Three-body correlations in the ground-state decay of 26O
Z. Kohley, T. Baumann, G. Christian, P. A. DeYoung, J. E. Finck, N. Frank, B. Luther, E. Lunderberg, M. Jones, S. Mosby, J. K. Smith, A. Spyrou, M. Thoennessen
aa r X i v : . [ nu c l - e x ] M a r Three-body correlations in the ground-state decay of O Z. Kohley,
1, 2
T. Baumann, G. Christian,
1, 3, ∗ P.A. DeYoung, J.E. Finck, N. Frank, B. Luther, E. Lunderberg, † M. Jones,
1, 3
S. Mosby,
1, 3, ‡ J. K. Smith,
1, 3, ∗ A. Spyrou,
1, 3 and M. Thoennessen
1, 3 National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, Michigan 48824, USA Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA Department of Physics & Astronomy, Michigan State University, East Lansing, Michigan 48824, USA Department of Physics, Hope College, Holland, Michigan 49423, USA Department of Physics, Central Michigan University, Mt. Pleasant, Michigan, 48859, USA Department of Physics & Astronomy, Augustana College, Rock Island, Illinois, 61201, USA Department of Physics, Concordia College, Moorhead, Minnesota 56562, USA (Dated: August 19, 2018)
Background:
Theoretical calculations have shown that the energy and angular correlations in the three-bodydecay of the two-neutron unbound O can provide information on the ground-state wavefunction, which has beenpredicted to have a dineutron configuration and 2 n halo structure. Purpose:
To use the experimentally measured three-body correlations to gain insight into the properties of O,including the decay mechanism and ground-state resonance energy.
Method: O was produced in a one-proton knockout reaction from F and the O + n + n decay productswere measured using the MoNA-Sweeper setup. The three-body correlations from the O ground-state resonancedecay were extracted. The experimental results were compared to Monte Carlo simulations in which the resonanceenergy and decay mechanism were varied.
Results:
The measured three-body correlations were well reproduced by the Monte Carlo simulations but werenot sensitive to the decay mechanism due to the experimental resolutions. However, the three-body correlationswere found to be sensitive to the resonance energy of O. A 1 σ upper-limit of 53 keV was extracted for theground-state resonance energy of O. Conclusions:
Future attempts to measure the three-body correlations from the ground-state decay of O willbe very challenging due to the need for a precise measurement of the O momentum at the reaction point in thetarget.
PACS numbers: 21.10.Tg, 23.90.+w, 25.60.-t, 29.30.Hs
I. INTRODUCTION
Exploring the limits of the chart of the nuclides pro-vides fundamental benchmarks for theoretical calcula-tions and opportunities to discover new phenomena [1–4]. Recently, experimental and theoretical studies oftwo-proton (2 p ) and two-neutron (2 n ) unbound systemshave garnered significant interest [5–7]. These systemsallow for the properties and decay mechanisms of nu-clei with extreme neutron-to-proton ratios, existing be-yond the driplines, to be examined. Of particular in-terest are the correlations present in the decay of thesethree-body systems which can offer new insights into theinitial structure and configuration of the nucleus [7–14].At the driplines, unique situations can present them-selves in which the sequential decay process is forbiddenand the “true” two-nucleon decay can be observed [15].While substantial progress has been made in the theoret- ∗ Present address: TRIUMF, Vancouver, British Columbia V6T2A3, Canada † Present address: National Superconducting Cyclotron Labora-tory, Michigan State University, East Lansing, Michigan 48824,USA ‡ Present address: Los Alamos National Laboratory, Los Alamos,New Mexico 87545, USA ical descriptions of the 2 p decay mechanism, resulting inimpressive reproductions of experimental measurements,theoretical frameworks for describing the full three-bodydecay of 2 n unbound systems are still at an early stageand appear to pose new challenges in comparison to the2 p decay [7, 9–11, 16, 17].While the correlations from the decays of a wide rangeof 2 n unbound systems have been measured ( H [18], He [12, 19], Li (excited state) [20], Li [12, 21], Be (excited state) [14], and Be [22]), the O sys-tem provides a particularly interesting case to examinein light of recent experimental and theoretical work. Cur-rently, constraints on the O ground-state resonance en-ergy of <
200 keV and <
40 keV have been reported bythe MoNA collaboration [23] and R3B collaboration [24],respectively. Thus, the sequential decay of O through O, with a ground state unbound by ∼
770 keV [24, 25],is forbidden and O must decay directly to O throughthe simultaneous emission of two neutrons. These con-straints have provided a sensitive observable for ab ini-tio -type calculations examining the role of three-nucleonforces and continuum effects [26–29]. Furthermore, the-oretical calculations of Grigorenko et al. suggested that O would be a candidate for 2 n radioactivity assum-ing a pure [ d / ] neutron configuration and near thresh-old ground-state resonance [30]. Through the use of thedecay-in-target technique [31], the MoNA collaborationextracted a half-life for O of 4.5 +1 . − . (stat) ± et al. a t / = 4 . <
