Design status of KOBRA for rare isotope production and direct measurements of radiative capture cross sections

Nuclear Instruments and Methods in Physics Research B 376 (2016) 188–193

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Design status of KOBRA for rare isotope production and direct measurements of radiative capture cross sections K. Tshoo a,⇑, H. Chae a,b, J. Park a,c, J.Y. Moon a, Y.K. Kwon a, G.A. Souliotis d, T. Hashimoto a, C. Akers a, G.P.A. Berg e, S. Choi b, S.C. Jeong a, S. Kato f, Y.K. Kim c, S. Kubono g, K.B. Lee a, C.-B. Moon h a

Rare Isotope Science Project, Institute for Basic Science, Daejeon 305-811, Republic of Korea Department of Physics and Astronomy, Seoul National University, Seoul 151-742, Republic of Korea Department of Nuclear Engineering, Hanyang University, Seoul 133-791, Republic of Korea d Department of Chemistry, National and Kapodistrian University of Athens and Hellenic Institute of Nuclear Physics, Athens GR-15771, Greece e Department of Physics and The Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, IN 46556, USA f Department of Physics, Yamagata University, Yamagata 990-8560, Japan g RIKEN Nishina Center, Saitama 351-0198, Japan h Department of Display Engineering, Hoseo University, Chung-Nam 336-795, Republic of Korea b c

a r t i c l e

i n f o

Article history: Received 6 September 2015 Received in revised form 30 November 2015 Accepted 12 December 2015 Available online 22 December 2015 Keywords: Rare Isotope Science Project (RISP) Recoil spectrometer Rare isotope production Radiative capture cross sections

a b s t r a c t KOBRA (KOrea Broad acceptance Recoil spectrometer and Apparatus) facility being designed at Rare Isotope Science Project in Korea will be utilized to produce rare isotope beams by employing multinucleon transfer reactions at about 20 MeV/nucleon for studies of nuclear structure. KOBRA will also provide high suppression of beam induced background for direct measurements of radiative-capture cross sections in the astrophysical energy range. The present design status of the KOBRA facility is reported along with a brief introduction to the facility. We have studied the feasibility of production of 44 Ti based on the present design of KOBRA as an example, and calculated the intensity of 44 Ti secondary beam, to be about 105 particles per second, for 1 pnA 46 Ti primary beam with a carbon target for a beam energy of 25 MeV/nucleon. A Monte Carlo simulation with a ray-tracing code has been performed to show that recoil products 66 Se are well separated from a 65 As beam by KOBRA for the 65 Asðp; cÞ66 Se reaction at a beam energy of 1 MeV/nucleon. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction A multi-purpose experimental instrument using stable or rare isotope (RI) beams, KOBRA (KOrea Broad acceptance Recoil spectrometer and Apparatus), is being designed for studies of various topics in low energy nuclear physics at Rare Isotope Science Project (RISP) of the Institute for Basic Science (IBS) in Korea. The stable ions and rare isotopes are provided by an Electron Cyclotron Resonance (ECR) ion source and an Isotope Separation On-Line (ISOL) facility, respectively. They are delivered to the KOBRA facility after acceleration by a superconducting linear accelerator up to about 20 MeV/nucleon. A detailed description of the accelerator complex named RAON was reported in Refs. [1–4]. The possible nuclear physics programs at RAON also have been extensively discussed in Ref. [5].

⇑ Corresponding author. E-mail address: [email protected] (K. Tshoo). http://dx.doi.org/10.1016/j.nimb.2015.12.025 0168-583X/Ó 2015 Elsevier B.V. All rights reserved.

