Double-folding Potential Research Articles

Hindrance of Heavy-Ion Fusion due to Nuclear Incompressibility

We propose a new mechanism to explain the unexpected steep falloff of fusion cross sections at energies far below the Coulomb barrier. The saturation properties of nuclear matter are causing a hindrance to large overlap of the reacting nuclei and consequently a sensitive change of the nuclear potential inside the barrier. We report in this Letter a good agreement with the data of coupled-channels calculation for the 64Ni + 64Ni combination using the double-folding potential with Michigan-3-Yukawa-Reid effective N - N forces supplemented with a repulsive core that reproduces the nuclear incompressibility for total overlap.

Excitation of nuclear collective states by heavy ions within the model of semimicroscopic optical potential

The (semi)microscopic double-folding nucleusAnucleus optical potentials are suggested for consid- eration of inelastic scattering with excitation of collective nuclear states by using the adiabatic approach and the elastic scattering amplitude in the high-energy approximation. The analytical expression for inelastic scattering amplitude is obtained keeping therst-order terms in the deformation parameter of a potential. Calculations of inelastic cross sections for the 17 O heavy ions scattered on different nuclei at about hundred MeV/nucleon are made, and the acceptable qualitative agreement with the experimental data is obtained without introducing free parameters. The prospect of the method for further applications is discussed. ²O · ¸¸³μE·¥´¨O ´¥E¶·E£μ£μ · ¸¸¥O´¨O ¸ ¢μ§iE|¤¥´¨¥³ ±μ²²¥±E¨¢´OI ¸μ¸EμO´¨° O¤¥· ¶·¥¤² - £ ¥E¸O ¨¸¶μ²O§μ¢ EO (¶μ²E)³¨±·μ¸±μ¶¨I¥¸±¨° O¤·μ-O¤¥·´O° μ¶E¨I¥¸±¨° ¶μE¥´I¨ ², ¤¨ i E¨I¥¸±¨° ¶μ¤Iμ¤ ¨ ³¶²¨EE¤E E¶·E£μ£μ · ¸¸¥O´¨O ¢ ¢O¸μ±μO´¥·£¥E¨I¥¸±μ³ ¶·¨i²¨|¥´¨¨. �μ²EI¥´μ ´ ²¨E¨- I¥¸±μ¥ ¢O· |¥´¨¥ ¤²O ³¶²¨EE¤O ´¥E¶·E£μ£μ · ¸¸¥O´¨O, £¤¥ E¤¥·|¨¢ OE¸O I²¥´O ¶¥·¢μ£μ ¶μ·O¤± ¢ · §²μ|¥´¨¨ ¶μE¥´I¨ ² ¶μ ¶ · ³¥E·E ¤¥Eμ·³ I¨¨. ‚O¶μ²´¥´O · ¸I¥EO ´¥E¶·E£¨I ¸¥I¥´¨° · ¸- ¸¥O´¨O EO|¥²OI ¨μ´μ¢ 17 O · §´O³¨ O¤· ³¨ ¶·¨ O´¥·£¨OI μ±μ²μ 100 ŒO‚/´E±²μ´, ¨ ¶μ²EI¥´μ E¤μ¢²¥E¢μ·¨E¥²O´μ¥ ¸μ£² ¸¨¥ ¸ O±¸¶¥·¨³¥´E ²O´O³¨ ¤ ´´O³¨ i¥§ ¢¢¥¤¥´¨O ¸¢μiμ¤´OI ¶ · ³¥E·μ¢. �i¸E|¤ OE¸O ¢μ§³μ|´μ¸E¨ ¶·¥¤²μ|¥´´μ£μ ¶μ¤Iμ¤ ¤²O ¤ ²O´¥°I¨I ¶·¨²μ|¥´¨°.

On temperature dependence of the optical potential for alpha-particles at low energies

Within the double folding formalism of the α-nucleus optical potential, used previously for a semi-microscopic analysis of the α-particle elastic scattering on A ∼ 100 nuclei at energies below 32 MeV, effects due to changes of the nuclear density at a finite temperature are considered. Parameterizations of the double-folding (DF) real potential as well as of a regional phenomenological potential have been used in the study of the ( n , α ) reaction cross sections for the target nuclei 92,95,98,100Mo. Taking into account the microscopic DF potentials based on nuclear density distributions, we are able to fully describe the excitation functions of the ( n , α ) reactions. It is shown that the temperature dependence of the nuclear density distribution function can be an important aspect that has to be included in statistical model calculations even for a nuclear temperature smaller than 2 MeV.

