Available online at www.sciencedirect.com
ScienceDirect Nuclear Physics A 922 (2014) 71–83 www.elsevier.com/locate/nuclphysa
Elastic and inelastic scattering of 6Li + 18O versus 7 Li + 18 O and 6 Li + 16 O Adam T. Rudchik a,∗ , Stanislaw Kliczewski b , Kostyantyn A. Chercas a , Kirby W. Kemper c , Evgeniy I. Koshchy d , Krzysztof Rusek e,f , Andryi A. Rudchik a , Sergyi Yu. Mezhevych a , Valeryi M. Pirnak a , Volodymyr A. Plujko g , Oleg A. Ponkratenko a , Jaroslaw Choi´nski f , Bronislaw Czech b , Regina Siudak b , Antoni Szczurek b , Anna Stolarz f , Ruslan M. Zelinskyi a a Institute for Nuclear Research, Ukrainian Academy of Sciences, Prospect Nauki 47, 03680 Kyiv, Ukraine b H. Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152,
PL-31-342 Cracow, Poland c Physics Department, Florida State University, Tallahassee, FL 32306-4350, USA d Kharkiv National University, pl. Svobody 4, 61077 Kharkiv, Ukraine e National Centre for Nuclear Research, ul. Ho˙za 69, PL-00-681 Warsaw, Poland f Heavy Ion Laboratory of Warsaw University, ul. L. Pasteura 5A, PL-02-093 Warsaw, Poland g Taras Shevchenko Kyiv National University, vul. Volodymyrs’ka 64, 01033 Kyiv, Ukraine
Received 24 May 2013; received in revised form 4 October 2013; accepted 4 October 2013 Available online 25 November 2013
Abstract Inverse kinematics scattering of 18 O on 6 Li at E lab (18 O) = 114 MeV was measured to obtain elastic and inelastic scattering cross sections. In this way cross sections for excited states in 6 Li and 18 O were determined. The data were analyzed within the optical model and coupled reaction channel method. The 6 Li + 18 O optical potential as well as the 6 Li and 18 O deformation parameters were deduced. Contributions of different nuclear processes to the 6 Li + 18 O elastic and inelastic scattering were explored. The isotopic differences between the 6,7 Li + 18 O and 6 Li + 16,18 O potential parameters were determined. © 2013 Elsevier B.V. All rights reserved.
* Corresponding author.
E-mail address:
[email protected] (A.T. Rudchik). 0375-9474/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysa.2013.10.013
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Keywords: N UCLEAR R EACTIONS 6 Li(18 O, 18 O), Elab (18 O) = 114 MeV; Measured elastic and inelastic σ (θ ); Deduced potential parameters; Scattering mechanism features; Optical model and coupled-reaction-channels analysis
1. Introduction It has been found over a period of years that the elastic and inelastic scattering data of lightheavy ions in a wide energy range are necessary to have an experimental base to study the energy and nuclear-structure dependences of the nucleus–nucleus interaction potentials as well as the properties and interaction of light unstable nuclei with nuclear reactions. As a rule, such research programs are realized with measurements of reaction products in a broad (A, Z)-region. As part of an ongoing program to determine elastic scattering potentials between light heavy ions, the results of a study of 6 Li + 18 O elastic and inelastic scattering at the energy E lab (18 O) = 114 MeV (c.m. 28.5 MeV) are presented here. Previously, only limited 6 Li + 18 O elastic scattering has been reported at the energy E lab (6 Li) = 32 MeV [1] (c.m. 24 MeV). The present data were taken in inverse kinematics, which allows the excitation of excited states in 6 Li, which are unbound, to be measured by detecting the outgoing scattered 18 O particles. Also, by detecting the recoil 6 Li particles it was possible to obtain large angle elastic scattering cross sections that are most sensitive to possible reaction processes other than pure potential scattering. In the present work, the 6 Li + 18 O data at both energies were analyzed within the optical model (OM) and coupled reaction channel (CRC) methods to account for the possible contributions of different mechanisms to the elastic scattering. In addition, the inelastic scattering deformation parameters for excited states in both 6 Li and 18 O were determined. The 6 Li + 18 O scattering data and deduced 6 Li + 18 O optical potential were compared with that of previously studied 7 Li + 18 O [2] and 6 Li + 16 O [3] elastic scattering to obtain information about the isotopic dependence of the nucleus–nucleus potentials. 