Elastic and inelastic scattering of 7Li + 18O versus 7Li + 16O

Nuclear Physics A 785 (2007) 293–306

Elastic and inelastic scattering of 7 Li + 18O versus 7Li + 16O A.A. Rudchik a , A.T. Rudchik a,∗ , S. Kliczewski b , E.I. Koshchy c , O.A. Ponkratenko a , K.W. Kemper d , K. Rusek e , A. Budzanowski b , J. Choi´nski f , B. Czech b , T. Czosnyka f , V.D. Chesnokova a , L. Głowacka g , E. Kozik b , V.M. Kyryanchuk a , S.Yu. Mezhevych a , A.V. Mokhnach a , O.A. Momotyuk a,d , I. Skwirczy´nska b , R. Siudak b , A. Szczurek b,h 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 Kharkiv National University, pl. Svobody 4, 61077 Kharkiv, Ukraine d Physics Department, Florida State University, Tallahassee, FL 32306-4350, USA e A. Soltan Institute for Nuclear Studies, 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 Institute of Applied Physics, MUT, ul. Kaliskiego 2, PL-00-908 Warsaw, Poland h University of Rzeszów, PL-35-959 Rzeszów, Poland

Received 31 October 2006; received in revised form 24 December 2006; accepted 3 January 2007 Available online 10 January 2007

Abstract Angular distributions of the 7 Li + 18 O elastic and inelastic scattering were measured at the energy Elab (18 O) = 114 MeV (32 MeV c.m.) in inverse kinematics. This technique allowed both small and large angle data to be collected simultaneously. The data were analyzed within the optical model and coupledreaction-channels method to determine the potential parameters of 7 Li + 18 O scattering and reaction channels dominating the scattering. 18 O inelastic scattering deformation parameters were obtained. The present data show that the 7 Li + 18 O system has a much stronger absorption when compared to previously

* Corresponding author.

E-mail address: [email protected] (A.T. Rudchik). 0375-9474/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2007.01.001

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measured 7 Li + 16 O data. The derived optical model parameters clearly show the scattering difference between two systems. © 2007 Elsevier B.V. All rights reserved. PACS: 25.70.Bc; 24.10.Eq; 24.10.Ht; 25.70.Hi Keywords: N UCLEAR REACTIONS 7 Li(18 O, 18 O), (18 O, 18 O ), Elab = 114 MeV; measured elastic and inelastic σ (θ); deduced potential parameter, scattering mechanism features. 18 O deduced deformation parameters. Optical model and coupled-reaction-channels analysis.

1. Introduction Determining the (A, Z)-dependence of the central nucleus–nucleus interaction potential for the scattering of stable nuclei is critical if we are to be able to recognize the new physics expected from the scattering of exotic nuclei. For example, it has already been shown that the elastic scattering of 6 He in a Coulomb potential dominated regime, with its low breakup threshold and large neutron–proton asymmetry, differs significantly from that of 6 Li [1–6]. The ultimate use of the observed potential differences is to be able to relate them to the underlying shell, cluster and halo structures of the interacting nuclei. In the present work, the scattering of 7 Li + 18 O has been measured and the data are analyzed with both the optical model (OM) and coupled-reaction-channels method (CRC) to extract the interaction potentials and to determine the strength of the inelastic and transfer channels that play a major role in the scattering process. To the best of our knowledge, the present data are the first to be reported for the system 7 Li + 18 O. The extracted potentials are then compared to those previously obtained for 7 Li + 16 O [7,8] whose structure and reaction Q-values are quite different from those of the 7 Li + 18 O system. The paper is organized as follows. Section 2 describes the experiment and data extraction, while Section 3 presents the OM- and CRC-calculations. The summary and conclusions are given in Section 4. 2. Experimental procedure Angular distributions for the 7 Li(18 O, X) reactions were measured by bombarding a self supporting 900 µg/cm2 foil of natural Lithium with an 18 O beam of energy Elab (18 O) = 114 MeV whose energy spread was about 0.5%. The experiment was performed at the Warsaw University C-200P cyclotron. The reaction products were detected by a ΔE–E Si telescope that was composed of a 67 µm ΔE- and 1 mm E-detectors. Standard CAMAC electronics were used with the data acquisition system SMAN [9]. The data were stored as (ΔE, E)-pairs and sorted into individual particle groups to form the spectra of interest. Fig. 1 shows a typical ΔE(E)-spectrum with the reaction products with Z = 3–8 identified. As can be seen, 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 for the detected 18 O and 7 Li products at the angle θlab = 13◦ are shown in Fig. 2. The measured spectrum of 18 O in the region of the elastic events is given in the upper panel. The markers show the peaks corresponding to the ground states of 7 Li, 12 C, 16 O and other heavy elements present in the target. The dashed curve represents the background produced

