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12C(15N, 14C)13N reaction at 81 MeV. Competition between one and two particle transfers
ScienceDirect Nuclear Physics A 992 (2019) 121638 www.elsevier.com/locate/nuclphysa
12 C(15 N, 14 C)13 N
reaction at 81 MeV. Competition between one and two particle transfers
A.T. Rudchik a,∗ , A.A. Rudchik a , O.E. Kutsyk a , K.W. Kemper b , K. Rusek c , E. Piasecki c , A. Trzci´nska c , S. Kliczewski h , E.I. Koshchy d , Val.M. Pirnak a , O.A. Ponkratenko a , I. Strojek e , V.A. Plujko f , S.B. Sakuta g , R. Siudak h , A.P. Ilyin a , Yu.M. Stepanenko a , Yu.O. Shyrma a , V.V. Uleshchenko a a Institute for Nuclear Research, Ukrainian Academy of Sciences, Prospect Nauki 47, 03680 Kyiv, Ukraine b Physics Department, Florida State University, Tallahassee, FL 32306-4350, USA c Heavy Ion Laboratory of Warsaw University, ul. L. Pasteura 5A, PL-02-093 Warsaw, Poland d Cyclotron Institute Texas A&M University, College Station, TX 77843, USA e National Center for Nuclear Research, ul. Ho˙za 69, PL-00-681 Warsaw, Poland f Taras Shevchenko National University, ul. Volodymyrska 64, 01033 Kyiv, Ukraine g Russian Research Center “Kurchatov Institute”, Kurchatov Sq. 1, 123182 Moscow, Russia h H. Niewodnicza´nski Institute of Nuclear Physics, Polish Academy of Sciences, ul. Radzikowskiego 152,
PL-31-342 Cracow, Poland Received 22 July 2019; received in revised form 20 September 2019; accepted 21 September 2019 Available online 25 September 2019
Abstract Angular distributions at both forward and backward angles for the 12 C(15 N, 14 C)13 N reaction were measured at the energy Elab (15 N) = 81 MeV for ground and exited states of 14 C and 13 N nuclei by detecting both particles at forward angles. Coupled-reaction-channels (CRC) calculations using spectroscopic amplitudes calculated within the translational invariant shell model (TISM) for transferring nucleons and clusters were carried out. These calculations describe the origin of the observed highly oscillatory large angle data as two neutron transfer while the less structured forward angle data is by proton transfer. Multi-step and other nucleon transfers were found to give small contributions to the current data. © 2019 Elsevier B.V. All rights reserved.
* Corresponding author.
E-mail address: [email protected] (A.T. Rudchik). https://doi.org/10.1016/j.nuclphysa.2019.121638 0375-9474/© 2019 Elsevier B.V. All rights reserved.
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A.T. Rudchik et al. / Nuclear Physics A 992 (2019) 121638
Keywords: N UCLEAR R EACTIONS 12 C(15 N, 14 C), E = 81 MeV; Measured particle spectra, σ (θ ); Deduced reaction mechanism features and Woods-Saxon potential parameters of the 14 C + 13 N potential using coupled-reaction-channels analysis
1. Introduction The present work continues the study of scattering and reactions between 1p-shell nuclei that allow the contributions from potential scattering and transfer reactions to be explored by acquiring data at both forward and backward angles through the detection of the incident beam and recoil particles. These studies have revealed the interplay between various reaction channels including reorientation of deformed nuclei and possible nucleon transfers. Even in the case of elastic scattering it has been shown that contributions from transfer or reorientation processes can be larger than potential scattering at large angles giving rise to cross sections factors of 10-100 greater than that if potential scattering dominated over the whole angular range. The 12 C(15 N, 14 C)13 N reaction measured in this work at the energy of 81 MeV has the interesting feature that the reaction can proceed via a single proton transfer or via two neutron transfer thus providing an opportunity to investigate the interplay between these two mechanisms. Early work demonstrated the power of heavy-ion reactions to probe nuclear structure with the possibility to measure both proton and neutron transfer cross sections at forward angles with the same detection system allowing for a very careful calibration of our understanding of heavy ion reactions. An example of such a case is the 12 C(14 N, 13 N/13 C) study [1] which showed that