Structure of 9C through proton resonance scattering with Texas Active Target detector

TL;DR

This study investigates the level structure of the exotic nucleus 9C using proton resonance scattering with an active target, identifying a new positive parity state and clarifying the sd-shell location in this neutron-deficient isotope.

Contribution

The paper reports the first identification of a 5/2+ resonance at 4.3 MeV in 9C, providing new insights into its shell structure and spin-parity assignments.

Findings

First positive parity state identified in 9C at 4.3 MeV

Determined the energy of the 2s shell in 9C

Confirmed the 5/2+ resonance as a broad L=0 state

Abstract

Background: Level structure of the most neutron deficient nucleon-bound carbon isotope, 9C, is not well known. Definitive spin-parity assignments are only available for two excited states. No positive parity states have been conclusively identified so far and the location of the sd-shell in A=9 T=3/2 isospin quadruplet is not known. Purpose: We have studied the level structure of exotic nucleus 9C at excitation energies below 6.4 MeV. Methods: Excited states in 9C were populated in 8B+p resonance elastic scattering and excitation functions were measured using active target approach. Results: Two excited states in 9C were conclusively observed, and R-matrix analysis of the excitation functions was performed to make the spin-parity assignments. The first positive parity state in A=9 T=3/2 nuclear system, the 5/2+ resonance at 4.3 MeV, has been identified. Conclusions: The new 5/2+ state at 4.3 MeV in 9C is a single-particle L=0 broad resonance and it determines the energy of the 2s shell. The 2s shell in this exotic nucleus appears well within the region dominated by the p-shell states.

Figures

Full text

Level structure of the most neutron deficient nucleon-bound carbon isotope, 9C, is not well known. Definitive spin-parity assignments are only available for two excited states. No positive parity states have been conclusively identified so far and the location of the sd-shell in A=9 T=3/2 isospin quadruplet is not known.

Purpose

We have studied the level structure of exotic nucleus 9C at excitation energies below 6.4 MeV.

Methods

Excited states in 9C were populated in 8B+p resonance elastic scattering and excitation functions were measured using active target approach.

Results

Two excited states in 9C were conclusively observed, and R-matrix analysis of the excitation functions was performed to make the spin-parity assignments. The first positive parity state in A=9 T=3/2 nuclear system, the 5/2+ resonance at 4.3 MeV, has been identified.

Conclusions

The new 5/2+ state at 4.3 MeV in 9C is a single-particle $\ell=0$ broad resonance and it determines the energy of the 2s shell. The 2s shell in this exotic nucleus appears well within the region dominated by the p-shell states.

I Introduction

Enormous progress has been achieved over the past two decades in describing the properties of light nuclei starting from interacting nucleons and using realistic two-nucleon and three-nucleon forces or chiral interactions. Sophisticated methods, such as Quantum Monte Carlo approach Pieper et al. (2002), No Core Shell Model Navrátil and Barrett (1998), No Core Configuration Interaction Maris et al. (2009), coupled-cluster theory Hagen et al. (2007) have been developed to make robust predictions of ground-state energies Binder et al. (2018), level structure Pieper et al. (2002), spectroscopic factors and partial widths Nollett (2012), scattering phase shifts Forssen et al. (2011), electromagnetic moments and transitions Pastore et al. (2013) in light nuclei. Reliable experimental benchmarks are necessary to facilitate further theoretical progress. The focus of this experimental study is 9C. The first ab initio calculations for A=9 T=3/2 systems have become available in 1998 Navrátil and Barrett (1998). Only few levels were experimentally known at the time, and robust spin-parity assignments were available only for two of them. Therefore, a detailed comparison to the experimental data was handicapped. Few experiments on 9Li and 9C have been performed since then, and more experimental information has become available. Yet, the spin-parity has been reliably established for only one more state. Moreover, all known states are negative parity (p-shell) states and no evidence for positive parity states have been observed so far, making the energy of the sd-shell in this system an open question. The goal of this study was to improve our knowledge of the level structure of 9C in general and locate the onset of the 2s-shell in this A=9 T=3/2 system in particular. The 2s shell plays an important role in the structure and stability of light exotic nuclei. The 2s ground state in 11Be is now a textbook case, and it is well recognized that the 2s shell dominated the structure of ground states of some exotic nuclei, such as 9He Uberseder et al. (2016), 10N Hooker et al. (2017), 11N Axelsson et al. (1996) and 14F Goldberg et al. (2010).