Fig. 1 represents a schematic view of KOBRA. The KOBRA facility is designed to include two stages, stage 1 and stage 2. Stage 1 is utilized not only for the production of low energy RI beams via multinucleon transfer reactions at about 20 MeV/nucleon or via direct reactions such as ðp; nÞ; ðd; pÞ; ðd; nÞ, and ð3 He; nÞ at a few MeV/ nucleon (production mode), but also to reject the primary beam for studies of direct capture reactions of astrophysical interest (radiative capture mode). Stage 2 placed downstream of stage 1 is employed to separate the fragments following reactions of the RI beam on a reaction target, or to reject the primary beam in the same manner as for the stage 1. We report on the present design status of KOBRA stage 1. Preliminary results of Monte Carlo simulations of the 44 Ti production by a multi-nucleon transfer reaction and of the direct capture reaction p (65 As,66 Se)c will be presented.

189

K. Tshoo et al. / Nuclear Instruments and Methods in Physics Research B 376 (2016) 188–193

F5: dispersive focal plane F4 F3: achromatic focal plane 10

Wien filter 2

Wien filter 1

m

F2

Curved-edge bending magnet (D2)

F1: dispersive focal plane Curved-edge bending magnet (D1)

F0 Beam Fig. 1. Schematic view of KOBRA consisting of stage 1 (F0–F3) and stage 2 (F3–F5). Curved-edge bending magnets are utilized to minimize high order aberrations. The total length of KOBRA is 51 m.

2. Multi-nucleon transfer reaction Multi-nucleon transfer reactions have been intensively studied around the Fermi energy (20 MeV/nucleon) over the last decade, see Refs. [6–9]. At the KOBRA facility, we employ multi-nucleon transfer reactions to produce rare isotopes at beam energies of 20 MeV/nucleon. The phenomenological model to describe this reaction mechanism known as Deep Inelastic Transfer (DIT) was implemented by Tassan-Got [10]. Veselsky and Souliotis modified the DIT model, called DITm, to reproduce the experimental data better [11]. The DITm model calculates stochastic nucleon exchange in peripheral and semi-peripheral collisions. The projectile and the target nuclei approach each other until they are within the range of the nuclear interaction, and then the stochastic nucleon transfer occurs. The transfer probabilities are calculated via a phase-space integral taking into account the barrier penetrability, nucleon occupancy, and Pauli blocking. To calculate the de-excitations of the fragments, the binary decay code GEMINI [12] was adopted. The GEMINI code performs a Monte Carlo calculation for a series of sequential binary decays, taking into account light particle evaporations, E1, E2 c-ray emission, as well as fission. We employed the DITm model with the GEMINI

code to predict the production cross sections of exotic nuclei.

3. Optical design of KOBRA stage 1 KOBRA stage 1 consists of two curved-edge bending magnets, a Wien filter (velocity filter), and fifteen quadrupole magnets. We determined the basic design parameters of KOBRA stage 1 to satisfy the requirements for the RI beam production using the multi-nucleon transfer reaction at an energy of 20 MeV/nucleon. The optical design of KOBRA was performed using the ion-optics code COSY INFINITY [13]. The multi-nucleon transfer reaction will be employed to produce RI beam in the mass range of A < 80. A first order momentum resolving power of p=Dp > 2000 is required to identify the fragments particle-by-particle taking into account the charge distributions with large angular and momentum acceptances. The