2. Experimental procedure Angular distributions for 6 Li + 18 O elastic and inelastic scattering were measured using an beam from the Warsaw University cyclotron at the energy E lab (18 O) = 114 MeV. The beam energy spread on the target was about 0.5%. A self-supporting ∼900 µg/cm2 lithium target enriched in 6 Li to about 85% was used in the experiment. Reaction products were detected with three E–E-telescopes consisting of silicon 30, 40 and 67 µm E-detectors and 1 mm E-detectors. The telescopes were positioned with an accuracy of about 0.3◦ . The angular resolution in the lab system was ∼0.5◦ . Standard CAMAC electronics were used with the data acquisition system SMAN [4]. The data were stored as (E, E)-pairs and sorted into E(E)-spectra. Fig. 1 shows a typical E(E)-spectrum with the reaction products with Z = 3–8 identified. As one can see, the individual elements as well as many isotope groups are well resolved. By using inverse kinematics, it is possible to measure both forward and backward angle cross sections at the same time. Typical energy spectra of the detected 18 O and 6 Li particles from the reactions 6 Li(18 O, 18 O)6 Li and 6 Li(18 O, 6 Li)18 O at the energy E (18 O) = 114 MeV are shown in Fig. 2: (a) lab and (c) with multiparticle reaction background, (b) and (d) obtained after subtraction of their backgrounds. In Figs. 2(a) and 2(c), the curves show the description of the background by form 18 O
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Fig. 1. Typical E(E)-spectrum from the 6 Li(18 O, X) reactions at energy E lab (18 O) = 114 MeV.
Fig. 2. Typical E-spectra of 18 O (a), (b) and 6 Li (c) and (d) from the reactions of 6 Li(18 O, 18 O)6 Li and 6 Li(18 O, 6 Li)18 O at the energy E lab (18 O) = 114 MeV: (a) and (c) measured spectra with backgrounds from the multi-particle reactions produced by interactions of 6,7 Li + 18 O (curves show the fitted background forms); upper scales show E lab (MeV); (b) and (d) after subtraction of the backgrounds and contributions from the 7 Li(18 O, 18 O)7 Li and 7 Li(18 O, 6 Li)19 O reactions (curves show the Gauss symmetric forms).
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Fig. 3. Angular θ c.m. [(a), (b)] and momentum transfer distributions qt of 6 Li + 18 O elastic scattering at the energy E lab (18 O) = 114 MeV (filled symbols) versus (c) 7 Li + 18 O elastic scattering at the same energy [2] (open symbols) and (d) 6 Li + 16 O elastic scattering at the energy E lab (6 Li) = 25.7 MeV [5] (open symbols). Curves show OM calculations [(a) and (b)].
E − E1i + E2i /2 −1 Nbg (E) = Ni (E) = N0i 1 + exp − h1i i i −1 E − E1i − E2i /2 × 1 − 1 + exp − h2i
(1)
with fitting parameters N0i , E1i , E2i , h1i , and h2i to the spectrum minima. The solid curve shows the sum of the individual forms (dashed curves). The residual spectra obtained by subtracting these backgrounds are shown in Figs. 2(b) and 2(d). To extract the yields, the peaks were fitted by the sum of Gauss symmetric functions, with the peak positions Ei determined by the corresponding kinetic energies and by fixing the parameters hi to the width of the elastic scattering peaks or to the natural level width [curves in Fig. 2(b) and 2(d)]. The extracted peak areas were used to calculate the cross sections of the 6 Li + 18 O elastic and inelastic scattering at the θ c.m. (18 O) angles from the 18 O spectra and at the θ c.m. (18 O) = 180◦ − θc.m. (6 Li) angles from the 6 Li spectra. The area errors of the peaks were estimated to be about 20%, if the peaks were well resolved, and 30–40% for poorly resolved peaks. The angular distribution of the elastic scattering was normalized to the optical model (OM) cross section at small angles, where there is little dependence on the OM parameters. In Figs. 3(a)
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Fig. 4. Coupling schemes for the transitions to the excited states of 6 Li and 18 O.