In addition, this experimental study was the commissioning run of the Texas Active Target detector system (TexAT) built for experiments with rare isotope beams at Texas A&M University Cyclotron Institute and elsewhere. The current state of experimental knowledge of 9C spectroscopy is reviewed below.

9C is a proton drip-line carbon isotope that has the largest Z/N ratio (2) among all nucleon-bound nuclei in the nuclear chart (same as 3He). It has a half-life of 126.5 ms, and proton separation energy of 1.3 MeV Tilley et al. (2004). The ground state of 9C was discovered in 1964 by Cerny et al. Cerny et al. (1964), the first excited state was observed in 1974 at 2.2 MeV Benenson and Kashy (1974), and an excited state at 3.3 MeV was reported in Golovkov et al. (1991), but it was not confirmed in later experiments. All of these studies used the 12C(3He,6He) reaction. More recently, the $5/2^{-}$ state at 3.6 MeV was observed in the excitation function for 8B+p elastic scattering, which was measured up to 4.5 MeV excitation energy at just one angle Rogachev et al. (2007). Finally, the structure of 9C was studied using inelastic scattering of a 9C beam on a 9Be target Brown et al. (2017). Two states were observed by measuring 8B and protons in coincidence, corresponding to the first and second excited states at 2.2 and 3.55 MeV, in good agreement with Refs. Benenson and Kashy (1974); Rogachev et al. (2007). The 7Be+2p decay channel was also measured and the authors claim to observe two resonances at 4.40 MeV and 5.69 MeV Brown et al. (2017).

We performed the study of 9C using 8B+p resonance elastic scattering to extend the excitation function to higher energies compared to the previous measurement Rogachev et al. (2007), and most importantly to obtain the angular distribution. The latter allowed us to conclusively identify the first positive parity state in 9C.

II Experiment and Analysis

The 8B beam was produced in the 6Li(3He,n)8B reaction using the Momentum Achromat Recoil Spectrometer (MARS) at the Cyclotron Institute at Texas A&M University Tribble et al. (1989). The primary 6Li beam of energy 13.2 MeV/u from K150 cyclotron was directed to the LN cooled, 9.2 cm long, gas cell with 4 $\mu$m thick and 19 mm diameter Havar entrance and exit windows. Pressure of the 3He gas inside the cell was 810 Torr. The resulting 8B beam had an energy of 60.8 MeV with an intensity of $10^{3}$ pps, energy spread of 1.2 MeV and a beam spot size of about 10 mm FWHM. The main contaminant was the scattered ions of primary 6Li beam at $\sim$1.6 % level.

A brief overview of the TexAT detector, shown in Fig. 1, is provided below. Technical details on TexAT detector system, the TexAT GEANT MonteCarlo simulation, and the TexAT 3D track reconstruction procedures are described in Ref. Koshchiy et al. .

TexAT is a time projection chamber (TPC) with a planar geometry. It is based on highly segmented Micromegas Giomataris et al. (1996) detector which provides particle ID and 3D tracking for the incoming beam ions and charged products of nuclear reactions. The Micromegas detector has an active area of 224x224 mm2 and consists of 1024 channels, of which 768 are in the central (beam) region of rectangular 3.5$\times$1.75 mm2 pads arranged into 6 columns and 128 rows along the beam axis. Pads in the “sides” region of the Micromegas detector are multiplexed into chains and strips, running parallel and perpendicular to the beam axis respectively, for a total of 64 chains and 64 strips per each side. The multiplexing is used to reduce the channel count. In the central region the 3D image of the tracks is produced using individual pads and ionization electrons drift times, while in the side regions the drift times are also used to match chains and strips. Further track recognition is performed using the Hough transform Duda and Hart (1972), which allows reliable identification of tracks even in sub-optimal noise conditions. In addition to the TPC, TexAT includes a windowless ionization chamber (IC) located near the scattering chamber entrance window, and an array of silicon detectors, backed by CsI(Tl) scintillators, that surround the TPC on all but the Micromegas sides. IC is used for incoming beam ions particle ID and overall normalization. Normally, a total of 50 5$\times$5 cm2 silicon detectors (700-1000 $\mu$m thick and each consisting of four 2.5$\times$2.5 cm2 square segments), backed by 50 5$\times$5$\times$4 cm3 CsI(Tl) scintillator detectors, read out by Si pin-diodes, are used by TexAT. However, only 9 Si+CsI(Tl) pairs were installed in the most forward region of TexAT for the commissioning run. General Electronics for TPCs (GET) Pollacco et al. (2018) is used for all TexAT channels. The data is recorded using Narval DAQ Grave et al. (2005).

