Energy dependence of total reaction cross sections for 17Ne on a proton target

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ScienceDirect Nuclear Physics A 994 (2020) 121663 www.elsevier.com/locate/nuclphysa

Energy dependence of total reaction cross sections for 17 Ne on a proton target T. Moriguchi a,∗ , M. Amano a , A. Ozawa a,b , W. Horiuchi c , Y. Abe d,1 , T. Fujii e , R. Kagesawa a , D. Kamioka a , A. Kitagawa f , M. Mukai a,b , D. Nagae d,2 , M. Sakaue e , S. Sato f , S. Suzuki a,3 , T. Suzuki e , T. Yamaguchi b,e , K. Yokota e a Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan b Tomonaga Center for the History of the Universe, University of Tsukuba, Ibaraki 305-8571, Japan c Department of Physics, Hokkaido University, Sapporo 060-0810, Japan d RIKEN Nishina Center, Wako, Saitama 351-0198, Japan e Department of Physics, Saitama University, Saitama 338-8570, Japan f National Institutes for Quantum and Radiological Science and Technology, Chiba 263-8555, Japan

Received 8 May 2019; received in revised form 17 October 2019; accepted 27 October 2019 Available online 30 October 2019

Abstract We measured the energy dependence of the total reaction cross sections (σR ) for the proton dripline nucleus of neon isotopes, 17 Ne, with a solid hydrogen target. The σR on a proton target in the low- and intermediate-energy regions were provided, where only a few values are available for unstable nuclei. The new data were compared with theoretical calculations using the Glauber model. In the lowenergy region (∼100A MeV), the theoretical cross sections overestimate the experimental ones, whereas the theoretical ones significantly underestimate the experimental data in the intermediate energy region (∼300-500A MeV). We discuss several possibilities for solving this discrepancy. This work suggests the necessity of more careful investigations of the energy dependence of σR for various nuclei on a proton target to determine the nuclear size properties precisely. © 2019 Elsevier B.V. All rights reserved.

* Corresponding author.

E-mail address: [email protected] (T. Moriguchi). 1 Present address: National Institutes for Quantum and Radiological Science and Technology, Chiba 263-8555, Japan. 2 Present address: Research Center for SuperHeavy Elements, Kyushu University, Fukuoka 819-0395, Japan. 3 Present address: Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China.

https://doi.org/10.1016/j.nuclphysa.2019.121663 0375-9474/© 2019 Elsevier B.V. All rights reserved.

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Keywords: N UCLEAR R EACTION p(17 Ne, X), p(20 Ne, X), E = 73–582A MeV; Total reaction cross section; Total charge-changing cross section; Solid hydrogen target