and 3(b), the curves show the OM calculations using 6 Li + 18 O optical potential of Woods– Saxon type with parameters deduced from CRC analysis of the 6 Li + 18 O [1], 7 Li + 18 O [2] and 6 Li + 16 O [3] elastic scattering data. One can see that diffraction maxima of these calculations well agree with the measured data normalized to the OM calculations with the 6 Li + 18 O potential parameters. The normalization error was smaller than 20%. The same factor was used to normalize the angular distributions for both elastic and inelastic scattering data at the forward and backward angles. In Fig. 3, the measured distribution of the 6 Li + 18 O elastic scattering at the energy E lab (18 O) = 114 MeV (filled symbols) is compared (c) with the 7 Li + 18 O elastic scattering at the same energy [2] (open symbols) and (d) with the 6 Li + 16 O elastic scattering at the energy E lab (6 Li) = 25.7 MeV [5] (open symbols) as a function of transferred momentum qt . One can see that there are differences in the scattering systems throughout the large momentum transfer range with 6 Li + 18 O less absorbing than is 7 Li + 18 O with its cross sections a factor of 10 smaller in the regions where data overlaps. 3. Data analysis 3.1. Calculation procedure A Woods–Saxon form optical potential as given by Eq. (2) in Ref. [6] with only the first two volume terms was used to extract the scattering potentials. The Coulomb potential was that of a uniform charged sphere as given by Eq. (3) in Ref. [6]. The radii forms used in the OM and CRC calculations for the scattering ions (P ) by target nuclei (T ) are given by: 1/3 1/3
(i = V , WS , C). Ri = ri AP + AT (2) The Coulomb parameter rC = 1.25 fm was used in all calculations.
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Fig. 5. Diagrams of one- and two-step transfers contributing to the 6 Li + 18 O scattering calculations.
Table 1 Deformation parameters of 6 Li and 18 O. Nucleus 6 Li
18 O
E∗ (MeV)
Jπ
λ
δλ (fm)
βλ a
Ref.
0.000 2.185
1+ 3+ 2+ 1+
−1.54 −1.54 1.00 −1.54 −1.54
−0.68 −0.68 0.44 −0.68 −0.68
[5] [5]
4.310 5.700
2 2 4 2 2
1.982 3.555 3.920 4.456 5.098 5.255
2+ 4+ 2+ 1− 3− 2+
2 4 2 1 3 2
1.00 1.00 1.00 1.00 1.00 1.00
0.30 0.30 0.30 0.30 0.30 0.30
b
[5] [5] [2] [2] [2] [2] [2] [2]
a β = δ /R, where R = 1.25A1/3 . λ λ b Deduced in this work.
The potential parameters Xi = {V0 , rV , aV , WS , rW , aW } were fitted with the optical model to obtain a description of the elastic scattering data for θc.m. < 90◦ . The optimal set of the potential parameters deduced from the OM fitting was then used as the initial ones in the CRC calculations. In the CRC analysis, the 6 Li + 18 O elastic and inelastic scattering for the transitions to the ground and excited states of 6 Li and 18 O, spin reorientation of 6 Li as well as the most important transfer reactions were included in the channels-coupling scheme. Fig. 4 shows the transitions to the excited states of 6 Li and 18 O and in particular the known strong Ei excitations to the spin–orbit triplet (3+ , 2+ and 1+ ) of unbound states in 6 Li [5]. The diagrams of one- (single-) and two-step transfers, which contribute to the 6 Li + 18 O scattering calculations, are presented in Fig. 5. We assume that the deformed rotations of 6 Li and 18 O as well as vibrations dominate the low-energy excitations. The transitions to these states were calculated using the form
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δλ dU (r) Vλ (r) = − √ 4π dr
77
(3)
