Coulomb Barrier Energies Research Articles

Observation of rotating nuclear molecules and determination of their lifetimes

Long-living rotating nuclear molecules (or “dinuclear systems”) have been observed at the velocity filter SHIP at GSI in reactions of 64Ni + 207Pb at Coulomb barrier energies. The rotation was directly revealed by the velocity spectra of deep inelastic target-like transfer products which are formed during the lifetime of the nuclear molecule and emitted after its breakup. The corresponding rotation angles were about 180 degree pointing to long nuclear interaction times or lifetimes of the system, respectively. We deduced the lifetimes from the lines in the velocity spectra originating from two different rotation angles. Further, the unambiguous correlation of a certain transfer product with its individual velocity spectrum allowed us to study the lifetimes as a function of the number of transferred protons.

A C-code for the double folding interaction potential for reactions involving deformed target nuclei

We present a C-code designed to obtain the interaction potential between a spherical projectile nucleus and an axial–symmetrical deformed target nucleus and in particular to find the Coulomb barrier, by using the double folding model (DFM). The program calculates the nucleus–nucleus potential as a function of the distance between the centers of mass of colliding nuclei as well as of the angle between the axis of symmetry of the target nucleus and the beam direction. The most important output parameters are the Coulomb barrier energy and the radius. Since many researchers use a Woods–Saxon profile for the nuclear term of the potential we provide an option in our code for fitting the DFM potential by such a profile near the barrier. Program summaryProgram title: DFMDEFCatalogue identifier: AENI_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENI_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 2245No. of bytes in distributed program, including test data, etc.: 215442Distribution format: tar.gzProgramming language: C.Computer: PC, Mac.Operating system: Windows XP (with the GCC-compiler version 2), MacOS, Linux.RAM: 100 MB with average parameters setClassification: 17.9.Nature of problem:The code calculates in a semimicroscopic way the bare interaction potential between a spherical projectile nucleus and a deformed but axially symmetric target nucleus as a function of the center of mass distance as well as of the angle between the axis of symmetry of the target nucleus and the beam direction. The height and the position of the Coulomb barrier are found. The calculated potential is approximated by a conventional Woods–Saxon profile near the barrier. Dependence of the barrier parameters upon the characteristics of the effective NN forces (like, e.g., the range of the exchange part of the nuclear term) can be investigated.Solution method:The nucleus–nucleus potential is calculated using the double folding model with the Coulomb and the effective M3Y NN interactions. For the direct parts of the Coulomb and the nuclear terms, the Fourier transform method is used. In order to calculate the exchange parts the density matrix expansion method is applied.Running time:Using a PC with 1.60 GHz processor under Windows XP less than 1 min in the case of reduced calculations and about 40 min in the case of full calculations for one value of angle. Using Apple computer under MacOS the code runs faster by a factor of 5.

RADIAL SENSITIVITY OF THE ELASTIC SCATTERING AROUND THE COULOMB BARRIER ENERGIES FOR WEAKLY-BOUND AND HALO NUCLEI

The radial sensitivity of the elastic scattering of the weakly-bound 6 Li and halo 6 He nuclei on medium-mass 64 Zn target and heavy target 208 Pb is examined around the Coulomb barrier energies. We present that very good agreement between theoretical and experimental results have been obtained with small χ2/N values. The fusion cross-section and volume integrals of the potentials have been deduced from the theoretical calculations for all studied systems at relevant energies. We have also analyzed the elastic scattering of the 6 He +208 Pb system at E lab = 14, 16, 18, 22, 27 MeV in order to investigate whether there is a dispersion relation between the real and imaginary parts of the optical potential.

Effect of the α production process on the direct reaction for the 7Li projectile

We investigate the effect of the breakup process on the direct reaction (DR) for 7Li. In order to study this effect, we introduce the theoretical ratio factor, R th, and the average value of the ratio factor is 0.92. The ratio factor is close to unity in the below-barrier region because many of the α particles separated from the breakup process of 7Li are not captured by the target nuclei. As a result, the α production cross sections become the main portion of the DR cross sections. However, the value of R th in the above-barrier region are gradually suppressed because the α particles at energies above the Coulomb-barrier energy can be captured easily by the target. Using the centerof-mass energy regions of α particles, we investigate the difference of the R th values between 6Li + 209Bi and 7Li + 209Bi systems in the above-barrier region, and we find that this difference is attributed to a reduction of the α capture cross-sections for the 7Li + 209Bi system.

