Observation of T=3/2 Isobaric Analog States in 9Be using p+8Li resonance scattering
C. Hunt, G.V. Rogachev, S. Almaraz-Calderon, A. Aprahamian, M. Avila, L.T. Baby, B. Bucher, V.Z. Goldberg, E.D. Johnson, K.W. Kemper, A.N. Kuchera, W.P. Tan, I. Wiedenhover
OObservation of T=3/2 Isobaric Analog States in Be using p+ Li resonance scattering
C. Hunt,
1, 2
G.V. Rogachev,
1, 2, 3, ∗ S. Almaraz-Calderon, A. Aprahamian, M. Avila, L.T. Baby, B. Bucher, V.Z. Goldberg, E.D. Johnson, K.W. Kemper, A.N. Kuchera, W.P. Tan, and I. Wiedenh¨over Department of Physics and Astronomy, Texas A & M University, 77843 TX Cyclotron Institute, Texas A & M University, 77843 TX Nuclear Solutions Institute, Texas A & M University, 77843 TX Department of Physics, Florida State University, 32306 FL Department of Physics, University of Notre Dame, 46556 IN Argonne National Laboratory, Lemont, 60439 IL Idaho National Laboratory, Idaho Falls, 83415 ID Department of Physics, Davidson College, Davidson, 28035 NC (Dated: May 25, 2020)
Background:
Resonance scattering has been extensively used to study the structure of exotic, neutron-deficientnuclei. Extension of the resonance scattering technique to neutron-rich nuclei was suggested more than 20 yearsago. This development is based on the isospin conservation law. In spite of broad field of the application, it hasnever gained a wide-spread acceptance.
Purpose:
To benchmark the experimental approach to study the structure of exotic neutron-rich nuclei throughresonance scattering on a proton target.
Method:
The excitation function for p+ Li resonance scattering is measured using a thick target by recordingcoincidence between light and heavy recoils, populating T=3/2 isobaric analog states (IAS) in Be.
Results:
A good fit of the Li(p,p) Li resonance elastic scattering excitation function was obtained using previ-ously tentatively known 5/2 − T=3/2 state at 18.65 MeV in Be and a new broad T=3/2 s-wave state - the 5/2 + at 18.5 MeV. These results fit the expected iso-mirror properties for the T=3/2 A=9 iso-quartet. Conclusions:
Our analysis confirmed isospin as a good quantum number for the investigated highly excitedT=3/2 states and demonstrated that studying the structure of neutron-rich exotic nuclei through IAS is a promis-ing approach.
I. INTRODUCTION
The understanding of nuclear structure evolution withincreasing values of isospin has been the mainstream incontemporary nuclear science for many decades. Devel-opment of rare isotope beams provided a major exper-imental advantage in these studies because simple andwell understood reactions, such as nucleon-transfer orCoulomb excitation reactions, could now be used to pop-ulate states in exotic nuclei over a range of isospins farremoved from the valley of stability.Resonance scattering with rare isotope beams usingthe thick target inverse kinematics (TTIK) approach [1]is a particularly powerful technique that has been ex-tensively used to establish the level structure of exoticproton-rich nuclei. Many nuclei have been studied thisway over the last 25 years, including the first observa-tions of ground states in several unbound nuclei ( N [2], N [3], F [4], F [5], Na [6]). Advantages of thistechnique, such as high efficiency, excellent energy res-olution ( ∼
20 keV in c.m.), and a well understood reac-tion mechanism described by R-matrix theory [7] madeit a technique of choice when applicable. However, ap-plication of the resonance scattering approach has beenlimited primarily to the proton-rich side of the nuclearchart. ∗ [email protected] Direct extension of TTIK to neutron-rich nuclei, whichwould involve resonance scattering of rare isotope beamsoff of neutron targets, is not possible due to lack of thelatter. However, one can employ isospin symmetry tostudy neutron-rich nuclei through the isobaric analogstates (IAS) which can be efficiently populated in res-onance scattering of neutron-rich ions off of a proton tar-get. This approach was first mentioned in an ENAM 1998conference proceedings [8], and originally implemented in He+p resonance scattering measurements [9]. The mainidea is that