Effects of N/Z on Post-Saddle γ Emission as an Observable of Post-Saddle Nuclear Friction

Based on a dynamical Langevin equation coupled with a statistical decay model, we calculate the variation of the post-saddle giant dipole resonance （GDR） q-ray multiplicity of the heavy nuclei 24^240Cf, ^246Cf, ^252Cf and ^240U with the post-saddle friction strength （13）. We find that the sensitivity of the post-saddle γ emission to β decreases considerably with increasing the neutron-to-proton ratio （N/Z） of the system. Moreover, for 240 U, the γ emission is no longer sensitive to 13. We suggest that to accurately obtain information of the post-saddle friction strength by measuring pre-scission GDR γ-ray multiplicities, it is optimal to choose among the various compound systems those with low N/Z.     

Effects of N/Z on Spin Distribution of Evaporation Residue Cross Section as a Probe of Nuclear Dissipation

The spin distribution of the evaporation residue cross section of nuclei ^194pb, ^200Pb, ^206Pb, and ^200 Os are calculated via a Langevin equation coupled with a statistical decay model. It is shown that with increasing the neutronto-proton ratio （N/Z） of the system, the sensitivity of the significantly. Moreover, for ^200Os this spin distribution is no spin distribution to the nuclear dissipation is decreased longer sensitive to the nuclear dissipation. These results suggest that to obtain a more accurate pre-saddle viscosity coefficient through the measurement of the evaporation residue spin distribution, it is best to yield those compound systems with low N/Z.     

Roles of Isospin in Evaporation Residue Cross Section as a Probe of Nuclear Dissipation

The influence of isospin on the excess of evaporation residue cross section over its standard statistical-model value for nuclei ^194pb, ^200Pb, and ^206pb is studied via a Langevin equation coupled with a statistical decay model. The magnitude of this excess for a low-isospin fissioning nucleus is shown to be larger and its dependence on the nuclear viscosity coefficient to be stronger than those of a high-isospin fissioning nucleus. These results suggest that to obtain a more accurate information of viscosity coefficient inside the saddle point by measuring evaporation residue cross sections, we had better choose those compound systems with small isospin.     

System size effects on probing nuclear dissipation with neutrons

Using a dynamical Langevin equation coupled with a statistical decay model, we calculate the excess of the pre-scission neutron multiplicities over its standard statistical-model values as a function of the nuclear dissipation strength for the three nuclei 19~Os, 2~~Hg, and 21~po which have the same neutron-to-proton ratio N/Z. We find that by decreasing the size of the fissioning nuclei, the effects of nuclear dissipation on the excess of the pre-scission neutron multiplicity are substantially amplified, and that the sensitivity of this excess to the nuclear friction strength is considerably increased as well. We suggest that for those fissioning systems with the same N/Z that are populated in fusion reactions, to obtain a more accurate information of the nuclear dissipation strength by measuring the pre-scission neutron multiplicity, it is best to choose a system with a small size.     

Formation region of emitted α and heavier particles inside radioactive nuclei

We investigate the formation distance(R_0) from the center of the radioactive parent nucleus at which the emitted cluster is most probably formed. The calculations are performed microscopically starting with the solution to the time-independent Schr?dinger wave equation for the cluster-core system, using nuclear potentials based on the Skyrme-SLy4 nucleon-nucleon interactions and folding Coulomb potential, to determine the incident and transmitted wave functions of the system. Our results show that the emitted cluster is mostly formed in the pre-surface region of the nucleus, under the effect of Pauli blocking from the saturated core density. The deeper α-formation distance inside the nucleus allows less preformation probability and indicates a more stable nucleus for a longer half-life. Furthermore, the α-particle tends to be formed at a slightly deeper region inside the nuclei, with larger isospin asymmetry, and in the closed shell nuclei. Regarding the heavy clusters, we observed that the formation distance of the emitted clusters heavier than α-particle increased via increasing the isospin asymmetry of the formed cluster rather than by increasing its mass number. The partial half-life of a certain cluster-decay mode increased with increase of either the mass number or the isospin asymmetry of the emitted cluster.     