1. Introduction Nuclear size properties such as radii and density distributions provide us with basic and important information for understanding the nuclear structure. In particular, at the limit of the nuclear binding, proton/neutron halo structure emerges, in which the density distribution shows an extended tail due to the one or two weakly-bound valence nucleons. Proton/neutron skin structure is also the representative phenomenon of unstable nuclei. The skin thickness is defined by the difference of the proton and neutron root-mean-square (RMS) radii (rp and rn ) of a nucleus. Since this quantity is closely related to the nuclear symmetry energy in the nuclear matter equation of state (EOS) [1–4], studies of the skin structure contribute not only to nuclear physics but also to the elucidations of the mechanism of supernova explosions and the internal structure of neutron stars. On the experimental side, measurements of the total reaction cross sections (σR ), interaction cross sections (σI ), and total charge-changing cross sections (σCC ) using high-energy radioactive beams from several tens of A MeV to 1A GeV have been standard approaches to extract the size properties of unstable nuclei [5–9]. The matter density distributions (ρm ) of halo nuclei such as 11 Li and 11 Be were deduced using incident energy and target mass dependence of σR and σI [10,11]. Recently, σCC measurements succeeded in deducing rp using the sensitivity of the charge-changing process to the proton density distribution (ρp ) [12–20]. The energy dependence of σR has been used to deduce the nucleon density distributions. In particular, σR on a proton target has the possibility to separate ρp and the neutron density distribution (ρn ) using the asymmetry of the nucleon–nucleon total cross sections (σNtotN ) [21]. The separation of ρp and ρn was successfully performed experimentally for 11 Li, 11 Be, and 8 B by σ measurements with a proton target at several tens of A MeV [22,23]. Theoretical R investigations suggested that the energy dependence of σR on a proton target is useful for the separation of rp and rn together with the practical prescriptions [24,25]. To extract the information on the nuclear size precisely from σR measurements, it is essential to understand the energy dependence of σR for unstable nuclei on a proton target in a wide energy range. A systematic measurement of σR with proton beams on stable nuclei has been studied well as compiled in Refs. [26,27]. However, only a few experimental σR for unstable nuclei on a proton target are available; especially, those at intermediate energies from 200 to 600A MeV have not been reported at this time. One of the reasons for this is the historical background. In the 1980s, σR and σI were intensively measured using high-energy unstable beams to study nuclear radii [11,28], and then those at low-energy beams (below ∼100A MeV) were used for the extraction of the density distributions at the nuclear surface such as the halo tail [22,23,29, 30]. Hence, σR on a proton target at intermediate energies have been missing for unstable nuclei. For experimental studies of collisions between unstable nuclei and a proton, hydrogen target has advantage that the number of atoms per unit mass of hydrogen is maximum compared with other materials [31]. This point is quite good for radioisotope (RI) beams with low intensity. In Ref. [32], σR for 22 C at low energies were measured by a liquid hydrogen target [33]. By optimization of the gas pressure in the target cell, a solid hydrogen target with thick and large size was developed for RI beams with intermediate energies (several 100A MeV) [34]. Actually, a windowless target was reported in Ref. [35].

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17 Ne (T 1/2 = 109.2(6) ms [36], S2p = 933.10(61) keV [37]), which is the proton drip-line nucleus of neon isotopes, is known to be a candidate for a two-proton halo nucleus [38,39], and there is a long standing controversy of how to interpret the different data. Experimental results of the asymmetry of β-decay probabilities indicate the existence of the proton halo [40]. σR and σI measurements suggest significant s-wave probability of the two valence protons [41,42]. This is consistent with the measurement of the longitudinal momentum distribution for two-proton removal from 17 Ne [43]. Experimental results of the optical isotope shift show the enhancement of the RMS charge radius (rch ) of 17 Ne, compared with those of other neon isotopes [44,45]. The observations of the two-proton emission from the excited states in 17 Ne support three-body structure of 15 O + 2p [46–49]. In contrast, a pronounced proton halo structure of 17 Ne is not exhibited from the magnetic moment measured using collinear laser spectroscopy [50]. Theoretical studies suggest that the two valence protons of 17 Ne dominantly occupy the 2s1/2 orbit in Refs. [51,52], but the 1d5/2 orbit in Refs. [53–55]. Meanwhile, the calculations in Refs. [56,57] suggest an almost equal occupation probabilities of (2s1/2 )2 and (1d5/2 )2 configurations. In the present study, we investigate the energy dependence of σR for 17 Ne on a proton target. σR were measured using a solid hydrogen target and those results were compared with standard Glauber model calculations using the density distribution of 17 Ne deduced from the previous σR measurement [42]. In Ref. [42], ρm of 17 Ne was deduced so as to reproduce experimental σR on several targets and energies with the Glauber model. The harmonic oscillator type for the core (15 O) plus a square of Yukawa function for the valence two protons was assumed for the fitting procedure. ρm deduced experimentally agrees with the Hartree-Fock calculation [58] within the uncertainties. The value of the RMS matter radius (rm ) obtained from Ref. [42] is consistent with those of the σI experiment [9] and the theoretical calculations [39,58,59]. Furthermore, the experimental value of rch of 17 Ne [44,45] is also consistent with that of the recent theoretical calculation [60]. The nuclear size properties of 17 Ne are studied well both experimentally and theoretically. Thus, 17 Ne offers an ideal example for unstable nuclei on a proton target.

