Bailey, S.

Bishop, J.

Curtis, N.

Dell’Aquila, D.

Faestermann, Th

Hertenberger, R.

Kokalova, Tz

Mengoni, D.

Pirrie, S.

Smith, Robin

Torresi, D.

Turner, A.

Wheldon, C.

Wirth, H-F

A series of proposed bands in 18O with potential nuclear molecular structures, such as 14C ⊗ - α or 12C ⊗ - 2n ⊗ - α, are being investigated. This was done through the use of the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory in Munich in conjunction with an array of double-sided silicon strip detectors (DSSDs). These detectors allowed for high resolution reconstruction of detected particles, enabling measurement of the branching ratios of the states that make up these bands. Here, a method is discussed for extracting the branching ratios of both material particles as well as γ-particles using the DSSD array to detect only charged decay fragments.</p

Smith, R.

Wirth, H. F.

Dell'Aquila, D.

University of Birmingham Research Portal

  A method to determine  branching ratios usingcharged particle detectors for states in 18OPirrie, Stuart; Kokalova, Tz; Wheldon, Carl; Bailey, Sam; Bishop, Jack; Curtis, Neil; Smith,Robin; Torresi, Domenico; Turner, Anthony; Hertenberger, R.; Wirth, H. F.; Faestermann, Th;Mengoni, D.; Dell'Aquila, D.DOI:10.1063/1.5078856License:Other (please specify with Rights Statement)Document VersionPeer reviewed versionCitation for published version (Harvard):Pirrie, S, Kokalova, T, Wheldon, C, Bailey, S, Bishop, J, Curtis, N, Smith, R, Torresi, D, Turner, A, Hertenberger,R, Wirth, HF, Faestermann, T, Mengoni, D & Dell'Aquila, D 2018, A method to determine  branching ratios usingcharged particle detectors for states in 18O. in M Barbui, CM Folden III, VZ Goldberg & GV Rogachev (eds),Proceedings of the 4th International Workshop on State of the Art in Nuclear Cluster Physics, SOTANCP 2018.,020037, AIP Conference Proceedings, no. 1, vol. 2038, AIP Publishing, 4th International Workshop on State ofthe Art in Nuclear Cluster Physics, SOTANCP 2018, Galveston, United States, 13/05/18.https://doi.org/10.1063/1.5078856Link to publication on Research at Birmingham portalPublisher Rights Statement:Checked for eligibility: 20/12/2018This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. Thefollowing article appeared in:Pirrie, S., Kokalova, T., Wheldon, C., Bailey, S., Bishop, J., Curtis, N., Smith, R., Torresi, D., Turner, A.,Hertenberger, R. and Wirth, H.F., 2018, November. A method to determine  branching ratios using charged particle detectors for states in18O. In AIP Conference Proceedings (Vol. 2038, No. 1, p. 020037). AIP Publishing and may be found at: https://doi.org/10.1063/1.5078856General rightsUnless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or thecopyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposespermitted by law.•	Users may freely distribute the URL that is used to identify this publication.•	Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of privatestudy or non-commercial research.•	User may use extracts from the document in line with the concept of ‘fair dealing’ under the Copyright, Designs and Patents Act 1988 (?)•	Users may not further distribute the material nor use it for the purposes of commercial gain.Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.When citing, please reference the published version.Take down policyWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has beenuploaded in error or has been deemed to be commercially or otherwise sensitive.If you believe that this is the case for this document, please contact UBIRA@lists.bham.ac.uk providing details and we will remove access tothe work immediately and investigate.Download date: 01. Feb. 2019A method to determine γ branching ratios using chargedparticle detectors for states in 18OS. Pirrie1,a),∗, Tz. Kokalova1, C. Wheldon1, S. Bailey1, J. Bishop1, N. Curtis1,R. Smith1, D. Torresi1, A. Turner1, R. Hertenberger2, H.-F. Wirth2,Th. Faestermann3, D. Mengoni4 and D. Dell’Aquila51School of Physics and Astronomy, University of Birmingham, Edgbaston Park Rd, Birmingham, UK, B15 2TT2Fakulta¨t fu¨r Physik, Ludwig-Maximilians-Universita¨t Mu¨nchen, D-85748 Garching, Germany3Physik Department, Technische Universita¨t Mu¨nchen, D-85748 Garching, Germany4Universita` degli Studi di Padova, Via 8 Febbraio 1848, 2, 35122 Padova PD, Italy5Universita` degli Studi di Napoli Fedorico II, Corso Umberto I, 40, 80138 Napoli NA, Italya)Corresponding author: S.Pirrie@PGR.bham.ac.ukAbstract. A series of proposed bands in 18O with potential nuclear molecular structures, such as 14C⊗α or 12C⊗2n⊗α, are being investigated. This was done through the use of the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory inMunich in conjunction with an array of double-sided silicon strip detectors (DSSDs). These detectors allowed for high resolutionreconstruction of detected particles, enabling measurement of the branching ratios of the states that make up these bands. Here, amethod is discussed for extracting the branching ratios of both material particles as well as γ-particles using the DSSD array todetect only charged decay fragments.INTRODUCTIONNuclear clustering is a well-established phenomenon observed in several nuclei, but the most common of these arelight, even N = Z nuclei [1] [2]. Clustering, however, is proposed to occur in many nuclei that are not purely alpha-conjugate. The addition of a pair of neutrons to the system can decrease the required threshold for an alpha particle toform in the nucleus, as in the case with 16O (7.16 MeV threshold for a 12C⊗α structure) going to 18O (6.23 MeVthreshold for a 14C⊗α structure).An excellent contender for the observation of cluster structure is 18O, particularly a core + alpha description dueto the properties of both the α and 14C nucleus. Like 16O (a cluster core observed most clearly in the core + alphadescription of 20Ne [3][4]), 14C has a closed p-shell and its first excited state lies at around 6 MeV, lending morecredence to the notion of a 14C⊗α configuration in 18O.An experiment performed at the Maier-Leibnitz Laboratory (MLL) of the Technical University and Ludwig-Maximillan University in Munich by W. von Oertzen et al. found 30 previously unobserved states in 18O [5]. Usingthese and previously measured states, rotational bands with different nucleon configurations were proposed. Thestates that make up these proposed rotational bands are shown in TABLE 1. As these proposed bands, each with anassociated positive and negative parity due to signature splitting, have a cluster structure, with the Kpi = 0+/−2 proposedto have a 14C⊗α structure and the kpi = 0+/−4 proposed to have a14C⊗α structure, the associated partial α decaywidths of the composite states can be used to confirm or refute the existence of each band as levels built upon thesame configuration should have similar decay properties.