Effect of Wigner energy on the symmetry energy coefficient in nuclei

The nuclear symmetry energy coefficient(including the coefficient a_(sym)~((4)) of the I~4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei.It is found that the extracted symmetry energy coefficient a_(sym)~*(A,I) decreases with increasing isospin asymmetry I,which is mainly caused by Wigner correction,since e_(sym)~* is the summation of the traditional symmetry energy e_(sym) and the Wigner energy ew.We obtain the optimal values J = 30.25±0.10 MeV,a_(ss)=56.18±1.25 MeV,a_(sym)~((4)) = 8.33±1.21 MeV and the Wigner parameter x= 2.38 ±0.12 through a polynomial fit to 2240 measured binding energies for nuclei with20 ≤ A ≤ 261 with an rms deviation of 23.42 keV.We also find that the volume symmetry coefficient J■ 30 MeV is insensitive to the value x,whereas the surface symmetry coefficient a_(ss) and the coefficient a_(sym)~((4)) are very sensitive to the value of x in the range 1≤x≤4.The contribution of the a_(sym)~((4)) term increases rapidly with increasing isospin asymmetry I.For very neutron-rich nuclei,the contribution of the a_(sym)~((4)) term will play an important role.     

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z^2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV L 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.     

The spin-isospin decomposition of the nuclear symmetry energy from low to high density

The energy per particle BA in nuclear matter is calculated up to high baryon density in the whole isospin asymmetry range from symmetric matter to pure neutron matter.The results,obtained in the framework of the Brueckner-Hartree-Fock approximation with two-and three-body forces,confirm the well-known parabolic dependence on the asymmetry parameterβ=(N?Z)/A(β^2 law)that is valid in a wide density range.To investigate the extent to which this behavior can be traced back to the properties of the underlying interaction,aside from the mean field approximation,the spin-isospin decomposition of BA is performed.Theoretical indications suggest that theβ^2 law could be violated at higher densities as a consequence of the three-body forces.This raises the problem that the symmetry energy,calculated according to theβ^2 law as a difference between BA in pure neutron matter and symmetric nuclear matter,cannot be applied to neutron stars.One should return to the proper definition of the nuclear symmetry energy as a response of the nuclear system to small isospin imbalance from the Z=N nuclei and pure neutron matter.     

A New Decomposition Approach of Dirac Brueckner Hartree—Fock G Matrix for Asymmetric Nuclear Matter

Asymmetric nuclear matter is investigated by the Dirac Brueckner Hartree-Fock (DBHF) approach with a new decomposition of the Dirac structure of nucleon self-energy from the G matrix.It is found that the isospin dependence of the scalar and vector potentials is relatively weak,although boty potentials for neutron (proton) become deep (shallow) in the neutron-rich nuclear matter.The results in asymmetric nuclear matter are rather different from those obtained by a simple method,where the nucleon self-energy is deduced from the single-particle energy.The nuclear binding energy as a function of the asymmetry parameter fulfils the empirical parabolic law up to very extreme isospin asymmetric nuclear matter in the DBHF approach.The behaviour of the density depandence of the asymmetry energy is different from that obtained by non-relativistic approaches,although both give similar asymmetry energy at the nuclear saturation density.     

Surveying post-saddle nuclear dissipation with protons and α particles as probes

Using a Langevin model, we calculate post-saddle proton and α-particle multiplicities as a function of the post-saddle dissipation strength （β） for the heavy systems 234Cf, 240Cf, 246Cf and 240U. We find that, with increasing isospin of the system, the sensitivity of post-saddle light charged-particle multiplicities to β decreases considerably and, moreover, for 240U the charged-particle multiplicities are no longer sensitive to β. These results suggest that in order to determine the post-saddle friction strength more accurately by measuring the multiplicities of pre-scission protons and α particles, it is best to populate those heavy compound systems with low isospin.     