100 keV [30]. However, the presence ofeven a small [ s / ] component in the O wavefunctionwould dominate the width of the decay (and lifetime).New detailed calculations from Grigorenko et al. usingthe three-body hyperspherical harmonics cluster modellowered the original constraint to E decay < O lifetime [17]. Estimates from the contin-uum shell-model, assuming a sequential decay, reporteda similar constraint of E decay . . O decay energy be furtherconstrained by experimental measurements.In addition to the theoretical constraints on the Odecay energy, full three-body calculations of the decaycorrelations have been reported by Grigorenko et al. [17]as well as by Hagino and Sagawa [34]. The results showthat the three-body correlations are sensitive to boththe initial wavefunction and the properties of the decaymechanism including the final-state nn interaction, recoileffects, and sub-barrier configuration mixing or rescatter-ing of the d − wave neutrons into lower ℓ orbitals duringthe decay [17, 34]. The predictions of the ground statewavefunction added additional interest since the modelof Grigorenko et al. suggested O would have a stronghalo structure with a rms radius of the valence neutronsaround 5.7 fm [17] and the model of Hagino and Sagawashowed the valence neutrons to be in a strong dineu-tron configuration [34]. Both theoretical frameworks pre-dicted that these configurations would be manifested inthe three-body decay correlations. One specific signatureshown in both models is that the distribution of anglesbetween the two neutrons ( θ nn ) would be peaked near180 ◦ .In this article, we extract the experimental energy andangular correlations in the Jacobi coordinate system fromthe three-body decay of the O ground-state resonance.The experimental distributions are compared to a dineu-tron model, a phase space model, and the theoretical cal-culation from Hagino and Sagawa. The sensitivity of theexperimental results to the decay mode and ground-stateresonance energy are presented.
II. EXPERIMENTAL DETAILS AND ANALYSIS
Since the experimental details have already been pro-vided in Refs. [23, 32, 35] where the ground state reso-nance and lifetime measurements were reported, only abrief overview is presented. An 82 MeV/u F radioactiveion beam was produced at the National SuperconductingCyclotron Laboratory at Michigan State University fromthe projectile fragmentation of a 140 MeV/u Ca pri-mary beam. The 2 n -unbound O was produced froma one-proton knockout of the F secondary beam us- ing a 705 mg/cm Be reaction target. The O decayedinto O + 2 n in the reaction target. The triple coinci-dence measurement was accomplished using the MoNA-Sweeper setup [36–40] and allowed for the invariant massand correlations between the decay products of O tobe determined.Measurements of 2 n decays require the discriminationof the “true” 2 n events from the “false” 2 n backgroundwhich is generated from a single neutron producing mul-tiple hits within the array. To remove the majority offalse 2 n events from the subsequent analysis, we appliedthe same causality cuts as used in our previous works re-porting on O [23, 32, 35]. The causality cuts requiredthe first two time ordered interactions within MoNA tohave a spatial separation of >
25 cm and a relative ve-locity > n component present in the experimental spectrais nearly negligible.In order to isolate the ground state decay of O, onlyevents with E decay < . O. Recent calcula-tions by Bogner et al. [27] and Hagino and Sagawa [41]indicate that the 2 + state is likely between 1 and 2 MeV.The E decay spectrum with the 0.7 MeV cut is shown inFig. 1(a). The full E decay spectrum can be seen in Fig. 1of Ref. [32].The T and Y Jacobi coordinate systems, illustratedin Fig. 2, were used to define the angular and energycorrelations in the three-body decay of O. The three-body correlations can be fully described by the energy, E x , and angle, cos( θ k ), defined in each Jacobi system as, E x = ( m + m ) k x m m (1a)cos( θ k ) = k x · k y k x k y (1b)with the Jacobi momenta k x and k y defined as, k x = m k − m k m + m (2a) k y = m ( k + k ) − ( m + m ) k m + m + m . (2b)The mass and momentum of each particle is labeled as m i and k i , respectively. As depicted in Fig. 2, E x representsthe energy in the two-body system defined by particles1 and 2, while θ k represents the angle between that two-body system and particle 3 . E x is often reported relativeto the total three body decay energy ( E T ). The exper-imental E x /E T and cos( θ k ) distributions for the T and Y systems, with the causality cuts and E decay < III. SIMULATIONS
Interpretation of the data requires comparisons withdetailed simulations of the experimental setup. A Monte C oun t s C oun t s E (MeV) decay
E /E x T
E /E x T
V (cm/ns) rel cos( ) q k cos( ) q k TT YY a) b) c)f)e)d)
Exp. Dineutron decayHaginoPhaseSpaceFalse2n
FIG. 1. (Color online) (a) Three-body decay energy spectrum, (b) Jacobi relative energy in T system, (c) Jacobi relative energyin the Y system, (d) relative velocity spectrum, (e) Jacobi angle in the T system, and (f) Jacobi angle in the Y system fromthe decay of O. The experimental data are compared with simulations using three different decay modes and a half-life of4 ps. All results are gated on E decay < . n component in thespectra, based on the Geant4 simulation, is shown as the solid grey area. T system Y system k x k y q k e nn k y k x e fn q k core core FIG. 2. Illustration of the T and Y Jacobi coordinate systemsused to define the energy and angular correlations of the threebody decay.