momentum resolving power is defined as Rp ¼ ðxjdÞ/½2x0 ðxjxÞ. For a total beam size of 2x0 = 2 mm, Rp  2200 is calculated for KOBRA stage 1. This optical design also satisfies the requirements for the RI beam production at a beam energy of a few MeV/nucleon. The optical design parameters of KOBRA stage 1 for the production mode at an energy of 20 MeV/nucleon are summarized in Table 1. In this mode the Wien filter is switched off. Fig. 2 shows a selection of rays of a 5th order optics calculation in stage 1 for the production mode. The production target will be installed at F0. The magnetic rigidity (Bq) is measured by the horizontal position at the dispersive focal plane F1. The nominal Bq of the bending magnet is 3 Tm, corresponding to a field strength of 1.5 T. There is an achromatic focus with zero dispersion ðxjdÞ ¼ 0 at F3. Two curved boundary bending magnets (D1 and D2) were designed to minimize the higher order aberrations. The curved boundaries of the bending magnets are described by polynomial functions up to 4th order. The polynomial functions were determined to minimize the high order (HO) aberrations taking into account the physical space between the D1 magnet and the down-stream quadrupole magnet, where a beam dump will be installed. The Wien filter 1 is employed to separate ions of the same Bq but different velocities/masses for both production and radiative capture modes, in the energy range less than a few MeV/nucleon. The effective field length of the Wien filter 1 is 2.5 m in the present design. Quadrupole magnet triplets are installed on both sides of the Wien filter 1 in order to increase the transmission by reducing the beam envelope. We avoided mirror symmetry between F0 and F2 to minimize the spherical aberration in the Wien filter section (from F2 to F3) by increasing both the horizontal and vertical magnifications at F2. Fig. 3 shows a selection of 1 MeV/nucleon 66 Se19+ rays of a first order optics calculation in stage 1 for the radiative capture mode. The electric and magnetic field strengths of the Wien filter are 2.67 kV/mm and 0.20 T, respectively. The mass dispersion was calculated to be ðxjmÞ = 8.64 cm/% at F3 with zero momentum dispersion. The beam rejection in this radiative capture mode will be discussed later. We are also working on the development of the ion- optics to include the second Wien filter in KOBRA stage 2 to increase the mass resolution of the radiative capture mode. The second Wien filter would increase the total mass resolving power by a factor of 2.

4. Present design of the curved-edge bending magnet Two curved-edge bending magnets (D1 and D2) are utilized not only for achromatic focusing of KOBRA stage 1 but also for correction of HO aberrations, and are, therefore important parts in the KOBRA design. The bending angles and bending radii are 60° and 2.0 m, respectively. The calculation requires that the relative field homogeneity should be about 104 within the horizontal range of x = 200 mm in a wide magnetic field range of 0.125 6B 6 1.5 T. The magnet design is similar to that of D2 of the high resolution SHARAQ spectrometer [14–16].

Table 1 Optical design parameters of KOBRA stage 1 for the production mode at an energy of 20 MeV/nucleon. The magnifications in horizontal and vertical directions and momentum dispersion are listed for each focal plane, F1, F2, and F3. ðxjxÞ F1 0.9 F2 3.2 F3 3.4 Momentum acceptance Angular acceptances

ðxjdÞ

ðyjyÞ

4.0 cm/% 0.0 0.0

5.3 3.0 4.6

Dp/p = 4% hx  40 mrad, hy  100 mrad

190

K. Tshoo et al. / Nuclear Instruments and Methods in Physics Research B 376 (2016) 188–193

Horizontal

High momentum Low momentum D2

410 mm

D1

F0

F1

F3

Wien filter 1

D2

410 mm

D1

F2

2.5 m

F3

25

(mrad)

50

0 -50 -200 -100 0 100 200

50

F3

25

y

(mrad)

F1

x

50

x

(mrad)

Vertical

0

0

-25

-25

-50 -50 -25

x (mm)

0

25

50

-50 -50 -25

0

25

50

y (mm)

x (mm)

Fig. 2. Horizontal and vertical rays of KOBRA stage 1 for the production mode from the 5th order ion-optics calculation with switched-off Wien filter. Beam trajectories with an angular spreads of 40 mrad (100 mrad) in horizontal (vertical) plane for beam size of 1 mm are shown. The blue-, green- and red-solid lines correspond to the trajectories with Dp=p = +4%, 0% and 4%, respectively. Images of the rays at the dispersive and achromatic focal planes, F1 and F3, in position-angle space are shown in the bottom. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this article.)

