Quasi-elastic Excitation Functions Research Articles

Fusion barrier distribution from measurement of quasielastic scattering at θ c.m. = 180°

Distribution of fusion barriers reveals the effect of structure of the collision partners on the dynamics of fusion between two heavy ions. Experimental barrier distribution can be extracted from precisely measured fusion excitation function. Quasielastic excitation function is related to fusion excitation function by conservation of incident flux. Hence, barrier distribution can also be extracted from quasielastic excitation function, which is usually measured at large angles, by detecting the back-scattered projectile-like ions. However, the reflectance coefficient is exactly complementary to the transmittance coefficient at θ c.m. = 180°, which corresponds to orbital angular momentum, ℓ = 0. We report here extraction of fusion barrier distribution for 16O+142 Ce from measurement of quasielastic scattering at θ c.m. = 180°, by detecting the target-like ions in the forward angles using a recoil mass spectrometer. Quasielastic excitation functions were also measured by detecting the projectile-like ions at two large angles. Barrier distributions extracted from both fusion and quasielastic measurements were found to be nearly identical. This work, thus, provided the first experimental verification of validity of the scaling property and the iso-centrifugal approximation in extracting barrier distribution from quasielastic excitation functions measured at large angles.

Fusion and back-angle quasielastic measurements in Si30+Gd156 near the Coulomb barrier

Background: Advancement in accelerator facilities has opened the door to dig deep to understand the interplay between nuclear reactions and structures. Although the influence of inelastic excitations on nuclear scattering and sub-barrier fusion is somewhat established, a clear understanding of nucleon transfer with a positive-$Q$ value is yet to achieve.Purpose: The objective of this paper is to examine the role of the $2n$-transfer channel with a positive $Q$ value on sub-barrier fusion and back-angle quasielastic (QE) scattering in the $^{30}\mathrm{Si}+^{156}\mathrm{Gd}$ reaction. Furthermore, extraction of barrier distributions (BDs) from fusion and QE scattering to infer their shapes is also a prime goal.Method: The excitation functions (EFs) of fusion and back-angle QE scattering have been measured over a wide range of incident beam energy around the Coulomb barrier using a recoil mass spectrometer. Furthermore, BDs have been extracted using the measured fusion and back-scattered QE data. The underlying findings have been analyzed within the framework of coupled-channel (CC) formalism using ccfull and ecc programs.Results: Fusion enhancement has been observed compared to those predicted from the one-dimensional barrier penetration model at sub-barrier energies. Fusion enhancement and QE EFs are explained by CC predictions considering the collective excitations among the colliding nuclei. The inclusion of $2n$ transfer and collective excitations in ccfull improves the fit to the experimental fusion data in a short span of energy window around the Coulomb barrier, whereas no significant effect has been observed at the sub-barrier region. However, no such effect of $2n$-pickup transfer has been observed from ecc model calculations. Thus, no firm conclusion can be made on the role of $2n$-pickup transfer with a positive $Q$ value in present measurements.Conclusion: Fusion EFs have been successfully explained by the CC calculations using ccfull and ecc model codes. No significant effect of the $2n$-pickup channel with a positive $Q$ value was observed on sub-barrier fusion enhancement. However, QE EFs are reproduced by considering the collective excitations and $2n$-transfer channel couplings. Fusion and QE BDs are similar in shape within the experimental uncertainty. One-dimensional barrier parameters extracted from the measured data agree with the different theoretical models. Also, the present system obeys the systematic based on deformation values after transfer at the exit.

Quasi-elastic scattering measurements of the 28Si + 142Nd system at back-angle

The barrier distribution of a system can be extracted from excitation function data obtained either through fusion reaction or through quasi-elastic scattering measurement. In the present work, the quasi-elastic excitation function has precisely been measured at back angle for the 28Si + 142Nd system at energies around the Coulomb barrier and the corresponding experimental barrier distribution has been extracted. The experimental data has been interpreted in the frame work of the coupled channel calculations which include couplings to different possible modes of excitations of the interacting target-projectile combination. The possible effect of the nature of projectile excitations on the derived barrier distribution has been presented.