Carlo simulation which included the incoming beam char-acteristics, reaction kinematics, and detector resolutionswas utilized in the subsequent analysis [42]. The interac-tions of the neutrons within MoNA were modeled usingthe
Geant4 framework [43, 44] with the custom neu-tron interaction model menate r [42, 45]. This allowedthe results of the Monte Carlo simulation to be treatedidentically to the experimental data.The ground state resonance of O was simulated witha Breit-Wigner lineshape having a resonance energy, E r ,and a decay width, Γ. The energy and angular corre-lations of the O + n + n system were simulated assuming three different decay models: a phase-spacedecay [46, 47], a dineutron decay [21], and a decaymodel based on the theoretical calculations of Haginoand Sagawa [34]. The phase-space decay model simu-lates the simultaneous breakup of O → O+ n + n as-suming that the particles do not interact during the de-cay process [21, 22, 46, 47]. The dineutron decay model,described in Refs. [21, 48], simulates a two-step pro-cess where a dineutron is emitted and then decays withan intrinsic energy defined by a nn -scattering length of a s = − . θ nn angular distribution from the fullthree-body calculations of Hagino and Sagawa (Fig. 3 ofRef. [34]). Examples of the input cos( θ k ) distributions inthe Y Jacobi system are shown in Fig. 3 for a 5 keV reso-nance energy. As shown, the flat distribution is producedby the phase-space model indicating no correlations be-tween the neutrons, whereas the dineutron and Haginomodels produces distributions that are strongly peakedat − ◦ and 180 ◦ , respectively. It is im-portant to clarify that the dineutron decay model simu-lates the emission of a dineutron and does not necessitatethe presence of a dineutron in the ground-state wavefunc-tion of O. In comparison, the correlations from Haginoand Sagawa are derived from a full three-body decay cal-culations which contain a dineutron configuration in theground-state structure of O. -1 -0.5 0 0.5 10123456 Dineutron decayHaginoPhaseSpace cos( ) q k Y i e l d ( a r b . un i t s ) FIG. 3. (Color online) Input cos( θ k ) distributions from the Y Jacobi coordinate system for the Monte Carlo simula-tions. The distributions from the phase-space, dineutron, andHagino decay models are presented.
The effects of a finite lifetime for O were also includedin the Monte Carlo simulation. As described in Ref. [32],a finite lifetime of O, in the range of picoseconds, willresult in decreased velocity distributions of the two neu-trons emitted after the O has traversed through partof the target. The decreased neutron velocity is repre-sented in the relative velocity spectrum, V rel , defined asthe difference in velocity between the neutron and the O fragment [Fig. 1(d)].
