Sharp Cutoff Model Research Articles

Investigation of Astrophysical S-Factor for 12C + 16O and 16O + 16O Reactions Within the Relativistic Mean-Field Approach

The fusion dynamics of 12C + 16O and 16O + 16O astrophysical reactions is investigated using the relativistic mean-field (RMF) formalism for the non-linear NL3* parameter set. The RMF densities, along with the widely adopted M3Y and relativistic R3Y nucleon-nucleon (NN) interaction potentials, are used to obtain the nuclear potential within the double folding approach. The ℓ-summed Wong model is used to obtain the fusion cross-section. The ℓmax values are extracted from the sharp cut-off model. The fusion cross-section is also represented in terms of the astrophysical S-factor, and the results are compared with the available experimental data. The microscopic R3Y NN potential is observed to give a reasonable fit to the experimental cross-section.

Properties of γ -decaying isomers in the Sn100 region populated in fragmentation of a Xe124 beam

A systematic study was performed of microsecond γ-decaying isomers around Sn100 produced in a fragmentation reaction of a Xe124 beam at 345 MeV/u at the Radioactive Ion Beam Factory of the RIKEN Nishina Center in Saitama, Japan. Half-lives of isomeric states in that region were remeasured allowing us to improve the currently available experimental information. Reduced transition probabilities were deduced and compared to shell-model calculations in various model spaces. The recently reported low-energy transitions in Rh92 and Ag96 were remeasured with improved precision. Additionally, experimental information on isomeric ratios, including five new ones, were extracted and compared to a previous experimental study and the sharp cutoff model of fragmentation reaction.

Effect of different nuclear density approximations on fusion dynamics within Skyrme Energy Density Formalism

The role of different density approximations such as frozen, sudden and modified sudden, investigated within the Skyrme Energy Density Formalism (SEDF), is compared with the phenomenological relaxed-density approach for Ni-based reactions. These approximations give different ways in which individual densities of projectile and target can be added for obtaining compound nucleus density. For the 58Ni + 58Ni reaction, unlike sudden, the frozen density approximation is known to give the realistic barrier parameters (Nucl. Phys. A 870-871, 42 (2011)) and addresses the experimental data with the use of the extended $ \ell$ -summed Wong model. In view of this, the barrier parameters within the sudden approximation are obtained, by modifying the central density term as an independent function of the surface thickness factor, which in turn, fits the data nicely at sub barrier energies. In comparison to this, the largest barrier height of the phenomenological potential of relaxed-density advocates the possibility of fusion hindrance. Additionally, for the 18O and 40Ca + 58Ni reactions, the frozen and modified sudden approximations address the data at below barrier-energies. For the case of a heavier-mass system, the barrier parameters cannot be extracted due to the disappeared pocket for the case of sudden and modified sudden density approximations. In such situation, the frozen and relaxed-density approaches behave in a similar manner and show a better fit to the data using the extended $ \ell$ -summed Wong formula. The $ \ell$-values are extracted using the sharp cut-off model for above-barrier energies and extrapolated at lower energies. Among the chosen approximations, the frozen approximation seems to provide a better option for the reactions considered from different mass regions. Further, on the basis of frozen and phenomenological approaches, the reduced cross-sections are calculated and compared with the Universal Fusion Function (UFF) for symmetric and asymmetric choices of nuclear partners.

Properties of γ -decaying isomers and isomeric ratios in the Sn100 region

Half-lives and energies of $\ensuremath{\gamma}$ rays emitted in the decay of isomeric states of nuclei in the vicinity of the doubly magic $^{100}\mathrm{Sn}$ were measured in a decay spectroscopy experiment at Rikagaku Kenkyusho (The Institute of Physical and Chemical Research) of Japan Nishina Center. The measured half-lives, some with improved precision, are consistent with literature values. Three new results include a 55-keV $E2\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$ ray from a new $({4}^{+})$ isomer with ${T}_{1/2}=0.23(6)\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{s}$ in $^{92}\mathrm{Rh}$, a 44-keV $E2\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$ ray from the $({15}^{+})$ isomer in $^{96}\mathrm{Ag}$, and ${T}_{1/2}({6}^{+})=13(2)$ ns in $^{98}\mathrm{Cd}$. Shell-model calculations of electromagnetic transition strengths in the $({p}_{1/2},{g}_{9/2})$ model space agree with the experimental results. In addition, experimental isomeric ratios were compared to the theoretical predictions derived with an abrasion-ablation model and the sharp cutoff model. The results agreed within a factor of 2 for most isomers. From the nonobservation of time-delayed $\ensuremath{\gamma}$ rays in $^{100}\mathrm{Sn}$, new constraints on the ${T}_{1/2}$, $\ensuremath{\gamma}$-ray energy, and internal conversion coefficients are proposed for the hypothetical isomer in $^{100}\mathrm{Sn}$.