2. Experiment In order to measure σR for 17 Ne, we adopted a transmission method expressed by the equation   1 Rin σR = − ln , (1) Nt Rout where Rin is the ratio of the number of outgoing particles (No ) to that of incoming particles (Ni ) for a target-in measurement and Rout is the same ratio for a target-out measurement. Target-out measurements are necessary to subtract the contribution of reactions with materials except for a reaction target. Outgoing particles indicate the non-interacting 17 Ne nuclei. The number of target nuclei per unit area is denoted as Nt . The experiment was performed using a fragment separator in the Heavy Ion Medical Accelerator in Chiba (HIMAC), which is referred to as SB2 [61]. Fig. 1 shows the schematic view of the fragment separator and the experimental setup. In the present experiment, we measured not only total reaction cross sections (σR ) for 17 Ne, but also the total charge-changing cross sections (σcc ) for 20 Ne at several incident energies to validate the experimental system. The experimental conditions are listed in Table 1. 20 Ne was used as a primary beam with three energies: 180, 400, and 600A MeV. A secondary beam was produced by bombardment of the 20 Ne beam on a beryllium target located at the entrance of the separator (F0). 17 Ne particles were identified using the

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Fig. 1. Schematic view of the fragment separator [61] and the experimental setup.

magnetic rigidity (Bρ), the time-of-flight (TOF) and the energy loss (ΔE). An aluminum energy degrader was installed at the momentum dispersive focal plane (F1). A plastic scintillation counter (0.5 or 1.0 mm thick) was also installed in F1 to detect the start signal of the TOF. At the second focal plane (F2), a 325-µm-thick silicon detector (Si) was installed to determine the ΔE. After a vacuum window (Al, 0.1 mm thick), a plastic scintillation counter (1.0 mm thick) was placed for the stop signal of the TOF and two parallel-plate avalanche counters (PPACs) [62] for beam tracking. A solid hydrogen target (SHT) was used as the reaction target [34]. Mylar foils (100 µm thick) were used for the entrance and exit windows of the vacuum chamber of the SHT. The SHT cell was made of copper, and thin Kapton foils (25 µm thick) were used for the entrance and exit windows of the cell. As listed in Table 1, two different thicknesses of SHTs were used, which correspond to φ50 × 30 mm3 (1.58 × 1023 /cm2 ) and φ50 × 100 mm3 (5.21 × 1023 /cm2 ). Downstream of the SHT, an ionization chamber (IC) [63] was placed to provide the ΔE for the determination of the atomic number (Z) of the particles ejected from the SHT. The IC was filled with a P10 (Ar 90% + CH4 10%) gas (approximately 760 Torr), and output signals were obtained from eight anode foils (4 µm-thick, Mylar aluminized on both sides). A NaI(Tl) scintillation counter (φ 3-in., 60 mm thick) was used to measure the total energy (E). In the case of the 600A MeV primary beam, a copper energy degrader was installed before the NaI(Tl) to stop the particles in the NaI(Tl). The beam energies of the target-out measurement with an empty SHT were adjusted to match those of the target-in measurements since both measurements should have the same reaction rates. 3. Analysis and results As mentioned in the experimental principle, Ni and No are needed to extract σR with Eq. (1) through particle identifications (PIDs) both before and after the reaction targets. Fig. 2 shows

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Table 1 Experimental conditions for the present experiments. The purity and the intensity of 17 Ne listed in this table are typical values. The unit of intensity, ppp, refers to particles per pulse. SHT stands for solid hydrogen target. The values in parentheses indicate the thickness of the SHT. Incident beam 17 Ne

20 Ne

Data number #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14

20 Ne energy

(A MeV)

Be (mm thick)

Degrader (mm thick)

Purity (%)

Intensity (ppp)

SHT (mm thick)

180 180 400 180 400 400 600 600 400 400 400 400 600 600

10 14 65 14 10 35 25 38 61 73 0 12 0 12

3.53 3.53 10.6 3.53 13.5 7.06 25.5 25.5 10.6 10.6 0 0 0 0

25 25 55 30 60 55 80 80

200 300 650 300 550 700 650 900

In (30) Out In (100) Out In (100) Out In (100) Out In (100) Out In (100) Out In (100) Out