while the T=5/2 (T-high) and T=3/2 (T-low)states in Li are populated in the He(T=2)+p(T=1/2)resonance scattering, the T=5/2 (T-high) states woulddominate the p+ He excitation function for resonanceelastic scattering. This is because only a few isospinallowed decay channels are open for these states, withproton decay back to He (elastic scattering) and isospinallowed neutron decay to the Li(T=2,0 + ), the IAS of He(g.s.), as the two main decay channels. The mostgraphic confirmation of this idea was demonstrated inthe experiment in which the excitation function for the He(p,n) Li(T=1,0 + ) reaction was measured [10]. TheT=3/2 (T-high) states completely dominate the spec-trum of Li measured in [10] while no evidence for T=1/2(T-low) states was observed. Yet, acceptance of this ap-proach was slow in the community. This is primarily dueto concerns associated with the role of the T-low statesand the validity of the isospin-symmetry hypotheses forvery exotic nuclei deep into the continuum. In addition a r X i v : . [ nu c l - e x ] M a y Li + + Be + ; 0 & 12 + ; 0 & 10 + ; 0 Li - - - Li+n Be - ; - ; 3/2 1/2 - ; 3/25/2 - ; 3/216.9818.6516.89 Li+p 1.66 Be+n5/2 + ; 3/218.50 C - - - B+p 4.3 5/2 + B + + FIG. 1. The level structure of the A=9, T=3/2 iso-quartet with levels for Li, Li, Be, Be, and B from [23] and C from[18–20]. to the already mentioned experiments, there were twomore applications of this approach to study the struc-ture of light, neutron rich nuclei, He [11] and B [12]and several recent studies in medium mass region [13–16] that applied the TTIK technique with rare isotopebeams to study Ar, Zn, Si, and Mg.The main goal of this work is to study a benchmarkcase that can be used to explore the applicability and lim-itations of the proposed experimental concept for spec-troscopic studies of neutron-rich nuclei. A convenientcase is the A=9 T=3/2 iso-quartet shown in Fig. 1, thatconsists of Li, Be(T=3/2), B(T=3/2), and C. Discus-sion if isospin is a good symmetry for the A=9 iso-quartetdates far back to the time when mass measurements for C first became available [17]. The structure of C hasbeen studied recently using resonance scattering and theinvariant mass technique [18–20] and its low-lying lev-els are well established now. The lowest states in Lihave been studied with the Li(d,p) reaction [21] andalso with Li(t,p) [22]. Experimental information on thethree lowest T=3/2 states in Be is also available [23].Therefore, one can expect that if the T=3/2 states dom-inate the Li+p resonance elastic scattering and if isospin is a good symmetry then the excitation function for thisreaction can be reasonably well constrained from the al-ready available data. A surprising claim to the contrarywas made recently in [24] where analysis of low energyresonances populated in Li+p scattering revealed sig-nificant isospin mixing for this specific case. We haveperformed kinematically complete measurements of theexcitation functions for Li+p elastic and inelastic scat-tering in the c.m. energy range from 1.46 MeV to 2.3MeV which corresponds to Be excitation energy rangefrom 18.35 MeV to 19.19 MeV. Combining spectroscopicinformation already available for the A=9 T=3/2 iso-quartet, two T=3/2 states are expected at these energiesin the spectrum of Be. It is the 5/2 − state at 18.65 MeVand the 5/2 + state at around 18.5 MeV (see detailed dis-cussion in sec. IV). The R-matrix analysis of the Li+pexcitation functions measured in this work conclusivelydemonstrates that these two T=3/2 states provide a per-fect description of the experimental data, lending strongsupport to the experimental approach proposed 22 yearsago [8]. No evidence for isospin mixing in Be has beenobserved. H Target Li Beam
FIG. 2. Schematic view of the experimental setup. Two Mi-cronsemiconductors Ltd. annular double-sided strip detectorsof “S2” type were installed after the polyethylene target. De-tectors were centered on the beam axis as shown. Positionsensitive E1 and E2 detectors were used to measure total en-ergy and hit location of the light and heavy recoils from the Li+p reactions, respectively.