where δλ is the length of the λ-multipole deformation. The deformation parameters for 6 Li and 18 O used in the present CRC calculations are listed in Table 1. The spectroscopic amplitudes 1/2 A Sx = ΨA |ΨC Ψx ; ϕCx (4) x of transferred nucleons or clusters x in the systems A = C + x required for the CRC calculation of the transfer reactions were obtained within the translationally invariant shell model (TISM) [7]. Here, the Ψi = |Ni [fi ](λi μi )αi Li Si Ji Ti > (i = A, C, x) are the TISM oscillatory wave functions with the SU (3)-symmetry (λi μi ) (orbital part) and SU (4)-symmetry [fi ] (Young scheme for spin–isospin part), describing internal states of A, C and x nuclei. The Ni are energy quantum numbers. The wave function ϕCx = |nLj describes the x-cluster motion relative to a core C. The code DESNA [8,9] and Boyarkina’s wave function tables [10] were used for the Sx -calculation. The calculations of the Clebsch–Gordon and Racah coefficients as well as 9(λμ)-symbols of S(3) group used in the Sx -calculation are described in Ref. [8]. The spin–isospin parts of Sx are taken from the corresponding tables of parentage coefficients listed in Refs. [11,12]. The amplitudes Sx are listed in Table 2. The spectroscopic notation of the ϕCx = |nLj wave functions are also given in Table 2. The bound cluster wave function was calculated by fitting the Woods–Saxon potential parameter V to the x-cluster binding energy in the system A = C + x for aV = 0.65 fm and rV = 1.25A1/3 /(C 1/3 + x 1/3 ) fm. The codes SPI-GENOA [13] and FRESCO [14] were used for the OM and CRC calculations, respectively. 3.2. Elastic scattering The angular distributions of the measured 6 Li + 18 O elastic scattering at the energy E lab (18 O) = 114 MeV are shown in Fig. 6 as (a) cross sections and (b) ratio to Rutherford scattering. The 6 Li + 18 O potential parameters deduced in the CRC fitting procedures are listed in Table 3. The curves show the CRC calculations for potential scattering (curves pot), spin reorientation of 6 Li (curves reor) and transfers of x and x + y, y + x nucleons and clusters x, y (curves x and xy, respectively) corresponding diagrams of which are shown in Fig. 5. As seen in Fig. 6, potential scattering dominates the angular region forward of about c.m. 90◦ . The 6 Li spin reorientation and transfers (curve tr) are important only for the scattering at large angles with the nucleon exchanges (curves nn and pp) dominating over transfers. Also Fig. 6 shows that the CRC coherent sum of all processes (curves Σ) describes the 6 Li + 18 O elastic scattering data satisfactorily. Fig. 7 shows the angular distributions of 6 Li + 18 O elastic scattering at the energy E lab (6 Li) = 32 MeV (E c.m. = 24 MeV [1]). The curves present the CRC calculations for the potential scattering (curve pot), spin reorientation of 6 Li (curve reor) and transfer reactions (curve tr). The 6 Li + 18 O potential parameters listed in Table 3, were used in the CRC calculations. The CRC angular distributions describe the data satisfactorily. In a study of nucleus–nucleus interactions, one important result is information on the isotopic differences of corresponding optical potentials. Here in Fig. 8, we compare the 6 Li + 18 O,
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Table 2 Spectroscopic amplitudes Sx of x-clusters in A = C + x systems. A
C
x
nLj
Sx
6 Li
2H
6 Li
4 He
6 Li
5 He
α d p
2S0 2S1 1P1/2
1.061 1.061 −0.596a
1P3/2
0.667
6 Li∗ 3.562 6 Li
5 He
p n
0.894a 0.596a −0.667 1.095 0.894a
6 Li∗ 2.185 6 Li∗ 3.562 7 Li
5 Li
n
1P3/2 1P1/2 1P3/2 1P3/2
5 Li
n
1P3/2
5 Li
6 Li
n
8 Li
6 Li∗ 2.185 6 Li∗ 3.562 6 Li
7 Be
6 Li
7 Be 8 Be
6 Li∗ 2.185 6 Li∗ 3.562 6 Li
10 B 18 O
7 Li 7 Li
7 Be
1P1/2 1P3/2 1P3/2
n
−0.657 −0.735a 0.738a
A
C
x
nLj
Sx
18 O
16 N 17 N
d p p
2P1/2 1P2 1P3/2
−1.304 1.198a −1.198a
17 N
p
1P1/2
1.198a
17 N
17 O
p 2n n n
1P3/2 3S0 1D5/2 2S1/2
−1.198a 0.615 1.406a 0.876