Fig. 2. Two-dimensional TOF-ΔE PID plot before the SHT in the case of 17 Ne at 289A MeV. The intensity is color coded. (For interpretation of the colors in the figures, the reader is referred to the web version of this article.)

the two-dimensional TOF-ΔE PID plot before the SHT in the case of 17 Ne at 289A MeV (data #5 in Table 1). This plot was obtained after selecting the beam position and angle ranges with good transmission using the beam tracking from position information of two PPACs. As shown in Fig. 2, 17 Ne particles were clearly separated from other nuclei. In order to determine Ni , Gaussian fits were performed on the TOF and the ΔE axes after projecting the main peak of 17 Ne to each axis. In the present analysis, we counted the number of 17 Ne within ±2 sigma as Ni . Figs. 3 (a) and (b) show the two-dimensional ΔE-E PID plots after the SHT for the target-in and the target-out measurements, respectively. These plots were obtained by selecting the 17 Ne before the SHT as mentioned above. Non-interacting 17 Ne events are seen as the main peaks in Figs. 3 (a) and (b). The tails from the main peaks towards low E correspond to the events due to the nuclear reactions inside the NaI(Tl) scintillation counter and should be counted as

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Fig. 3. Particle identification (PID) after the SHT in the case of 17 Ne at 289A MeV. (a) and (b) are two-dimensional ΔE-E PID plots of the target-in and target-out measurements, respectively. The intensity is color coded. (c) and (d) are projections onto the ΔE axis of (a) and (b), respectively. The shaded areas indicate the non-interacting 17 Ne for the determination of No .

non-interacting 17 Ne. Inelastic-scattering events were neglected in the present analysis since these events are not seen in Fig. 3 and the bound excited states of 17 Ne have not been reported yet. One-neutron removal reaction events are not seen in these plots since 17 Ne is a proton drip-line nucleus. Moreover, neutron pickup reactions were also neglected since a solid hydrogen was used as the reaction target. Consequently, non-interacting 17 Ne can be identified solely from the ΔE, which is provided by the IC. Figs. 3 (c) and (d) are the ΔE projection of Figs. 3 (a) and (b), respectively. As shown in Fig. 3 (c), the main peak is non-interacting 17 Ne, and the peaks of carbon, nitrogen, and oxygen isotopes are seen as the fragment events. Fluorine isotopes are not seen since the 16 F produced by one-proton removal reactions is an unbound nucleus. Proton pickup events such as sodium isotopes were not seen in the present experiment. In the target-out measurement shown in Figs. 3 (b) and (d), while almost all events are non-interacting 17 Ne, a few reaction events with some materials are seen. In order to determine N , the width of o non-interacting 17 Ne peak in Figs. 3 (c) and (d) was obtained from Gaussian fits. In the present analysis, we counted the number of events in the gate from −3.5 sigma to +5 sigma as No , which is indicated by each shaded area in Figs. 3 (c) and (d), to prevent contamination from the oxygen isotopes.

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Table 2 Experimental results for the total reaction cross sections (σR ) for 17 Ne and the total charge-changing cross sections (σCC ) for 20 Ne on a proton target. The energies of the present work are given for the middle of the target.

Present work

Incident particle

Energy (A MeV)

σR (mb)

17 Ne

73 100 289 432 163 379 582 290 400 600

353.1(8.6) 322.6(5.9) 282.4(2.8) 300.2(2.2)

20 Ne

Previous work [64]

20 Ne

σCC (mb)

289.3(3.0) 304.8(3.0) 333.2(2.6) 272(16) 311(15) 319(13)