II. EXPERIMENT
This experiment was carried out at the RESOLUT [25]radioactive nuclear beam facility at the John D. Fox Su-perconducting Accelerator Laboratory at Florida StateUniversity using the hybrid Thick/Thin Target in In-verse Kinematics approach [26, 27]. In this approach,the target is thick enough for the beam particles to losea significant fraction of their energy, but thin enoughfor the heavy recoil particles to exit the target and bedetected. A radioactive Li beam (t / = 838 ms) wasproduced using the H( Li, Li) H reaction. The primary Li beam was accelerated by a 9 MV FN tandem Van deGraaff accelerator followed by a linear accelerator boosterto kinetic energies of 27 MeV and 23.5 MeV (two beamenergies were used in this experiment). The primary tar-get was a liquid-nitrogen-cooled, 4 cm long deuterium gascell with pressure of 400 Torr and 2.5 µ m thick Havar en-trance and exit windows. The secondary Li beam wasmomentum selected, bunched and separated from othercontaminants by the superconducting resonator, and thequadrupole and dipole magnets of the RESOLUT sepa-rator. The composition of the radioactive beam was 95% Li and 5 % Li contaminant at the secondary tar-get position. The typical intensity of the Li beam was ≈ × pps. We measured the excitation function for Li+p in the energy region between 1.46 and 2.3 MeVin the c.m. system. The proton decay threshold in Beis at excitation energy of 16.888 MeV (Fig. 1), so wecovered the excitation energy range from 18.35 to 19.19MeV. The light and heavy reaction residues were mea-sured in coincidence. Two Li-beam energies were usedin this experiment: 22.0 MeV and 18.6 MeV. A polyethy-lene (C H ) target thickness was optimized for each beamenergy to ensure that both light and heavy recoils get outof the target with enough energy to be detected. By care- fully choosing the combination of the beam energy andthe target thickness, it was possible to measure the con-tinuous excitation functions for Li+p elastic scatteringfrom 1.46 to 2.3 MeV in the c.m. system in just twobeam energy steps. The thickness of the polyethylenetarget was 4.13 mg/cm for the Li beam energy of 22.0MeV. Two different target thicknesses, 4.13 mg/cm and2.75 mg/cm , were used with the 18.6 MeV Li beamenergy.Two Micron Semiconductors Ltd. [28] annular siliconstrip detectors of the S2 type were installed downstreamof the target along the beam axis. A schematic viewof the experimental setup is shown in Fig. 2. The S2detectors have annular geometry and they consist of 48rings on one side, that were combined into groups of threefor a total of sixteen channels, and sixteen segments onthe other side. The first S2 detector (E1), which had athickness of 1000 µ m, was placed at 7.6 cm to measurelight recoils, covering an angular range from 8.2 ◦ to 24.7 ◦ in the laboratory reference frame. The second S2 detector(E2), which had a thickness of 500 µ m for measuringheavy recoils, was located at 26.8 cm downstream fromthe target, covering an angular range from 2.4 ◦ to 7.4 ◦ . III. EXPERIMENTAL RESULTS
In this experiment we measured the complete kine-matics for the binary reactions. The trigger was setto coincidence mode between the E1 and E2 detectors.Only those events that produced signals in both nearand far S2 detectors simultaneously (within 100 ns) wererecorded. In addition to measuring energies of heavyand light recoils, direction of the momentum vectors canbe recovered for both particles from the location of thehits, extracted from the double-sided annular strip de-tectors. Coincidence between light and heavy recoils intwo S2s and complete kinematics allows for unambiguousand background-free identification of the binary reactionchannels.Fig. 3 shows a 2D identification scatter plot. Energydeposited by the heavy ion in the E2 detector is plot-ted versus energy deposited by the light ion in the E1detector. The calculated kinematics curve for variousreaction channels is shown for comparison. The most in-tense group is due to the Li+p elastic scattering. Thisis not surprising, of course, because the cross section forelastic scattering is high and the geometry of the experi-mental setup was optimized for this channel. Since therewas a 5% contamination of Li in the secondary beamwe also expect to see Li(p,p) elastic scattering, whichis clearly visible in Fig. 3 at higher total energy. Thisis just as expected because the kinetic energy of the Libeam was higher than that of the Li it produced. Thereare three more reaction channels that can be identifiedin Fig. 3: inelastic scattering, Li(p,p’), populating thefirst excited state in Li (the 1 + at 0.98 MeV), and the Li(p,d) reactions populating the ground and the first ex-