Failure of the standard coupled-channels method in describing inelastic reaction data: on the use of a new shape for the coupling potential

We present the failure of the standard coupled-channels method in explaining inelastic scattering together with other observables such as elastic scattering, excitation function and fusion data. We use both microscopic double-folding and phenomenological deep potentials with shallow imaginary components. We argue that the solution of the problems for the inelastic scattering data is not related to the central nuclear potential, but to the coupling potential between excited states. We demonstrate that these problems can be addressed in a systematic way by using a different shape for the coupling potential instead of the usual one based on Taylor expansion.

Threshold anomaly with weakly bound projectiles: Elastic scattering ofBe9+Al27

Elastic scattering of the weakly bound $^{9}\mathrm{Be}$ on $^{27}\mathrm{Al}$ was measured at near barrier energies. The optical model data analysis with the real and imaginary parts of a global double-folding potential does not show strong evidence of the usual threshold anomaly. The same result was obtained by using a Woods-Saxon shape optical potential and calculating the potential strengths at the strong absorption radius. The reason for this behavior may be explained by the presence of break-up and∕or transfer channels at low energies.

Recent Theoretical Activities of Heavy-Ion Fusion Reactions in Sendai

We discuss three topics. The first is the effect of difference of the deformation of the neutron and proton density distributions predicted for some nuclei on their fusion cross section. The second is the results of calculations of the fusion cross section based on the double folding potential. We discuss the sensitivity of the fusion cross section to the surface properties of nuclei, and the necessity of normalization of the potential to reproduce the experimental data at high energies. The third is related to the synthesis of superheavy elements. We show that the quantum effects originating from the finite curvature of the fission barrier play significant roles in describing the synthesis of superheavy elements, i.e. the evolution from the fusion to the fission barriers, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability to cross the fission barrier.

Folding model and coupled-channels analysis of 6,7 Li elastic and inelastic scattering

The double-folding optical potentials of 6,7Li nuclei have been constructed using the S1Y effective nucleon-nucleon interaction. Angular distributions of the differential cross-section of 6,7Li elastic and inelastic scattering from 12 C, 28 Si and 58 Ni targets in the energy range 12-35 MeV/u were analyzed using the derived potentials through the coupled-channels mechanism. Successful descriptions of the data were obtained using the derived potentials.

16O-induced transfer reactions on 90Zr

Cross-section for transfer reactions 90Zr(16O, X) have been measured at an incident energy of 90 MeV. The angular distribution of the elastic scattering 90Zr(16O,16O)90Zr, the inelastic scattering to excited states of 90Zr, the one-nucleon transfer reactions 90Zr(16O,15N)91Nb (g.s., 0.104 and 3.37 MeV states), 90Zr(16O,15O)91Zr (g.s. and 2.17 MeV state) 90Zr(16O,17O)91Zr (g.s.) and the two-nucleon transfer reactions 90Zr(16O,14C)92Mo (ground and 1st excited states) are analyzed in the coupled-reaction-channel (CRC) formalism. Starting with a double-folded real potential, the elastic-scattering angular distribution is calculated using the CRC code FRESCO. The absorptive potential is then generated through the coupling of various inelastic and transfer processes that occur at the nuclear surface. Addition of a short-range imaginary potential in the coupling scheme, whose purpose was to take into account the effect due to loss of flux in fusion channel, reproduces the measured elastic-scattering angular distribution. A good description of all the quasi-elastic data has been achieved and the absolute magnitudes are reproduced without any arbitrary normalization. The relative importance of the one-step cluster transfer of two protons vs. the two-step successive transfer has been studied.

DOUBLE FOLDING ANALYSIS OF 6Li SCATTERING BY 12C, 40Ca, 90Zr AND 208Pb

A double folding potential has been used to calculate the real part of optical potential of 6 Li scattering by 12 C , 40 Ca , 90 Zr and 208Pb. In this model the effective nucleon-nucleon interaction potential has been developed to include an energy and density dependent in a simple form. The real part of the optical potential calculated by the double folding model is then reduced to an equivalent Wood–Saxon form using a fitting program. The obtained Wood–Saxon potentials have been used to calculate the differential cross sections for elastic scattering of 6 Li nucleus by 12 C , 40 Ca , 90 Zr and 208 Pb . This method gives satisfactory agreement of the calculated differential scattering cross section with the corresponding experimental values.