A model for explaining fusion suppression using the classical trajectory method

A two-dimensional classical trajectory model is used to explain the projectile breakup and above-barrier fusion suppression for the reactions 6Li+209Bi, 6Li+152Sm and 6Li+144Sm. To obtain the initial conditions of the equations of motion, a simplified model of the 6Li nucleus has been developed. Numerical solutions of the equations lead to the classification of orbits into breakup and no-breakup trajectories. The breakup fraction is studied as a function of the impact parameter. Using quantum mechanical arguments, the cut-off impact parameter for fusion is determined by proposing a sharp cut-off model which assumes that there is an angular momentum limit to fusion. We introduce a simple formula for the explanation of fusion suppression, according to which fusion suppression is given by the average of the breakup fractions evaluated at impact parameters ranging from head-on collision up to the cut-off impact parameter. We find that there is excellent agreement between the experimental fusion cross section (σexp) and the calculated fusion cross section (σcal) for the systems studied.

STUDY OF (14.0MeV/u) URANIUM IONS INTERACTION WITH VANADIUM TARGET

We have investigated Uranium ions interaction at energy 14.0 MeV /u incident on a Vanadium target using mica as nuclear track detector. The detector exposure was made from ions beam facility at UNILAC accelerator of GSI Darmstadt, Germany. The etched detector was scanned using an optical microscope. From the total binary tracks data events, elastic track events were separated using angular correlation criterion. The elastic scattering data have been separated from the binary events and used for the determination of quarter-point angle θ1/4(grazing angle). Total and partial reaction cross-sections are measured using the statistic of inelastic two-pronged and higher multiplicity tracks. The experimental measured cross-sections are compared with the cross-sections calculated using sharp cut-off model. The theoretical prediction of reaction parameters of interacting heavy ions have also been determined, that are comparable with experimental measured values.

Cross Section of Heavy Ion Reaction (14.5 MeV/u) 132Xe +Bi

We investigate the cross section of the heavy ion reaction (14.5 MeV/u)132Xe + Bi by using a CR-39 plastic track detector. Thetarget-detector assembly is exposed at UNILAC beam facility of GSI,Germany. After etching under appropriate etching conditions, thedetector is scanned for multipronged events produced as a result ofinteractions of projectile ions with target atoms. The elastic eventsare separated from binary events and used for the determination of thequarter-point angle. The quarter-point angle obtained is used todetermine the total reaction cross section. The total experimentalreaction cross section is determined by using statistics of inelasticevents of two-pronged and higher multiplicity events. The experimentalreaction cross sections determined by using elastic and inelastic dataobserved in the reaction under study are found to be in good agreementwith the theoretically calculated value of reaction cross section usinga sharp cutoff model.

Local chain motions in a dilute solution of phenolphthalein poly(ether sulfone)

Abstract13C and 1H relaxation times were measured as a function of temperature in two magnetic fields for dilute solutions of phenolphthalein poly(ether sulfone) (PES‐C) in deuterated chloroform. The spin‐lattice relaxation times were interpreted in terms of segmental motion characterized by the sharp cutoff model of Jones and Stockmayer (J. S. model). The phenyl group rotation is treated as a stochastic diffusion by the J. S. model. The restricted butterfly motion of the phenyl group attached to the cardo ring in PES‐C is mentioned but is not discussed in detail in this work. Correlation times for the segmental motion are in the picosecond range which indicates the high flexibility of PES‐C chains. The correlation time for the phenyl group internal rotation is similar to that of the segmental motion. The temperature dependence of these motions is weak. The apparent activation energy of the motions considered is less than 10kJ/mol. The simulating results for PES are also reasonable considering the differences in structure compared with PES‐C. The correlation times and the apparent activation energy obtained using the J. S. model for the main chain motion of PES‐C are the same as those obtained using the damped orientational diffusion model and the conformational jump model.

NMR spectra of polyimides: Interpretation and local chain motion study

AbstractThree kinds of high‐performance polyimides 1 (poly(ketone‐imide) PKI), 2 (poly(ether‐imide) PEI) and 3 (poly(oxy‐imide) POI) were studied using nuclear magnetic resonance (NMR). The NMR spectra of the polyimides were assigned according to the comprehensive consideration of the substitution effect of different substituting groups, viz. distortionless enhancement by polarization transfer (DEPT), no nuclear Overhauser effect (NNE), analysis of relaxation time, and two‐dimensional correlated spectroscopy (COSY) techniques. The structural units of these three polyimides were determined. Carbon‐13 and proton relaxation times for PEI and PKI were interpreted in terms of segmental motion characterized by the sharp cutoff model of Jones and Stockmayer (JS model) and anisotropic group rotation such as phenyl group rotation and methyl group rotation. Correlation times for the main‐chain motion are in the tens of picosecond range which indicates the high flexibility of polyimide chains. Correlation times for phenyl group and methyl group rotations are more than 1 order of magnitude lower and approximately 1 order of magnitude higher than that of the main chain, respectively.