Light Recoil Energy (MeV)0 2 4 6 8 10 12 H ea vy R e c o il E ne r g y ( M e V ) Li(p,p') Li(p,p) Li(p,d') Li(p,d) Li(p,p) FIG. 3. Scatter plot of energy measured in the heavy recoildetector (E2) plotted against the energy measured in the lightrecoil detector (E1). The curves show calculated heavy recoilenergy vs light recoil energy correlation for binary reactionsof Li beam on the proton target. The red curves represent Li+p elastic and inelastic scattering populating the first ex-cited state in Li. The blue curve is the Li+p elastic scat-tering and the magenta curves are the Li(p,d) Li(g.s.) and Li(p,d’) Li(0.48 MeV) reactions. cited states in Li. Statistics are very low for the Li(p,p’)inelastic scattering, but it still carries useful information.It indicates that the cross section for inelastic scatter-ing is smaller than the cross section for elastic scatteringby a factor of 30 and therefore this channel can be ne-glected in the R-matrix analysis described in sec. IV.The Li(p,d) Li(g.s.) reaction channel was used to verifythe overall normalization, which was obtained using theratio of the Li ions to the primary beam current. Weverified that the Li(p,d) Li(g.s.) reaction cross sectionmeasured in this experiment is in good agreement withthe cross section for the time-reverse Li(d,p) Li reac-tion measured in [29] and converted using the detailedbalance principle.Gating on the Li(p,p) elastic scattering using the 2Dscatter plot shown in Fig. 3 and calculating the c.m.energies at the interaction point for each event usingenergies and scattering angles of both light and heavyrecoils (see [26]) the excitation function for Li+p res-onance elastic scattering was obtained (Fig. 4). Thisexcitation function includes c.m. angles from 138 ◦ to155 ◦ in c.m. The smallest and largest angles were ex-cluded to avoid geometric effects of loosing coincidencebetween the light and heavy reaction residues due to an-gular divergence and finite spot size of the beam. Energyresolution is dominated by the intrinsic energy resolutionof the E1 detector and is about 30 keV in c.m. d σ / d Ω ( m b / s r) Be Excitation Energy (MeV)
FIG. 4. Excitation function for Li+p elastic scattering foran angular range between 138 ◦ and 155 ◦ in c.m. The solidcurve is the best R -matrix fit with T=3/2 5/2 − at 18.65 MeVand T=3/2 5/2 + at 18.5 MeV states in Be with parametersshown in Table I. The blue dashed curve is the R -matrix cal-culation with the T=3/2 5/2 − state at 18.65 MeV only. IV. R-MATRIX ANALYSIS
Analysis of the excitation function for Li+p elasticscattering was performed with the R -matrix code MinR-Matrix [30]. As was mentioned in the introduction sec-tion, some spectroscopy information on the level struc-ture of Li, C, and T=3/2 states in Be in the relevantenergy region is available. Therefore, many R -matrixparameters can be fixed a priori for this system. TwoT=3/2 states at 14.3922 and 16.9752 MeV are well knownin Be [23]. These are the IAS of the ground (3/2 − ) andthe first excited (1/2 − ) states of Li and C. Note thatthese states are very narrow - 380 eV each [23]. Thisis because the isospin allowed nucleon decay channelsare energetically forbidden and the resonance widths aredominated by small isospin violating admixtures. Thethird T=3/2 state is a tentative 5/2 − at 18.65(5) MeV[23] and it is a rather broad resonance ( ∼
300 keV) be-cause the isospin allowed proton and neutron decays areopen for this state (see Fig. 1). There is a good reason toassume that the 5/2 − spin-parity assignment is correct.The 5/2 − state in C has been clearly identified at an
TABLE I. Best fit R -matrix parameters for the T=3/2 states in Be with channel radius of 4.5 fm and γ sp =1.25 MeV. E ex isan excitation energy in Be, E λ is an energy eigenvalue, Γ is a total width and S is a spectroscopic factor. Natural boundarycondition is used so that it is equal to the shift function calculated at the resonance energy, making E λ equal to p+ Li c.m.energy. The parameters that were varied in the R -matrix fit are boldfaced. The remaining values were recalculated based onthe values of the boldfaced parameters and Eq. (1)-(4). The spectroscopic factor for the 5/2 + state was set to unity.J π E ex E λ Γ S γ p γ n (16 . γ n (16 . MeV MeV keV keV keV keV −
410 610
52 + excitation energy of 3.6 MeV and well characterized asnearly a single particle state in three recent experiments[18–20]. Therefore, one is justified to use a simple po-tential model to predict the Thomas-Ehrman [31] shiftbetween the T=3/2, A=9 isobars for this state. Usingconventional parameters for the Woods-Saxon potentialwith R=1.25 × √ a = 0 .