∗Work supported by STFC (UK)TABLE 1: The preliminary measured excitation energies and FWHMs of states in the proposed rotational bandscompared to the literature values for the excitation energies and widths from Ref. [5]. Spins and parities that wereassigned based on fitting the rotational properties are shown in brackets, and states with a small cross-section (<2µb/sr) with an asterisk (*). The resolution of the focal plane varied across its length and was determined for theground state (measured FWHM of 86(5) keV) and the 1st excited state (measured FWHM of 76(3) keV), measuredat separate ends of the focal plane detector. Unmeasured states lay outside of the excitation regions investigated.Kpi = 0+2 Kpi = 0−2Ex(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitEx(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitunmeasured 3.558(4) - 0+ 8.037(1)∗ 93(19) 8.035(5) <10 1−unmeasured 5.254(5) - 2+ 9.737(4) 118(7) 9.715(5) 15(4) (3−)7.114(1) 80 (2) 7.115(4) - 4+ 13.617(3) - 13.624(6) 22(7) (5−)11.716(4) 95 (11) 11.702(6) 27 6+ unmeasured 18.630(10) 100(20) (7−)unmeasured 18.058(8) 83 8+*Kpi = 0+4 Kpi = 0−4Ex(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitEx(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLit7.798(1)∗ - 7.796(5) <10 0+ 10.595(4) 105(7) 10.59(1) 70(16) (1−)8.217(1) 66(3) 8.216(4) <10 2+ 10.937(4) 99(6) 10.92(1) 30(9) (3−)10.297(5) 84(5) 10.293(4) 23(8) 4+ 13.827(3) 80(4) 13.82(2) 27(8) (5−)12.559(1) 114(7) 12.557(6) 22(8) 6+ unmeasured 16.99(1) 50(12) (7−)unmeasured 15.810(10) 20(8) (8+) unmeasured 20.28(3) 120(21) (9−)unmeasured 20.385(15) 155(25) (10+)EXPERIMENTAL METHODA subsequent experiment was performed, also at MLL Munich, to determine the branching ratios of the high-energyexcited states in 18O and hence extract their partial α decay widths. The reaction chosen to populate states in 18O was12C(7Li,p)18O∗ (Q0 = +8.401 MeV) as this reaction, used by von Oertzen et al., was known to be well-populated. The15 MV tandem Van de Graaff accelerator at MLL was used to produce a 44 MeV 7Li beam. The Q3D spectrograph wasset at an angle of −39◦ in the horizontal beam plane, with an angular acceptance of ±3◦ in x (horizontal) and ±2◦ in y(vertical). The Birmingham array of 50 mm by 50 mm, 500 µm thick double-sided silicon strip detectors (DSSDs) wasused in conjunction with the Q3D spectrograph in order to extract both energy and momentum information, allowingfor high-resolution reconstruction. The experimental set-up and DSSD array are depicted in FIGURE 1.The Q3D spectrograph was configured to allow for the detection of the resulting protons from the reaction. TheQ3D consists of a scintillator for measuring the energy of an incident particle, two upstream horizontal wires in a gasvolume for measuring the energy loss and a 255 strip cathode foil for measuring the position of incident particles [6].Using the information from the scintillator and the horizontal wires, particle identification was achieved and henceproton-only events were selected. The energy of the proton is obtained from the detected position at the focal plane[7] and enables an excitation spectrum for 18O to be produced. An example of this is shown later in FIGURE 5. Itshould be noted that the position of the proton at the focal plane was independent of the angle at which it entered theQ3D. The corresponding 18O or its decay products would then, in the majority of cases, be detected by the DSSDarray, which had a total angular coverage of 14◦ to 92◦ in-plane, and −36◦ to 40◦ out-of-plane. When an event wasregistered in the Q3D, all events in the ADC channels of the DSSDs were read out, allowing for events with Q3D andDSSD coincidences as well as Q3D-only events.RESULTSAs the particles incident on the DSSDs were not directly identified, a technique to identify a detected particle-speciesbased on its energy and momentum was adopted. In the break-up of 18O∗ into particles A and B, using events with asingle hit in the DSSD array (for example, a detection of A), the momentum of the undetected B can be reconstructed:(a) (b)FIGURE 1: Diagrams illustrating the experimental set-up used at MLL. The plan view in the chamber is shown in (a),while the double-sided silicon strip detector (DSSD) array is shown in more detail in (b). The in-plane center angle ofdetectors 1 and 2 was +28±1◦ and for detectors 3 and 4 was +67±1◦. The out-of-plane center angles of detectors 1-4were +21±1◦, −15±1◦, +25±1◦ and −18±1◦ respectively.~pB = ~pbeam − ~pQ3D − ~pA, (1)where ~pA is the momentum of the particle detected in the DSSD array, ~pbeam is the momentum of the beam particle and~pQ3D is the momentum of the proton detected at the Q3D focal plane [8]. The momentum in each Cartesian directioncan be calculated using the angles of detection of any detected particles in conjunction with their energies and masses.Using particle A as an example:pA =√2EAmA, (2)pAx = pA sin θx cos θy,pAy = pA sin θy andpAz = pA cos θx cos θy,with θx and θy being the angles of detection in-plane and out-of-plane respectively. In order to calculate the totalmomentum of the detected particle, the mass (mA) must be assumed.Using this information, the total momentum of the missing particle can then be substituted into the Q valueexpression for the 12C(7Li,p)A+B reaction,Q = EA + EQ3D +p2B2mB− Ebeam, (3)where the energy of particle B has been related to its momentum by EB =p2B2mB. Rearranging this to be in the formy = mx + c gives the following expression,Ebeam − EA − EQ3D =p2B2mB− Q, (4)which allows the calculated value of p2B2 to be plotted against the measured value of Ebeam − EA − EQ3D, generatinga locus with a gradient of 1/mB and a y-intercept of −Q if the correct assumption has been made regarding the massof the particle in Equation 2. If a detected particle does not have the same mass as the one assumed, the associatedlocus will not lie on the line described by this gradient and y-intercept. Such a diagram is known as a Catania plot,and FIGURE 2 shows a labeled example.(a) (b)FIGURE 2: A comparison of experimental (a) and simulated (b) data plotted on a Catania plot. The simulated datawere produced using Resolution8.1 [9][10], an in-house Monte Carlo simulation package, and contain 2 types ofbreak-up: 12C(7Li,p)α+14C (Q = +2.173 MeV) and 12C(7Li,p)n+17O (Q = +0.355 MeV). The momenta for all parti-cles detected in the DSSD were calculated assuming they were 14C, allowing correct events to lie on the locus definedby the red line with y-intercept = −Q = −2.173 MeV and gradient = 1mα . Incorrect assumption of the particle masscause the other visible loci to arise, but these are still distinct from one another and allow for particle identificationwhen compared with simulation.