the same spectroscopic factor was obtained from the reaction analysis of these data for both single neutron and proton transfers. A further analysis of these data demonstrated the importance of the Coulomb interaction in understanding these mirror final states [2]. The possibility of elastic transfer between light heavy ion scattering was recognized early ion and its presence was clearly shown in the analysis of 13 C(12 C,12 C) and 18 O(16 O,16 O) scattering [3]. Two proton cluster transfers versus that of two-step single proton transfers were studied for the reaction 14 C(16 O,14 C) in Ref. [4], to assess their contributions to the elastic scattering 14 C(16 O,16 O)14 C at the energies Elab (16 O) = 132 MeV and 281 MeV using the experimental data from Ref. [5]. The power of studies with light heavy ion beams for probing more exotic structures in nuclei is shown further in by the heavy-ion induced two neutron transfer reactions 12 C(16 O,14 O), 12 C(14 N,12 N) and 12 C(15 N,13 N), carried out at far forward angles, that used the property of angular momentum matching to selectively probe the structure of nuclei such as 14 C Ref. [6]. Another interesting example is the use of the 14 C(12 C,14 O) and 10 Be(14 N,12 N) to develop the band structure of 12 Be [7]. To study the interplay between the allowed single proton and two neutron transfers, coupledreaction channels (CRC) calculations that include spectroscopic amplitudes of transferred nucleons and clusters calculated within the translation invariant shell model (TISM) are reported. The entrance optical potential needed for the reaction calculation has been determined from an analysis of the 12 C(15 N,15 N) elastic scattering taken at the same time as the reaction data in this work and is reported in Ref. [8,9]. The results of this reaction analysis along with the new data are presented in the current work. The paper is organized as follows. Section 2 contains a brief summary of the experimental procedure, Section 3 gives the results of CRC-analyses of the reaction experimental data and the last section provides a summary of this work.
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Fig. 1. Typical energy spectra of 14 C and 13 N nuclei from the 12 C(15 N, 14 C)13 N reaction with the backgrounds from multi-particle reactions (a, c) (curves show the backgrounds) and after subtraction of these backgrounds (b, d) (curves show the Gauss symmetric fitted forms).
2. Experimental procedure Experimental details for producing the angular distributions of the 12 C(15 N, 14 C)13 N reaction for ground and exited states of 14 C and 13 N nuclei are the same as those given in a recent report of the 12 C + 15 N elastic scattering Ref. [8,9]. In summary, the 81 MeV 15 N beam was produced by the U-200P cyclotron of the Heavy Ion Laboratory of the University of Warsaw. The detection and electronics systems are well described in Ref. [9] as is the data reduction method. This system allows both the 14 C and 13 N reaction products to be measured simultaneously at forward angles thus giving angular distributions over the full angular range since the forward angle 13 N data corresponds to large angles in the center-of-mass. Typical energy spectra of the reaction products 14 C and 13 N are shown in Fig. 1: (a) and (c) with backgrounds from multi-particle reactions (curves show background forms), (b) and (d) after subtraction of the backgrounds (curves show the symmetric Gauss functions fitted to the spectra peaks). The areas under the peaks of the residual 14 C and 14 N spectra were used for the calculation of the angular distributions at the angles θc.m. (14 C) and θc.m. (14 C) = 180o −θc.m. (13 N), respectively. In this way, the angular distributions for the 12 C(15 N, 14 C)13 N reaction were determined over the whole angular range. 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.
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Fig. 2. Angular distributions of the 12 C(15 N, 14 C)13 N reaction cross-sections for different states of 14 C and 13 N. The lines through the data are to guide the eye. Table 1 Parameters of WS optical potentials. P +T
Ec.m. (MeV)
V0 (MeV)
rV (fm)
aV (fm)
WS (MeV)
rW (fm)
aW (fm)
Ref.