65 fm and adjust-ing the depth to reproduce the 3.6 MeV excitation energyof the 5/2 − in C, one gets an excitation energy of 5/2 − in Li at 4.26 MeV. This is less than 40 keV different fromthe known tentative 5/2 − state at 4.296 MeV in Li [23].Using excitation energies of the 5/2 − in Li and C anexcitation energy of the T=3/2 5/2 − IAS in Be can beestimated at 18.5 MeV. Therefore we expect to observe asingle-particle T=3/2 5/2 − state in the measured excita-tion energy region - between 18.35 and 19.19 MeV. More-over, its R -matrix parameters can be tightly constrainedby the fact that neutron decay to the T=0 states in Beshould be strongly suppressed due to the isospin conser-vation. We set the reduced widths associated with thesedecays to zero. The reduced widths for neutron decayto the isospin mixed T=0+1 states at 16.626 and 16.922MeV in Be and proton decay to Li(g.s.) are defined bythe isospin Clebsch-Gordan coefficients, the nearly unityspectroscopic factor of the 5/2 − state [18, 20] and theknown isospin mixture of the T=0+1 2 + states in Be[32]. They are given by the equations below: γ p = Sγ sp (cid:16) C −
12 3212 (cid:17) (1) γ n = Sγ sp (cid:16) C (cid:17) (2) γ n (16 . = γ n × . γ n (16 . = γ n × . , (4)where γ sp is the single particle reduced width whichwas set to 1.25 MeV to reproduce the single particlewidth of a p-wave resonance calculated with the potentialmodel mentioned above at an R -matrix channel radius of4.5 fm. The boundary condition was set equal to the shiftfunction calculated at the resonance energy. Using con-siderations above, all R -matrix parameters for the T=3/25/2 − state at 18.65(5) MeV in Be are constrained.The R -matrix calculations that include only theT=3/2 5/2 − state at 18.65 MeV are shown in Fig. 4 with a dashed blue curve. Parameters for the 5/2 − stateare given in Table I and are consistent with [23]. Ob-viously, the dashed blue curve does not reproduce theexperimental data. Rather, one more T=3/2 state needsto be included. A very broad, purely single-particle (cid:96) = 05/2 + state has been observed in C at around 4 MeV ex-citation energy [20]. Its IAS should be located at around18.7 MeV in Be. The single-particle nature of this statein C allows one to fix the spectroscopic factor to unityand calculate the reduced width using Eq. (1)-(4). Toproduce the final fit we allowed the excitation energies ofthe 5/2 + and 5/2 − states to vary. We also allowed vari-ation of the total width of the 5/2 − state but we keptthe ratio of the reduced widths fixed, as defined by eq.