17 O
n
1D5/2
1.406a
17 O
n n n
1D5/2 1D5/2 2S1/2
0.403a 0.527 −0.889
n
1D5/2
0.471
n p p
2S1/2 2S1/2 1D5/2
0.470 0.699 1.315
p
2S1/2
−0.522
p d α
1D5/2 2D2 5S0
1.315 0.380 −0.566
18 O
16 O
18 O
17 O
18 O∗ 1.982 18 O∗ 3.634 18 O∗ 3.921 19 O
18 O
18 O∗ 1.982 18 O∗ 3.634 18 O∗ 3.921 18 O
19 O
n
1P3/2
−0.569
19 O
2n p
1D2 1P1/2 1P3/2
−0.667a −0.657 −0.735a
19 O
p
1P3/2
0.738a
19 F
6 Li
p d α
6 Li
12 B
1P3/2 2S1 2D2 3D1
0.569 1.217 −0.125 0.022
17 N
18 O∗ 1.982 18 O∗ 3.634 18 O∗ 3.921 18 O
19 F
20 F
18 O∗ 1.982 18 O∗ 3.635 18 O∗ 3.921 18 O
22 Ne
18 O
19 F 19 F
a S J +j −JA S = −S . x x FRESCO = (−1) C
Table 3 Parameters of nucleus–nucleus potentials of Woods–Saxon type. System
V (MeV)
rV (fm)
aV (fm)
WS (MeV)
rWS (fm)
aWS (fm)
WD (MeV)
rWD (fm)
aWD (fm)
6 Li + 18 O A
175.6 174.5 174.0
0.800 0.806 0.782
0.763 0.900 0.790
14.0 13.0 13.5
1.250 1.470 1.100
0.763 0.900 0.650
0 0 5.500
0.974
0.450
7 Li + 18 O B 6 Li + 16 O C
Ref.
[2] [3]
7 Li + 18 O and 6 Li + 16 O optical potentials of Woods–Saxon type, parameters of which are listed
in Table 3. Fig. 8 shows that the peripheries of both parts of the 7 Li + 18 O optical potential are more extended than those of the 6 Li + 18 O and 6 Li + 16 O potentials. The real potential for 6 Li scattering is almost identical for 18 O and 16 O scattering, whereas the imaginary potential for scattering by 16 O is much shorter ranged than that for 18 O. The double-folding model using the Reid M3Y [15] and DDM3Y1 [16] nucleon–nucleon potentials was used to calculate the 6 Li + 18 O interaction potential for comparison with the potential obtained from the Woods–Saxon analysis of the scattering. The codes DFPOT [17] and DFMSPH [18] were used for the folding-potential calculations. The nucleon distributions in 6 Li and 18 O were calculated using charge distributions in these nuclei [19]. As can be seen in panel (c) of Fig. 8, there is good agreement between these three real potentials in the peripheral region of the interaction.
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Fig. 6. Angular distributions of the 6 Li + 18 O elastic scattering at the energy E lab (18 O) = 114 MeV. The curves show the CRC calculations for the potential scattering (curve pot), spin reorientation of 6 Li (curve reor) and transfers of x and x + y, y + x nucleons or clusters x, y (curves x and xy, respectively). Σ - and tr-curves show the coherent sums of all processes and transfer reactions, respectively.
Fig. 7. Angular distributions of the 6 Li + 18 O elastic scattering at the energy E lab (6 Li) = 32 MeV [1]. The labels for the curves are the same as in Fig. 6.
To determine whether the isotopic differences of the 6 Li + 18 O (A), 7 Li + 18 O (B) and + 16 O (C) optical potential parameters affect the CRC calculations of the 6 Li + 18 O elastic scattering, CRC angular distributions were calculated with the sets of potential parameters A, B and C listed in Table 3. The results of these calculations are shown in Fig. 9 (curves A,
6 Li
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Fig. 8. Comparison of (a) real and (b) imaginary parts of the 6 Li + 18 O, 7 Li + 18 O and 6 Li + 16 O optical potentials of Woods–Saxon type, from the parameters listed in Table 3 (parameter sets A, B and C, respectively). In figure part (c), the 6 Li + 18 O double-folding potentials calculated with nucleus–nucleus potentials M3Y and DDM3Y1 are compared with real part of this potential deduced from the data analysis.
Fig. 9. Angular distributions of the 6 Li + 18 O elastic scattering at the energy E lab (18 O) = 114 MeV. The curves A, B and C show the CRC calculations with potential parameters A, B and C, respectively (see Table 3).