(a) (b)FIGURE 3: A comparison of simulated data (a) and experimental data (b), scaled to show low reconstructed energyevents, which demonstrates the agreement between the simulation of the 7.115 MeV 4+ state in 18O decaying to the6.404 MeV 3− state and the 7.969 MeV state 3+/4− photon decaying to the 6.880 MeV 0− state (both highlighted inblack ellipses). The simulation includes the decay modes mentioned in FIGURE 2, which are labelled in both (a) and(b) and can be seen to be in good agreement.Photon EventsStates that have a significant γ decay branch, such as unnatural parity states below the n decay threshold (8.045 MeV),will also be present on a Catania plot, but due to the small amount of momentum taken by the photon the loci formedby γ decay events will contaminate other loci from massive particle decay with a large variability depending on the γ-ray energy of the associated decay. As one of the excitation regimes investigated in this analysis was centered around(a) (b)FIGURE 4: Two-dimensional plots showing the number of events hitting each pixel of the detector, with eventssmeared randomly across the area of the pixel (9 mm2). Experimental data are shown in (a) while simulated data areshown in (b). The region in the center of the Gaussian profiles with the largest number of counts is largely formedby the focused nature of the 18O distribution, which is confirmed using the simulation to identify features. The pixelcenters of the detectors of the detectors are shown by the grid of points for both experimental and simulated data.7500 keV, several states might be expected to decay via photon emission. An example of this contamination can beseen in FIGURE 3, along with simulation comparisons using two states (7.115 MeV and 7.969 MeV) which matchwell to the observed features in the data.As the γ events prevent gating on the loci formed due to massive particles, they must be removed in order toestablish branching ratios for the various decay modes. This can be achieved through plotting the in-plane and out-of-plane Cartesian angles for detections in the DSSD array on a 2D histogram and observing the Gaussian distributionsdue to each particle, as shown in FIGURE 4. The momentum of an 18O nucleus detected in the DSSD array is largelydefined by the momentum of the proton detected at the focal plane (as the photon takes very little), which resultsin a very small Gaussian distribution for 18O relative to other similar particles which share momentum with massivedecay products, such as 17O with the n. Thus, by putting a gate around the possible 18O detection region, which wasconfirmed through comparison with Monte Carlo simulation, γ events were removed from the Catania plot to facilitateaccurate measurement of the branching ratios for each decay mode. FIGURE 5 shows the comparison of the totalexcitation spectrum to that formed when looking at Q3D events coincident with a hit in the DSSD array inside the 18Ogate.The 18O gate also contained events from the other decay modes which needed to be accounted for in the branchingratio determination. Considering a single excitation and a single decay mode, the fraction of events outside of the 18Ogate was calculated from the Monte Carlo simulations using the relationshipf =Nsimtot − NsimgateNsimtot, (5)where Nsimtot is the total number of simulated events and Nsimgate is the number of these events in 18O the gate.Using this fraction, the total number of erroneous events in the 18O gate, Ngate, belonging to this decay mode wasdetermined from the number of events in the γ-removed Catania plot, Ncat, byNgate =Ncatf− Ncat. (6)Hence, Ngate was hence subtracted for each state in the 18O-gated excitation spectrum, leaving only true γ decay eventsonce this process was done for all decay modes. The γ decay branching ratio was then established for each state.Excitation Energy (keV)6500 7000 7500 8000 8500 9000Counts/20 keV050100150200250300350+7155 keV 4_7619 keV 1_7702 keV 2_7855 keV 5) +/4 _7969 keV (3 +8214 keV 2_8284 keV 38508 keV+7796 keV 0(a)Excitation energy (keV)6500 7000 7500 8000 8500 9000Counts/20 keV020406080100120140160+7155 keV 4_7619 keV 1_7702 keV 2) +/4 _7969 keV (3_7855 keV 5 +8214 keV 2_8284 keV 38508 keV(b)FIGURE 5: A comparison of the total excitation spectrum produced centered at 7500 keV (a) with the excitationspectrum produced when gating on DSSD array hits in the 18O gate (b). States that are likely to γ decay are shown inred, due to low barrier penetrability in the case of the 7.115 MeV state and the unnatural parity of the 7.770 MeV and7.969 MeV states, which are below the n threshold of 8.045 MeV. Enhancements of these states relative to the stateslabelled in blue can be observed in (b).CONCLUSIONThe experimental method for measuring the branching ratios of excited states in 18O has been discussed, includinga technique that allows for the measurement of the γ decay branching ratio through the use of a DSSD array solelydetecting charged particles. States which are expected to γ decay due to their spin-parity and excitation energy relativeto decay thresholds have been investigated through use of Monte Carlo simulations and found to match observedfeatures in experimental data Catania plots, which can then be removed and hence accurate determination of bothmassive particle decay and γ decay branching ratios achieved.ACKNOWLEDGMENTSThe authors would like to thank Andy Bergmaier for his help loaning equipment during the set-up of the experiment, aswell as the operators of the tandem Van de Graaff accelerator at the Maier-Leibnitz Laboratory in Munich for providingand maintaining the 7Li beam. This work was funded by the UK Science and Technology Facilities Council (STFC)under Grant No. ST/L005751/1 and from the European Unions Horizon 2020 research and innovation programmeunder the Marie Skłodowska-Curie Grant Agreement No. 65F9744.REFERENCES[1] M. Freer, Rep. Prog. Phys 70, 2149–2210 (2007).[2] B. Fulton, Contemp. Phys 40(5), 299–311 (1999).[3] W. von Oertzen et al., Eur. Phys. J. A 11, 403–411 (2001).[4] J. Hiura et al., Progr. Theor. Phys 42, 555–580 (1969).[5] W. von Oertzen et al., Eur. Phys. J. A 43, 17–33 (2010).[6] H.-F. Wirth, Ph.D. thesis, Technischen Universita¨t, Mu¨nchen 2001.[7] H.-F. Wirth et al., Beschleuniger Laboratorium Munchen, Annual Report (unpublished), p. 71 (2000).[8] C. Wheldon et al., Phys. Rev. C 83, 2503–2504 (2011).[9] N. Curtis et al., Phys. Rev. C 51, 1554–1557 (1995).[10] N. Curtis et al., Phys. Rev. C 53, 1804–1810 (1996).[11] N. Curtis et al., Phys. Rev. C 66, 024315:1–10 (2002).[12] H. Fortune, Phys. Rev. C 18, p. 1053 (1978).[13] K. Artemov, Sov. J. Nucl. Phys. 37, p. 805 (1983).[14] G. Morgan, Nucl. Phys. A 148, p. 480 (1970).