The 8B beam enters the TexAT scattering chamber through a 4 $\mu$m thick Havar window. The target Methane gas (CH4, research grade 99.999% purity) pressure was adjusted to stop the incoming 8B beam ions before the last 16 rows of the central pads - 435 Torr. The profile of average energy losses of the beam ions, shown in Fig. 2, reflects the location of the Bragg peak and the range of 8B ions. Anode biasing scheme is utilized in TexAT for the Micromegas detector, with specific sets of pads biased individually.

This arrangement makes it possible to apply different voltages for different regions of the detector, and as a result to have different gas gains. Hence, we used low gas gain (400 V tension) in the first 7/8 of the central pads region to record tracks of the beam ions, and high gas gain (600 V tension) in the last 1/8 - the furthermost 16 rows from the Havar entrance window. This allowed us to record tracks of light (proton) recoils in the last Micromegas section. The side regions all had high (570 V) tension for high gas gain.

The event ID for 8B+p elastic scattering with TexAT is robust. We first gate on the energy deposition in the ionization chamber to select the events associated with 8B (see Fig. 3). We then identify proton events using the $\Delta$E-E scatter plot of specific energy loss per unit pad in the Micromegas detector vs total energy measured in Si+CsI(Tl) (Fig. 4). For higher energy protons that punch through the silicon detectors, we apply an additional cut in the $\Delta$E-E scatter plot of energy deposition in silicon detector vs energy in CsI(Tl) (Fig. 5). This additional step was not strictly necessary but we used it to check that the first $\Delta$E-E selection produced a clean proton event identification. The kinetic energy of protons at the vertex location was determined as the sum of the measured energies in the Si and CsI(Tl) detectors and the calculated proton energy loss in the gas on event by event basis. For the latter we used code SRIM Ziegler et al. (2010) and the measured reaction vertex location (see below). For the reference, energy loss in the gas for 8.7 MeV protons that correspond to zero degrees 8B+p elastic scattering events at 2.45 MeV in c.m. is $\sim$600 keV on average.

We then used 3D tracking in the TPC to reconstruct the complete kinematics of the event. The details of the tracking procedure are described in Ref. Koshchiy et al. . Briefly, the reaction vertex location for the proton tracks in the side region is determined using fitting of the three tracks (beam ion track, proton recoil track in the side region, and heavy ion recoil track) with straight lines. A typical event that has a proton scattered into the side region of the micromegas detector is shown in Fig. 6. If the reaction vertex is outside of the active area of the TPC then only the proton track was used to reconstruct the vertex location, in which case the vertex location was determined as a crossover point between a proton track (projected onto the plane of the micromegas detector) and the beam axis. Vertex location reconstructed this way is plotted against the sum of the energies measured by the Si and CsI(Tl) detectors in the bottom panel of Fig. 8. Negative values for the reaction vertex location correspond to reaction events that occurred before the active region of micromegas detector, but produced light recoils that punched through the gas and hit the Si array. For the events with proton tracks that appear only in the central region (small lab. scattering angles) the vertex location was reconstructed using the location of the Bragg peak for the heavy recoils. We have chosen this approach because it allows for an extension of the vertex location reconstruction into the region outside of the TPC’s active area. Vertex location reconstructed using the Bragg peak is plotted against the energy in the Si and CsI(Tl) detectors in the top panel of Fig. 8. The downside of this approach is that it does not work for the higher energy events which produce heavy recoils too far to reach the active region of the TPC. This is why the top panel of Fig. 8 does not extend as far back as the bottom panel, that does not suffer from this limitation. Elastic scattering kinematics results in a well-defined trend of vertex location vs total energy of light recoil, and it was used for additional selection of elastic scattering events. Histogram of reconstructed vertex locations for c.m. energies of $2.4-2.5$ MeV is shown in Fig. 9. An obvious peak between 55 and 90 mm (measured from the start of the micromegas active region) corresponds to the elastic scattering events.