The physical shape of the curved edge was determined so that the curve of effective field boundary agrees with that of ion optics, using a polynomial function up to 4th order. The round-shaped fillets of 150 mm radius are introduced on both sides of the pole piece in order to reduce field saturation. They are approximated by 10-step functions. 1 mm-thick Rose shims of 65 mm widths are further provided to improve the field homogeneity in the full field range with the pole width of 950 mm. The field saturation effects at both entrance and exit pole edges are minimized by adopting the Rogowski function [17] approximated by a 10-step function. The Rogowski shape provides better field saturation properties than the round shape, reducing the field strength dependence of the effective field boundary curve. The iron yoke at the exit was extended by 100 mm to accommodate the curved edge. The position of the exit pole boundary was shifted to inside of the magnet by 75 mm in order to make the effective lengths of magnetic field along the central trajectory at both entrance and exit the same. The tails of the fringe fields are cut off by field clamps on both the entrance and the exit sides. The magnetic field distribution was calculated in 3 dimensions using the finite-element code OPERA 3D, where the magnetization

property of S1010 annealed steel reported in Ref. [18] was used in the calculation. Fig. 4 shows the layout of the curved-edge bending magnet D1 and the calculated field distributions in the center and in the midplane (y = 0) for low (B = 0.12 T) and high (B = 1.52 T) field strengths, respectively. The calculated field homogeneity is DBy =By  4 104 in the field range from 0.12 to 1.5 T.

5. Production of

44

Ti in KOBRA

The long lived isotope 44 Ti (life time = 85.3  0.4 years) is of great interest not only for understanding the core-collapse supernovae but also for the study of nucleosynthesis in the explosions of massive stars [19]. For example, the c-ray lines of 44 Ti (67.86 and 78.36 keV) detected in the Cassiopeia A remnants strongly support the production of 44 Ti in supernovae [20,21]. Recently, Grefenstette et al. [22] suggested the low-mode convection of supernovae explosions from the spatial distribution of the c-ray emission of 44 Ti in the Cassiopeia A remnants. A Monte Carlo simulation combined with a ray-tracing code was performed in order to examine the particle identification

191

K. Tshoo et al. / Nuclear Instruments and Methods in Physics Research B 376 (2016) 188–193

D2

410 mm

D1

High momentum Low momentum m+ m

m

m

F0

F1

F2

F3

Wien filter 1

D2

410 mm

D1

m

2.5 m Vertical

By (T)

Fig. 3. 1 MeV/nucleon 66 Se19+ rays of KOBRA stage 1 for the radiative capture mode from the first order ion-optics calculation. Beam trajectories with an angular spreads of 15 mrad (15 mrad) in horizontal (vertical) plane are shown. The blue, green- and red-solid lines correspond to the trajectories with Dp=p = +1.5%, 0% and 1.5%, respectively, where Dm=m is 1/66. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this article.)

Field clamp Iron yoke

0.1240 0.1235 0.1230

y

By/By = 4.2 10

4

0.1225 x Pole

By (T)

Ex it

Coil

-200

0

The secondary beams were generated using the DITm model with the decay code GEMINI for a 25 MeV/nucleon 46 Ti primary beam and a 0.1 mm-thick 12 C production target. The 46 Ti primary beam has a much larger production rate of 44 Ti compared to heavier projectiles, owing to the small mass difference of 44 Ti and 46 Ti. The production cross section of 44 Ti was calculated to be rcal ð44 TiÞ = 49 mb. A light target such as 12 C has the advantage of small angular and energy spread of the fragments, thereby increasing the transmission. We assumed a mono-energetic pencil-like primary beam with a Gaussian spatial distribution of r = 1 mm at F0. The Bq-TOF-DE method was employed to identify the charged fragments. The Bq of the secondary beam is determined particle-by-particle by the positions at the focuses F1 and F2, assuming that parallel-plate avalanche counters (PPACs) are installed at the focuses with a position resolution of 0.35 mm in r. We assumed that the timeof-flight (TOF) is determined by an RF signal of accelerator with a time width of 1 nsec (r) and a 100 lm-thick plastic-scintillation detector placed at F3 with a timing resolution of 50 psec (r). The energy loss (DE) is determined by a 20 lm-thick silicon detector with an energy resolution of 1% (r) at F3. Fig. 5 represents the particle-identification spectra, showing the clear separation of the 44 Ti22+ secondary beam. The most abundant charge states of the fragments were calculated following the formulation reported in Ref. [23], along with the width of equilibrium charge distribution formulated by Nikolaev et al. [24]. Secondary particles originating from the beam hitting the wall of the vacuum chamber were not included in this simulation. Since the 46 Ti primary beams with charge states of 21+ and 22+ are separated near the quadrupole magnet just upstream of F1, a beam dump will be installed inside the vacuum chamber at this location. The intensities of the cocktail beam at F1 and 44 Ti22+ beam at F3 were calculated to be 106 and 105 particles per second (pps), respectively, for 1 pnA (6.25  109 pps) of 46 Ti primary beam. The calculated intensity of the 44 Ti beam is comparable with those reported in Refs. [25–27]. The kinetic energy of 44 Ti downstream of F3 was calculated to be about 14 MeV/nucleon.