A method to determine γ branching ratios using charged particle detectors for states in <sup>18</sup>O

S. Pirrie

Tz. Kokalova

C. Wheldon

S. Bailey

J. Bishop

N. Curtis

R. Smith

D. Torresi

A. Turner

R. Hertenberger

H.-F. Wirth

Th. Faestermann

D. Mengoni

D. Dell’Aquila

Crossref

A method to determine γ branching ratios using charged particle detectors for states in 18O

  University of BirminghamA method to determine  branching ratios usingcharged particle detectors for states in 18OPirrie, S.; Kokalova, Tz; Wheldon, C.; Bailey, S.; Bishop, J.; Curtis, N.; Smith, R.; Torresi, D.;Turner, A.; Hertenberger, R.; Wirth, H. F.; Faestermann, Th; Mengoni, D.; Dell'Aquila, D.DOI:10.1063/1.5078856License:Other (please specify with Rights Statement)Document VersionPeer reviewed versionCitation for published version (Harvard):Pirrie, S, Kokalova, T, Wheldon, C, Bailey, S, Bishop, J, Curtis, N, Smith, R, Torresi, D, Turner, A, Hertenberger,R, Wirth, HF, Faestermann, T, Mengoni, D & Dell'Aquila, D 2018, A method to determine  branching ratios usingcharged particle detectors for states in 18O. in M Barbui, CM Folden III, VZ Goldberg & GV Rogachev (eds),Proceedings of the 4th International Workshop on State of the Art in Nuclear Cluster Physics, SOTANCP 2018.,020037, AIP Conference Proceedings, no. 1, vol. 2038, AIP Publishing, 4th International Workshop on State ofthe Art in Nuclear Cluster Physics, SOTANCP 2018, Galveston, United States, 13/05/18.https://doi.org/10.1063/1.5078856Link to publication on Research at Birmingham portalPublisher Rights Statement:Checked for eligibility: 20/12/2018This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. Thefollowing article appeared in:Pirrie, S., Kokalova, T., Wheldon, C., Bailey, S., Bishop, J., Curtis, N., Smith, R., Torresi, D., Turner, A.,Hertenberger, R. and Wirth, H.F., 2018, November. A method to determine  branching ratios using charged particle detectors for states in18O. In AIP Conference Proceedings (Vol. 2038, No. 1, p. 020037). AIP Publishing and may be found at: https://doi.org/10.1063/1.5078856General rightsUnless a licence is specified above, all rights (including copyright and moral rights) in this document are retained by the authors and/or thecopyright holders. The express permission of the copyright holder must be obtained for any use of this material other than for purposespermitted by law.•	Users may freely distribute the URL that is used to identify this publication.•	Users may download and/or print one copy of the publication from the University of Birmingham research portal for the purpose of privatestudy or non-commercial research.•	User may use extracts from the document in line with the concept of ‘fair dealing’ under the Copyright, Designs and Patents Act 1988 (?)•	Users may not further distribute the material nor use it for the purposes of commercial gain.Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document.When citing, please reference the published version.Take down policyWhile the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has beenuploaded in error or has been deemed to be commercially or otherwise sensitive.If you believe that this is the case for this document, please contact UBIRA@lists.bham.ac.uk providing details and we will remove access tothe work immediately and investigate.Download date: 01. Mar. 2020A method to determine γ branching ratios using chargedparticle detectors for states in 18OS. Pirrie1,a),∗, Tz. Kokalova1, C. Wheldon1, S. Bailey1, J. Bishop1, N. Curtis1,R. Smith1, D. Torresi1, A. Turner1, R. Hertenberger2, H.-F. Wirth2,Th. Faestermann3, D. Mengoni4 and D. Dell’Aquila51School of Physics and Astronomy, University of Birmingham, Edgbaston Park Rd, Birmingham, UK, B15 2TT2Fakulta¨t fu¨r Physik, Ludwig-Maximilians-Universita¨t Mu¨nchen, D-85748 Garching, Germany3Physik Department, Technische Universita¨t Mu¨nchen, D-85748 Garching, Germany4Universita` degli Studi di Padova, Via 8 Febbraio 1848, 2, 35122 Padova PD, Italy5Universita` degli Studi di Napoli Fedorico II, Corso Umberto I, 40, 80138 Napoli NA, Italya)Corresponding author: S.Pirrie@PGR.bham.ac.ukAbstract. A series of proposed bands in 18O with potential nuclear molecular structures, such as 14C⊗α or 12C⊗2n⊗α, are being investigated. This was done through the use of the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory inMunich in conjunction with an array of double-sided silicon strip detectors (DSSDs). These detectors allowed for high resolutionreconstruction of detected particles, enabling measurement of the branching ratios of the states that make up these bands. Here, amethod is discussed for extracting the branching ratios of both material particles as well as γ-particles using the DSSD array todetect only charged decay fragments.INTRODUCTIONNuclear clustering is a well-established phenomenon observed in several nuclei, but the most common of these arelight, even N = Z nuclei [1] [2]. Clustering, however, is proposed to occur in many nuclei that are not purely alpha-conjugate. The addition of a pair of neutrons to the system can decrease the required threshold for an alpha particle toform in the nucleus, as in the case with 16O (7.16 MeV threshold for a 12C⊗α structure) going to 18O (6.23 MeVthreshold for a 14C⊗α structure).An excellent contender for the observation of cluster structure is 18O, particularly a core + alpha description dueto the properties of both the α and 14C nucleus. Like 16O (a cluster core observed most clearly in the core + alphadescription of 20Ne [3][4]), 14C has a closed p-shell and its first excited state lies at around 6 MeV, lending morecredence to the notion of a 14C⊗α configuration in 18O.An experiment performed at the Maier-Leibnitz Laboratory (MLL) of the Technical University and Ludwig-Maximillan University in Munich by W. von Oertzen et al. found 30 previously unobserved states in 18O [5]. Usingthese and previously measured states, rotational bands with different nucleon configurations were proposed. Thestates that make up these proposed rotational bands are shown in TABLE 1. As these proposed bands, each with anassociated positive and negative parity due to signature splitting, have a cluster structure, with the Kpi = 0+/−2 proposedto have a 14C⊗α structure and the kpi = 0+/−4 proposed to have a14C⊗α structure, the associated partial α decaywidths of the composite states can be used to confirm or refute the existence of each band as levels built upon thesame configuration should have similar decay properties.