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Fig. 1. Typical ΔE(E)-spectra from the 7 Li(18 O, X) reactions at energy Elab (18 O) = 114 MeV.

by multiparticle-reactions of the type 7 Li(18 O, 18 O){αt, n6 Li, and so on} that occurred. The background N(E) was described by the reverse sigmoidal form   1 N(E) = N0 1 − , 0 1 + exp(− E−E h ) where the parameters N0 , E0 and h were fitted to the spectrum minima. The residual spectrum of 18 O obtained after excluding this background, is given in the central panel and the residual spectrum of 7 Li is shown in the lower panel. The energy resolution of the experiment was about 0.2 MeV allowing the often strongly excited 0.48 MeV first excited state of 7 Li to be resolved. The energy spectra were analyzed with a standard peak-fitting procedure using symmetric Gaussian functions to describe a spectrum peak. The excited states of 18 O and 7 Li observed in the scattering of 7 Li, 16 O, 12 C + 18 O were included in the analysis of the 18 O spectra. The contribution of the ejectiles of 7 Li from the 12 C(18 O, 7 Li)23 Na and 16 O(18 O, 7 Li)27 Al reactions to the 7 Li spectra were small. The measured angular distributions of the elastic and inelastic scattering of 7 Li + 18 O at Elab (18 O) = 114 MeV for transitions to the 0.478 MeV (1/2− ), 4.63 MeV (7/2− ) + 4.456 MeV

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Fig. 2. Typical E-spectra of 18 O and 7 Li isotopes from the 7 Li(18 O, X) reactions at energy Elab (18 O) = 114 MeV.

(1− ) (18 O), 6.68 MeV (5/2− ), 7.467 MeV (5/2− ) excited states of 7 Li and 1.982 MeV (2+ ), 3.555 MeV (4+ ) + 3.635 MeV (0+ ), 3.92 MeV (2+ ), 5.098 MeV (3− ), 5.26 MeV (2+ ) excited states of 18 O are shown in Figs. 3–5. In these figures, we show the sum of statistical errors of the data and uncertainties that arise from the fitting of the overlapping peaks. 3. Analysis of the data 3.1. Calculation procedure The 18 O + 7 Li data were analyzed within the optical model and coupled-channels method using scattering potentials of the Woods–Saxon type: U (r) = Vf (r, RV , aV ) + iWS f (r, RW , aW )

(1)

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Fig. 3. The angular distributions of 7 Li + 18 O elastic scattering at energy Elab (18 O) = 114 MeV. The curves show the OM and CRC angular distributions of the potential scattering (curves OM), reorientation of 7 Li (curves reor) and transfers (other curves). The solid and dashed B1  curves represent the coherent sum of these processes, calculated with the potential parameters A and B1 (see Table 3), respectively.

and the Coulomb potential of a uniform charged sphere of radius RC , where    r − Ri −1 , f (r, Ri , ai ) = 1 + exp ai  1/3 1/3  Ri = ri AP + AT , i = V , W, C,

(2) (3)

and AP and AT are the projectile and target masses, respectively. The radius of the Coulomb potential was fixed at the value of rC = 1.25 fm. To take into account the Pauli principle for the nucleus–nucleus interaction at small distances, the parameter rV was limited by the relation  1/3 1/3  rV  Rcomp / AP + AT , (4) where Rcomp is the radius of the compound-nucleus C = AP + AT : Rcomp ≈ 1.25(AP + AT )1/3 .

(5)

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Fig. 4. The angular distributions of 7 Li + 18 O inelastic scattering at energy Elab (18 O) = 114 MeV for the transitions to the excited states of 7 Li and the 4.456-MeV state of 18 O. The curves A and Bi  (i = 2, 4, 5, 10) show the CRC calculations for collective excitations using A and Bi potential parameters, respectively.