15 N + 12 C
36.0 27.7 58.0
195 190 150
0.790 0.790 0.812
0.750 0.870 0.722
8.0 6.0 35.4
1.250 0.900 0.958
0.750 0.870 0.789
[8,9] This work [11]
14 C + 13 N 14 N + 14 C
The final angular distributions of the 12 C(15 N, 14 C)13 N reaction cross-sections for ground and exited states of 14 C and 13 N are shown in Fig. 2. Total angular distributions of the reaction were measured for the unresolved states in 13 N 3.511 MeV + 3.547 MeV states and 6.590 MeV + 6.728 MeV and 6.902 MeV + 7.012 MeV states of 14 C. 3. Data analysis The 12 C(15 N, 14 C)13 N reaction data were analyzed with CRC methods using optical model potentials U(r) in the entrance and exit channels of Woods-Saxon form (WS) with parameter values taken from Ref. [8] for 12 C(15 N, 15 N) scattering. The 14 C + 13 N WS exit channel potential parameters were deduced from fitting the reaction CRC-calculations to the reaction experimental data. These deduced parameters and previously found 14 C + 14 N WS potential parameters [11] are listed in Table 1. In the CRC analysis of the 12 C(15 N, 14 C)13 N reaction, the 12 C + 15 N elastic scattering and most important one- and two-step transfers were included in the coupling channels scheme. The
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Fig. 3. Diagrams of nucleon and cluster transfers in the 12 C(15 N, 14 C)13 N reaction. Table 2 Spectroscopic amplitudes Sx of x-clusters in A = C + x systems. A
C
x
nLj
Sx
A
C
x
nLj
Sx
12 C
11 B
15 N
12 C
13 C
12 C
15 N
13 C
d t d
14 C
11 B
-1.706a 1.706a 0.601 0.368a 0.615 0.615 0.615 0.615 0.246 0.246 -1.094a 0.203 0.125 0.375a 0.601 0.601 0.601 0.101 -0.461 -0.163a
12 C
11 C
1P3/2 1P3/2 1P1/2 2P3/2 2S0 1P1 2S0 2S0 1D2 1D2 1P1/2 2S1 1D1 1D2 1P1/2 2S1/2 1P3/2 1D5/2 1P1/2 1P3/2
14 N
12 C
p n n t 2n 2n 2n 2n 2n 2n n d
15 N
14 C
1D1 2P1/2 2S1 1D1 1P1/2 2S1/2 1P1/2 1P1/2 1P3/2 1P3/2 2S0 2S0 1D2 1D2 1P1/2 1P3/2 2P2 1D3/2 2P1/2 1P1/2
0.246 0.380 0.248a 0.444a -0.598 0.598 -0.598 -0.598 1.336 1.336 0.608 -0.608 -0.544 -0.246 -1.091a 0.386 0.380 -0.270 -0.910a -1.461a
14 C
12 C
14 C∗ 6.09 14 C∗ 6.59 14 C∗ 6.90 14 C∗ 7.01 14 C∗ 7.34 14 C
12 C
13 N
11 C
13 N
13 N∗ 2.36 13 N∗ 3.51 13 N∗ 3.55 14 N
12 C 12 C 12 C 12 C 13 C
12 C 12 C 12 C 12 C 13 N
p p p p n
15 N 15 N 15 N 15 N 15 N 15 N
14 C∗ 6.09 14 C∗ 6.59 14 C∗ 6.90 14 C∗ 7.01 14 C∗ 7.34 13 N
15 N
13 N∗ 2.36 13 N∗ 3.51 13 N∗ 3.54 14 N
16 N
14 C
16 N
15 N
16 O
13 N
16 O
15 N
15 N 15 N 15 N
p p p p p p 2n 2n 2n 2n n d n t p
a S J +j −JA S = −S . x x F RESCO = (−1) C
diagrams of these transfers are shown in Fig. 3. The code FRESCO [10] was used for the CRC calculations. The needed spectroscopic amplitudes Sx of nucleons and clusters x in the A = C + x systems transferred in the 12 C(15 N, 14 C)13 N reaction (Fig. 3) were calculated within the translational invariant shell model (TISM) [12] using code DESNA [13,14]. These Sx are listed in Table 2. Note the presence of the two neutron amplitudes in this table. The wave function of the bound state of cluster x was calculated by fitting the energy eigenvalue to the x-cluster binding energy in the A = C + x system by adjusting the depth of the Woods-Saxon potential with aV = 0.65 fm and rV = 1.25A1/3 /(C 1/3 + x 1/3 ) fm. The angular distribution of the measured 12 C(15 N, 14 C)13 N reaction cross-sections for 14 C and 13 N in their ground states are presented in Fig. 4. The curves show the CRC calculations for the transfers of protons p (curve
), 2n-clusters (curve <2n>), sequential transfers of t + p and <2n> in Figs. 6–8 show the CRC calculations for the transfers of protons p and 2n-clusters for the exited state 2.365 MeV of 13 N and exited states 6.094 MeV, 7.341 MeV of 14 C. The sums of these transfers for these states of 14 C and 13 N are shown with curves W S . The curves k show the sums of p- and 2n-transfer calculations for unresolved states k of 14 C and 13 N nuclei and curves k+j show sums of CRC-calculations for such k- and j -states of these nuclei. One can see, that the CRC cross-sections calculated with the 12 C + 15 N and 14 C + 13 N14 potential parameters of Table 2 and spectroscopic amplitudes for the transfer protons p and 2n-clusters give a satisfactory description of the data. 4. Summary and conclusions New experimental data for the 12 C(15 N, 14 C)13 N reaction at the energy Elab (15 N) = 81 MeV were measured for ground and exited states of 14 C and 13 N by detecting both the 14 C and recoil 13 N at forward angles. , <2n> and E show the reaction CRC cross-sections for the corresponding transfers and their sums (see text).