(1)-(4). The best three-parameter fit is shown in Fig.4 as a black solid curve and the best fit parameters aregiven in Table I. The normalized χ of the best fit is 0.98.The best fit parameters for the 5/2 − state are close tothe expected values. The excitation energy of 18.5 MeVfor the 5/2 + state is in agreement with the predictions ofthe potential model discussed in [20], which works wellfor the broad 2s1/2 (cid:96) = 0 scattering states in B, C, and N and predicts that the 5/2 + partial wave should peakat around 1.8 MeV of p+ Li c.m. energy (18.7 MeV).The uncertainties for the fitted parameters were estab-lished using the Monte Carlo technique, which randomlyvaried all three fitting parameters simultaneously and ac-cepted only those sets that resulted in χ values within90% confidence level.For completeness we note that while proton decay ofthe T=3/2 states in Be to the first excited state in Li(1 + at 0.98 MeV) is energetically possible, it is stronglysuppressed by the penetrability factors. We have ob-served events associated with the inelastic scattering (seeFig. 3), but the cross section was a factor of 30 smaller,therefore inelastic scattering cannot have significant in-fluence on the elastic scattering cross section and was ex-cluded from the R -matrix fit to reduce the number of freeparameters. Also, the 5/2 − state has two sets of reducedwidths - one for channel spin 3/2 and one for channelspin 5/2. As it was discussed in [18, 20], channel spin5/2 should dominate and we have excluded the reducedwidths associated with the channel spin 3/2. An excellentagreement between the three-parameter R -matrix fit andthe experimental data validates these approximations. V. CONCLUSION
The excitation function for Li+p resonance elasticscattering was measured in the energy range that cor-responds to the range between 18.35 MeV and 19.19MeV excitation energy in Be. The main goal of thesemeasurements was to provide benchmark data to verifythe validity of the isospin symmetry considerations andcheck if the application of the TTIK approach for spec-troscopy studies of neutron rich nuclei with rare isotopebeams leads to reliable results. The measured excita-tion function was perfectly described by the R -matrix ap-proach, which included the two T=3/2 states only (5/2 − and 5/2 + ). Moreover, the best fit reduced widths, totalwidths, and resonance energies are in agreement with thevalues expected based on the isospin symmetry consider-ations and most recent experimental information on the level structure of the T=3/2 A=9 iso-quartet. We con-firm that the excited state at 18.65 MeV in Be [23] isindeed a 5/2 − T=3/2 IAS. We have also identified a newbroad 5/2 + T=3/2 state at 18.5(1) MeV. It appears thatthe T=1/2 states play only a minor role in this case. Thisis probably due to the presence of strong, single-particleT=3/2 resonances which dominate the cross section for Li+p elastic scattering. It was shown that isospin sym-metry considerations are still valid in this case, whichfeatures broad states in the continuum. This is encour-aging and validates the application of the TTIK methodfor future spectroscopy studies of neutron-rich nuclei withrare isotope beams.This work was funded in part by the Department ofEnergy, Office of Science, under Award No. DE-FG02-93ER40773, and by the National Science Foundation un-der grant No. PHY-1712953 and No. PHY-1713857. [1] K. P. Artemov, O. P. Belyanin, A. L. Vetoshkin, R. Wol-ski, M. S. Golovkov, V. Z. Goldberg, M. Madeja, V. V.Pankratov, I. N. Serikov, V. A. Timofeev, V. N. Shardin,and J. Szmider, Sov. J. Nucl. Phys. , 408 (1990).