∗Work supported by STFC (UK)TABLE 1: The preliminary measured excitation energies and FWHMs of states in the proposed rotational bandscompared to the literature values for the excitation energies and widths from Ref. [5]. Spins and parities that wereassigned based on fitting the rotational properties are shown in brackets, and states with a small cross-section (<2µb/sr) with an asterisk (*). The resolution of the focal plane varied across its length and was determined for theground state (measured FWHM of 86(5) keV) and the 1st excited state (measured FWHM of 76(3) keV), measuredat separate ends of the focal plane detector. Unmeasured states lay outside of the excitation regions investigated.Kpi = 0+2 Kpi = 0−2Ex(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitEx(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitunmeasured 3.558(4) - 0+ 8.037(1)∗ 93(19) 8.035(5) <10 1−unmeasured 5.254(5) - 2+ 9.737(4) 118(7) 9.715(5) 15(4) (3−)7.114(1) 80 (2) 7.115(4) - 4+ 13.617(3) - 13.624(6) 22(7) (5−)11.716(4) 95 (11) 11.702(6) 27 6+ unmeasured 18.630(10) 100(20) (7−)unmeasured 18.058(8) 83 8+*Kpi = 0+4 Kpi = 0−4Ex(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitEx(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLit7.798(1)∗ - 7.796(5) <10 0+ 10.595(4) 105(7) 10.59(1) 70(16) (1−)8.217(1) 66(3) 8.216(4) <10 2+ 10.937(4) 99(6) 10.92(1) 30(9) (3−)10.297(5) 84(5) 10.293(4) 23(8) 4+ 13.827(3) 80(4) 13.82(2) 27(8) (5−)12.559(1) 114(7) 12.557(6) 22(8) 6+ unmeasured 16.99(1) 50(12) (7−)unmeasured 15.810(10) 20(8) (8+) unmeasured 20.28(3) 120(21) (9−)unmeasured 20.385(15) 155(25) (10+)EXPERIMENTAL METHODA subsequent experiment was performed, also at MLL Munich, to determine the branching ratios of the high-energyexcited states in 18O and hence extract their partial α decay widths. The reaction chosen to populate states in 18O was12C(7Li,p)18O∗ (Q0 = +8.401 MeV) as this reaction, used by von Oertzen et al., was known to be well-populated. The15 MV tandem Van de Graaff accelerator at MLL was used to produce a 44 MeV 7Li beam. The Q3D spectrograph wasset at an angle of −39◦ in the horizontal beam plane, with an angular acceptance of ±3◦ in x (horizontal) and ±2◦ in y(vertical). The Birmingham array of 50 mm by 50 mm, 500 µm thick double-sided silicon strip detectors (DSSDs) wasused in conjunction with the Q3D spectrograph in order to extract both energy and momentum information, allowingfor high-resolution reconstruction. The experimental set-up and DSSD array are depicted in FIGURE 1.The Q3D spectrograph was configured to allow for the detection of the resulting protons from the reaction. TheQ3D consists of a scintillator for measuring the energy of an incident particle, two upstream horizontal wires in a gasvolume for measuring the energy loss and a 255 strip cathode foil for measuring the position of incident particles [6].Using the information from the scintillator and the horizontal wires, particle identification was achieved and henceproton-only events were selected. The energy of the proton is obtained from the detected position at the focal plane[7] and enables an excitation spectrum for 18O to be produced. An example of this is shown later in FIGURE 5. Itshould be noted that the position of the proton at the focal plane was independent of the angle at which it entered theQ3D. The corresponding 18O or its decay products would then, in the majority of cases, be detected by the DSSDarray, which had a total angular coverage of 14◦ to 92◦ in-plane, and −36◦ to 40◦ out-of-plane. When an event wasregistered in the Q3D, all events in the ADC channels of the DSSDs were read out, allowing for events with Q3D andDSSD coincidences as well as Q3D-only events.RESULTSAs the particles incident on the DSSDs were not directly identified, a technique to identify a detected particle-speciesbased on its energy and momentum was adopted. In the break-up of 18O∗ into particles A and B, using events with asingle hit in the DSSD array (for example, a detection of A), the momentum of the undetected B can be reconstructed:(a) (b)FIGURE 1: Diagrams illustrating the experimental set-up used at MLL. The plan view in the chamber is shown in (a),while the double-sided silicon strip detector (DSSD) array is shown in more detail in (b). The in-plane center angle ofdetectors 1 and 2 was +28±1◦ and for detectors 3 and 4 was +67±1◦. The out-of-plane center angles of detectors 1-4were +21±1◦, −15±1◦, +25±1◦ and −18±1◦ respectively.~pB = ~pbeam − ~pQ3D − ~pA, (1)where ~pA is the momentum of the particle detected in the DSSD array, ~pbeam is the momentum of the beam particle and~pQ3D is the momentum of the proton detected at the Q3D focal plane [8]. The momentum in each Cartesian directioncan be calculated using the angles of detection of any detected particles in conjunction with their energies and masses.Using particle A as an example:pA =√2EAmA, (2)pAx = pA sin θx cos θy,pAy = pA sin θy andpAz = pA cos θx cos θy,with θx and θy being the angles of detection in-plane and out-of-plane respectively. In order to calculate the totalmomentum of the detected particle, the mass (mA) must be assumed.Using this information, the total momentum of the missing particle can then be substituted into the Q valueexpression for the 12C(7Li,p)A+B reaction,Q = EA + EQ3D +p2B2mB− Ebeam, (3)where the energy of particle B has been related to its momentum by EB =p2B2mB. Rearranging this to be in the formy = mx + c gives the following expression,Ebeam − EA − EQ3D =p2B2mB− Q, (4)which allows the calculated value of p2B2 to be plotted against the measured value of Ebeam − EA − EQ3D, generatinga locus with a gradient of 1/mB and a y-intercept of −Q if the correct assumption has been made regarding the massof the particle in Equation 2. If a detected particle does not have the same mass as the one assumed, the associatedlocus will not lie on the line described by this gradient and y-intercept. Such a diagram is known as a Catania plot,and FIGURE 2 shows a labeled example.(a) (b)FIGURE 2: A comparison of experimental (a) and simulated (b) data plotted on a Catania plot. The simulated datawere produced using Resolution8.1 [9][10], an in-house Monte Carlo simulation package, and contain 2 types ofbreak-up: 12C(7Li,p)α+14C (Q = +2.173 MeV) and 12C(7Li,p)n+17O (Q = +0.355 MeV). The momenta for all parti-cles detected in the DSSD were calculated assuming they were 14C, allowing correct events to lie on the locus definedby the red line with y-intercept = −Q = −2.173 MeV and gradient = 1mα . Incorrect assumption of the particle masscause the other visible loci to arise, but these are still distinct from one another and allow for particle identificationwhen compared with simulation.