In the coupled-channels analysis of the elastic and inelastic scattering the possible reorientations of 7 Li and 18 O and most important transfers were included. The diagrams of the investigated transfers are shown in Fig. 6. The cross-section for populating the excited states of 7 Li and 18 O were calculated within the rotational and vibrational models, using the form-factors δλ dU (r) , Vλ (r) = − √ 4π dr

(6)

where δλ is the length of the λ-multipole deformation. The deformation parameters from Refs. [10,11] were used for 7 Li in the present calculations: δ2 = 2.0 fm, δ4 = 1.0 fm. The parameters δλ for 18 O were obtained by matching the calculated cross-sections to the data. The 18 O deformation parameters δλ , obtained in the present work and those previously known from Refs. [12–20], are listed in Table 1. The diagrams of the transitions to the excited states of 7 Li and 18 O which were included in the channels-coupling scheme, are shown in Fig. 7.

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Fig. 5. The same as in Fig. 4 but for the excited states of 18 O. Curve Σ shows the incoherent sum of 3.555-MeV rotational model transition and 3.635-MeV 2n-cluster excitation of 18 O (curve B8 , A2n ).

The spectroscopic amplitudes Sx of transferred clusters (nucleons) x for the A = C + x systems were calculated within the translational-invariant-shell-model (TISM) [21] using the code DESNA [22,23] and Boyarkina’s wave function tables [24]. The amplitudes Sx are 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 for a = 0.65 fm and rV = 1.25A1/3 /(C 1/3 + x 1/3 ) fm. The codes SPI-GENOA [25] and FRESCO [26] were used for the OM- and CRC-calculations, respectively. The potential parameters X = {Xi } = {V0 , rV , aV , WS , rW , aW } were obtained by fitting the elastic data with the OM and then independently through the CRC-calculations. The OM-analysis was carried out first and the parameters obtained were used as starting values for the CRC-calculations. These parameters are given in Table 3 (set A). For comparison we give the 7 Li + 16 O optical model parameters in Table 3 that were derived from the energy dependent

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Fig. 6. Diagrams of one- and two-step transfers contributing to the 7 Li + 18 O elastic-scattering calculations.

Table 1 Deformation parameters of 18 O Jπ

λ

δλ (fm)

βλ a

Ref.

Ex (MeV)

Jπ

λ

δλ (fm)

βλ a

Ref.

1.982

2+ 1

2

1 3

5.255

2+ 3

2

4

3.920

2+ 2

2

π + [12] π − [12] n [13] p [13] p [14] p [15] p [16] α [17] 18 O [18–20] Average This work p [16] This work n [13] p [13] p [16] α [17] Average This work

1− 3−

4+

0.46 0.74 0.33 0.36 0.32 0.30 0.33 0.30 0.30 0.38 0.30 0.28 0.30 0.16 0.13 0.25 0.19 0.18 0.30

4.456 5.098

3.555

1.51 2.43 1.07 1.18 1.04 0.98 1.07 0.99 1.00 1.25 1.00 0.92 1.00 0.52 0.43 0.81 0.62 0.60 1.00

1.00 1.38 1.01 1.45 0.90 1.61 1.33 0.68 1.19 1.00 0.52 0.58 0.55 1.00

0.30 0.42 0.31 0.44 0.28 0.49 0.41 0.21 0.36 0.30 0.16 0.18 0.17 0.30

This work n [13] p [13] p [14] p [15] p [16] α [17] 18 O [20] Average This work n [13] p [16] Average This work

Ex (MeV)

a β = δ /R, R = 1.25 · A1/3 = 3.28 fm. λ λ

analysis of Refs. [7,8] (sets B1 –B12 ). For each potential, Table 3 contains also the logarithms of the well-known relations between the potential parameters     RV RW , CW = WS exp . (7) CV = V exp aV aW One can see that the values ln(CV ) ≈ 10.7 and ln(CW ) ≈ 11.3 are constant for all Bi -parameters, e.g. these parameters are almost energy independent in the given energy range.

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Fig. 7. Coupling schemes for the transitions to the excited states of 7 Li and 18 O.