B and C, respectively), where as can be seen, they produce dramatically different elastic scattering patterns. 3.3. Inelastic scattering The measured angular distributions of the 6 Li + 18 O inelastic scattering at the energy E lab (18 O) = 114 MeV are shown in Figs. 10–12. Some excited states of 6 Li and 18 O were unresolved in the experiment so summed cross sections are presented for such peaks. The curves show the CRC calculations for the transitions to the excited states of 6 Li and 18 O, the schemes
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Fig. 10. Angular distributions of the 6 Li + 18 O inelastic scattering at the energy E lab (18 O) = 114 MeV. The curves show the CRC calculations for the collective excitations of 6 Li and 18 O and transfer reactions (curve tr). The curve Σ shows the incoherent sum of the two angular distributions.
Fig. 11. Angular distributions of the 6 Li + 18 O inelastic scattering at the energy E lab (18 O) = 114 MeV. The curves show the CRC calculations for the collective excitations of 6 Li and 18 O.
and reaction diagrams of which are shown in Figs. 4 and 5, respectively. In Fig. 10, the coherent sum of transfers for the transition to the 3.921 MeV (2+ ) state of 18 O are shown by the curve tr. As Fig. 10 shows, the transfer contributions are small to this transition and also for other transitions as well.
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Fig. 12. Angular distributions of the 6 Li + 18 O inelastic scattering at the energy E lab (18 O) = 114 MeV. The curves show the CRC calculations for the collective excitations of 6 Li and 18 O.
As was stated above, the low-energy excited states of 6 Li and 18 O were assumed to be collective in nature. In the CRC calculations, the transitions without changes of parity were calculated within a rotational model, and for those with parity changes, a vibration model was used. In both cases, the form-factors determined with Eq. (3) were used. The transitions within rotational bands shown with corresponding schemes of Fig. 4, were calculated within a rotational model. The reorientations for the states of the rotational bands based on the vibration states were also calculated. It was found that its contributions to the corresponding inelastic scattering of 6 Li + 18 O are very small. Therefore, these reorientations were not included in the CRC calculations. The direct transitions to the 3.635 MeV (0+ ) excited state of 18 O and the 3.562 MeV (0+ , T = 1) state in 6 Li are possible by transfer reactions. The CRC calculations of these transitions are shown in Fig. 11 by the curves 3.635 and 3.562. As Fig. 11 shows, these transitions are much smaller than the transition to the collective 3.555 MeV (4+ ) state of 18 O. The deformation parameter δ4 for 6 Li deduced in the fitting procedure is listed in Table 1. Other deformation parameters for 6 Li and 18 O were taken from Refs. [2,5]. 4. Summary and conclusions New angular-distribution data for 6 Li + 18 O elastic and inelastic scattering at the energy E lab (18 O) = 114 MeV (c.m. 28.5 MeV) were measured for transitions to Eex = 0.0–5.26 MeV
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states of 18 O and Eex = 0.0–5.7 MeV states of 6 Li. These data and previously published 6 Li + 18 O elastic scattering data at E (6 Li) = 32 MeV [1] (c.m. 24 MeV) were analyzed with lab the optical model and coupled reaction channel methods. The transitions to the excited states were calculated using rotational and vibration models. The elastic and inelastic channels as well as the most important particle transfers were included in the coupling scheme. In the 6 Li + 18 O elastic channel, potential scattering dominates at all angles with spin reorientation of 6 Li and one- and two-step transfers making only small contributions to the elastic scattering at backward angles. The collective transitions to excited states in 6 Li and 18 O dominate the inelastic scattering over the full angular region. The deduced 6 Li + 18 O Woods–Saxon optical potential when compared to that for 6 Li + 16 O was found to have a similar real potential but a much longer range imaginary potential, which might be due to the greater importance of transfer reactions for the 18 O target. The 7 Li + 18 O potential however, is much longer ranged in both its real and imaginary potentials than those for 6 Li scattering. It was found that there is good agreement of the real part of the deduced 6 Li + 18 O Woods–Saxon potential with the folding-potential in the peripheral region that is most important in the nucleus–nucleus interaction increasing the confidence in the presently obtained 6 Li interaction. The present work clearly demonstrates that the internal structure of the colliding nuclei greatly impacts their interaction making the search for universal optical potentials for the scattering of light heavy ions difficult. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
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