Clearly visible gaps in the spectrum of protons in Figs. 4 and 8 are due to the threshold of the CsI(Tl) detectors. These gaps occur in the energy ranges 9-9.5 MeV and 12.5-13 MeV for the 700 $\mu$m and the 1000 $\mu$m thick detectors respectively. As no narrow resonances have been observed or are expected in the measured excitation energy region in 9C, and to avoid discontinuities in the excitation function, the events with energies 0.5 MeV below the observed gaps were randomly sampled and energy was added back to some of them. This sampling was guided by the Monte Carlo simulation of the punch-through events, taking into account the CsI(Tl) detectors threshold. The c.m. energy regions affected by this procedure are 2.4-2.7 MeV for the larger c.m. scattering angles (Fig. 10a) and 4.1-4.4 MeV for the smaller scattering angles (Fig. 10b).

The inelastic p+8B scattering have also been observed. There are no proton-bound excited states in 8B. Therefore, any p+8B inelastic scattering event will produce two protons and a 7Be recoil. An example of such event is shown in Fig. 7. These events are excluded from the analysis presented in this paper.

III Results

The excitation functions for 8B+p elastic scattering for two angular ranges are shown in Fig. 10. The scattering angle for the detected proton recoils is a function of energy - the smaller the energy the larger the scattering angle in the lab. frame, and therefore the smaller it is in the c.m. for detected proton recoils. Note that zero proton scattering angle in the lab frame corresponds to 180*∘* in c.m. frame in inverse kinematics. We will refer to the “direct kinematics” c.m. scattering angle throughout this paper. The absolute normalization of the cross section was performed by summing the total number of 8B ions measured in the IC, and taking into account the actual solid angle as determined by the average vertex location for each energy bin. The only systematic uncertainty in absolute normalization is related to the uncertainty of the effective target thickness per energy bin, which was calculated using specific energy losses given by code SRIM Ziegler et al. (2010) and considered to be negligible as compared to the statistical uncertainty. Note that the shape of the 8B+p excitation function around 164*∘* scattering angle (Fig. 10a) is very similar to the results of the previous study (Ref. Rogachev et al. (2007), Fig. 7), but the absolute normalization is different by about 10-15%. This is not surprising, given that various backgrounds had to be subtracted in Rogachev et al. (2007) and that the number of accumulated 8B ions was not counted directly, but evaluated using Faraday cup for the primary beam and an assumption that 8B/6Li ratio remains constant.