[2] J. Hooker, G. Rogachev, V. Goldberg, E. Koshchiy,B. Roeder, H. Jayatissa, C. Hunt, C. Magana, S. Upad-hyayula, E. Uberseder, and A. Saastamoinen, PhysicsLetters B , 62 (2017).[3] L. Axelsson, M. J. G. Borge, S. Fayans, V. Z. Gold-berg, S. Gr´evy, D. Guillemaud-Mueller, B. Jonson, K. M.K¨allman, T. L¨onnroth, M. Lewitowicz, P. Manng˚ard,K. Markenroth, I. Martel, A. C. Mueller, I. Mukha,T. Nilsson, G. Nyman, N. A. Orr, K. Riisager, G. V. Ro-gatchev, M. G. Saint-Laurent, I. N. Serikov, O. Sorlin,O. Tengblad, F. Wenander, J. S. Winfield, and R. Wol-ski, Phys. Rev. C , R1511 (1996).[4] V. Goldberg, B. Roeder, G. Rogachev, G. Chubarian,E. Johnson, C. Fu, A. Alharbi, M. Avila, A. Banu,M. McCleskey, J. Mitchell, E. Simmons, G. Tabacaru,L. Trache, and R. Tribble, Physics Letters B , 307(2010).[5] W. A. Peters, T. Baumann, D. Bazin, B. A. Brown,R. R. C. Clement, N. Frank, P. Heckman, B. A. Luther,F. Nunes, J. Seitz, A. Stolz, M. Thoennessen, andE. Tryggestad, Phys. Rev. C , 034607 (2003).[6] M. Assi, F. De Oliveira Santos, F. De Grancey,L. Achouri, J. Alcantara-Nunez, J.-C. Anglique,C. Borcea, L. Caceres, I. Celikovic, V. Chudoba,D. Pang, T. Davinson, C. Ducoin, M. Fallot, J. Kiener,A. Lefebvre-Schuhl, G. L. Lotay, J. Mrazek, L. Per-rot, A. M. Sanchez-Benitez, F. Rotaru, M.-G. Saint-Laurent, Y. Sobolev, M. Stanoiu, R. Stanoiu, I. Stefan,K. Subotic, P. Woods, P. Ujic, and R. Wolski, Inter-national Journal of Modern Physics E , 971 (2011),https://doi.org/10.1142/S0218301311019088.[7] A. M. Lane and R. G. Thomas, Rev. Mod. Phys. , 257(1958).[8] V. Z. Goldberg, AIP Conference Proceedings , 319(1998).[9] G. V. Rogachev, V. Z. Goldberg, J. J. Kolata, G. Chubar-ian, D. Aleksandrov, A. Fomichev, M. S. Golovkov, Y. T. Oganessian, A. Rodin, B. Skorodumov, R. S. Slepnev,G. Ter-Akopian, W. H. Trzaska, and R. Wolski, Phys.Rev. C , 041603 (2003).[10] G. V. Rogachev, P. Boutachkov, A. Aprahamian, F. D.Becchetti, J. P. Bychowski, Y. Chen, G. Chubarian,P. A. DeYoung, V. Z. Goldberg, J. J. Kolata, L. O.Lamm, G. F. Peaslee, M. Quinn, B. B. Skorodumov, andA. W¨ohr, Phys. Rev. Lett. , 232502 (2004).[11] E. Uberseder, G. Rogachev, V. Goldberg, E. Koshchiy,B. Roeder, M. Alcorta, G. Chubarian, B. Davids, C. Fu,J. Hooker, H. Jayatissa, D. Melconian, and R. Tribble,Physics Letters B , 323 (2016).[12] B. B. Skorodumov, G. V. Rogachev, P. Boutachkov,A. Aprahamian, V. Z. Goldberg, A. Mukhamedzhanov,S. Almaraz, H. Amro, F. D. Becchetti, S. Brown,Y. Chen, H. Jiang, J. J. Kolata, L. O. Lamm, M. Quinn,and A. Woehr, Phys. Rev. C , 024607 (2007).[13] J. Bradt, Y. Ayyad, D. Bazin, W. Mittig, T. Ahn, S. B.Novo], B. Brown, L. Carpenter, M. Cortesi, M. Kuchera,W. Lynch, S. Rost, N. Watwood, J. Yurkon, J. Barney,U. Datta, J. Estee, A. Gillibert, J. Manfredi, P. Mor-fouace, D. Prez-Loureiro, E. Pollacco, J. Sammut, andS. Sweany, Physics Letters B , 155 (2018).