Structure and dynamics of poly(1-naphthyl acrylate) in solution by carbon-13 NMR spectroscopy

13 C Relaxation data for poly(1-naphtyl acrylate) (PNA) in 1,1,2,2-tetrachloroethane-d 2 were interpreted in terms of chain segmental motion and naphtyl internal rotation by using the sharp cutoff model of Jones and Stockmayer and the Hall-Weber-Helfand correlation function. Both models describe in a satisfactory and comparable manner the local chain motions of PNA. Naphtyl internal rotation is described by a hindered rotation about the C(1)-O bond superimposed on segmental motions described by both models.

A simple microscopic approach to the energy dependence of the real and imaginary parts of the heavy-ion interaction potential

A simple microscopic model has been presented to calculate the energy dependence of the real and imaginary parts of the heavy-ion interaction potential. The results obtained from a simple effective interaction and Skyrme interaction in this formalism show that the imaginary part of the potential becomes more and more attractive with increasing relative centre-of-mass energy ECM unlike the real part of the potential which exhibits a 'switching over' phenomenon. The elastic scattering cross sections for 16O+40Ca (ECM=28.57 MeV) and 40Ca+40Ca (ECM=71.8, 88, 93, 112.5 and 120 MeV) calculated from such potentials are in good agreement with the phenomenological results. Values of the Fresnel interaction radius, the grazing angular momentum and the total cross section obtained in the sharp cut-off model from the elastic scattering angular distributions of 40Ca+40Ca are consistent with their corresponding values computed from the optical model calculation. The position and height of the fusion barrier and fusion cross sections of 40Ca+40Ca at different values of ECM calculated in the Hill-Wheeler parabolic approximation also compare well with the experimental results.

Elastic and inelastic scattering of uranium ions by holmium, gold, and bismuth targets.

Angular distributions for elastic scattering of /sup 238/U ions by /sup 165/Ho, /sup 197/Au, and /sup 209/Bi at 2380 MeV have been obtained in a 2..pi.. geometry using solid state nuclear track detectors. The angular distributions of the elastic differential cross section ratios sigma/sub el/(expt.)/sigma(Ruth) are analyzed using (a) the generalized Fresnel model and (b) the parametrized S-matrix method. Quarter-point angles obtained are converted to reaction parameters such as grazing angular momenta, interaction radii, and total reaction cross sections. Values of inelastic total reaction cross sections were obtained by directly counting the three-, four-, and five-prong events along with the two-prong inelastic events as observed in the 2..pi.. geometry. Experimental total reaction cross sections are compared with optical and sharp cutoff model calculations. There is good agreement among the total reaction cross sections evaluated from elastic and inelastic data as well as with model calculations.

Spin distribution of the compound nucleus in heavy ion reactions at near-barrier energies.

Gamma ray multiplicities and the (HI,xn) cross sections for the dominant reaction channel were measured at near-barrier bombarding energies for the systems \ensuremath{\alpha}${+\mathrm{}}^{154}$Sm and $^{12}$C${+\mathrm{}}^{154}$Sm. The mean value of the spin distribution of the compound nucleus was obtained for each of the systems studied. The results of these measurements together with the results of an earlier study on $^{16}$O${+\mathrm{}}^{154}$Sm indicate that at bombarding energies near and below the Coulomb barrier the spin distributions of the compound nucleus are broader than the triangular distributions expected from a sharp cutoff model, these deviations being larger for the more massive projectiles. The different behavior of the three systems clearly indicates the importance of the centrifugal barrier penetrability in determining the spin distribution of the compound nucleus. The absolute values of the mean angular momentum can be accounted for if one also includes deformation effects. A one-dimensional barrier-penetration model including the effect of averaging over the orientation of the deformed target can account for the experimental results.

The influence of the spectroscopic deformation of Li-isotopes on their interaction with51V

The energy dependence of the total reaction cross sectionσr and its tensor analyzing powerT20r was measured for the7Li−51V interaction in the energy rangeELi=10–20 MeV using two different experimental methods. Reaction residues were observed directly by their characteristicγ-emission, and the elastic scattering of7Li from51V was investigated. Additionally, the elastic scattering of6Li from51V was measured at 9.8, 12 and 14 MeV. The tensor analyzing power data can be interpreted as being caused by the spectroscopic mass deformation of the Li-ions. The energy dependence of σr andT20r above the Coulomb barrier can be described in terms of the classical sharp-cutoff model.

