dr. P.R. Natarajan, Head of the Radiochemistry Division for his keen interest in the work.     

Tangential friction in nuclear reactions studied with the time-dependent Hartree-Fock model

The dissipation of orbital angular momentum is studied by analyzing TDHF calculations of the damped nuclear reaction 280 MeV ⁴⁰Ca+⁴⁰Ca in terms of the nucleon exchange transport model. While the overall results of the TDHF calculation are well accounted for by the NET model, the more detailed behavior reveals evidence of a finite intrinsic nuclear relaxation time.     

Quasi-fission and other strongly damped collisions between 63Cu ions and 197Au nuclei

The interaction of ⁶³Cu ions with ¹⁹⁷Au nuclei have been studied experimentally at incident energies of 365 and 443 MeV (1.1 and 1.4 times the Coulomb barrier). Mass and kinetic energy distributions of reaction products have been measured at several angles. Near the grazing angle, a continuous transition was found from elastic events to partially damped (PD) events, and to fully damped events (quasi-fission, QF). Away from the grazing angle a clean separation between elastic and QF events was observed. Events that may be due to fission following fusion (CF) were also obtained. Results are discussed in terms of decomposition into PD, QF, and CF components. The QF kinetic energy is independent of the incident energy (implying full damping of the initial relative motion). It is lower than the Coulomb barrier and close to the kinetic energies from the fission of similar systems. The angular distribution is peaked somewhat forward of the grazing angle for low mass transfers. For large mass transfers the yield increases slowly with decreasing angle. At 443 MeV a large contribution from negative angles is present. σ_QF accounts for more than 65 % of the reaction cross section σ_R at 443 MeV and for more than 50 % at 365 MeV. The upper limit on CF is about 10 % of σ_R, and σ_PDis of the order of 25 % of σ_R.     

Studies on strongly damped components in relatively light heavy ion reaction systems

Strongly damped components have been studied in relatively light heavy ion reaction systems;²⁰Ne(E _lab=93, 120 and 146MeV)+⁵⁰Cr,²⁰Ne(E _lab=146MeV)+⁵⁴Cr and²⁰Ne(E _lab=146MeV)+⁹²Mo,¹⁰⁰Mo. The kinetic energy, angular and charge distributions have been observed for those products. The yields of symmetric-mass-splitting products for²⁰Ne+⁵⁰Cr were found about three times larger than those for²⁰Ne+⁵⁴Cr. There was also observed a similar difference in the cross sections of the symmetric-mass-splitting products between²⁰Ne+⁹²Mo and²⁰Ne+¹⁰⁰Mo reactions. In order to explain the bombarding energy dependence of the cross sections of symmetric-mass-splitting products by the transport theory, it was found necessary to assume that the mean life of the composite nucleus was dependent on the bombarding energy. However, the target isotope dependence of the cross sections could not be explained by such an assumption. They could be partly explained by fission calculations.     

Quadrupole interactions in MoCl5 intercalated in graphite

The time-differential perturbed angular correlation technique was used to investigate quadrupole interactions following the decay of⁹⁹Mo as a probe in the intercalation compound graphite-molybdenum pentachloride. Analysis of the 740-(44) 141 keV γ-γ correlation in⁹⁹Tc reveals the presence of two sites with static electric field gradient interactions, one of which corresponds to a moderately damped (δ∼16%), high-frequency interaction (v _q∼630 MHz), the other to a heavily damped (δ∼28%), low-frequency (v _q∼283 MHz) component.     

The transition between quasi elastic and completely damped collisions studied in the40Ar (280 MeV)+58Ni reaction

A careful exploration of the angular distribution for the products emitted mainly below the grazing angle shows the continuous evolution from Q.E. to completely damped collisions. The relative relaxation time of the collective degrees of freedom is considered.     

A fast-fission component with small mass drift in the reaction84Kr+27Al atE lab=5.9 MeV/u

All reaction products in the range from target- and projectile-like to fission-like fragments were measured for the system⁸⁴Kr+²⁷Al at 5.9 MeV/u beam energy. They are assigned to the various reaction mechanisms on the basis of experimental signatures (energy dissipation, mass and angular distribution). The sum of the measured partial cross sections, including the evaporation residue yield obtained previously, agrees with the total reaction cross section derived from elastic scattering. A small fast-fission component was found, discernible from deep-inelastic reactions by its 1/sin θ angular distribution, and distinguished from compound-nucleus fission by an incomplete mass asymmetry relaxation.     

Quasi-fission — The mass-drift mode in heavy-ion reactions

The binary and ternary products from reactions of ²³⁸U beams with targets of ¹⁶O, ²⁷Al, ⁴⁸Ca, ⁴⁵Sc, ⁴⁸Ti, ⁵⁸Fe, ⁶⁴Ni and ⁸⁹Y have been recorded at 6.0 MeV/u bombarding energy with four position-sensitive avalanche detectors, operated in coincidence. A few runs at 5.4 MeV/u have also been performed. Accurate triple-differential cross sections, $\text{d}{}^3\text{σ}\text{d}\text{A}\text{d}\text{θ}{}_{\mathrm{<mtext>c.m.</mtext>}}\text{dTKE}$, are obtained for the binary events within the full range of mass A and total kinetic energy TKE, and within almost the full range of center-of-mass angle θ_c.m.. Similar cross sections are obtained with somewhat less accuracy for triple events stemming from the sequential fission of uranium-like products. The distributions are discussed in terms of quasielastic and strongly damped scattering, where the products have partially relaxed energies and negligible average drift in mass, as opposed to capture where the products emerge with fully relaxed energies after a more or less pronounced mass drift towards symmetry. Apart from the reaction with ¹⁶O, all the capture product distributions are dominated by the non-equilibrium quasi-fission (or fast fission) process. The central feature of this reaction mechanism is the evolution of the reaction complex towards mass symmetry. With the ²⁷Al target the evolution towards symmetry is almost complete, whereas the heavier targets show very broad mass distributions with clear evidence of dissociation taking place before symmetry is reached. At the same time, the cross section for quasi-fission diminishes as the target Z-value increases. With the ⁸⁹Y target the strongly damped scattering component dominates completely. The capture cross sections are discussed in terms of the extra-push concept, and the mass and angular distributions in quasi-fission are analyzed in terms of interaction time and mass rearrangement as functions of target Z-value and excess kinetic energy in the entrance channel.     