Two-dimensional Langevin modeling of fission dynamics of the excited compound nuclei ~(188)Pt,~(227)Pa and ~(251)Es

A stochastic approach based on one-and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity,fission probability,anisotropy of fission fragment angular distribution,fission cross section and the evaporation cross section for the compound nuclei ~(188)Pt,~(227)Pa and ~(251)Es in an intermediate range of excitation energies.The chaos weighted wall and window friction formula are used in the Langevin equations.The elongation parameter,c,is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis,K,considered as the second dimension in Langevin dynamical calculations.A constant dissipation coefficient of K,γk=0.077(MeV zs)~(-1/2),is used in two-dimensional calculations to reproduce the above mentioned experimental data.Comparison of the theoretical results of the pre-scission neutron multiplicity,fission probability,fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data.Furthermore,it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K,γk=0.077(MeV zs)~(-1/2),can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus(251)~Es.However,a larger value of γk=0.250(MeV zs)~(-1/2)is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus(227)Pa.     

Simulation of the fission dynamics of the excited compound nuclei ~(206)Po and ~(168)Yb produced in the reactions ~(12)C+~(194)Pt and ~(18)O+~(150)Sm

A two-dimensional dynamical model based on the Langevin equation was used to study the fission dynamics of the compound nuclei ~(206)Po and ~(168)Yb produced in the reactions ~(12)C+~(194)Pt and ~(18)O+~(150)Sm,respectively.The fission cross section and average pre-scission neutron multiplicity were calculated for the compound nuclei ~(206)Po and ~(168)Yb,and results of the calculations compared with the experimental data.The elongation coordinate was used as the first dimension and the projection of the total spin of the compound nucleus onto the symmetry axis,K,considered as the second dimension in the Langevin dynamical calculations.In the two-dimensional calculations,a constant dissipation coefficient of K and a non-constant dissipation coefficient have been used to reproduce the abovementioned experimental data.It is shown that the two-dimensional Langevin equation can satisfactorily reproduce the fission cross section and average pre-scission neutron multiplicity for the compound nuclei ~(206)Po and ~(168)Yb by using constant values of the dissipation coefficient of K equal to γκ=0.18(MeV zs)~(-1/2) and γκ= 0.20(MeV zs)~(-1/2)for the compound nuclei ~(206)Po and ~(168)Yb,respectively.     

Photo-transmutation based on resonance γ-ray source

High intensity γ-ray source can be obtained through resonance reaction induced by protons. In this work, the possibility of using such high intensity MeV-range γ-ray source to transmute nuclear waste is investigated through Mont Carlo simulation.~(197) Au(γ, n)~(196)Au experiment is performed to obtain the transmutation rate and compared with the simulation result. If the current of the proton beam is 10 mA at the resonance energy of 441 keV, with the γ photons emitted from~7 Li(p, γ)~8 Be, then the corresponding transmutation yield for~(129)I in 2π direction can reach 9.4 × 10~9 per hour. The result is compared with that of LCS γ-ray source.     

Isospin Effect of Charged Particle Multiplicity in Intermediate Energy Heavy Ion Collisions

The dependences of He and intermediate mass fragments (IMF) production rates in the reactions 55 MeV/u ^40Ar ^58,64 Ni on the isospin, impact parameter and primary excitation energy of the reaction nuclear system were studied by using the 4π charged particle multi-detector array system (MUDAL). For the mentioned two reaction systems, the measured He particle contribution in the total charged particle multiplicity increases with increasing the total charged particle multiplicity but for the contribution of IMFs in the total charged particle multiplicity increases with increasing the total charged particle multiplicity at lower total charged particle multiplicities, and latter on it drops down with further increasing of the total charged particle multiplicities (see Fig.l). The experimental results of these two reaction systems with the same nuclear charge indicate that the contribution of He and IMFs in the total charged particle multiplicities are obviously isospin dependent.     

Decomposition of the equation of state of asymmetric nuclear matter into different spin-isospin channels

We investigate the equation of state of asymmetric nuclear matter and its isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach extended to include a microscopic three-body force（TBF） . It is shown that the potential energy per nucleon in the isospinsinglet T = 0 channel is mainly determined by the contribution from the tensor SD coupled channel. At high densities,the TBF effect on the isospin-triplet T = 1 channel contribution turns out to be much larger than that on the T =0 channel contribution. At low densities around and below the normal nuclear matter density,the isospin dependence is found to come essentially from the isospin-singlet SD channel and the isospin-triplet T = 1 component is almost independent of isospin asymmetry. As the density increases,the T = 1 channel contribution becomes sensitive to the isospin asymmetry and at high enough densities its isospin dependence may even become more pronounced than that of the T = 0 contribution. The present results may provide some microscopic constraints for improving effective nucleon-nucleon interactions in a nuclear medium and for constructing new functionals of effective nucleon-nucleon interaction based on microscopic many-body theories.     