Strong neutron-transfer coupling effects in the reaction mechanism of the O18+Zn64 system at energies near the Coulomb barrier

The precise quasielastic excitation function for the $^{18}\mathrm{O}+^{64}\mathrm{Zn}$ system was measured at energies near and below the Coulomb barrier at ${\ensuremath{\theta}}_{\mathrm{lab}}={161}^{\ensuremath{\circ}}$, from which its correlated quasielastic barrier distribution was derived. The excitation functions for the two-neutron, $\ensuremath{\alpha}$, and tritium transfer reactions have also been measured at the same conditions. These data were well described by the coupled channel and coupled reaction channel calculations. The comparison of the data with theoretical calculations shows the strong influence of three inelastic channels in the coupling process: the quadrupole and octupole vibrational states of $^{64}\mathrm{Zn}$, ${2}_{1}^{+}$ and ${3}_{1}^{\ensuremath{-}}$, and the quadrupole vibrational state of $^{18}\mathrm{O}$, ${2}_{1}^{+}$. In addition, theoretical calculations indicate that the two-neutron stripping is mostly due to a one-step process, which has a striking effect on the reaction mechanism of this system.

Scattering of O16,18 beams on Cu63,65 targets: A systematic study of different reaction channels

Precise quasielastic experimental excitation function for the $^{18}\mathrm{O}+^{65}\mathrm{Cu}$ system has been measured and its barrier distribution has been derived. Several reaction channels have been observed on the experimental spectra, revealing the presence of two-neutron and $\ensuremath{\alpha}$-stripping processes, as well as the proton pickup transfer, for which excitation functions were also measured. Extensive coupled channel and coupled reaction channel calculations have been performed to describe the experimental data. The inelastic couplings of target and projectile, and the ground state reorientation of the target, were important to the proper description of data. The transfer data were well described by calculations; however, it was shown that they almost do not affect the excitation function of $^{18}\mathrm{O}+^{65}\mathrm{Cu}$ quasielastic scattering. Whenever possible, structure shell model calculations have been performed to obtain the spectroscopic amplitudes of projectile and target overlaps. The two-neutron and $\ensuremath{\alpha}$-transfer reactions have been calculated considering the transferred particle as a cluster with spin 0.

Reaction mechanisms of the O18+Cu63 system at near-barrier energies

A precise quasielastic excitation function for the $^{18}\mathrm{O}+^{63}\mathrm{Cu}$ system has been measured at energies around the Coulomb barrier at ${\ensuremath{\theta}}_{\mathrm{LAB}}={161}^{\ensuremath{\circ}}$. The corresponding quasielastic barrier distribution has been derived. Two-neutron-, one-proton-, and \ensuremath{\alpha}-transfer-excitation functions have also been measured at the same energies and angle. Coupled reaction channels calculations were performed to describe the experimental data. Large-scale shell-model calculations were performed to derive most of the spectroscopic amplitudes. No surface imaginary potential was necessary for the interaction potential because almost all relevant reaction channels were explicitly included in the calculation. The theoretical results were compared to the experimental quasielastic barrier distribution and a very good agreement was achieved. The comparison of the coupled reaction channel calculations and data has put in evidence several important details of the reaction mechanism of the $^{18}\mathrm{O}+^{63}\mathrm{Cu}$ system. The collectivity of the $^{63}\mathrm{Cu}$ nucleus has important contribution to the reaction mechanism of this system, mainly due to its first $5/{2}^{+}$ and $7/{2}^{+}$ states. It was also observed a striking influence on the reaction dynamics of the $^{18}\mathrm{O}$(${2}^{+}$) state, the two-neutron transfer and the reorientation of the target ground-state spin. The best agreement to data was achieved when the nuclear matter diffuseness for the $^{18}\mathrm{O}$ was assumed equal to 0.60 fm, value that we have derived in a previous paper and that is 10% greater than the $^{16}\mathrm{O}$ diffuseness. Another significant result was that the two-neutron transfer process is much more relevant than the one-neutron-transfer process, which suggests that the pairing correlation could play an important role in the transfer process of this system.

Predicting reaction observables from back-scattering measurements in low-energy heavy-ion collisions

A simplified, reliable and useful method, based on reaction theory, for calculating a number of integrated and differential cross sections in low-energy heavy-ion collisions is presented. Simplified formulae provide predictions of reaction, capture and elastic-scattering differential cross sections, using experimental information about elastic and quasi-elastic back-scattering excitation functions.