200

1.5175 1.5150

By/By = 3.9 10

4

Z

Horizontal

1.5125

ce Entran

1.5100

a)

24

44Ti22+

22 -200 0 200 x position (mm)

102

20 10

18

Fig. 4. Layout of the curved-edge bending magnet D1. The center field distributions in the midplane (y = 0) for low (B = 0.12 T) and high (B = 1.52 T) field strengths are shown as calculated using the finite-element code OPERA 3D.

16

and to predict the intensity of the 44 Ti secondary beam. The raytracing code has been developed taking into account the beam profile, the geometry, the magnetic field distributions, the energy losses and multiple scatterings in materials, the detector resolutions, and the charge distribution. In the code, the variations of momentum and position vectors of the particles are calculated by the Lorentz force exerted by the sum of magnetic fields of all magnets, with position steps of typically 4 mm, where the momentum is normalized to satisfy the energy–momentum conservation for each step. The particle trajectories calculated using a raytracing code were in good agreement with the results of the 5th order ion optics calculation. We also confirmed that the first order transfer matrix elements extracted from the ray-tracing code are consistent with those of the calculation using COSY INFINITY.

Counts

560 104

580 b)

44Ti22+

103 102

600

620 640 m/q (arbitray unit)

45Ti22+

1

46Ti22+ 47Ti22+ 44Ti21+

43Ti22+

45Ti21+

10 560

580

600 620 m/q (arbitray unit)

Fig. 5. (a) Monte Carlo simulation of particle identification spectrum of multinucleon transfer reactions using a 25 MeV/nucleon 46 Ti primary beam with 12 C production target. (b) m=q (ratio of mass to charge) spectrum of the Ti isotopes.

192

K. Tshoo et al. / Nuclear Instruments and Methods in Physics Research B 376 (2016) 188–193

6. Beam rejection for p(65 As,66 Se)c

Counts

The radiative-capture (p; c) reaction on 65 As in inverse kinematics was calculated at an energy of 1 MeV/nucleon. Since the extremely small cross sections of the order of nanobarns–picobarns for the (p; c) reactions in the astrophysical energy range, a large acceptance detector system with very high rejection of the primary beam are necessary with sufficiently intense beams. For instance, although 65 As(p; c)66 Se is an astrophysically important reaction to understand nucleosynthesis in X-ray bursts as discussed in Refs. [28,29], there is no direct measurement of the cross section owing to the lack of sufficient beam intensity. To achieve high beam rejection the mass separation has to be of the order of larger than 10r of the beam distribution at F3 assuming a Gaussian distribution. The direct measurement of the p(65 As,66 Se)c reaction is one of the challenging experiments for the future KOBRA facility. The Monte Carlo simulation has been performed with the raytracing code for the p(65 As,66 Se)c reaction at the beam energy of 1 MeV/nucleon in order to examine the rejection of the primary beam in KOBRA stage 1. Since the magnetic rigidity difference between 65 As and 66 Se is only about 104 for the same charge state of 20+ i.e., too small for a separation, the Wien filter is utilized to separate 66 Se from 65 As on the basis of their mass differences. The most abundant charge state of 66 Se leaving the H2 gas jet target was calculated to be 14+ using the empirical formula proposed by Schiwietz [23]. This formula reproduced the charge state of Kr at an energy of 1.04 MeV/nucleon for He gas [30,31]. We note that the separation can be improved more if we use a stripper foil after the target, because the higher charge state leads to larger velocity dispersion of the Wien filter, for a given field strength. We assumed that a 350 nm-thick Al stripper foil is placed just downstream of the target, from which the most abundant charge state of 65 As leaving the Al foil was calculated to be 19+. For the direct measurements of the radiative-capture cross sections, the intense RI beams will be provided by the ISOL facility. For the simulation, the primary 65 As19+ beam started at F0, assuming