Total cross sections for 4,6He + 28Si reactions measured at 10–28 MeV/A

New results on the energy dependence of the total cross section (σ R) for 6He scattering on 28Si in the incident energy range 10–28 MeV/A are obtained. The α-particle-production cross sections for the 28Si(6He, 4He)X channel are measured as well. The secondary beam of 6He with an intensity of up to 5×104 particle/s was generated by bombarding a thick beryllium target with ∼32-MeV/A 7Li ions. In the energy region below 17 MeV/A, σ R increases sharply. The experimental dependences of the total cross sections are compared with the results of σ R calculations using the double-folding potential within the optical model. The energy dependence of σ R for 6He differs from that for the neighboring nuclei, which can be associated with the structural features of the former nucleus. The energy spectra of α particles produced in the 6He interactions with silicon indicate two mechanisms of their production: transfer reaction and 6He breakup in the field of the 28Si nucleus.

Elastic scattering and breakup of17Fat 10 MeV/nucleon

Angular distributions of fluorine and oxygen produced from 170 MeV 17^F incident on 208^Pb were measured. The elastic scattering data are in good agreement with optical model calculations using a double-folding potential and parameters similar to those obtained from 16^O+208^Pb. A large yield of oxygen was observed near \theta_lab=36 deg. It is reproduced fairly well by a calculation of the (17^F,16^O) breakup, which is dominated by one-proton stripping reactions. The discrepancy between our previous coincidence measurement and theoretical predictions was resolved by including core absorption in the present calculation.

Folding model analysis of 6,7Li elastic scattering at 12.5–53 MeV/u

6,7Li-nucleus double-folding optical potentials have been constructed using the JLM and a gaussian shape of the effective nucleon–nucleon interaction. Angular distributions of the differential cross sections of 6,7Li elastic scattering from 12C, 28Si, 40Ca, 58Ni, 90Zr and 208Pb targets at 12.5–53 MeV/u were analyzed using the derived potentials. An energy-dependent reducing renormalization coefficient was required for the real component of the JLM optical potential in order to obtain successful predictions of the observed cross sections even when the projectile density-dependence was considered. A similar behavior was found for calculations based on the density-independent gaussian version of the effective nucleon–nucleon interaction. However, no renormalization was needed when a density-dependence approximation was involved. The energy- and target mass number-dependence in the renormalization factor, real volume integrals and total reaction cross sections are investigated.

Improving explosive nucleosynthesis models via (n,α) measurements

Within the double folding formalism of the α-nucleus optical potential, used previously for a semi-microscopic analysis of the α-particle elastic scattering on A∼100 nuclei at energies below 32 MeV, effects due to changes of the nuclear density at a finite temperature are considered. Parameterizations of the double-folding (DF) real potential as well as of a regional phenomenological potential have been used in the study of the (n,α) reaction cross sections for the target nuclei 92,95,98,100Mo. Taking into account the microscopic DF potentials based on nuclear density distributions, we are able to fully describe the excitation functions of the (n,α) reactions. It is shown that the temperature dependence of the nuclear density distribution function can be an important aspect that has to be included in statistical model calculations even for a nuclear temperature smaller than 2 MeV.

New results for reaction cross sections of intermediate energy [formula omitted]-particles on targets from [formula omitted]Be to [formula omitted]Pb

Reaction cross sections for α-particles have been measured for 9Be, 12C, 16O, 28Si, 40Ca, 58,60Ni, 112,116,120,124Sn, and 208Pb at 117.2, 163.9 and 192.4 MeV and for the lighter nuclei also at 69.6 MeV. The results are compared with predictions from optical model calculations using phenomenological, global and double-folded optical potentials. Comparisons are also made with predictions using the Glauber model approach suggested by Bertsch, Brown and Sagawa.

α-nucleus potentials for the neutron-deficientpnuclei

$\ensuremath{\alpha}$-nucleus potentials are one important ingredient for the understanding of the nucleosynthesis of heavy neutron-deficient p nuclei in the astrophysical $\ensuremath{\gamma}$ process where these p nuclei are produced by a series of $(\ensuremath{\gamma},n),$ $(\ensuremath{\gamma},p),$ and $(\ensuremath{\gamma},\ensuremath{\alpha})$ reactions. I present an improved $\ensuremath{\alpha}$-nucleus potential at the astrophysically relevant sub-Coulomb energies which is derived from the analysis of $\ensuremath{\alpha}$ decay data and from a previously established systematic behavior of double-folding potentials.

Half-lives of trinuclear molecules

Recent discoveries of ${}^{10}\mathrm{Be}$ and ${}^{12}\mathrm{C}$ accompanied cold fission in the spontaneous fission of ${}^{252}\mathrm{Cf}$ lead to the surprising result that long living trinuclear molecules may exists. For the description of the dynamics and decay of such molecules, we used a coplanar three body cluster model (two deformed fragments and an \ensuremath{\alpha} particle) with a three body potential computed by a double folding potential generated by M3Y effective interaction. A repulsive compression term was included. The computed \ensuremath{\alpha} ternary cold fission yields are in agreement with the experiment. The energy and angular distributions of the three clusters at infinity and the half-lives are strongly dependent of the initial positions of the \ensuremath{\alpha} particle relative to the two fragments and of mass asymmetry of the fragments. The evaluated lifetimes of such trinuclear molecules are quite large, of the order of one second.

