Nuclear rainbow structures in the elastic scattering of 16O on 16O at EL=350 Me

doi:10.1016/0370-2693(89)91604-3

Physics Letters B

Volume 223, Issues 3–4, 15 June 1989, Pages 291-295

https://doi.org/10.1016/0370-2693(89)91604-3 Get rights and content

Abstract

The elastic scattering of ¹⁶O on ¹⁶O has been measured at 22MeV/u in a large angular range up to θ_cm=61° with high accuracy. Besides the Fraunhofer diffractive patterns at forward angles a clear oscillatory structure is observed at large angles. It is shown in a semi-classical analysis that this structure is due to a rainbow interference of two refractive amplitudes (the second Airy maximum is identified). These data show a nuclear rainbow structure for the first time in heavy-ion scattering (A>6) with unambiguous clarity.

References (19)

G.R. Satchler
Phys. Lett. B
(1983)
S. Kubono
Phys. Lett. B
(1983)
M. Buenerd
Nucl. Phys. A
(1984)
K.W. McVoy et al.
Nucl. Phys. A
(1984)
G. Bertsch
Nucl. Phys. A
(1977)
Y. Sakuragi et al.
Phys. Lett. B
(1984)
J. Knoll et al.
Phys. Rep.
(1977)
D.H.E. Gross et al.
Phys. Rep.
(1978)
Th. Delbar
Phys. Rev. C
(1978)

There are more references available in the full text version of this article.

Cited by (120)