Data number in Table 1 #1, #2 #3, #4 #5, #6 #7, #8 #9, #10 #11, #12 #13, #14

The thickness of the SHT depends on the position of incident particles since the surfaces of the SHT with the thin entrance and exit windows swell owing to the inner pressure. This expansion is approximated by a second-order polynomial function [34]. In this study, the effective thickness was used as Nt by considering the statistical weight of the beam position at the exit of the SHT. Moreover, we measured σCC for 20 Ne on a proton target using Eq. (1). In the case of σCC , No corresponds to the number of neon isotopes after the SHT. The analysis procedure for σCC is similar to that of σR for 17 Ne, as mentioned above. The neon isotopes after the SHT were seen as the main peak of ΔE provided by the IC, and the gate from −2.8 sigma to +4 sigma was used for No to prevent contamination from isotopes such as the fluorine. As listed in Table 1, we applied this analysis procedure to data #1−#8 and #9−#14 to obtain σR for 17 Ne and σCC for 20 Ne, respectively. The experimental results are summarized in Table 2. The experimental errors take into account the statistical errors and the uncertainty of the target thickness. As listed in Table 2, the present results of σCC for 20 Ne are consistent with those of the previous study [64] within uncertainties at comparable energies, and the validation of our experimental system is confirmed. The analysis of the partial charge-changing cross section [15, 19,64,65] is still in progress, and will be reported separately. 4. Discussion We investigate the energy dependence of σR for 17 Ne on a proton target with the Glauber model [66], which is a widely accepted method to extract the nuclear size properties from σR. The Glauber model is formulated based on the multiple-product of the nucleon–nucleon (N N ) scattering. σR is calculated using the optical-phase-shift function, eiχ(b) :       iχ(b) 2 σR = db 1 − e (2)  , where b is the impact parameter vector perpendicular to the beam direction. In this paper, we take a standard approximation, the optical limit approximation (OLA) [66] for the nucleus-proton scattering    iχ(b) = − dr ρp (r)pp (b − s) + ρn (r)pn (b − s) , (3)

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where r = (s, z) is the single-particle coordinate from the center-of-mass of the projectile nucleus with z being the beam direction. In the OLA, the basic inputs are ρp , ρn , and the profile function N N , which is responsible for describing the nucleon–nucleon collision. The profile function, N N , is often parameterized as follows [67]:  1 − iαN N tot b2 N N (b) = σ exp − , (4) 4πβN N N N 2βN N where αN N is the ratio of the real to the imaginary part of the N N scattering amplitude in the forward direction, and σNtotN is the N N total cross section. βN N (fm2 ) is the slope parameter of the NN elastic differential cross section and is related to the effective range of the nuclear interaction. We have the following relation between βN N and αN N [68,69]: σNelN =

2

tot 2 1 + αN N σ , 16πβN N N N

(5)

with σNelN being the N N elastic scattering cross section. Note that σNelN = σNtotN holds below ∼ 300 MeV, where is the threshold of the pion production. In this study, the parameter set used is listed in Ref. [68]. The validity of this profile function has been tested in many examples of proton–nucleus [25,68] and nucleus–nucleus collisions [70–74] as well as experimental analyses of σR [75,76] and σcc [14,16,17,20,77]. The proton and neutron density distributions of 17 Ne are needed for the calculation of σR using the Glauber model. The matter density distribution (ρm ) of 17 Ne was experimentally deduced from σR on beryllium, carbon, and aluminum targets [42]. We adopted the harmonic-oscillator (HO) core + Yukawa function density of 17 Ne used in Ref. [42] and slightly modified it for separating ρp and ρn as follows. The RMS matter radius (rm ) of 17 Ne is obtained from ρm which was deduced by σR measurements [42]. The RMS charge radius (rch ) of 17 Ne is experimentally known from the optical isotope shift measurement [45]. rch can be converted to the RMS point–proton radius (rp ) using the following equation: 2 rp2 = rch − Rp2  −

N 2 3h¯ 2 , Rn  − Z 4m2p c2

(6)

where Rp2 , Rn2 , and mp are the RMS charge radius of the proton [78], that of the neutron [79], and the proton mass, respectively. The last term on the right-hand side indicates the Darwin–Foldy correction [80]. rm , rp , and the RMS point-neutron radius (rn ) show the following relationship:     Z 2 N 2 rm = (7) rp + r 2, A A n where Z, N , and A are the atomic number, the neutron number, and the mass number, respectively. rn can be obtained by substituting rm and rp into Eq. (7). The RMS radii of 17 Ne obtained from the above procedure are listed in the first row of Table 3 along with the previous experimental results. To deduce ρp and ρn from ρm , the width parameters of the HO core density of ρp and the HO-type ρn are adjusted so as to reproduce rp (2.92 fm) and rn (2.29 fm), keeping rm (2.68 fm) and the Yukawa-type tail density distribution for ρp fixed. Fig. 4 displays ρm , ρp , and ρn of 17 Ne. The ρp shows a long tail which characterizes the proton halo structure of 17 Ne. These densities are used as the input densities for the Glauber model calculations.