[14] N. Imai, Y. Hirayama, H. Ishiyama, S. Jeong, H. Miy-atake, Y. X. Watanabe, H. Makii, S. Mitsuoka, D. Nagae,I. Nishinaka, K. Nishio, and K. Yamaguchi, Eur. Phys.J. A , 157 (2010).[15] N. Imai, Y. Hirayama, Y. X. Watanabe, T. Teranishi,T. Hashimoto, S. Hayakawa, Y. Ichikawa, H. Ishiyama,S. C. Jeong, D. Kahl, S. Kubono, H. Miyatake, H. Ueno,H. Yamaguchi, K. Yoneda, and A. Yoshimi, Phys. Rev.C , 034313 (2012).[16] N. Imai, M. Mukai, J. Cederk¨all, H. Aghai, P. Golubev,H. T. Johansson, D. Kahl, J. Kurcewics, T. Teranishi,and Y. X. Watanabe, Phys. Rev. C , 011302 (2014).[17] G. F. Trentelman, B. M. Preedom, and E. Kashy, Phys.Rev. Lett. , 530 (1970).[18] G. V. Rogachev, J. J. Kolata, A. S. Volya, F. D. Bec-chetti, Y. Chen, P. A. DeYoung, and J. Lupton, Phys.Rev. C , 014603 (2007).[19] K. W. Brown, R. J. Charity, J. M. Elson, W. Reviol, L. G. Sobotka, W. W. Buhro, Z. Chajecki, W. G. Lynch,J. Manfredi, R. Shane, R. H. Showalter, M. B. Tsang,D. Weisshaar, J. R. Winkelbauer, S. Bedoor, and A. H.Wuosmaa, Phys. Rev. C , 044326 (2017).[20] J. Hooker, G. V. Rogachev, E. Koshchiy, S. Ahn, M. Bar-bui, V. Z. Goldberg, C. Hunt, H. Jayatissa, E. C. Pol-lacco, B. T. Roeder, A. Saastamoinen, and S. Upad-hyayula, Phys. Rev. C , 054618 (2019).[21] A. H. Wuosmaa, K. E. Rehm, J. P. Greene, D. J. Hen-derson, R. V. F. Janssens, C. L. Jiang, L. Jisonna, E. F.Moore, R. C. Pardo, M. Paul, D. Peterson, S. C. Pieper,G. Savard, J. P. Schiffer, R. E. Segel, S. Sinha, X. Tang,and R. B. Wiringa, Phys. Rev. Lett. , 082502 (2005).[22] R. Middleton and D. Pullen, Nuclear Physics , 50(1964).[23] D. Tilley, J. Kelley, J. Godwin, D. Millener, J. Purcell,C. Sheu, and H. Weller, Nuc. Phys. A , 155 (2004).[24] E. Leistenschneider, A. L´epine-Szily, M. A. G. Al-varez, D. R. Mendes, R. Lichtenth¨aler, V. A. P. Aguiar,M. Assun ¸c ao, R. P. Condori, U. U. da Silva, P. N.de Faria, N. Deshmukh, J. G. Duarte, L. R. Gasques,V. Guimar˜aes, E. L. A. Macchione, M. C. Morais,V. Morcelle, K. C. C. Pires, V. B. Scarduelli, G. Scotton, J. M. B. Shorto, and V. A. B. Zagatto, Phys. Rev. C ,064601 (2018).[25] I. Wiedenh¨over, L. T. Baby, D. Santiago-Gonzalez,A. Rojas, J. C. Blackmon, G. V. Rogachev, J. Belarge,E. Koshchiy, A. N. Kuchera, L. E. Linhardt, J. Lai, K. T.Macron, M. Matos, and B. C. Rascol, Proceedings of the5th International Conference on “Fission and propertiesof neutron-rich nuclei” (ICFN5) , 144 (2014).[26] G. V. Rogachev, E. D. Johnson, J. Mitchell, V. Z. Gold-berg, K. W. Kemper, and I. Wiedenhver, AIP Conf.Proc. , 137 (2010).[27] S. Almaraz-Calderon, Study of resonances in light nucleifor nuclear structure and nuclear astrophysics , Ph.D. the-sis, University of Notre Dame (2011).[28] “Micron semiconductors ltd.” .[29] J. M. Lombaard and E. Friedland, Z. Physik , 713(1974).[30] E. D. Johnson, Ph.D. thesis, Florida State University(2008).[31] J. B. Ehrman, Phys. Rev. , 412 (1951).[32] R. B. Wiringa, S. Pastore, S. C. Pieper, and G. A. Miller,Phys. Rev. C88