4 10 104

41.12

a)

P1 P2 P3 P4 P5 P6 P7 P8 P9

3 10 103 66Se19+

2 10 102

1010

65As19+

1 Counts

-50 -50

5000 4000

/ 50 5925. 135.0 6.396 768.4 132.1 8.559 160.8 135.3 8.571

0

50 50

100 150 100 150 x position at F3 (mm)

b) 65As19+ (

1015)

that beam size, angular spread, and momentum spread are represented by Gaussian distributions with r = 1 mm, 1 mrad, and 0.1%, respectively. 66 Se19+ was generated isotropically in the center of the momentum system of 66 Se + c at F0, where the Q value was calculated to be 2.03 MeV using the mass excess taken from Ref. [32]. A thickness of the H2 gas was 6.62 lg/cm2 in this study. A slit placed at F1 was fully open, leading to no loss of 66 Se19+ at this location. The first order mass resolving power was calculated to be m=Dm = 720 from the ion optics calculation. Fig. 6(a) shows the simulated position distributions of 65 As19+ and 66 Se19+ at the achromatic focus F3. The blue-solid line represents the best fit of the position distribution of 65 As19+ using a linear combination of three Gaussian functions to describe the tail of the distribution. Here, we note that the distributions of 65 As is well described by the fitting function. The widths of the distributions for 65 As and 66 Se were calculated to be 6.83 and 7.06 mm, respectively, by a Gaussian fit. The position distribution of 66 Se was compared with the fitted distribution of 65 As, assuming that the yield of 65 As is extremely higher than that of 66 Se by 15 orders of magnitude, which is represented by Fig. 6 (b). 66 Se is clearly separated from 65 As, if we can neglect the non-Gaussian tail of the beam (see Fig. 6 (b)) and other background sources like scattering and charge exchange on residual gas and vacuum chamber walls. The separation can be further improved by utilizing the second Wien filter of KOBRA stage 2. 7. Summary The KOBRA facility is being designed to satisfy the requirements for the RI beam production using multi-nucleon transfer reaction at an energy of 20 MeV/nucleon and for high background rejection for direct measurements of radiative-capture cross sections in the astrophysical energy range. We have performed a Monte Carlo simulation of the 44 Ti production, as an example, showing that the 44 Ti22+ secondary beam is clearly separated particle-by-particle by measuring the position, the energy loss, and the time-of-flight. The intensity of 44 Ti22+ was calculated to be 105 pps for 1 pnA 46 Ti beam at a beam energy of 25 MeV/nucleon. For direct measurements of the radiative-capture cross sections, the Wien filters of KOBRA stage 1 and 2 will be utilized to separate the recoils from the beam in the mass range of A < 65. The simulated position distributions of 65 As and 66 Se for the p (65 As,66 Se)c reaction at an energy of 1 MeV/nucleon are indicative of a possibility of high rejection of the beam in KOBRA. The design study of KOBRA is still ongoing, and its construction will be completed by the end of 2019 or earlier. It is planned to perform the commissioning in the year 2020. We expect that KOBRA will give an opportunity to study the nuclear structure of exotic nuclei in the energy range of 1020 MeV/nucleon, as well as a variety of astrophysically interesting reactions.