(a) (b)FIGURE 3: A comparison of simulated data (a) and experimental data (b), scaled to show low reconstructed energyevents, which demonstrates the agreement between the simulation of the 7.115 MeV 4+ state in 18O decaying to the6.404 MeV 3− state and the 7.969 MeV state 3+/4− photon decaying to the 6.880 MeV 0− state (both highlighted inblack ellipses). The simulation includes the decay modes mentioned in FIGURE 2, which are labelled in both (a) and(b) and can be seen to be in good agreement.Photon EventsStates that have a significant γ decay branch, such as unnatural parity states below the n decay threshold (8.045 MeV),will also be present on a Catania plot, but due to the small amount of momentum taken by the photon the loci formedby γ decay events will contaminate other loci from massive particle decay with a large variability depending on the γ-ray energy of the associated decay. As one of the excitation regimes investigated in this analysis was centered around(a) (b)FIGURE 4: Two-dimensional plots showing the number of events hitting each pixel of the detector, with eventssmeared randomly across the area of the pixel (9 mm2). Experimental data are shown in (a) while simulated data areshown in (b). The region in the center of the Gaussian profiles with the largest number of counts is largely formedby the focused nature of the 18O distribution, which is confirmed using the simulation to identify features. The pixelcenters of the detectors of the detectors are shown by the grid of points for both experimental and simulated data.7500 keV, several states might be expected to decay via photon emission. An example of this contamination can beseen in FIGURE 3, along with simulation comparisons using two states (7.115 MeV and 7.969 MeV) which matchwell to the observed features in the data.As the γ events prevent gating on the loci formed due to massive particles, they must be removed in order toestablish branching ratios for the various decay modes. This can be achieved through plotting the in-plane and out-of-plane Cartesian angles for detections in the DSSD array on a 2D histogram and observing the Gaussian distributionsdue to each particle, as shown in FIGURE 4. The momentum of an 18O nucleus detected in the DSSD array is largelydefined by the momentum of the proton detected at the focal plane (as the photon takes very little), which resultsin a very small Gaussian distribution for 18O relative to other similar particles which share momentum with massivedecay products, such as 17O with the n. Thus, by putting a gate around the possible 18O detection region, which wasconfirmed through comparison with Monte Carlo simulation, γ events were removed from the Catania plot to facilitateaccurate measurement of the branching ratios for each decay mode. FIGURE 5 shows the comparison of the totalexcitation spectrum to that formed when looking at Q3D events coincident with a hit in the DSSD array inside the 18Ogate.The 18O gate also contained events from the other decay modes which needed to be accounted for in the branchingratio determination. Considering a single excitation and a single decay mode, the fraction of events outside of the 18Ogate was calculated from the Monte Carlo simulations using the relationshipf =Nsimtot − NsimgateNsimtot, (5)where Nsimtot is the total number of simulated events and Nsimgate is the number of these events in 18O the gate.Using this fraction, the total number of erroneous events in the 18O gate, Ngate, belonging to this decay mode wasdetermined from the number of events in the γ-removed Catania plot, Ncat, byNgate =Ncatf− Ncat. (6)Hence, Ngate was hence subtracted for each state in the 18O-gated excitation spectrum, leaving only true γ decay eventsonce this process was done for all decay modes. The γ decay branching ratio was then established for each state.Excitation Energy (keV)6500 7000 7500 8000 8500 9000Counts/20 keV050100150200250300350+7155 keV 4_7619 keV 1_7702 keV 2_7855 keV 5) +/4 _7969 keV (3 +8214 keV 2_8284 keV 38508 keV+7796 keV 0(a)Excitation energy (keV)6500 7000 7500 8000 8500 9000Counts/20 keV020406080100120140160+7155 keV 4_7619 keV 1_7702 keV 2) +/4 _7969 keV (3_7855 keV 5 +8214 keV 2_8284 keV 38508 keV(b)FIGURE 5: A comparison of the total excitation spectrum produced centered at 7500 keV (a) with the excitationspectrum produced when gating on DSSD array hits in the 18O gate (b). States that are likely to γ decay are shown inred, due to low barrier penetrability in the case of the 7.115 MeV state and the unnatural parity of the 7.770 MeV and7.969 MeV states, which are below the n threshold of 8.045 MeV. Enhancements of these states relative to the stateslabelled in blue can be observed in (b).CONCLUSIONThe experimental method for measuring the branching ratios of excited states in 18O has been discussed, includinga technique that allows for the measurement of the γ decay branching ratio through the use of a DSSD array solelydetecting charged particles. States which are expected to γ decay due to their spin-parity and excitation energy relativeto decay thresholds have been investigated through use of Monte Carlo simulations and found to match observedfeatures in experimental data Catania plots, which can then be removed and hence accurate determination of bothmassive particle decay and γ decay branching ratios achieved.ACKNOWLEDGMENTSThe authors would like to thank Andy Bergmaier for his help loaning equipment during the set-up of the experiment, aswell as the operators of the tandem Van de Graaff accelerator at the Maier-Leibnitz Laboratory in Munich for providingand maintaining the 7Li beam. This work was funded by the UK Science and Technology Facilities Council (STFC)under Grant No. ST/L005751/1 and from the European Unions Horizon 2020 research and innovation programmeunder the Marie Skłodowska-Curie Grant Agreement No. 65F9744.REFERENCES[1] M. Freer, Rep. Prog. Phys 70, 2149–2210 (2007).[2] B. Fulton, Contemp. Phys 40(5), 299–311 (1999).[3] W. von Oertzen et al., Eur. Phys. J. A 11, 403–411 (2001).[4] J. Hiura et al., Progr. Theor. Phys 42, 555–580 (1969).[5] W. von Oertzen et al., Eur. Phys. J. A 43, 17–33 (2010).[6] H.-F. Wirth, Ph.D. thesis, Technischen Universita¨t, Mu¨nchen 2001.[7] H.-F. Wirth et al., Beschleuniger Laboratorium Munchen, Annual Report (unpublished), p. 71 (2000).[8] C. Wheldon et al., Phys. Rev. C 83, 2503–2504 (2011).[9] N. Curtis et al., Phys. Rev. C 51, 1554–1557 (1995).[10] N. Curtis et al., Phys. Rev. C 53, 1804–1810 (1996).[11] N. Curtis et al., Phys. Rev. C 66, 024315:1–10 (2002).[12] H. Fortune, Phys. Rev. C 18, p. 1053 (1978).[13] K. Artemov, Sov. J. Nucl. Phys. 37, p. 805 (1983).[14] G. Morgan, Nucl. Phys. A 148, p. 480 (1970).