R-matrix analysis of the excitation functions was performed using the code MinRmatrix Johnson (2008). Only two channels were included explicitly in the analysis, the elastic scattering and the inelastic scattering populating the first excited state of 8B, the 1+ at 0.77 MeV. A channel radius of 4.5 fm was used for both of these channels. First, we tried to reproduce the observed excitation functions using only the known states in 9C - the 3/2- ground state, 1/2- at 2.2 MeV, and the 5/2- at 3.6 MeV, as in Rogachev et al. (2007). It is typical to include the “background” resonances at high energy in the R-matrix calculations to emulate the contribution from the higher lying resonances that are not taken into account explicitly. These “background” resonances are normally considered free parameters. In the attempt to reduce the number of free parameters and to make the R-matrix analysis as realistic as possible we have adopted a different approach in this paper. The 1/2-, 3/2-, and 5/2- p-waves were constrained by solving the Schrödinger equation for a single proton in the field of 8B(g.s.). A Woods-Saxon shape for the p+8B interaction potential was adopted, with diffuseness set to 0.65 fm and the reduced radius set to r=1.2 fm (R=1.2$\sqrt[3]{8}$ fm). The potential well depth was adjusted to fit the energies of the known states in 9C with respect to the proton decay threshold. For example, the 3/2- ground state is bound by 1.3 MeV and the potential depth required to reproduce this binding energy is 50.45 MeV. The Coulomb interaction was approximated by a potential of a uniformly-charged sphere with reduced radius of $r_{c}$=1.3 fm. The parameters of the high energy “background” resonances in R-matrix calculations were then tuned for each partial wave so that the resulting R-matrix phase shift reproduces that of the Schrödinger equation in the energy range relevant for this analysis (from 1 to 5 MeV in c.m.), as shown in Fig. 11. A perfect match is achieved for the 3/2- and 5/2- partial waves. The 1/2- R-matrix phase shift deviates from the solution of the single-particle Schrödinger equation because its width is about a factor of two smaller than a single-particle width, if we adopt the most recent experimental value ($\Gamma$= 52$\pm$11 keV) Brown et al. (2017). Since the 1/2- state is below the energy range measured in this work, the overall influence of the 1/2- partial wave on the excitation function is minimal and the specific choice made above has no influence on the final result.

Further reduction of the number of free parameters in the R-matrix fit was achieved by noticing that each of the $\ell=1$ partial waves is dominated by one of the possible channel spins (S=3/2 or S=5/2) in the entrance channel. Naturally, the 1/2- and 7/2- p-shell states can only be populated with channels spins 3/2 and 5/2 respectively (if we exclude the $\ell=3$ contribution). The 3/2- ground state is known to be dominated by a proton in the 1p3/2 shell, and the 5/2- state corresponds to a proton in the 1p1/2 shell Wuosmaa et al. (2005); Rogachev et al. (2007). Re-coupling from JJ coupling scheme to the LS coupling leads to the dominant contribution of the S=3/2 channel spin for the 3/2-, and the S=5/2 channel spin for the 5/2-. Therefore, we have restricted the R-matrix calculation to channel spin 3/2 for the 1/2- and 3/2- partial waves, and to channel spin 5/2 for the 5/2- and 7/2- partial waves.

This way the excitation function calculated using R-matrix approach and shown in Fig. 10 by the dashed red curve has no free parameters.

While the shape of the 155*∘* - 170*∘* angular range excitation function is described, the absolute magnitude of the cross section is underestimated. Most importantly, the shape of the excitation function for the 105*∘* - 145*∘* angular range is wrong. Adding the tentative 3/2- at 4.1 MeV (as it was done in Rogachev et al. (2007)) improves the fit at large c.m. scattering angle but does not help to reproduce the 105*∘* - 145*∘* angular range. We have found that fitting the deep minimum observed in the 8B+p excitation functions at 1.5 MeV for smaller c.m. scattering angles (around 110*∘) requires a strong destructive interference between the $\ell$=0 partial wave and Coulomb amplitude. A broad $J^{\pi}=5/2^{+}$ state, located at an excitation energy around 4.3 MeV, achieves the desired effect at smaller c.m. scattering angles, and also improves the fit at large c.m. scattering angles. The R-matrix calculation that includes the 1/2-, 5/2-, and 5/2+ states is shown in Fig. 10 with the short-dashed blue curve. Other spin-parity assignments for the new state were considered. The 1/2+ cannot decay to the 8B(2+) ground state with $\ell=0$ (only $\ell=2$) and therefore does not produce the required interference pattern. The 3/2+ spin-parity assignment was tried, but it resulted in substantially worse agreement. Further improvements are achieved by introducing an $\ell=1$ $J^{\pi}=7/2^{-}$ state with an excitation energy of 6.4 MeV (5.1 MeV in c.m.) and a width of 1.1 MeV as shown in Fig. 10 with the solid black curve. Although our spectrum does not extend beyond 5.0 MeV and therefore we cannot make definitive conclusions, a $7/2^{-}$ was suggested by the Continuum Shell Model calculations at 6.3 MeV Volya and Zelevinsky (2014). Also, there is a state in the mirror nucleus, 9Li, at similar excitation energy - 6.43 MeV, the spin-parity assignment for which is unknown. We included the 7/2-* at 6.4 MeV into our final fit, but consider it tentative.