Understanding the effect of channel coupling on fusion of6Li+64Ni

The effect of inelastic excitation and single particle transfer reactions on fusion have been investigated for the system 6 Li+ 64 Ni at near barrier energies. The calculations show that a simultaneous coupling to the inelastic excitation of projectile and target along with positive Q-value 1n- and 1p-stripping channels, describes the experimental CF cross sections reasonably well in the below barrier region. Exploring the interplay of different reaction channels in the collision of weakly bound systems is a subject of interest, both experimentally and theoretically, over the past several years [1–4]. In a recent work [5], the effect of coupling to inelastic excitations and single particle transfer channels on the back angle quasi-elastic excitation function had been reported for the system 6 Li+ 64 Ni. To investigate the effect of these couplings on fusion excitation function, a complementary experimental observable, for 6 Li+ 64 Ni is the primary motivation of the present work. Unlike the heavy targets, for the lower medium mass targets like 64 Ni the measured fusion cross sections with weakly bound projectiles provide total fusion (TF) cross sections instead of the cross sections for complete fusion (CF) of the whole projectile. The TF cross section for 6 Li+ 64 Ni system includes along with CF cross section the contributions from incomplete

Barrier distribution functions for the systemLi6+Ni64and the effect of channel coupling

Background: The barrier distribution function is an important observable in low-energy nucleus-nucleus collisions because it carries the distinct signature of the channel-coupling effect that is dominant at low energies. It can be derived from the fusion excitation function as well as from the back-angle quasi-elastic excitation function. The barrier distribution functions derived from the two complimentary measurements, in general, appear to peak at an energy close to the Coulomb barrier for strongly bound systems. But for weakly bound projectiles, like $^{6}\mathrm{Li}$, a relative shift is observed between the distributions.Purpose: The present work investigates the barrier distribution functions from fusion as well as from the back-angle quasi-elastic excitation function for the $^{6}\mathrm{Li}+^{64}\mathrm{Ni}$ system. The purpose is to look for the existence of a shift, if any, between the two measured distribution functions, as reported for $^{6}\mathrm{Li}$ collision with heavy targets. A detailed coupled-channel calculation to probe the behavior of the distribution functions and their relative shift has been attempted.Measurement: A simultaneous measurement of fusion and back-angle quasi-elastic excitation functions for the system $^{6}\mathrm{Li}+^{64}\mathrm{Ni}$ was performed. The fusion excitation function was measured for the energy range of 11 to 28 MeV while the quasi-elastic excitation function measurement extended from 11 to 20 MeV. The barrier distribution functions were subsequently extracted from both the excitation functions and compared.Results: A small shift of around 450 keV peak to peak is observed between the barrier distribution functions derived from the complementary measurements. Detailed coupled channel and coupled reaction channel calculations reproduced both the excitation functions and barrier distributions. The shift of about 550 keV resulted from the model predictions corroborate the experimentally observed value for $^{6}\mathrm{Li}+^{64}\mathrm{Ni}$ system.Conclusions: The coupling to inelastic channels are found to be sufficient to describe the fusion-barrier distribution. The positive $Q$-value one-proton and one-neutron stripping channels, leading to three-body final states, on the other hand, play dominant roles in reproducing the barrier distribution from the back-angle quasi-elastic excitation function.

1n-transfer reaction using6Li with heavy mass target

Influence of 1n-transfer coupling on quasi-elastic scattering excitation function has been investigated for 6 Li + 209 Bi system. Coupled Reaction Channels Calculations have been carried out for the energies around the Coulomb barrier. Corresponding barrier distributions obtained with and without including 1n-transfer cou- pling, have been compared with experimental data. 1n-transfer effect on quasi-elastic excitation function has been observed to be insignificant for the present system. In the reaction of 6 Li with 208 Pb and 209 Bi, an ex- perimental relative contributions for breakup and 1n-transfer channels have been reproduced by simultaneous calculation using CDCC and CRC formalism.

Deriving capture and reaction cross sections from observed quasi-elastic and elastic backscattering

Based on reaction theory, we suggest a useful method for extracting total and partial reaction and capture (complete fusion) cross sections from the experimental elastic and quasi-elastic backscattering excitation functions taken at a single angle. We also propose a method to predict the differential reaction cross section from the observed elastic-scattering angular distribution.

Disagreement between capture probabilities extracted from capture and quasi-elastic backscattering excitation functions

Experimental quasi-elastic backscattering and capture (fusion) excitation functions are usually used to extract the s-wave capture probabilities for the heavy-ion reactions. We investigated the $^{16}$O+$^{120}$Sn,$^{144}$Sm,$^{208}$Pb systems at energies near and below the corresponding Coulomb barriers and concluded that the probabilities extracted from quasi-elastic data are much larger than the ones extracted from fusion excitation functions at sub and deep-sub barrier energies. This seems to be a reasonable explanation for the known disagreement observed in literature for the nuclear potential diffuseness derived from both methods.