3.2. Elastic scattering Fig. 4 shows the angular distributions of the 7 Li + 18 O elastic scattering data and OM and CRC calculations for the potential scattering (curves OM), reorientation of 7 Li (curves reor) and transfers of 11 B-cluster (curve 11 B), sequential exchange of neutrons, protons and 2nclusters (curves nn, pp and 2n, respectively). The solid and B1  curves represent the coherent sums of all processes calculated with the potential parameters A and B1 , respectively. One can see, that the potential scattering dominates at forward angles. The large angle scattering is due to the reorientation of the 7 Li ground state. Transfers contribute weakly to the elastic scattering channel. The B1 -parameters (curves B1 ), obtained from the energy dependence of the potential parameters for the 7 Li + 16 O elastic scattering [7,8], fail to describe the 7 Li + 18 O elastic scattering data. One can see, that the curve B  has slope smaller than the slope of 1

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Table 2 Spectroscopic amplitudes Sx of x-clusters in A = C + x systems with bound energies Eb A

C

x

Eb (MeV)

7 Li

6 He

7 Li

6 Li

p n

9.975 7.250

8 Li

7 Li

8 Be

7 Li

n p

18 O

7 Li

11 B

2.033 17.254 24.357

18 O

17 N

18 O

16 O

p 2n 2n n n p

15.942 12.188 8.554 8.004 3.957 7.994

18 O 18 O

16 O

3.635

17 O

19 O

18 O

19 F

18 O

nLj

Sx

1P3/2 1P1/2 1P3/2 1P1/2 1P3/2 4S3/2 3D3/2 1P1/2 3S0 3S0 1D5/2 1D5/2 2S1/2

0.805 −0.657 −0.735a 0.478 1.234a −0.184a −0.121a −1.198a −0.833 0.615 0.891a −0.155 0.633

a S J +j −JA S = −S . x x FRESCO = (−1) C

Table 3 Parameters of Woods–Saxon potential for 7 Li + 18 O scattering Eex (MeV)

Jπ

0.0

Ec.m. (MeV)

Sets

31.92

A B1

13.0 14.9

1.470 1.250

0.900 0.660

9.22 10.66

9.97 11.29

14.8 14.5 14.2 14.1

1.250 1.250 1.250 1.250

0.660 0.660 0.660 0.660

10.66 10.70 10.73 10.74

11.28 11.26 11.24 11.23

14.7

1.250

0.660

10.68

11.27

0.660 0.660 0.950 0.660 0.660 0.660 0.660

14.6 14.8 29.6 14.6 14.5 14.5 14.4

1.250 1.250 0.878 1.250 1.250 1.250 1.250

0.660 0.660 0.810 0.660 0.660 0.660 0.660

10.69 10.68 9.35 10.69 10.70 10.71 10.71

11.27 11.28 8.30 11.27 11.26 11.26 11.25

0.803 0.803 1.050 0.804 0.804 0.805 0.805

B6

3.920 4.456 5.098 5.255

2+ 2 1− 3− 2+ 3

28.00 27.46 26.82 26.66

B7 B8 A2n [21] B9 B10 B11 B12

175.8 174.3 77.0 176.1 176.6 177.1 177.2

2+ 1

0.900 0.660 18 O 0.660 0.660 0.660 0.660 18 O 0.660

18 O

28.36 28.28

1.982

ln CW

+ 0.806 0.802 + 0.802 0.804 0.807 0.808 + 0.803

29.94

B2 B3 B4 B5

ln CV

7 Li

4+ 0+

31.44 27.29 25.24 24.45

aW (fm)

aV (fm)

3.555 3.634

1/2− 7/2− 5/2− 5/2−

rW (fm)

rV (fm)

174.5 172.9 7 Li 173.3 176.7 178.3 178.9 7 Li 174.5

0.478 4.652 6.604 7.454

WS (MeV)

V (MeV)

experimental angular distribution. This curve lays above the experimental data for large angles. A good description of the data was achieved with the fitted parameters A, for which ln(CV ) ≈ 9.2 and ln(CW ) ≈ 10.0. These potential parameters are smaller than those for B1 (see Table 3). The fitted A and predicted B1 potentials differ mainly in the geometry parameters aV = aW = 0.9 fm versus 0.66 fm and rW = 1.47 fm versus 1.25 fm. It was found that the slope of the calculated angular distribution depends mainly on the imaginary part of the 7 Li + 18 O potential. This is presented by the dotted curve in Fig. 3 (lower panel). This dotted curve represents the result of calculation with the 7 Li + 18 O potential. It consists of the real part of the B1 potential and imaginary part of potential A.

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Fig. 8. 7 Li + 16,18 O data plotted as a function of momentum transfer. The data show that the elastic scattering from 18 O is more strongly absorbed than that for 16 O.