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Fig. 4. Angular distribution of the 12 C(15 N, 14 C)13 N reaction for 14 C and 13 N in their ground states. The curves show the CRC calculations for different transfers of nucleons and clusters x (see text).
and p + t (curve
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Fig. 5. Comparing CRC-calculations of the 12 C(15 N, 14 C)13 N reaction with the 14 C + 13 N WS potential parameters deduced in this work (curve W S(13N +14C) ) and with the 14 C + 14 N potential parameters [11] (curve W S(14N +14C) ).
Fig. 6. Angular distributions of the 12 C(15 N, 14 C)13 N reaction cross-sections for the 2.365 MeV and 3.511 + 3.547 MeV exited states of 13 N. The curves show the CRC calculations for the p- and 2n-cluster transfers. The curves
The data were analyzed within the CRC method. The 12 C + 15 N elastic scattering and oneand multi-step transfer reactions were included in the coupled-channels scheme. The spectroscopic amplitudes of transfer nucleons and clusters were calculated within the translational
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Fig. 7. The same as in Fig. 6, but for the exited states of 14 C.
Fig. 8. The same as in Fig. 6, but for the exited states of 14 C.
invariant shell model (TISM). It was found that proton transfer dominates in the reaction for all states of 14 C and 13 N at small angles. The 2n-cluster transfer dominates at the highly oscillatory data at mid and large angles with other cluster transfers and multi-step contributions providing little contribution. The present data allow the competition between two strong transfer modes in
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a single reaction to be investigated thus furthering our understanding of reactions between light nuclei of similar masses. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
K.G. Nair, H. Voit, C.W. Towsley, et al., Phys. Rev. C 12 (1975) 1575. K.G. Nair, K. Nagatani, H. Voit, Phys. Rev. Lett. 36 (1976) 1293. A. Vitturi, C.H. Dasso, Nucl. Phys. A 458 (1986) 157. A.T. Rudchik, Yu.O. Shyrma, K.W. Kemper, et al., Eur. Phys. J. A 47 (2011) 50. A.S. Demyanova, Yu.A. Glukhov, W. Trzaska, et al., Bull. Russ. Acad. Sci., Phys. 67 (2003) 83. W. Von Oertzen, H.G. Bohlen, M. Milin, et al., Eur. Phys. J. A 21 (2004) 193. H.G. Bohlen, W. Von Oertzen, et al., Int. Mod. Phys. E 17 (2008) 2067. A.T. Rudchik, A.A. Rudchik, O.E. Kutsyk, et al., Nucl. Phys. At. Energy 19 (2018) 210. A.T. Rudchik, A.A. Rudchik, O.E. Kutsyk, et al., Acta Phys. Pol., B 50 (2019) 733. I.J. Thompson, Comput. Phys. Rep. 7 (1988) 167. A.T. Rudchik, V.A. Ziman, et al., Nucl. Phys. A 589 (1995) 535. Yu.F. Smirnov, Yu.M. Tchuvil’sky, Phys. Rev. C 15 (1977) 84. A.T. Rudchik, Yu.M. Tchuvil’sky, The code DESNA, report KINR-82-12, Kiev Institute for Nuclear Researches, 1982. [14] A.T. Rudchik, Yu.M. Tchuvil’sky, Ukr. Fiz. Zh. 30 (1985) 819.