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Table 3 The root-mean-square matter (rm ), proton (rp ), neutron (rn ), and charge (rch ) radii of 17 Ne. The radii given in the first row indicate those of the density distributions shown in Fig. 4. The details are described in the text. The previous experimental results are taken from Refs. [9,42,45]. The unit is fm.

Density shown in Fig. 4 Previous experiments

rm

rp

rn

2.68 2.68(6) 2.75(7)

2.92

2.29

rch

References

3.0413(88)

[42] [9] [45]

Fig. 4. Density distributions of 17 Ne used as the input densities for the Glauber model calculations. The solid, dashed, and dotted lines indicate matter, proton, and neutron density distributions (ρm , ρp , and ρn ), respectively.

The solid lines in Figs. 5 (a) and (b) show the results of the OLA calculations of 17 Neproton and 12 C-proton collisions [68], respectively, along with the experimental cross sections. As shown in Fig. 5 (a), the calculated σR slightly overestimate the experimental cross sections of 17 Ne at 73 and 100A MeV, whereas they significantly underestimate those at 289 and 432A MeV. Even though the uncertainties of the RMS radii are taken into account, it is difficult to reproduce these experimental σR at low and intermediate energies simultaneously. This trend of the 17 Ne-proton collision is also seen in the 12 C-proton one. That is, the calculated σ is larger R (smaller) than the experimental cross sections at low (intermediate) energies, as shown in Fig. 5 (b). We also calculate σR on a carbon target with the nucleon-target profile function in the Glauber model (NTG) [81,82] which only requires the same inputs as the OLA, but includes the multiplescattering contributions effectively. The results perfectly reproduce the experimental σR for 17 Ne on 12 C [42] as shown in Fig. 5 (c). We discuss possible reasons for this discrepancy in the 17 Ne-proton cross sections. In the present calculations, we use σNtotN in the free space, but it can be modified in the nuclear medium owing to, e.g., Fermi motion and Pauli blocking. As discussed in Ref. [83], the Fermi-motion effect increases the free σNtotN especially at low energies (several tens A MeV), but does not affect it strongly at intermediate and high energies. This Fermi-motion effect is unlikely to explain the differences of σR between the experimental results and the Glauber model calculations shown in Figs. 5 (a) and (b). As discussed in Refs. [84–87], the Pauli-blocking effect plays a role to

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Fig. 5. Energy dependence of the reaction cross section (σR ) of (a) 17 Ne-proton, (b) 12 C-proton, (c) 17 Ne-12 C, and (d) 12 C-12 C collisions. Note that the energy per mass number A of an incident nucleus (A MeV) in the proton-fixed frame corresponds to that of an incident proton (MeV) in the nucleus-fixed frame. Closed circles and open squares in (a) indicate the present experimental results and previous one [88], respectively. Open circles in (b) and (d) are the experimental results taken from previous studies [9,26,27,83,89]. Open triangles in (c) are taken from previous σR measurements of 17 Ne [42]. Solid lines indicate the Glauber model calculations which adopted the optical limit approximation (OLA) in (a) and (b) [68], and the nucleon-target profile function in the Glauber model (NTG) in (c) and (d) [81,82], using the original slope parameter, βN N . Dashed lines indicate the Glauber model calculations using the original βN N plus 0.1 (fm2 ).