Woods-Saxon and São Paulo optical model calculations of the threshold anomaly of the 6,7Li+28Si systems near Coulomb barrier energies

Two types of optical model interactions, namely the double-folding density dependent São Paulo potential (SPP) and the Woods-Saxon potential (WSP) are used to study the appearance of the Theshold Anomaly (TA) or the Breakup Threshold Anomaly (BTA) for the nuclear systems 6,7Li+28Si for energies around the Coulomb barrier. In the first case, the presence of the anomaly is determined from the energy dependence of the normalization parameters NR and NI as found from fittings to elastic scattering angular distributions. In the second case, the presence of the anomaly is investigated by the energy variation of the fusion and direct reaction parts of the Woods-Saxon potential. In this case, the parameters of the fusion and direct reaction potentials are calculated by a simultaneous analysis of elastic scattering, fusion and total reaction cross sections. It is found in both cases that the BTA appears for the 6Li+28Si reaction. As for 7Li+28Si, the calculation with the SPP shows that the usual TA appears but the dispersion relation is not satisfied, however the WSP indicates that indeed the BTA shows up.

Strong reaction channels for the system 17F + 58Ni at Coulomb barrier energies

The reaction dynamics induced by the 17F Radioactive Ion Beam on the proton-shell closed 58Ni target was studied at two colliding energies slightly above the Coulomb barrier. Charged reaction products were detected at forward angles and the quasi-elastic differential cross section was analyzed within the framework of the optical model in order to extract the reaction cross section and to investigate the relevance of direct reaction channels (inelastic scattering, breakup and transfer) at near-barrier energies. The comparison with the reaction induced by double-magic tightly-bound 16O projectiles on the same target showed that the 17F reaction cross section is moderately enhanced at the lower secondary beam energy. Direct reaction channels were also found to be more relevant than for the corresponding 16O-induced reaction.

Two-Particle Separation Energies in the Superdeformed Well

The location of nuclear closed shells, as evidenced through discontinuities in binding energy and one- and two-particle separation energy systematics, remains one of the simplest tests of global nuclear models. How shell gaps evolve, whether with increasing mass, increasing neutron:proton ratio or increasing deformation, is still uncertain, and it has recently been suggested that one must go beyond a static meanfield picture to include the effects of dynamic fluctuations in the nuclear shape even in the ground state. The identification of key properties which may distinguish between competing approaches is thus vital. Comparison of the binding energies of superdeformed nuclei in the A ≈ 190 region shows that two-proton separation energies are higher in the superdeformed state than in the normal state, despite the probably lower Coulomb barrier and lower total binding energy. Possible reasons for this difference are discussed. This somewhat counterintuitive result provides a critical test for global nuclear models.

Complete and incomplete fusion in 9Be+124Sn system

Abstract Complete and incomplete fusion cross-sections for the 9Be+124Sn system have been measured around the Coulomb barrier energies (E lab C.B=28 MeV) using the on-line gamma ray detection technique. The complete fusion cross-sections of this system have been compared with the two stable projectiles on the same 124Sn target to provide information on the projectile dependence. The brief comparison of the present 9Be+124Sn data with a comprehensive and recent study of the neighbouring system 9Be+144Sm is also given.

Heavy ion reactions around the Coulomb barrier

The angular distributions of fission fragments for the 32S+184W reaction near Coulomb barrier energies are measured. The experimental fission excitation function is obtained. The measured fission cross sections are decomposed into fusion-fission, quasi-fission and fast fission contributions by the dinuclear system (DNS) model. The hindrance to completing fusion both at small and large collision energies is explained. The fusion excitation functions of 32S+90,96Zr in an energy range from above to below the Coulomb barrier are measured and analyzed within a semi-classical model. The obvious effect of positive Q-value multi-neutron transfers on the sub-barrier fusion enhancement is observed in the 32S+96Zr system. In addition, the excitation functions of quasi-elastic scattering at a backward angle have been measured with high precision for the systems of 16O + 208Pb, 196Pt, 184W, and 154,152Sm at energies well below the Coulomb barrier. Considering the deformed coupling effects, the extracted diffuseness parameters are close to the values extracted from the systematic analysis of elastic and inelastic scattering data. The elastic scattering angular distribution of 17F+12C at 60 MeV is measured and calculated by using the continuum-discretized coupled-channels (CDCC) approach. It is found that the diffuseness parameter of the real part of core-target potential has to be increased by 20% to reproduce the experimental result, which corresponds to an increment of potential depth at the surface region. The breakup cross section and the coupling between breakup and elastic scattering are small.