The lowest order constrained variational (LOCV) method for the many-body problems and its applications
2023, Progress in Particle and Nuclear Physics
One always looks for a simplified technique and desirable formalism, to solve the Hamiltonian, and to find the wave function, energy, etc, of a many-body system. The lowest order constrained variational ( $L O C V$ ) method is designed such that, to fulfill the above requirements. The $L O C V$ formalism is based on the first two, i.e., lowest order, terms of the cluster expansion theory with the $J a s t r o w$ correlation functions as its inputs. A constraint is imposed for the normalization of the total correlated two-body wave functions, which also forces the cluster expansion series to converge very rapidly. The variation of $J a s t r o w$ correlation functions subjected to the above normalization constraint, leads to the sets of Euler–Lagrange equations, which generates the required correlation functions. In order to satisfy the normalization constraint exactly, one has to define the long-range behaviors, for the two-body correlation functions, i.e., the Pauli function. The primary developments of $L O C V$ formalism, and some of its applications were reviewed in this journal by Max Irvine in 1981. Since then (1981–2022), the various extensions and applications of the $L O C V$ method are reported through the several published articles (nearly 180 items), which are the subjects of this review. (i) It is shown that the $L O C V$ results can be, as good as, the various more complicated and computer time-consuming techniques, such as the Fermi $h y p e r n e t t e d$ chain ( $F H N C$ ), Monte Carlo ( $M C$ ), G-matrix, etc, calculations. (ii) Moreover, the $L O C V$ method is further developed to deal with the more sophisticated interactions, such as the $A V 18$ , $U V 14$ , etc, nucleon–nucleon potentials, using the state-dependent correlation functions, and applicable to perform the finite temperature calculations. The extended $L O C V$ ( $E L O C V$ ) method is also introduced for the state-independent media. (iii) Its convergence is tested through the calculation of three-body cluster series, with the state-dependent correlation functions, which confirm the old (1979) state-averaged predictions. Finally, its application to the $n u c l e o n i c$ and $β -$ stable matter with and without the three-body force, the finite nuclei, the liquid helium 3, the neutron star, etc are performed and compared with the other many-body techniques. As we stated before, in this review, we definitely go through the most of above items.
The role of the tightly bound core in the refractive scattering of 17F+12C
2021, Nuclear Physics A
Citation Excerpt :
In the last five decades, a lot of effort has been put into discovering the mechanisms of the nuclear rainbow scattering. Many reaction experiments of light heavy ions have been carried out and the nuclear rainbow is also observed clearly in the elastic scattering of 12C+12C, 16O+16O and 16O+12C [9–11]. The nuclear rainbow phenomenon is believed to be very helpful in determining the optical potential strength and extracting the key information about the nuclear interaction and the nuclear matter [3,12].
The refractive scattering of ¹⁷F+¹²C is analyzed systematically by using the optical model with the cluster folding potentials. First of all, the applicability of the cluster folding approach is validated by analyzing the elastic scattering data of ¹³C+¹²C and ¹²C+¹²C at 20 A MeV. To perform the optical model calculations of ¹⁷F+¹²C, the less ambiguous optical potentials of ¹⁶O+¹²C and the global optical potential of p+¹²C are used to give the cluster folding potentials. Apart from the reproduction of the experimental data of the elastic scattering of ¹⁷F+¹²C at 10 A MeV, the Airy patterns are noticeable from about 10 to 40 A MeV. For comparison, the optical model calculations of ¹⁷O+¹²C at the same energies per nucleon are also performed through the cluster folding approach, of which the results are very similar to those of ¹⁷F+¹²C. For both ¹⁷F+¹²C and ¹⁷O+¹²C, the energy dependence of the Airy minima is extracted and compared with that in the case of ¹⁶O+¹²C. It is found that the Airy minima characteristic of ¹⁷F+¹²C is nearly identical with that of ¹⁷O+¹²C and similar to that of ¹⁶O+¹²C, which indicates the strong contributions from the ¹⁶O core to the appearance of the nuclear rainbow effects in ¹⁷F scattering. At last, the calculated total reaction cross sections are compared with the strong absorption model, which verifies the reasonableness of the present optical model calculations.
The C12−12C and O16−16O elastic scattering folding analysis using the LOCV effective interaction and the FRESCO code
2020, Nuclear Physics A
To describe the elastic scattering cross sections of ${}^{12}C -^{12} C$ and ${}^{16}O -^{16} O$ systems, in our recent work (RM1), the double-folding (DF) model potentials was calculated via the density-dependent averaged effective two-body nucleon-nucleon (NN) interaction (DDAEI). The DDAEI can be generated through the lowest order constrained variational (LOCV) method for the symmetric nuclear matter (SNM), with the input bare Reid68 NN potential. Then the DF potentials were directly inserted into the FRESCO code to find the differential cross-sections (DCS). The result was encouraging with respect to the experimental data and the other theoretical works. In the present report, the above folded potentials are fitted through a Woods-Saxon (WS) shell model potential, which can easily be used (through the WS parameters) as an input to the FRESCO code, without any approximation. The calculated DCS are compared with the corresponding calculations coming from the fitting procedures with the input finite range DDM3Y1-Reid68 potential, RM1 and the available experimental data at different incident energies. As in RM1, it is shown that a reasonable description of scattering data at the low and the medium energies for the elastic scattering of the ${}^{12}C -^{12} C$ and ${}^{16}O -^{16} O$ systems can be obtained in the framework of the above LOCV-DDAEI, without any need for defining a parameterized density dependent function in the effective NN potential, which is formally considered in the typical DDM3Y1-Reid68 interactions. The $χ^{2}$ fits are calculated and discussed. Our result based on DF WS potential parameters, i.e., WS-FRESCO DCS, are approximately in agreement to those of RM1. Finally, the generated energy dependent WS potentials can be directly used in the future calculations and considered as an approximate energy dependent shell model one-body potential which is based on the phenomenological NN interaction.
The breakup coupling effects on the rainbow scattering of 6Li at 35 AMeV
2019, Nuclear Physics A
Citation Excerpt :
Sometimes the Airy structure is heavily mixed with the diffractive part and only the structureless fall-off can be seen. It has been observed in the elastic scattering measurements of α particle and some other strongly bound light heavy-ions (such as 12C and 16O) at intermediate energies (several tens AMeV) [3–9]. The information about the nuclear rainbow is proved to be very useful in extracting the optical potential between the colliding pair at small internuclear distances, probing the density dependence of the in-medium nucleon-nucleon interaction and determining the incompressibility of the cold nuclear matter [2].
To investigate the breakup coupling effects on the formation of the nuclear rainbow, the existing experimental data of the refractive elastic scattering of ⁶Li on ¹²C, ⁴⁰Ca, ⁵⁸Ni and ⁹⁰Zr targets at 35 AMeV are analyzed. The continuum discretized coupled-channel (CDCC) method is adopted to calculate the elastic scattering angular distributions including the coupling effects from the breakup of ⁶Li into α and d. The one-channel (1-ch) calculations that switch off the breakup coupling are also performed for comparison. In the calculated angular distributions given by both approaches, the first Airy (A1) minimum shows a trend of moving to larger angles as the target mass increases. Comparing the calculated results through two approaches, one can find that the breakup coupling shifts the A1 minima to larger angles. This shows that the breakup coupling can boost the nuclear rainbow, although it also damps the elastic scattering cross sections. We also find that the stronger the breakup coupling is, the larger the A1 shift becomes.
Double-folding potentials from chiral effective field theory
2018, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Citation Excerpt :
In particular, we use local chiral EFT interactions [16–22], because this simplifies the double-folding calculation. In this first study, we explore and test this idea for 16O–16O reactions, comparing our calculations to elastic-scattering [23–30] and fusion data [31–35]. For this system, phenomenological Woods–Saxon potentials [30] and potentials obtained through inversion techniques [36,37] also exist.
The determination of nucleus–nucleus potentials is important not only to describe the properties of the colliding system, but also to extract nuclear-structure information and for modelling nuclear reactions for astrophysics. We present the first determination of double-folding potentials based on chiral effective field theory at leading, next-to-leading, and next-to-next-to-leading order. To this end, we construct new soft local chiral effective field theory interactions. We benchmark this approach in the ¹⁶O–¹⁶O system, and present results for cross sections computed for elastic scattering up to 700 MeV in energy, as well as for the astrophysical S-factor of the fusion reaction.
Influence of long-range correlation on the scaling properties of the normalized factorial correlators in relativistic heavy-ion collisions
2013, International Journal of Modern Physics E

View all citing articles on Scopus

¹: Also Fachbereich Physik (WE3), Freie Universität Berlin, D-1000 Berlin, Germany.

View full text

Article preview

Physics Letters B

Abstract

References (19)

Phys. Lett. B

Phys. Lett. B

Nucl. Phys. A

Nucl. Phys. A

Nucl. Phys. A

Phys. Lett. B

Phys. Rep.

Phys. Rep.

Phys. Rev. C

Cited by (120)

The lowest order constrained variational (LOCV) method for the many-body problems and its applications

The role of the tightly bound core in the refractive scattering of <sup>17</sup>F+<sup>12</sup>C

The C12−<sup>12</sup>C and O16−<sup>16</sup>O elastic scattering folding analysis using the LOCV effective interaction and the FRESCO code

The breakup coupling effects on the rainbow scattering of <sup>6</sup>Li at 35 AMeV

Double-folding potentials from chiral effective field theory

Influence of long-range correlation on the scaling properties of the normalized factorial correlators in relativistic heavy-ion collisions