Due to the nature of this excitation function that is defined by broad overlapping resonances - we used additional a priori constrains to reduce the number of free parameters in the fitting procedure. The excitation energy of the 5/2- state is well established and is in good agreement between the Refs. Rogachev et al. (2007) and Brown et al. (2017). In particular, in Ref. Brown et al. (2017) the 5/2- resonance energy is well defined (but not necessarily the width, see comments in section IV), so the excitation energy of this state was fix at 3.6 MeV (within the uncertainties given in Brown et al. (2017)). We have studied the quality of the fit as a function of the widths of the 5/2- state by manually varying it around the best fit value and fitting the parameters of the 5/2+ and 7/2- states for each manual iteration. The best fit is achieved for the 5/2- width of 1.1 MeV with one standard deviation of 300 keV. The sensitivity of the fit to the parameters of the 5/2+ state was evaluated by fixing the 5/2- at its best fit values and manually varying the excitation energy and widths for the 5/2+. The result for the 5/2+ is E∗ = 4.3$\pm$0.3 MeV and $\Gamma$=4.0${}^{+2.0}_{-1.4}$ MeV.

IV Discussion

The excitation function for 8B+p elastic scattering at large c.m. angles is dominated by the 5/2- state, confirming the results of Ref. Rogachev et al. (2007). There are two main advantages of the presented data over that of Ref. Rogachev et al. (2007): (1) no background subtraction was necessary, and (2) the much wider range of scattering angles is measured in the present active target experiment. The latter provides clear evidence for a broad $\ell=0$ 5/2+ state, which plays a dominant role at smaller c.m. scattering angles (close to 90 ∘). We confirm the previous findings of Ref. Rogachev et al. (2007) that there is no evidence for an excited state at 3.3 MeV reported in Golovkov et al. (1991). The 5/2- state has also been recently observed in the inelastic scattering of a 9C beam on a 9Be target Brown et al. (2017). The best fit total width for this state is notably different in this work and in Rogachev et al. (2007), as compared to Brown et al. (2017). It is 630 keV in Brown et al. (2017) and 1.1 MeV in the present work. It is possible that the background subtraction procedure applied in Brown et al. (2017) is a cause for this discrepancy. The background constitutes 2/5 of the observed yield in Ref. Brown et al. (2017) at the 5/2- resonance maximum, while there is no background in the excitation function for 8B+p elastic scattering obtained in this work. The observed 1.1 MeV width of the 5/2- state corresponds to the single particle width - the p+8B(g.s.) spectroscopic factor (SF) for this state is 0.8+/-0.2. This is in agreement with the SF of 0.93(20) measured for the mirror 5/2- state in 9Li Wuosmaa et al. (2005) using 8Li(d,p) reaction and also with predictions of the ab initio models Wuosmaa et al. (2005). The result of Ref. Brown et al. (2017) would infer the SF of 0.45 for this state - in disagreement with ab initio calculations and experimental data on SF in 9Li. For completeness we note that the total width of the 5/2- state at 4.3 MeV in 9Li was measured in three different experiments and the results are not consistent. It is 250(30) keV in Young and Stokes (1971), 100(30) keV in Ajzenberg-Selove et al. (1978), and 60(45) keV in Heilbronn et al. (1989). The single particle width for this state in 9Li is 180 keV, so while the former value would be more in agreement with the results of this work as well as the ab initio predictions Wuosmaa et al. (2005); Nollett (2012) and the results of the 8Li(d,p) measurements Wuosmaa et al. (2005), the latter would be more in-line with the Ref. Brown et al. (2017).

A broad ($\Gamma$=2.75(11) MeV) excited state has been observed at 4.4 MeV excitation energy in Ref. Brown et al. (2017). This state was assigned a positive parity in Brown et al. (2017), but reasons for that assignment were not discussed. We have observed clear evidence for a broad $\ell=0$ 5/2+ ($\Gamma$=4.0${}^{+2.0}_{-1.4}$ MeV) state at 4.3 MeV, which is in good agreement with Brown et al. (2017).