Fusion barrier distributions inLi6,7+Bi209reactions from quasi-elastic and fusion excitation function measurements

Fusion barrier distributions have been obtained from the measurement of the quasi-elastic scattering excitation functions at a backward angle in the reactions of $^{6,7}\mathrm{Li}$ with $^{209}\mathrm{Bi}$. Comparisons have been carried out among barrier distributions, obtained from quasi-elastic scattering by considering elastic + inelastic and elastic + inelastic + [breakup(BU) and/or transfer] and also from fusion excitation function measurements. It has been observed that representations of barrier distributions obtained from elastic + inelastic + [breakup(BU) and/or transfer] and from fusion excitation functions are in good agreement showing the importance of the inclusion breakup channels for the correct fusion barrier representations in the $^{6,7}\mathrm{Li}+^{209}\mathrm{Bi}$ reactions. The observed discrepancy in the resultant barrier distributions with and without including breakup and/or transfer has been interpreted in terms of the capture barrier distribution. The results obtained from the continuum discretized coupled channels calculations also follow the fusion barrier distributions which have been obtained from the fusion excitation functions measurements. It has been observed that the inclusion of direct breakup $\ensuremath{\alpha}$ with the elastic and inelastic channels in quasi-elastic scattering play an important role in explaining consistently the fusion barrier distributions for both the $^{6,7}\mathrm{Li}+^{209}\mathrm{Bi}$ systems.

Role of neutron transfer on fusion barrier distributions of theSi28,30 + Sn124systems

The fusion barrier distributions for $^{28,30}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ systems were extracted from quasielastic excitation function measurements at backward angles. The experimental barrier distributions were then compared with coupled-channel (CC) calculations. The fusion barrier distribution for the $^{30}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ reaction was well reproduced by the CC calculations with the inclusion of projectile and target inelastic couplings and only one possible positive $Q$-value 2$n$-transfer channel coupling using the ccfull code. However, CC calculations with similar coupling schemes for inelastic excitation of target and projectile with the 4$n$-transfer channel corresponding to the highest positive $Q$ value failed to reproduce the barrier distribution for the $^{28}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ reaction, because it has many positive $Q$-value multi-neutron transfer channels. A better agreement between the experimental fusion barrier distribution for the $^{28}\mathrm{Si}$ + $^{124}\mathrm{Sn}$ system and the prediction of semiempirical CC calculations based on the Zagrebaev framework [V. I. Zagrebaev, Phys. Rev. C 67, 061601(R) (2003)] was obtained only after considering positive $Q$-value multi-neutron transfer couplings. The sensitivity of the fusion barrier distribution to the hexadecapole deformation parameter ${\ensuremath{\beta}}_{4}$ of the projectile was also discussed.

Breakup following neutron transfer for the 7Li + 144Sm system

We have analyzed the backward angle quasi-elastic excitation function and the barrier distribution for the 7Li + 144Sm system by considering not only the direct breakup of the projectile, the inelastic excitations of the target and the one-neutron transfer channel, but also the sequential breakup of 7Li as a two-step process: the stripping of one neutron followed by the breakup of 6Li. The agreement of the theoretical calculations with the experimental barrier distribution is good, even without any fit procedure. This result confirms some recent experimental evidences showing the importance of this two-step process to 7Li breakup.

Quasi-elastic processes of the48Ca + 120Sn system and the48Ca nuclear matter density

We present the results of a high-precision quasi-elastic excitation function measurement for the ${}^{48}$Ca + ${}^{120}$Sn system at ${\ensuremath{\theta}}_{\mathrm{LAB}}$ = 160\ifmmode^\circ\else\textdegree\fi{} at near-barrier energies in steps of 1.0 MeV. The corresponding quasi-elastic barrier distribution is derived. A large-scale coupled-channel calculation was performed to investigate the role of several reaction channels in the reaction mechanism. An excellent agreement between theory and data was obtained for the barrier distribution. The first quadrupole vibrations of the ${}^{48}$Ca and ${}^{120}$Sn, the 2$n$, and the ${}^{4}$He transfers have a strong influence on the reaction mechanism and are responsible for the good agreement achieved. The 1$n$ transfer has a minor importance in the result when compared with the 2$n$ transfer, which suggests that the pairing correlation might play an important role in the 2$n$-neutron transfer process. However, if the octupole vibration of the projectile is included in the coupling scheme, the agreement with the data gets worse. The comparison of the coupled-channel calculations with experimental data leads to the conclusion that the nuclear matter diffuseness of the ${}^{48}$Ca nucleus is 0.56 fm in agreement with most of the double-magic nuclei.

