Energy dependence of the 8Be + 13C interaction
Introduction
The interaction of radioactive heavy-ion beams with atomic nuclei is one of the most interesting problems of nuclear physics studied in many nuclear research centers. Unfortunately, the experiments with radioactive beams are expensive and strongly restricted by the life time of radioactive ions and beam intensities. At present, only elastic scattering of radioactive ions can be effectively investigated experimentally. To study an interaction of very short-lived ions with atomic nuclei one needs an alternative method. One of such methods is to use nuclear reactions with radioactive (or unstable) ions in the exit channels (we shall call them the reactions with radioactive channels or RC reactions for brevity). The quasi-elastic RC reactions with well-known mechanisms are preferable for this purpose. The RC reactions can be successfully investigated within the coupled reaction channels (CRC) model. In this case the optical model (OM) potential parameters of the exit channel are fitted to describe the reaction angular distributions.
The RC reactions can be effectively used to study the interaction of unstable nuclei provided that the OM potential for the entrance channel was already obtained in the analysis of elastic, inelastic scattering and other reaction channels in a broad energy range, spectroscopic amplitudes were determined experimentally or calculated in a model and the mechanism of the reaction was very carefully studied. These conditions can be easily fulfilled for the 9Be(12C,13C)8Be reaction for which the energy-dependent OM potential for the 9Be + 12C elastic scattering was recently obtained in the work [1] and where the n-transfer evidently dominates.
This article is devoted to the 9Be(12C,13C)8Be reaction at the energy of Elab(12C) = 65 MeV. The angular distributions for the transitions to the ground and low-energy excited states of the 13C and 8Be nuclei were measured using the Kiev cyclotron U-240. These data together with the available data for the 9Be(12C,13C)8Be reaction at Elab(12C) = 12, 15 MeV [2] and 12C(9Be,8Be)13C reaction at Elab(8Be) = 20 MeV [3] were analyzed within the CRC model using the energy-dependent OM potential found in Ref. [1] for the 9Be + 12C interaction. The spectroscopic amplitudes were calculated within translation-invariant shell model (TISM) [5], which was tested in the analysis of various reaction data. The mechanism of the 9Be(12C,13C)8Be reaction was carefully studied and the results are presented in this article. In the CRC calculations we used two OM potentials for the 8Be + 13C interaction: the same as for the entrance channel and the OM potential obtained in the fitting procedure. It is shown that the first potential failed in the description of the experimental data and the second possibility must be considered. The energy dependence of this potential was studied using the approach described in detail in Ref. [1]. It was compared with the energy dependence of the OM potential for the 9Be + 12C elastic scattering. Some differences were found.
The present paper is organized as follows. In Section 2 we present the experimental procedure and experimental data for the angular distributions of the 9Be(12C,13C)8Be reaction at the energy of Elab(12C) = 65 MeV. Results of analysis of all available experimental data at Elab = 12–65 MeV are presented in Section 3. The energy-dependent OM potential obtained in the analysis for the 8Be + 13C interaction is discussed in Section 4. A summary and conclusions close our paper.
Section snippets
Experimental procedure
The angular distributions of the 9Be(12C,13C)8Be reaction for the transitions to the ground and low-energy excited states of the 13C and 8Be nuclei were measured using the Kiev U-240 cyclotron at the beam energy Elab(12C) = 65 MeV in the angular range θcm≈24°–95°. The spread of the beam energy on the target was ∼0.6%. The 9Be target was prepared on the thin nickel foil (∼300μg/cm2). The 9Be layer was equal to g/cm2. Two ΔE−E spectrometers with ΔE (40 μm) and E (1 mm) silicon detectors and
Analysis of the data
The angular distributions of the 9Be(12C,13C)8Be reaction at the energy of Elab(12C) = 65 MeV (Ecm = 27.86 MeV) for the transitions to the ground and excited states of 13C and 8Be nuclei together with similar data at Elab(12C) = 12, 15 MeV (Ecm = 5.14, 6.43 MeV) [2] and Elab(9Be) = 20 MeV (Ecm = 11.43 MeV) for the 12C(9Be,8Be)13C reaction [3] were analyzed within the CRC model using the code FRESCO [4]. The one- and two-step transfer reactions corresponding to the diagrams are presented in Fig.
Energy dependence of OM potential parameters
The values of OM potential parameters listed in Table 1 for the 8Be + 13C interaction are plotted as functions of the center-of-mass energy in Figs. 7 and 8. The errors ΔXi of the parameters Xi=V0, WS=WCRC, rV, rW shown in Figs. 7 and 8, were estimated by using the following simple criterion [1]:If the error ΔXi determined in such a way was smaller than 0.1×Xi, then it was assumed to be ΔXi=0.1×Xi.
In the region of the Coulomb barrier one may
Summary and conclusions
The angular distributions of the 9Be(12C,13C)8Be reaction were measured at the energy Elab(12C) = 65 MeV for the transitions to the ground states of the 8Be and 13C nuclei and to the 2.94 MeV (2+) (state of 8Be) + 3.09 MeV (1/2+) (state of 13C) and 3.68 MeV (3/2−) + 3.85 MeV (5/2+) excited states of 13C nucleus in the angular range θcm≈ 24° - 90°.
These data together with the angular distribution of the 9Be(12C,13C)8Be reaction at the energies Elab(12C) = 12, 15 MeV [2] and the 12C(9Be,8Be)13C
Acknowledgements
This work was supported in part by the Polish State Committee for Scientific Research.
References (9)
Nucl. Phys. A
(1970)Nucl. Phys. A
(1979)Comp. Phys. Rep.
(1988)Nucl. Phys. A
(1986)
Cited by (18)
<sup>7</sup>Li(<sup>15</sup>N, <sup>14</sup>C)<sup>8</sup>Be reaction at 81 MeV and <sup>14</sup>C + <sup>8</sup>Be interaction versus that of <sup>13</sup>C + <sup>8</sup>Be
2018, Nuclear Physics ACitation Excerpt :These data sets along with new data for the 9Be(12C, 13C)8Be reaction taken at a much higher beam energy were then analyzed within the coupled reaction channels (CRC) method. It was shown that n-transfer dominates the forward angle from 5.1 MeV up to 28 MeV in the center of mass, and alpha particle transfer being responsible for the large cross sections at the backward angles [12]. The paper is organized as follows.
<sup>6</sup>Li(<sup>18</sup>O, <sup>17</sup>O)<sup>7</sup>Li reaction and comparison of <sup>6, 7</sup>Li+<sup>16, 17, 18</sup>O potentials
2014, Nuclear Physics ACitation Excerpt :By using well-studied nucleus–nucleus stable beam interactions in the entrance channel and then varying the properties of the exit channel it has been possible to extract the interaction potentials and spectroscopic amplitudes for a range of reactions involving systems of light nuclei. This transfer-reaction method has been used to extract nucleus–nucleus potentials for the interactions of 8Be + {13C, 15N, 9Be, 17N} [1–4], 8Li + 17O [5] and 9Be + 16N [6]. The paper is organized as follows.
Energy levels of light nuclei A = 8,9,10
2004, Nuclear Physics AMechanism of large angle enhancement of the <sup>9</sup> Be+ <sup>11</sup> B scattering
2003, Nuclear Physics A