CARIBU: a new facility for the study of neutron-rich isotopes

The Californium Rare Ion Breeder Upgrade (CARIBU) to the ATLAS superconducting linac facility is currently being commissioned. It provides low-energy and re-accelerated beams of neutron-rich isotopes obtained from 252Cf fission. The fission products from a 252Cf source are stopped in a large high-intensity gas catcher, thermalized and extracted through an RFQ cooler, accelerated to 50 kV and mass separated in a high-resolution separator before being sent to either an ECR charge breeder for post-acceleration through the ATLAS linac or to a low-energy experimental area. This approach gives access to beams of very neutron-rich isotopes, many of which have not been available at low or Coulomb barrier energies previously. These beams provide unique opportunities for measurements along the r-process path. To take advantage of these unique possibility, the reaccelerated beams from CARIBU will be made available at the experimental stations of ATLAS to serve equipment such as Gammasphere, HELIOS and the reaction spectrometers. In addition, the Canadian Penning Trap (CPT) mass spectrometer has been moved to the CARIBU low-energy experimental area and a new injection line has been built. The new injection line consists of a RFQ buncher sitting on a 50 kV high-voltage platform that will accumulate the mass separated 50 kV radioactive beams, cool and extract them as a pulsed beam of 3 keV. This beam can be sent either to a tape station for diagnostics and tuning, or a cryogenic linear trap for preparation before transfer to the high-precision Penning trap where the mass measurements will take place. Initial CARIBU commissioning is proceeding with a 2 mCi source that will be replaced by a 100 mCi source as the commissioning proceeds. Final operation will use a 1 Ci source and attain yield in excess of 107 ions/sec for the most intense beams at low energy, an order of magnitude less for reaccelerated beams.

Analysis of alpha-cluster transfer in 16O+12C and 12C+16O at energies near Coulomb barrier

The aim of this work is to track the phenomenon of α-cluster transfer mechanism at low energies 1.25, 1.5 and 1.75 MeV/n, close to the Coulomb barrier energy for 12 C( 16 O, 12 C) 16 Oa nd 16 O( 12 C, 16 O) 12 C nuclear systems. The measurements of the angular distribution show a significant increase in the differential cross section at large angles due to alpha-transfer mechanism. The optical model code SPI-GENOA could be used effectively for fitting the experimental data with the theoretical predictions nearly up to angle 90 ◦ , where the differential cross section decreases steadily with increasing the scattering angle. For the second hemisphere, at angles greater than 100 ◦ , there is a large increase in cross section due to the contribution of α-transfer mechanism, and the Distorted Wave Born Approximation (DWBA) method could be used effectively for fitting the experimental data with the theoretical predictions at this region using (DWUCK5) code.

Fission fragment mass distributions in reactions forming theFr213compound nucleus

The fission fragment mass angle correlations and mass ratio distributions have been investigated for the two systems $^{16}\mathrm{O}+^{197}\mathrm{Au}$ and $^{27}\mathrm{Al}+^{186}\mathrm{W}$, leading to the same compound nucleus $^{213}\mathrm{Fr}$ around the Coulomb barrier energies. Systematic analysis of the variance of the mass distributions as a function of temperature and angular momentum suggests true compound nuclear fission for both the reactions, indicating the absence of nonequilibrium fission processes.

12C+16O sub-barrier radiative capture cross-section measurements

We have performed a heavy ion radiative capture reaction between two light heavy ions, $^{12}$C and $^{16}$O, leading to $^{28}$Si. The present experiment has been performed below Coulomb barrier energies in order to reduce the phase space and to try to shed light on structural effects. Obtained $\gamma$-spectra display a previously unobserved strong feeding of intermediate states around 11 MeV at these energies. This new decay branch is not fully reproduced by statistical nor semi-statistical decay scenarii and may imply structural effects. Radiative capture cross-sections are extracted from the data.

Coupled channel effect in elastic scattering and fusion for6,7Li+28Si

The fusion excitation and elastic angular distribution were measured for 6,7 Li+28 Si from below to above Coulomb barrier (≤ 3Vb ) energies. The barrier distribution derived from the fusion data was found to be broad and asymmetric at the sub-barrier region, compared to 1D BPM estimation. Effect of rotational coupling on fusion was found to be not so dominant. Phenomenological optical potential parameters, with surface and volume type imaginary potentials, were obtained from f tting of elastic scattering data and energy dependence of real and imaginary surface strengths were investigated around the barrier. CDCC calculations considering only breakup of projectile were performed for 6,7 Li+28 Si with the elastic scattering data, using the code FRESCO. The effects of breakup of projectile on elastic cross section do not agree with the energy dependence of real and imaginary strength with volume type imaginary potential around the barrier.

Two-Particle Separation Energy Trends in the Superdeformed Well

A measurement of the energy and spin of superdeformed states in 190Hg, obtained through the observation of transitions directly linking superdeformed and normal states, expands the number of isotopes in which binding energies at superdeformation are known. Comparison with neighboring nuclei shows that two-proton separation energies are higher in the superdeformed state than in the normal state, despite the lower Coulomb barrier and lower total binding energy. This unexpected result provides a critical test for nuclear models.