IV. RESULTS AND DISCUSSION
The results from the simulations with the three differ-ent decay modes were simultaneously fit to the experi-mental decay energy, relative velocity, and Jacobi plotsin Fig. 1. The ground-state resonance energy was a freeparameter varying from 0 keV to 100 keV in the fit. Thewidth of the decay, Γ, was fixed at 1 keV since the widthof the resonance is completely dominated by the experi-mental resolutions [23, 32]. The influence of the O life-time was also investigated with t / = 0 ps and 4 ps. Thebest fit (shown in Fig. 1) of the phase-space, dineutron,and Hagino decay modes corresponds to E r = 15 keV,15 keV, and 10 keV, respectively, with t / = 4 ps.The experimental results were well reproduced by allof the models indicating that the angular-energy correla-tions are relatively insensitive to the decay mode. This isunexpected as previous works have shown E x /E T fromthe T system and cos( θ k ) from the Y system to be par-ticularly sensitive to the decay mode [21, 22, 35]. For ex-ample, the input cos( θ k ) distribution should be stronglypeaked at − O at Y i e l d ( A r b . U n i t s ) cos( ) q k E = 200 keV, 705mg/cm E = 200 keV, 0.5mg/cm E = 5 keV, 0.5mg/cm E = 5 keV, 125mg/cm Experimental Beam CharacteristicsIdeal Beam Characteristicsa)b) Y i e l d ( A r b . U n i t s ) FIG. 4. (Color online) cos( θ k ) distributions from the Y Ja-cobi system for simulations using the Hagino decay mode withvarying Be target thicknesses and decay energies for O. Theresults are shown (a) with and (b) without the inclusion ofthe experimental incoming beam characteristics in the simu-lations. the reaction point in the target and the near thresholdenergy of the O ground-state resonance. The Jacobivariables, which describe the three-body correlations, aredirectly related to the relative momenta of the particlesin the decay. When the decay energy is very low, therelative momentum between the particles is then verysmall. Thus, a small uncertainty in the momentum ofthe O fragment can cause a large change in the relativemomentum between the neutrons and fragment. Thisproduces a false enhancement in the correlation betweenthe two neutrons relative to the O fragment which ismanifested as the observed dineutron signatures shown inpanels (b) and (f) of Fig. 1. This effect is diminished withincreasing decay energy. For example, in Fig. 4(a) thethe cos( θ k ) distribution is shown for a resonance energyof 200 keV with the Hagino decay model (black dash-dotline). With the 200 keV resonance energy, the angulardistribution peaks at cos( θ k ) = 1 reproducing the overallfeature of the input distribution from Hagino.The uncertainty in the momentum of the O stemsmainly from two factors: (1) the uncertainty in the po-sition at which the F( − p ) reaction occurs within thetarget and (2) the size and angular spread of the incom-ing beam. While the momentum, or Bρ , of the outgoing O is defined by the path of the fragment through theSweeper magnet, the momentum at the reaction pointrequires the location of the reaction in the target to beknown so that the energy-loss within the target can beaccurately calculated. Since the reaction location is un-known, it was assumed that the reaction took place atthe mid-point of the target in the present analysis. InFig. 4(a), the effect of the target thickness is shown. Fora 200 keV resonance, decreasing the target thickness from705 mg/cm to 0.5 mg/cm improves the agreement be-tween the results of the simulation and the input Haginodistribution. However, decreasing the target thicknessdoes not improve the results when E r = 5 keV and thedineutron signature still prevails. This is due to the char-acteristics of the incoming F beam which can produceuncertainties in the Bρ analysis of the O through theSweeper magnet. Again, if the decay energy of O isnear threshold any uncertainty in the O momentum ismagnified in the three-body correlations. From the ex-periment, the beam spot on the target was estimated tobe 5 mm x 5 mm and the incoming angular distributionof the beam was approximated as a Gaussian distributionwith a mean of 0 ◦ and σ = 7 mrad (2 mrad) in the dis-persive (non-dispersive) direction. These deviations froman ideal beam could be corrected event-by-event usingtracking detectors upstream of the target, however suchdetectors were not available for the present experiment.Fig. 4(b) shows the expected angular distributions as-suming ideal beam characteristics. While the simulationswith the 200 keV resonance energy are not significantlyaltered with the ideal beam characteristics, the dineu-tron signature is no longer present in the simulation witha 5 keV resonance energy. A relatively flat cos( θ k ) distri-bution is observed with a 125 mg/cm target and a slightpeaking towards cos( θ k ) = 1 is shown with a 0.5 mg/cm target with E r = 5 keV. The results from the simula-tion, therefore, indicate that an experimental measure-ment sensitive to the angular and energy correlationsin the three body decay of O will be extremely diffi-cult assuming the ground state resonance is near thresh-old. Even with an increased F beam rate, the use ofa 0.5 mg/cm target would pose a significant challengein obtaining the required statistics to identify the decaymode of O. While future experiments will likely en-counter a similar situation, it is important to emphasisthat these results and sensitivity studies are specific tothe present experiment and MoNA-Sweeper setup.