Derivation of capture cross sections from quasi-elastic excitation functions

The relationship between the quasielastic excitation function and the capture cross section is derived. The quasielastic data is shown to be a useful tool to extract the capture cross sections and the angular momenta of the captured systems for the reactions $^{16}$O+$^{144,154}$Sm,$^{208}$Pb, $^{20}$Ne+$^{208}$Pb, and $^{32}$S+$^{90,96}$Zr at near and above the Coulomb barrier energies.

Near-barrier quasielastic scattering as a sensitive tool to derive nuclear matter diffuseness

Quasielastic excitation functions for the ${}^{16,18}$O $+$ ${}^{60}$Ni systems were measured at energies near and below the Coulomb barrier, at the backward angle \ensuremath{\theta}${}_{\mathrm{LAB}}$ $=$ 161\ifmmode^\circ\else\textdegree\fi{}. The corresponding quasielastic barrier distributions were derived. The data were compared with predictions from coupled channel calculations using a double-folding potential as a bare potential. For the ${}^{16}$O-induced scattering, good agreement was obtained for the barrier distribution by using the projectile default nuclear matter diffuseness obtained from the S\~ao Paulo potential systematic, that is, 0.56 fm. However, for the ${}^{18}$O-induced scattering, good agreement was obtained only when the projectile nuclear matter diffuseness was changed to 0.62 fm. Therefore, in this paper we show how near-barrier quasielastic scattering can be used as a sensitive tool to derive nuclear matter diffuseness.

Systematic study of projectile-structure effect on the fusion-barrier distribution

Quasielastic excitation function measurement has been carried out for the ${}^{4}$He $+$ ${}^{232}$Th system at ${\ensuremath{\theta}}_{\text{lab}}={160}^{\ensuremath{\circ}}$ with respect to the beam direction, to obtain a representation of the fusion-barrier distribution. Using the present data along with previously measured barrier distribution results on ${}^{12}$C, ${}^{16}$O, and ${}^{19}$F $+$ ${}^{232}$Th systems, a systematic analysis has been carried out to investigate the role of target and/or projectile structures on fusion-barrier distribution. It is observed that for ${}^{4}$He, ${}^{12}$C, and ${}^{16}$O $+$ ${}^{232}$Th reactions, the couplings due to target states only are required in coupled-channel fusion calculations to explain the experimental data, whereas for the ${}^{19}$F $+$ ${}^{232}$Th system along with the coupling of target states, inelastic states of ${}^{19}$F are also required to explain the experimental results on fusion-barrier distribution. The width of the barrier distribution shows interesting transition behavior when plotted with respect to the target-projectile charge product for the above systems.

Quasi-elastic barrier distribution of theO17 + Zn64system and the derivation of theO17nuclear matter diffuseness

The quasi-elastic excitation function for the $^{17}\mathrm{O}$ $+$ $^{64}\mathrm{Zn}$ system was measured at energies near and below the Coulomb barrier, at the backward angle ${\ensuremath{\theta}}_{\mathrm{lab}}={161}^{\ifmmode^\circ\else\textdegree\fi{}}$. The corresponding quasi-elastic barrier distribution was derived. The excitation function for the neutron stripping reactions was also measured, at the same angle and energies, and the experimental values of the spectroscopic factors were deduced by fitting the data. A reasonably good agreement was obtained between the experimental quasi-elastic barrier distribution with the coupled-channel calculations including a very large number of channels. Of the channels investigated, three dominated the coupling matrix: two inelastic channels, $^{64}\mathrm{Zn}$(2${}_{1}^{+}$) and $^{17}\mathrm{O}$(1/2${}^{+}$), and one-neutron transfer channel, particularly the first one. On the other hand, a very good agreement is obtained when we use a nuclear diffuseness for the $^{17}\mathrm{O}$ nucleus larger than the one for $^{16}\mathrm{O}$. We verify that quasi-elastic barrier distribution is a sensitive tool for determining nuclear matter diffuseness.