This result firmly establishes the onset of the 2s1/2 shell in T=3/2 A=9 and gives us an opportunity to discuss systematics for the 2s-shell in light proton rich p-shell nuclei 8B, 9C, and 10N. To do that we employ the potential model mentioned above. We fit the potential depth to reproduce the 5/2+ resonance energy in 9C. Since the corresponding phase shift never reaches 90*∘*, we investigate the resonance behavior by plotting the square of the amplitude of the wave function at certain fixed distance from the origin (1.0 fm) as a function of c.m. energy Mukhamedzhanov et al. (2010). The dashed curve in Fig. 12 corresponds to the single-particle 5/2+ in 9C at 4.3 MeV (3.0 MeV in c.m.), as observed experimentally. We can now explore the s-wave in 8B and 10N by making an assumption that the s-wave proton-core interaction is the same for all three nuclei (8B, 9C, and 10N). So, keeping parameters of the Woods-Saxon potential exactly the same (only the reduced mass and charge are different) we get the 2s resonances in all three nuclei, as shown in Fig. 12. This result is in remarkable agreement with the experimental data. The 2s-shell is located at c.m. energy of 2.3$\pm$0.2 MeV in 10N Hooker et al. (2017). This is where a maximum of the amplitude of the wave function for the 10N is predicted by the potential model (Fig. 12). For the 7Be+p the most recent comprehensive R-matrix analysis Paneru et al. (2019) gives -3.18${}^{+0.55}_{-0.50}$ fm scattering length for the $\ell=0$ 2- partial wave. The potential model $\ell=0$ phase shift for the 7Be+p scattering calculated using parameters given in the caption for Fig. 12 corresponds to the scattering length of -5.5 fm, in fair agreement with the actual experimental value, especially considering the simplicity of the underlying approach that completely ignores the possible isospin dependence of the nucleon-core interaction potential. It is also in perfect agreement with the ab initio calculation by P. Navratil, et al., Navrátil et al. (2011), which predicts -5.2 fm.

V Conclusion

We have studied the structure of 9C by measuring an excitation function for 8B+p elastic scattering in a broad energy and angular range using the active target approach. This experiment was a commissioning run for Texas Active Target detector system (TexAT). In addition to the two previously known negative parity excited states in 9C, $J^{\pi}=1/2^{-}$ and $5/2^{-}$, a broad positive parity state $J^{\pi}=5/2^{+}$ has been observed at around 4 MeV. This state has a single-particle nature and therefore we have an opportunity to experimentally determine the location of the 2s-shell in the A=9 T=3/2 system for the first time. It would be interesting to compare this result with predictions of the ab initio models, but these are not available at the moment. Since the state is very broad, the meaningful comparison with theory can only be made if continuum is consistently taken into account. Therefore, it is not a surprise that the bound-state AMD calculations Kanada-En’yo and Horiuchi (2001) significantly overestimate the 2s shell energy in 9C - by a factor of two. In addition to the $J^{\pi}=5/2^{+}$ state at 4 MeV, there is some evidence for a $J^{\pi}=7/2^{-}$ state at 6.4 MeV with a width of 1.3 MeV. Although we cannot make definitive conclusions regarding this state since the excitation function has not been measured to high enough excitation energies and we’ve only observed the low energy tail of this resonance, it does agree with the prediction of the CSM Volya and Zelevinsky (2014) for the 7/2- excitation energy. The $J^{\pi}=5/2^{+}$ observed in this measurement is the first conclusive observation of any sd-shell state in 9C or any other member of A=9 T=3/2 isospin multiplet. This observation was made possible by application of an active target approach that allowed to measure the 8B+p excitation functions in wide range of scattering angles.

We thank Rui de Oliviera & Bertrand Mehl at CERN for their technical assistance in developing the Micromegas pad plane. This work was supported by the U.S. Department of Energy, Office of Science under grant number #DE-FG02-93ER40773, by the National Nuclear Security Administration through the Center for Excellence in Nuclear Training and University Based Research (CENTAUR) under grant number #DE-NA0003841, and by the Nuclear Solutions Institute at Texas A&M University.