V. CONSTRAINTS ON THE OGROUND-STATE RESONANCE ENERGY
Although not sensitive to the decay mode, the mea-sured three-body correlations are sensitive to the Odecay energy and, therefore, can allow for improved con-straints to be extracted through a self-consistent fit of allthe spectra presented in Fig. 1. As mentioned previously,the width of the resonance was kept constant, Γ = 1 keV.The fitting procedure was completed for t / = 0 ps and c r ed E (keV) decay
E (keV) decay
Dineutron decayHaginoPhaseSpace t = 0ps t = 4ps a) b)
FIG. 5. (Color online) Reduced chi-squared as a function of O ground-state decay energy for (a) t / = 0 ps and (b) 4 pswith the three different decay modes used in the simulation.TABLE I. 1 σ limits on the O ground-state resonance en-ergy extracted from the simultaneous fitting of the three-bodycorrelations and decay energy spectrum with different decaymodes in the simulation. 1 σ limitModel t / = 0 ps t / = 4 psHagino <
15 keV <
31 keVPhase-Space <
33 keV <
53 keVDineutron 6 −
42 keV 6 −
53 keV V rel distribution [Fig. 1(d)] has been shown tobe best fit with t / ∼ t / = 0 ps.The results of the simultaneous fitting procedure for t / = 0 ps and 4 ps are presented in Fig. 5 where thereduced chi-squared value ( χ red ) from each fit is shownas a function of the O resonance energy for the threesimulated decay modes. In all cases, it is clear that the in-clusion of the three-body correlations into the fit greatlyenhances the sensitivity of the results to the decay en-ergy relative to our previous work where a constraint of E decay <
200 keV was extracted using only the decayenergy spectrum [23]. The strong correlations present inthe input distributions of the Hagino and dineutron de-cay models (Fig. 3) produce a strong sensitivity of theresults at high and low decay energies, respectively. Atlow decay energies, the correlation between the emittedneutrons are severely overestimated by the dineutron de-cay resulting in the large χ red . Similarly, as the decayenergy increases the correlations from the Hagino decay,with cos( θ k ) peaking near 1, become more prominent pro-ducing a rapid increase in χ red . The phase-space decayis the least sensitive to the decay energy since it does notexhibit such strong features in the correlations.For all three models, the χ red rises with the decay en-ergy increasing beyond ∼
20 keV due to the poor fittingof the three-body correlations. From the chi-squared fits,the 1 σ limits for the ground-state O resonance energywere extracted and are shown in Table I. The resultsstrongly support the conclusion that the ground-stateresonance energy is near threshold, with upper-limitsranging from 15 keV to 50 keV depending on the decaymode and half-life. The extracted 1 σ limits are in excel-lent agreement with the 40 keV upper-limit reported bythe R3B collaboration [24]. It is worth noting that theresults using the correlations from the full three-bodycalculations of Hagino and Sagawa [34] (which also agreewith the detailed calculations of Grigorenko et al. [17])should provide the most realistic model for the decay andproduces 1 σ upper-limits of 15 keV and 31 keV for thecases of t / = 0 ps and 4 ps, respectively. VI. CONCLUSIONS
The three-body energy and angular correlations in theground-state resonance decay of O → O + n + n were experimentally measured using the MoNA-Sweepersetup. The experimental results were compared to MonteCarlo simulations using three different decay models: aphase-space model, dineutron model, and three-body de-cay model based on the theoretical calculations of Haginoand Sagawa [34]. The experimental three-body correla-tions were well reproduced by all three of the decay mod-els indicating an insensitivity of the experimental datato the decay mode. This was shown to be due to thelow decay energy of O which, therefore, requires veryprecise measurements of the relative momentum of the O and two neutrons to reconstruct the correlations.Monte Carlo simulations showed that the target thick-ness and tracking of the incoming beam characteristicslargely define the experimental resolutions for measuringthe three-body correlations. Even with improving theseaspects of the experiment, the simulation results indicatethat future attempts to measure the three-body correla-tions from the decay of O will face a difficult challengedue to the near threshold ground-state resonance energy.Through simultaneous and self-consistent fitting of thedecay energy spectrum and the Jacobi three-body corre-lation variables strict constraints on the O decay en-ergy were extracted. While the results were dependenton the decay mode and half-life of O, a maximum 1 σ upper-limit of 53 keV was obtained. Furthermore, if oneassumes that the correlations from the full three-bodydecay calculations of Hagino and Sagawa [34] are cor-rect (noting that similar correlations are also predictedby Grigorenko et al. [17]), then the 1 σ upper-limit for the O ground-state is 31 keV. Additional measurements, re-quiring increased statistics, are strongly desired to pro-vide a precise measurement ground-state resonance en-ergy for O. ACKNOWLEDGMENTS
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