Influence of the Static Deformation ofLi7on theLi7-V51Total Reaction Cross Section

The energy dependence of the reaction cross section and the corresponding tensor analyzing power has been measured for the system $^{7}\mathrm{Li}$-$^{51}\mathrm{V}$ by two different methods. The tensor analyzing powers observed can be interpreted in a sharp-cutoff model as caused entirely by the static deformation of the $^{7}\mathrm{Li}$ projectiles.

Dynamics of Coulomb fission

A general formalism is described for the treatment of Coulomb fission, within the framework of the semiquantal theory. We develop a model for the fission probabilities of levels excited in Coulomb excitation. This model contains penetration of the double-humped fission barrier, competition from gamma and neutron emission, and the spreading of the collective states into noncollective compound states. For $_{74}^{184}\mathrm{W}$ + $_{92}^{238}\mathrm{U}$, the fission probability at ${\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}=180\ifmmode^\circ\else\textdegree\fi{}$ is increased by a factor of 3.9, 3.3, and 2.0 at $\frac{E}{{E}_{\mathrm{Coul}}}=0.77, 0.85, \mathrm{and} 0.935$, respectively, compared to the simplified sharp cutoff model used in earlier model calculations. The enhancement comes from barrier penetration. The damping of the fission probability due to spreading into noncollective compound states is small. Prompt Coulomb fission (near the distance of closest approach) is studied in a one-dimensional model. The results clearly imply that prompt fission is negligible. We have also studied the sudden approximation for collective rotational levels in connection with Coulomb fission. At high spins ($I\ensuremath{\approx}20$), it leads to significant errors. Contrary to the basic assumption of the sudden approximation that the nuclear symmetry axis remains fixed during the collision, it is shown that Coulomb excitation results in a strong alignment of the nuclear symmetry axis perpendicular to the beam axis at small internuclear distances.

Isomer ratios in antimony and tellurium isotopes

Isomer ratios have been measured in Sb and Te isotopes prepared in the 115In( alpha ,n), 115In( alpha ,3n), 118,120,122,124Sn( alpha ,pn), and 120Sn( alpha ,3n) reactions, using a range of bombarding energies between 16.6 and 38.4 MeV. In most of the product nuclei the isomer ratios are smaller than the predictions of the sharp cut-off model, showing that the isomer is less than 100% efficient in trapping high-spin products. The variation of isomer ratio with bombarding energy is described by a simple expression for the trapping efficiency.

Interaction times for damped heavy-ion collisions

Angular-momentum dependent interaction times for damped heavy-ion reactions are deduced from experimental angular distributions. The angular momentum l is related to the experimental kinetic-energy loss assuming the energy loss to increase monotonically with decreasing l and the experimental cross section to be given by the sharp cutoff model. Although the analysis depends on the moment of inertia of the intermediate double-nucleus system, rather short interaction times are obtained ranging from 10/sup -22/ to several times 10/sup -21/ sec. Assuming this time scale, nucleon diffusion coefficients are deduced from experimental fragment charge distributions.

Cross sections for the Ni, Cu,Zn(O16,18,xn)reactions near the Coulomb barrier

Cross sections for neutron emitting reactions induced by $^{16,18}\mathrm{O}$ bombardment of $^{58,60,61,62,64}\mathrm{Ni}$, $^{63,65}\mathrm{Cu}$, and $^{64,66,67,68,70}\mathrm{Zn}$ targets have been measured for projectile energies between 36 and 55 MeV by means of a large graphite sphere with embedded $^{10}\mathrm{BF}_{3}$ detectors. Comparisons were made with the total reaction cross section calculated with (1) the optical model, (2) the sharp cutoff model, and (3) the parabolic-barrier model. The data are generally in good agreement with the optical-model predictions above the Coulomb barrier if the neutrons are assumed to be emitted statistically from a compound nucleus and if fusion is the predominant mechanism. Interaction barriers obtained from the parabolic-barrier model yield interaction radii with values of (1.54 to 1.65) ($A_{T}^{\frac{1}{3}}+A_{P}^{\frac{1}{3}}$) fm.NUCLEAR REACTIONS $^{58,60,61,62,64}\mathrm{Ni}$, $^{63,65}\mathrm{Cu}$,$^{64,66,67,68,70}\mathrm{Zn}(^{16,18}\mathrm{O},xn)$: $E=36\ensuremath{-}55$ MeV. Measured total neutron yields.

Consistent asymptotic expansion of the partial wave sum of the scattering amplitude

A consistent asymptotic expansion of the partial wave sum for the quantal scattering amplitude is given to arbitrary order of large ħ −1, the Sommerfeld parameter n or the grazing angular momentum Λ. It is explicitly shown that the leading term of this expansion is the familiar semiclassical expression, and how in the sharp cut-off model the Fraunhofer diffraction pattern arises from the second-order term.