Photoactivation experiment of ~(197)Au(γ, n) performed with 9.17-MeV γ-ray from ~(13)C(p, γ)~(14)N

High energy γ-ray can be used for nuclear waste transmutation by using the giant dipole resonance(GDR). The photonuclear reaction ~(197)Au(γ, n) is known as a standard for studies on photoactivation experiments. The previous experiments on ~(197)Au(γ, n) have been performed with bremsstrahlung, positron annihilation in flight or laser Compton scattering γ-ray.In this work, a new mono-energetic γ-ray source based on ~(13)C(p, γ)~(14)N reaction is used to measure the cross section of ~(197)Au(γ, n) and the measured value is compared with the results obtained with other ways.     

Effect of Gamma-Ray Beaming on the Fluxes of Gamma-Ray Pulsars

We study the effect of γ-ray beaming on γ-ray emission of the pulsars in a self-sustained outer gap model. In this model, averaged γ-rav flux is a function of period, magnetic field, magnetic inclination angle and solid angle of γ-ray beaming for a γ-ray pulsar. We generate a sample of γ-ray pulsars with their ages less than 10^6 ears by using the Monte Carlo method, and then study the γ-ray beaming effect. The comparison of distributions of periods, magnetic fields, distances, γ-ray energy fluxes and period derivatives of the simulated γ-ray pulsars with those of observed γ-ray pulsars by the detector EGRET shows that γ-ray beaming has an important role on the detection of γ-ray pulsars. Furthermore, possible γ-ray pulsars observed by the detector GLAST are predicted.     

Fluxes and Death Lines of Gamma-Ray Pulsars

We study the fluxes and the death lines of γ-ray emission of the pulsars with outer gaps.In a self-sustained outer gap,we derive that the fractional size of the outer gap is a function of period,period derivative,radial distance and magnetic inclination angle for a pulsar.Our results indicate that (i) averaged typical γ-ray energy and γ-ray flux of a pulsar with an outer gap increase with the magnetic inclination angle;we estimate the averaged γ-ray fluxes for observed canonical pulsars with outer gaps and compare them with the sensitivities of AGILE and GLAST,and (ii) if the fractional size of the outer gap at the inner boundary of the outer gap is not greater than unity,then an outer gap exists;such a condition gives the death lines of the pulsars with outer gaps.     

New empirical formula for(γ, n) reaction cross section near GDR peak for elements with Z ≥ 60

A new empirical formula has been developed that describes the(7,n) nuclear reaction cross sections for isotopes with Z ≥ 60.The results were supported by calculations using TALYS-1.6 and EMPIRE-3.2.2 nuclear modular codes.The energy region for incident photon energy has been selected near the giant dipole resonance(GDR) peak energy.The evaluated empirical data were compared with available data in the experimental data library EXFOR.The data produced using TALYS-1.6 and EMPIRE-3.2.2 are in good agreement with experimental data.We have tested and presented the reproducibility of the present new empirical formula.We observe the reproducibility of the new empirical formula near the GDR peak energy is in good agreement with the experimental data and shows a remarkable dependency on key nuclei properties:the neutron,proton and atomic number of the nuclei.The behavior of nuclei near the GDR peak energy and the dependency of the GDR peak on the isotopic nature are predicted.An effort has been made to explain the deformation of the GDR peak in(γ,n) nuclear reaction cross sections for some isotopes,which could not be reproduced with TALYS-1.6 and EMPIRE-3.2.2.The evaluated data have been presented for the isotopes ~(180)W,~(183)W,~(202)Pb,~(203)Pb,~(204)Pb,~(205)Pb,~(231)Pa,~(232)U,~(237)U and ~(239)Pu,for which there are no previous measurements.