reduce the σNtotN , depending on the Fermi momentum of the nucleons in the nucleus. As shown in Figs. 5 (a) and (b), the reduction of σN N may affect the agreement with experimental σR at low energies, but not with those at intermediate energies. Therefore, it is difficult to explain the experimental σR of the nucleus-proton collision at low and intermediate energies simultaneously with the in-medium effects. Another possibility is the uncertainties of the N N used in the Glauber model. As discussed in Ref. [68], the slope parameter βN N was not well constrained from the low-energy differential elastic scattering cross sections owing to the large uncertainties. Thus, we calculate σR on proton and carbon targets for 17 Ne and 12 C by varying βN N in Eq. (4). We adopted the NTG [81,82] for the calculations of σR on a carbon target. With this modification, the original αN N is also changed using the relation given in Eq. (5), although the σR calculations with the OLA does not depend on the αN N value. Solid and dashed lines in Fig. 5 indicate the results of the Glauber model calculations using original βN N and original plus 0.1 (fm2 ), respectively. As shown in Fig. 5, σR on a carbon target are somewhat sensitive to the βN N value, whereas those on a proton target show much less dependence with respect to the changes of βN N . Since the Glauber calculations with the original profile function reproduce the experimental σR values of the nucleus–nucleus collision perfectly as shown in Figs. 5 (c) and (d), it is unlikely to explain σR for both on proton and carbon targets with the same N N .

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The OLA ignores the higher-order multiple scattering effects which will be important for a nucleus with such a spatially extended density distribution. However, these effects are small (at most 1%) even in the very extended halo nucleus 22 C [74]. The proton tail of 17 Ne is not as extended as the neutron tail of 22 C. The multiple-scattering effects are even smaller in the case of 17 Ne and are not enough to explain the discrepancy of σR . It was shown in Ref. [25] that for heavy nuclei (120 Sn, 208 Pb), the Glauber model calculations tend to be larger than the experimental σR at low energies, which is the same trend as 17 Ne and 12 C at low energies. However, the results reproduced the experimental data at intermediate energies. At present, the discrepancy of σR for the nucleus–proton collision between experimental results and the Glauber model calculations remains an open question. To understand the energy dependence of σR for the nucleus–proton collision, we need to measure more σR for not only unstable nuclei but also stable nuclei and verify them with theoretical calculations to establish a method of a precise determination of the nuclear size properties. 5. Summary We studied the energy dependence of the total reaction cross sections (σR ) for 17 Ne using a solid hydrogen target. The low- (∼100A MeV) and intermediate- (∼300–500A MeV) energy data were measured where only a few values were available for unstable nuclei. The new σR data were compared with a standard theoretical calculation, the Glauber model. Though we found complete agreement between the theory and experiment with a carbon target, the Glauber model calculations slightly overestimated at the low energies (73 and 100A MeV) and significantly underestimated at the intermediate energies (289 and 432A MeV). We discussed possible reasons for this discrepancy: Fermi motion, Pauli blocking, uncertainties of the profile functions used in the Glauber calculations, and multiple-scattering effects. However, we found that they were not sufficient to explain both the σR behavior on carbon and proton targets simultaneously. At present, the discrepancy of σR for the nucleus–proton collision between experimental results and the Glauber model calculation is still an open question. More experimental σR on a proton target for various nuclei are desired to understand the behavior of σR of the nucleus–proton collisions over the whole energy range. Furthermore, to understand the reaction mechanism, exclusive measurements to study the structure of halo nuclei and the correlation of the valence nucleons are important. Acknowledgements We thank AEC staff of HIMAC for steady operation of the accelerators and appreciate the technical support. This work was supported by the Research Project with Heavy Ions at NIRSHIMAC project number 16H365. We also thank D. Nishimura and M. Fukuda for fruitful discussions on the analysis and experimental results. This work was supported by JSPS KAKENHI Grant Number JP16K17678. References [1] [2] [3] [4]

X. Roca-Maza, et al., Phys. Rev. Lett. 106 (2011) 252501. W. Horiuchi, S. Ebata, K. Iida, Phys. Rev. C 96 (2017) 035804. F.J. Fattoyev, J. Piekarewicz, C.J. Horowitz, Phys. Rev. Lett. 120 (2018) 172702. C.A. Bertulani, J. Valencia, Phys. Rev. C 100 (2019) 015802.

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