English

Sheffield Hallam University Research Archive

A method to determine γ branching ratios using charged particle detectors for states in 18OPIRRIE, S., KOKALOVA, Tz, WHELDON, C., BAILEY, S., BISHOP, J., CURTIS, N., SMITH, Robin <http://orcid.org/0000-0002-9671-8599>, TORRESI, D., TURNER, A., HERTENBERGER, R., WIRTH, H-F, FAESTERMANN, Th, MENGONI, D. and DELL’AQUILA, D.Available from Sheffield Hallam University Research Archive (SHURA) at:http://shura.shu.ac.uk/23424/This document is the author deposited version.  You are advised to consult the publisher's version if you wish to cite from it.Published versionPIRRIE, S., KOKALOVA, Tz, WHELDON, C., BAILEY, S., BISHOP, J., CURTIS, N., SMITH, Robin, TORRESI, D., TURNER, A., HERTENBERGER, R., WIRTH, H-F, FAESTERMANN, Th, MENGONI, D. and DELL’AQUILA, D. (2018). A method to determine γ branching ratios using charged particle detectors for states in 18O. In: PEDAPATI, Srinivasa Rao, SOON, William Pao King, NASIF, Mohammad Shakir, YA, Handan, SULAIMAN, Shaharin Anwar B and MAMAT, Othman B, (eds.) 6th International Conference on Production, Energy and Reliability 2018: World Engineering Science & Technology Congress (ESTCON). AIP Conference Proceedings (2035). AIP. Copyright and re-use policySee http://shura.shu.ac.uk/information.htmlSheffield Hallam University Research Archivehttp://shura.shu.ac.ukA method to determine γ branching ratios using charged particle detectors for states in18OS. Pirrie, Tz. Kokalova, C. Wheldon, S. Bailey, J. Bishop, N. Curtis, R. Smith, D. Torresi, A. Turner, R.Hertenberger, H.-F. Wirth, Th. Faestermann, D. Mengoni, and D. Dell’AquilaCitation: AIP Conference Proceedings 2038, 020037 (2018); doi: 10.1063/1.5078856View online: https://doi.org/10.1063/1.5078856View Table of Contents: http://aip.scitation.org/toc/apc/2038/1Published by the American Institute of PhysicsArticles you may be interested inAn improved upper limit on the direct 3α decay of the Hoyle stateAIP Conference Proceedings 2038, 020035 (2018); 10.1063/1.5078854Enhanced 3α radius in 12C probed by nuclear reactionsAIP Conference Proceedings 2038, 020016 (2018); 10.1063/1.5078835Evidence for resonances in the 7α disassembly of 28SiAIP Conference Proceedings 2038, 020021 (2018); 10.1063/1.5078840C-burning at astrophysical energies via the Trojan Horse MethodAIP Conference Proceedings 2038, 020012 (2018); 10.1063/1.5078831Some lessons from invariant mass spectroscopy about light nucleiAIP Conference Proceedings 2038, 020025 (2018); 10.1063/1.5078844Resonance reactions at Astana cyclotronAIP Conference Proceedings 2038, 020030 (2018); 10.1063/1.5078849A method to determine γ branching ratios using chargedparticle detectors for states in 18OS. Pirrie1,a),∗, Tz. Kokalova1, C. Wheldon1, S. Bailey1, J. Bishop1, N. Curtis1,R. Smith1, D. Torresi1, A. Turner1, R. Hertenberger2, H.-F. Wirth2,Th. Faestermann3, D. Mengoni4 and D. Dell’Aquila51School of Physics and Astronomy, University of Birmingham, Edgbaston Park Rd, Birmingham, UK, B15 2TT2Fakulta¨t fu¨r Physik, Ludwig-Maximilians-Universita¨t Mu¨nchen, D-85748 Garching, Germany3Physik Department, Technische Universita¨t Mu¨nchen, D-85748 Garching, Germany4Universita` degli Studi di Padova, Via 8 Febbraio 1848, 2, 35122 Padova PD, Italy5Universita` degli Studi di Napoli Fedorico II, Corso Umberto I, 40, 80138 Napoli NA, Italya)Corresponding author: S.Pirrie@PGR.bham.ac.ukAbstract. A series of proposed bands in 18O with potential nuclear molecular structures, such as 14C⊗α or 12C⊗2n⊗α, are being investigated. This was done through the use of the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory inMunich in conjunction with an array of double-sided silicon strip detectors (DSSDs). These detectors allowed for high resolutionreconstruction of detected particles, enabling measurement of the branching ratios of the states that make up these bands. Here, amethod is discussed for extracting the branching ratios of both material particles as well as γ-particles using the DSSD array todetect only charged decay fragments.INTRODUCTIONNuclear clustering is a well-established phenomenon observed in several nuclei, but the most common of these arelight, even N = Z nuclei [1] [2]. Clustering, however, is proposed to occur in many nuclei that are not purely alpha-conjugate. The addition of a pair of neutrons to the system can decrease the required threshold for an alpha particle toform in the nucleus, as in the case with 16O (7.16 MeV threshold for a 12C⊗α structure) going to 18O (6.23 MeVthreshold for a 14C⊗α structure).An excellent contender for the observation of cluster structure is 18O, particularly a core + alpha description dueto the properties of both the α and 14C nucleus. Like 16O (a cluster core observed most clearly in the core + alphadescription of 20Ne [3][4]), 14C has a closed p-shell and its first excited state lies at around 6 MeV, lending morecredence to the notion of a 14C⊗α configuration in 18O.An experiment performed at the Maier-Leibnitz Laboratory (MLL) of the Technical University and Ludwig-Maximillan University in Munich by W. von Oertzen et al. found 30 previously unobserved states in 18O [5]. Usingthese and previously measured states, rotational bands with different nucleon configurations were proposed. Thestates that make up these proposed rotational bands are shown in TABLE 1. As these proposed bands, each with anassociated positive and negative parity due to signature splitting, have a cluster structure, with the Kpi = 0+/−2 proposedto have a 14C⊗α structure and the kpi = 0+/−4 proposed to have a14C⊗α structure, the associated partial α decaywidths of the composite states can be used to confirm or refute the existence of each band as levels built upon thesame configuration should have similar decay properties.