Level structure of120Sn:High resolution(p,t)reaction and shell model description

The $(p,t)$ reaction on ${}^{122}\mathrm{Sn}$ has been studied in a high resolution experiment at an incident proton energy of 26 MeV. The cross section angular distributions for transitions to 38 levels of ${}^{120}\mathrm{Sn}$ with an excitation energy up to $\ensuremath{\sim}3500\mathrm{keV}$ have been measured. Distorted wave Born approximation analysis of experimental angular distributions using double-folded potential for the exit channel has been done. This has made it possible to confirm previous spin and parity values and to propose new assignments for a large number of states. A shell-model study of ${}^{120}\mathrm{Sn}$ has been performed using a realistic effective interaction derived from the Paris nucleon-nucleon potential. The calculations have been carried out within the framework of the seniority scheme including states with seniority up to 4. Comparison of the calculated and experimental spectra shows a one-to-one correspondence between levels up to about 2.7 MeV excitation energy and lends support to some of the spin-parity assignments given in this work.

One-particle exchange in the double-folded potential in a semiclassical approximation

The one-particle exchange in the double-folded model is analysed. The extended Thomas-Fermi approach to the one-body density matrix is used. The nucleon-nucleon force with Yukawa, Gauss and Coulomb-type form factors are considered. The energy dependence of the exchange part of the double-folded potential is investigated and a comparison with former approaches is carried out.

Cluster description of cold (neutronless) α ternary fission of252Cf

A coplanar three body cluster model (two deformed fragments and an \ensuremath{\alpha} particle) similar to the model used for the description of cold binary fission was employed for the description of cold (neutronless) \ensuremath{\alpha} accompanied fission of ${}^{252}\mathrm{Cf}.$ No preformation factors were considered. The three body potential was computed with the help of a double folding potential generated by the M3Y-NN effective interaction and realistic fragment ground state deformations. From the minimum action principle, the \ensuremath{\alpha} particle trajectory equations, the corresponding ternary barriers, and an approximate WKB expression for the barrier penetrability are obtained. The relative cold ternary yields were calculated as the ratio of the penetrability of a given ternary fragmentation and the sum of the penetrabilities of all possible cold ternary fragmentations. Different scenarios were considered depending on the trajectories of the fragments. It was shown that two regions of cold fragmentation exist, a deformed one corresponding to large fragment deformations and a spherical one around ${}^{132}\mathrm{Sn},$ similarly to the case of the cold binary fission of ${}^{252}\mathrm{Cf}.$ We have shown that for the scenario corresponding to the Lagrange point, where all forces acting on the \ensuremath{\alpha} particle are in equilibrium, the cold \ensuremath{\alpha} ternary yields of ${}^{252}\mathrm{Cf}$ are strongly correlated with the cold binary yields of the daughter nucleus ${}^{248}\mathrm{Cm}$ into the same heavy fragments. For all other scenarios only the spherical splittings are favored. We concluded that due to the present available experimental data on cold \ensuremath{\alpha} ternary yields only the Lagrange scenario could describe the cold \ensuremath{\alpha} ternary fission of ${}^{252}\mathrm{Cf}.$

Cold-fission modes in [sup 252]Cf

The binary and ternary cold fragmentations of heavy nuclei are studied in the framework of a deformation-dependent cluster model in which the final fragments are produced in their respective ground states and interact via a double-folded potential with M3Y forces. The deformation effects are taken into account up to multipolarity λ=4. It is shown that two regions of cold fragmentation arise. The first one has large quadrupole and even hexadecapole deformations and mass number of the heavy fragment ranging between 138 and 158. In the second region, the Q-value principle dictates the occurrence of a few spherical nuclei around the doubly magic nucleus 132 Sn , which is similar to the case of heavy-cluster radioactivity, where the daughter nuclei are around 208 Pb . This structure is similar for binary and ternary cold fission. The cold-fission yields are computed for the binary fragmentation and for the alpha-accompanied fission of 252 Cf . For the ternary cold-fission mode we derive the most likely geometrical and dynamical characteristics of the fragments at the moment of release of the light particle and perform classical trajectory calculations, in order to compute the final kinetic energy of the alpha particle. The recent observation of 10 Be in cold ternary fission is discussed in connection with the concept of a giant nuclear molecule.