3000 Acknowledgments

66Se19+

2000

This work has been supported by the Rare Isotope Science Project of Institute for Basic Science funded by the Ministry of Science and NRF of Korea (2013M7A1A1075765).

1000 0

0

100 50 100 x position at F3 (mm) 65

66

References 65

66

Fig. 6. (a) Simulated position distributions of As and Se at F3 for the p( As, Se)c reaction at an energy of 1 MeV/nucleon. The blue-solid line represents the best fit result obtained using a linear combination of three Gaussian functions. (b) Tail of the fitted distribution of 65 As (blue-dashed line) and the position distribution of 66 Se, assuming that the yield of 65 As is higher then that of 66 Se by 15 order of magnitudes (see text). (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this article.)

[1] M.S. Ryu, B.H. Kang, Y.K. Kim, S.C. Jeong, C.C. Yun, J. Korean Phys. Soc. 60 (2012) 19. [2] Baseline Design Summary, Rare Isotope Science Project, 2012. [3] Y.K. Kwon et al., Few-Body Syst. 54 (2013) 961. [4] K. Tshoo, Y.K. Kim, et al., Nucl. Instrum. Methods B 317 (2013) 242. [5] C.-B. Moon, AIP Adv. 4 (2014) 041001. [6] G.A. Souliotis et al., Phys. Lett. B 543 (2002) 163.

K. Tshoo et al. / Nuclear Instruments and Methods in Physics Research B 376 (2016) 188–193 [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]

G.A. Souliotis et al., Phys. Rev. Lett. 91 (2003) 022701. G.A. Souliotis et al., Phys. Rev. C 84 (2011) 064607. P.N. Fountas et al., Phys. Rev. C 90 (2014) 064613. L. Tassan-Got, C. Stefan, Nucl. Phys. A 524 (1991) 121. M. Veselsky, G.A. Souliotis, Nucl. Phys. A 765 (2006) 252. R. Charity et al., Nucl. Phys. A 483 (1988) 371. K. Makino, M. Berz, Nucl. Instrum. Methods Phys. Res., Sect. A 558 (2006) 346. T. Uesaka et al., Nucl. Instrum. Methods Phys. Res., Sect. B 266 (2008) 4218. T. Uesaka et al., CNS Annual Report 2005. T. Uesaka et al., CNS Annual Report 2006. W. Rogowski, Arch. Elektrotech. 12 (1923) 1. J.K. Cobb, R.A. Early, SLAC-TN-89-04 (1989). L.-S. The et al., Astrophys. J. 504 (1998) 500. J. Vink et al., Astrophys. J. Lett. 560 (2001) L79.

193

[21] M. Renaud et al., Astrophys. J. Lett. 647 (2006) L41. [22] B.W. Grefenstette et al., Nature 506 (2014) 339. [23] G. Schiwietz, P.L. Grande, Nucl. Instrum. Methods Phys. Res., Sect. B 175 (2001) 125. [24] V.S. Nikolaev, I.S. Dmitriev, Phys. Lett. A 28 (1968) 277. [25] J. Görres et al., Phys. Rev. Lett. 80 (1998) 2554. [26] A.A. Sonzogni et al., Phys. Rev. Lett. 84 (2000) 1651. [27] V. Margerin et al., Phys. Lett. B 731 (2014) 358. [28] A. Parikh, J. Jose, G. Sala, AIP Adv. 4 (2014) 041002. [29] Y.H. Lam et al., arXiv:1505.02275. [30] R.B. Clark, I.S. Grant, R. King, Nucl. Instrum. Methods 133 (1976) 17. [31] H. Kuboki et al., Phys. Rev. ST Accel. Beams 17 (2014) 123501. [32] G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729 (2003) 337.