Further evidence that the scattering of 7 Li by 16 O requires a different potential from that for the scattering by 18 O can be seen from Fig. 8, where the data for the two systems are plotted as a function of momentum transfer [27]. This figure shows that the 16 O data does not decrease as rapidly at larger momentum transfer as does the 18 O data meaning that the imaginary potential for 16 O is weaker from that for 18 O. Fig. 9 shows the actual potentials and as anticipated, the 18 O potentials are stronger at large distances where the more favorable Q-values for transfer reactions decrease the chance for elastic scattering. Since the breakup threshold for both 16 O and 18 O is almost the same and large (∼ 6 MeV), it would not play a major role in the elastic scattering. 3.3. Inelastic scattering Measured and calculated angular distributions of 7 Li + 18 O inelastic scattering are shown in Figs. 4 and 5, with Fig. 7 giving the cross-sections for the excited states in 7 Li and 18 O. The solid A and dashed B1  curves represent CRC-calculations within rotational and vibrational models with the A and B1 parameters, respectively. One can see that the B1 parameters fail to describe the data. A good description of the data was achieved using potential parameters A and the deformation parameters δλ for 7 Li from Refs. [4,5] and δλ for 18 O listed in Table 1 with the notation of “This work”. In this table we give also the δλ values taken from other work that

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Fig. 9. Real V (r) and imaginary W (r) potentials of the 7 Li + 18 O elastic scattering for the parameters A (curves VA and WA ) and B1 (curves VB1 and WB1 ).

were obtained from different analyses of the inelastic scattering data of π ± -mesons, nucleons, α-particles and 18 O ions. One can see that in many cases the δλ values for 18 O obtained in the present work, are close to the average of that of other work with the exception of transitions to the 3.92-MeV and 5.255-MeV states of 18 O. The 3.555-MeV (4+ ) and 3.635-MeV (0+ ) states of 18 O were not resolved in the present experiment. The angular distribution for the sum of the transitions to these states is shown in Fig. 5. In this figure, the dotted curve A represents the rotational transition 0+ → 4+ to the 3.555-MeV (4+ ) state of 18 O. The transition 0+ → 0+ to the 3.635-MeV (0+ ) state of 18 O was assumed to be the 2n-cluster excitation in the system 18 O = 16 O+2n. In the CRC-calculations for these transitions, the potentials B8 and A2n were used for 7 Li + 16 O and 7 Li + 2n interactions, respectively. The potential A2n of the 7 Li + 2n interaction was assumed to be close to that of the 7 Li + d interaction [28]. In Fig. 5, the curve B8 , A2n  shows the CRC-calculation for the particle-excitation transition 0+ → 0+ to the 3.635-MeV (0+ ) state of 18 O. The incoherent sum of both transitions (solid curve Σ) describes the data satisfactorily. 4. Summary and conclusions Angular distributions of the elastic and inelastic scattering of 7 Li + 18 O have been measured in inverse kinematics at the lab energy of 114 MeV (Ec.m. = 31.9 MeV). Both 7 Li and 18 O inelastic cross-sections have been determined. The data were analyzed in terms of the optical model and coupled reaction channels. The optical model analysis showed that the scattering of 7 Li by 18 O produces a very different potential than that for scattering by 16 O. The fact that the 7 Li + 18 O scattering system is more absorbing than that where 16 O is the target is seen by comparing the elastic data for 18 O scattering with that from 16 O. The radial difference in the optical model potentials indicates that reactions that take place at larger distances produce the