Investigation of deep inelastic reactions in 238U + 238U at Coulomb barrier energies

We investigated deep inelastic reactions in 238U + 238U collisions at 6.09, 6.49, 6.91, 7.1 and 7.35×A MeV at the VAMOS spectrometer (GANIL). A large transfer of neutrons and protons was observed at all beam energies. For a transfer of more than 10 nucleons the total kinetic energy of the detected fragments becomes independent of the beam energy and reaches values far below the Coulomb barrier for spherical fragments. This points to the formation of a di-nuclear system in the entrance channel which develops an elongated shape and a strong neck. For such reactions we expect an enhanced lifetime of the di-nuclear system which is significantly longer than the time scale for elastic and quasi-elastic reactions. Different theoretical approaches predict delay times of more than 5×10-21 s for a subset of our data.

ENERGY DISSIPATION IN FUSION REACTIONS FROM DYNAMICAL MEAN-FIELD THEORY

Nucleus-nucleus interaction potentials and friction coefficients associated with one-body energy dissipation in the entrance channel of fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory. They show center-of-mass energy dependence close to the Coulomb barrier energy. This dependence indicates dynamical reorganization of internal degrees of freedom. We give a simple estimate of excitation energy from microscopic nucleon exchange.

A C-code for the double folding interaction potential of two spherical nuclei

We present a C-code designed to obtain the nucleus–nucleus potential by using the double folding model (DFM) and in particular to find the Coulomb barrier. The program calculates the nucleus–nucleus potential as a function of the distance between the centers of mass of colliding nuclei. The most important output parameters are the Coulomb barrier energy and the radius. Since many researchers use a Woods–Saxon profile for the nuclear term of the potential we provide an option in our code for fitting the DFM potential by such a profile. Program summary Program title: DFMSPH Catalogue identifier: AEFH_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEFH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5929 No. of bytes in distributed program, including test data, etc.: 115 740 Distribution format: tar.gz Programming language: C Computer: PC Operating system: Windows XP (with the GCC-compiler version 2) RAM: Below 10 Mbyte Classification: 17.9 Nature of problem: The code calculates in a semimicroscopic way the bare interaction potential between two colliding spherical nuclei as a function of the center of mass distance. The height and the position of the Coulomb barrier are found. The calculated potential is approximated by a conventional Woods–Saxon profile near the barrier. Dependence of the barrier parameters upon the characteristics of the effective NN forces (like, e.g. the range of the exchange part of the nuclear term) can be investigated. Solution method: The nucleus–nucleus potential is calculated using the double folding model with the Coulomb and the effective M3Y NN interactions. For the direct parts of the Coulomb and the nuclear terms, the Fourier transform method is used. In order to calculate the exchange parts the density matrix expansion method is applied. Running time: Less than 1 minute using a PC with a 1.60 GHz processor.

Reaction mechanism study of 7Li(7Li,6He) reaction at above Coulomb barrier energies

The elastic scattering and the 6He angular distributions were measured in 7Li + 7Li reaction at two energies, Elab = 20 and 25 MeV. FRDWBA calculations have been performed to explain the measured 6He data. The calculations were very sensitive to the choice of the optical model potentials in entrance and exit channels. The one-step proton transfer was found to be the dominant reaction mechanism in 6He production.

Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier

The nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory for the mass symmetric reactions ${}^{16}\mathrm{O} + {}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca} + {}^{40}\mathrm{Ca}$, and ${}^{48}\mathrm{Ca} + {}^{48}\mathrm{Ca}$ and the mass asymmetric reactions ${}^{16}\mathrm{O} + {}^{40, 48}\mathrm{Ca}$, ${}^{40}\mathrm{Ca} + {}^{48}\mathrm{Ca}$, ${}^{16}\mathrm{O} + {}^{208}\mathrm{Pb}$, and ${}^{40}\mathrm{Ca} + {}^{90}\mathrm{Zr}$. When the c.m. energy is much higher than the Coulomb barrier energy, potentials deduced with the microscopic theory identify with the frozen density approximation. As the c.m. energy decreases and approaches the Coulomb barrier, potentials become energy dependent. This dependence indicates dynamical reorganization of internal degrees of freedom and leads to a reduction of the ``apparent'' barrier felt by the two nuclei during fusion of the order of 2--3% compared to the frozen density case. Several examples illustrate that the potential landscape changes rapidly when the c.m. energy is in the vicinity of the Coulomb barrier energy. The energy dependence is expected to have a significant role on fusion around the Coulomb barrier.