Energy damping feature in light heavy-ion reactions

The energy damped reaction products from³⁷Cl+¹²C,²⁷Al,⁴⁸Ti and¹⁶O+⁴⁸Ti were measured over a wide range of angles (typically 18°<θ _lab<70°), incident energies (160 <E _lab(³⁷Cl)<200 MeV,E _lab(¹⁶O)=118 MeV) and charges Z, including two systems (³⁷Cl+³⁷Al and¹⁶O+⁴⁸Ti) which lead to the same compound nucleus⁶⁴Zn with the same excitation energy and comparable angular momenta. The angular dependences of total kinetic energy (TKE) and dσ/dθ were decomposed into two components (forward peaked and nearly constant at backward angles), and the elemental TKE and cross sections were derived. The backward components of³⁷Cl+²⁷Al and¹⁶O+⁴⁸Ti exhibit very different Z-distributions, indicating that the fragments do not originate from compound nucleus decay. The results can be understood in terms of an energy damping process.     

Elastische und unelastische Streuung von Deuteronen an Aluminium bei 11,8 MeV

Using the 11.8 MeV deuteron beam of a cyclotron, a study has been made of the angular dependence of the deuteron spectrum from interactions on Al²⁷. Separation of the deuterons from other products of the deuteron reactions was accomplished by recordingdE/dx, measured by a three fold proportional counter, andE, measured by a CsI-counter, on an oscilloscope screen. The experimental inelastic angular distributions have the shape of a direct interaction process. The elastic angular distribution shows pronounced diffraction maxima.     

Evolution from deep inelastic transfer to quasi-fission

Recoil techniques have been used to study the evolution of the features of four-charge transfer reactions in ¹⁴⁸Sm targets when the mass and energy of the projectile are varied. Beams of ⁶³Cu and ⁵⁶Fe were used, and their energies were chosen in order to be equal to 1.2B and 1.5B for both projectiles, B being the interaction barrier. The residual nuclei ^149gTb, ¹⁵⁰Dy and ¹⁵¹Dy were identified by their radioactive properties. This study has shown a continuous evolution of the characteristics of the c.m. angular distributions, especially the position of the maxima, from typical deep inelastic transfer to quasi-fission features, when the value of $\text{E}\text{B}$ decreases. For equal values of this ratio, no difference was observed between Fe and Cu induced reactions. The c.m, energies corresponding to the maximum cross section increases when the incident energy is increased, for a given projectile. At low incident energies (igE = 1.2B), the relative motion appears to be completely damped, and the distance of the two nuclei after separation is equal to about 5 fm. At higher incident energies, the c.m. energy is significantly higher. This may mean that the relative motion is not completely damped. Part of the effect may be explained by the differences in the angular momenta involved in the reaction.     

Projectile break-up with two outgoing intermediate-mass fragments in 26 AMeV32S+197Au

Correlations between two intermediate-mass fragments resulting from 840 MeV³²S projectiles interacting with¹⁹⁷Au were measured. The angular correlations and absolute two-fragment cross sections agree with predictions of a semi-microscopic model for direct dynamic projectile break-up. This suggests a predominantly direct mechanism for the production of intermediate-mass fragment pairs. It is argued that the intensity of such a channel which, compared to decays yieldingα particles, is much larger than observed for the sequential decay of corresponding primary excited nuclei, supports the direct-break-up interpretation. The model mechanism yields also strongly damped projectile fragments of intermediate mass.     

Large contribution of deep inelastic processes to reactions of40Ar and48Ca with238U

Differential recoil range distributions have been measured for heavy-reaction products ranging from Te(Z=52) to quasielastic transfer products near the charge and mass of the targets for the reactions of 276 MeV⁴⁸Ca+²³⁸U, 237MeV and 250 MeV⁴⁰Ar+²³⁸U, and 259 MeV⁴⁰Ar+¹⁹⁷Au. The measured recoil range distributions for the⁴⁰Ar+¹⁹⁷Au reaction agree with range distributions calculated from the known projectile-like fragment angular distributions for this reaction. The angular distributions of recoil products formed in the uranium target reactions are deduced and show that the products in the₇₅Re to₈₃Bi region have backward peaked angular distributions characteristic of deep inelastic reactions. The heavy product angular distributions smoothly vary from a (1/sinθ) shape to an exponential shaped backward peak as the atomic number of the product increases from 52 to 83. The trend in the deduced angular distributions for those elements for which recoil range distributions were determined in the⁴⁰Ar+¹⁹⁷Au reaction and the 250 MeV⁴⁰Ar+²³⁸U reaction is similar, suggesting that just as for the Ar+Au system the composite system for the uranium target reaction is also not fully equilibrated along the mass asymmetry coordinate. These conclusions show that the fraction of the total reaction cross section resulting in complete fusion must be re-evaluated for the⁴⁰Ar+²³⁸U reaction and similar heavy-target reactions.