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observed scattering difference. The fact that the breakup threshold is similar for the two target nuclei would suggest that breakup of the target does not play a role in the difference in the observed scattering of the two system. The coupled channel reaction analysis showed that the greater than expected large angle elastic cross-section arises from the ground state reorientation of 7 Li. This effect has now been observed with targets from mass seven to those of mass eighteen. The target and projectile inelastic scattering is well described and the deformation parameters obtained by matching the calculated cross-section to the data are consistent with those found for their inelastic scattering with a wide range of other probes. Acknowledgements One of us (K.W. Kemper) acknowledges support of the US National Science Foundation in this work. References [1] O.R. Kakuee, M.A.G. Alvarez, M.V. Andres, S. Cherubini, T. Davinson, A. Di Pietro, W. Galster, J. GomezCamacho, A.M. Laird, M. Lamehi-Rachti, I. Martel, A.M. Moro, J. Rahighi, A.M. Sanchez-Benitez, A.C. Shotter, W.B. Smith, J. Vervier, P.J. Woods, Nucl. Phys. A 765 (2006) 294. [2] K. Rusek, I. Martel, J. Gomez-Camacho, A.M. Moro, R. Raabe, Phys. Rev. C 72 (2005) 037603. [3] A.M. Sanchez-Benitez, D. Escrig, M.A.G. Alvarez, M.V. Andres, C. Angulo, M.J.G. Borge, J. Cabrera, S. Cherubini, J.M. Espino, P. Figuera, M. Freer, J.E. Garcia-Ramos, J. Gomez-Camacho, M. Gulino, O.R. Kakuee, I. Martel, C. Metelco, A.M. Moro, J. Rahighi, K. Rusek, D. Smirnov, O. Tengblad, P. Van Duppen, V. Ziman, J. Phys. (London) G 31 (2005) S1953. [4] K. Rusek, N. Alamanos, N. Keeley, V. Lapoux, A. Pakou, Phys. Rev. C 70 (2004) 014603. [5] O.R. Kakuee, J. Rahighi, A.M. Sanchez-Benitez, M.V. Andres, S. Cherubini, T. Davinson, W. Galster, J. GomezCamacho, A.M. Laird, M. Lamehi-Rachti, I. Martel, A.C. Shotter, W.B. Smith, J. Vervier, P.J. Woods, Nucl. Phys. A 728 (2003) 339. [6] K. Rusek, N. Keeley, K.W. Kemper, R. Raabe, Phys. Rev. C 67 (2003) 041604. [7] A.A. Rudchik, A.T. Rudchik, K.W. Kemper, V.K. Kyryanchuk, O.A. Ponkratenko, Nucl. Phys. At. Energy 1 (17) (2006) 9. [8] A.T. Rudchik, K.W. Kemper, A.A. Rudchik, A.M. Crisp, V.D. Chesnokova, V.K. Kyryanchuk, F. Maréchal, O.A. Momotyuk, O.A. Ponkratenko, B.T. Roeder, K. Rusek, Phys. Rev. C, in press. [9] M. Kowalczyk, SMAN: A code for nuclear experiments, Warsaw University report, 1998. [10] J. Cook, A.K. Abdallah, M.N. Stephens, K.W. Kemper, Phys. Rev. C 35 (1987) 126. [11] A.A. Rudchik, A.T. Rudchik, G.M. Kozeratska, O.A. Ponkratenko, E.I. Koshchy, A. Budzanowski, B. Czech, S. Kliczewski, R. Siudak, I. Skwirczy´nska, A. Szczurek, S.Yu. Mezhevych, K.W. Kemper, J. Choi´nski, T. Czosnyka, L. Głowacka, Phys. Rev. C 72 (2005) 034608. [12] Md.A. Rahman, H.M. Sen Gupta, M. Rahman, Phys. Rev. C 44 (1991) 2484. [13] P. Grabmayr, J. Rapaport, R.W. Finlay, Nucl. Phys. A 350 (1980) 167. [14] D.T. Khoa, Phys. Rev. C 68 (2003) 011601. [15] E. Khan, Y. Blumenfeld, N. Van Giai, et al., Phys. Lett. B 490 (2000) 45. [16] J.L. Escudi˙e, R. Lombard, M. Pignanelli, F. Resmini, A. Tarrats, Phys. Rev. C 10 (1974) 1645. [17] H.F. Lutz, S.F. Eccles, Nucl. Phys. 81 (1966) 423. [18] H. Essel, K.E. Rehm, H. Bohn, H.J. Körner, H. Spieler, Phys. Rev. C 19 (1979) 2224. [19] A. Christy, O. Häusser, Nucl. Data Tables A 11 (1972) 281. [20] K.E. Rehm, W. Henning, J.R. Erskine, D.G. Kovar, Phys. Rev. C 26 (1982) 1010. [21] Yu.F. Smirnov, Yu.M. Tchuvil’sky, Phys. Rev. C 15 (1977) 84. [22] A.T. Rudchik, Yu.M. Tchuvil’sky, A code DESNA, Kiev Institute for Nuclear Research, report KIYAI-82-12, 1982. [23] A.T. Rudchik, Yu.M. Tchuvil’sky, Ukr. Fiz. Zh. 30 (1985) 819. [24] A.N. Boyarkina, Structure of 1p-Shell Nuclei, Moscow State University, 1973. [25] B.S. Nilsson, SPI-GENOA: an optical model search code, Niels Born Institute report, 1976.

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