∗Work supported by STFC (UK)Proceedings of the 4th International Workshop on “State of the Art in Nuclear Cluster Physics” (SOTANCP4)AIP Conf. Proc. 2038, 020037-1–020037-6; https://doi.org/10.1063/1.5078856Published by AIP Publishing. 978-0-7354-1764-9/$30.00020037-1TABLE 1: The preliminary measured excitation energies and FWHMs of states in the proposed rotational bandscompared to the literature values for the excitation energies and widths from Ref. [5]. Spins and parities that wereassigned based on fitting the rotational properties are shown in brackets, and states with a small cross-section (<2µb/sr) with an asterisk (*). The resolution of the focal plane varied across its length and was determined for theground state (measured FWHM of 86(5) keV) and the 1st excited state (measured FWHM of 76(3) keV), measuredat separate ends of the focal plane detector. Unmeasured states lay outside of the excitation regions investigated.Kpi = 0+2 Kpi = 0−2Ex(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitEx(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitunmeasured 3.558(4) - 0+ 8.037(1)∗ 93(19) 8.035(5) <10 1−unmeasured 5.254(5) - 2+ 9.737(4) 118(7) 9.715(5) 15(4) (3−)7.114(1) 80 (2) 7.115(4) - 4+ 13.617(3) - 13.624(6) 22(7) (5−)11.716(4) 95 (11) 11.702(6) 27 6+ unmeasured 18.630(10) 100(20) (7−)unmeasured 18.058(8) 83 8+*Kpi = 0+4 Kpi = 0−4Ex(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLitEx(MeV)FWHM(keV)Ex,Lit(MeV)ΓLit(keV) JpiLit7.798(1)∗ - 7.796(5) <10 0+ 10.595(4) 105(7) 10.59(1) 70(16) (1−)8.217(1) 66(3) 8.216(4) <10 2+ 10.937(4) 99(6) 10.92(1) 30(9) (3−)10.297(5) 84(5) 10.293(4) 23(8) 4+ 13.827(3) 80(4) 13.82(2) 27(8) (5−)12.559(1) 114(7) 12.557(6) 22(8) 6+ unmeasured 16.99(1) 50(12) (7−)unmeasured 15.810(10) 20(8) (8+) unmeasured 20.28(3) 120(21) (9−)unmeasured 20.385(15) 155(25) (10+)EXPERIMENTAL METHODA subsequent experiment was performed, also at MLL Munich, to determine the branching ratios of the high-energyexcited states in 18O and hence extract their partial α decay widths. The reaction chosen to populate states in 18O was12C(7Li,p)18O∗ (Q0 = +8.401 MeV) as this reaction, used by von Oertzen et al., was known to be well-populated. The15 MV tandem Van de Graaff accelerator at MLL was used to produce a 44 MeV 7Li beam. The Q3D spectrograph wasset at an angle of −39◦ in the horizontal beam plane, with an angular acceptance of ±3◦ in x (horizontal) and ±2◦ in y(vertical). The Birmingham array of 50 mm by 50 mm, 500 µm thick double-sided silicon strip detectors (DSSDs) wasused in conjunction with the Q3D spectrograph in order to extract both energy and momentum information, allowingfor high-resolution reconstruction. The experimental set-up and DSSD array are depicted in FIGURE 1.The Q3D spectrograph was configured to allow for the detection of the resulting protons from the reaction. TheQ3D consists of a scintillator for measuring the energy of an incident particle, two upstream horizontal wires in a gasvolume for measuring the energy loss and a 255 strip cathode foil for measuring the position of incident particles [6].Using the information from the scintillator and the horizontal wires, particle identification was achieved and henceproton-only events were selected. The energy of the proton is obtained from the detected position at the focal plane[7] and enables an excitation spectrum for 18O to be produced. An example of this is shown later in FIGURE 5. Itshould be noted that the position of the proton at the focal plane was independent of the angle at which it entered theQ3D. The corresponding 18O or its decay products would then, in the majority of cases, be detected by the DSSDarray, which had a total angular coverage of 14◦ to 92◦ in-plane, and −36◦ to 40◦ out-of-plane. When an event wasregistered in the Q3D, all events in the ADC channels of the DSSDs were read out, allowing for events with Q3D andDSSD coincidences as well as Q3D-only events.RESULTSAs the particles incident on the DSSDs were not directly identified, a technique to identify a detected particle-speciesbased on its energy and momentum was adopted. In the break-up of 18O∗ into particles A and B, using events with asingle hit in the DSSD array (for example, a detection of A), the momentum of the undetected B can be reconstructed:020037-2(a) (b)FIGURE 1: Diagrams illustrating the experimental set-up used at MLL. The plan view in the chamber is shown in (a),while the double-sided silicon strip detector (DSSD) array is shown in more detail in (b). The in-plane center angle ofdetectors 1 and 2 was +28±1◦ and for detectors 3 and 4 was +67±1◦. The out-of-plane center angles of detectors 1-4were +21±1◦, −15±1◦, +25±1◦ and −18±1◦ respectively.~pB = ~pbeam − ~pQ3D − ~pA, (1)where ~pA is the momentum of the particle detected in the DSSD array, ~pbeam is the momentum of the beam particle and~pQ3D is the momentum of the proton detected at the Q3D focal plane [8]. The momentum in each Cartesian directioncan be calculated using the angles of detection of any detected particles in conjunction with their energies and masses.Using particle A as an example:pA =√2EAmA, (2)pAx = pA sin θx cos θy,pAy = pA sin θy andpAz = pA cos θx cos θy,with θx and θy being the angles of detection in-plane and out-of-plane respectively. In order to calculate the totalmomentum of the detected particle, the mass (mA) must be assumed.Using this information, the total momentum of the missing particle can then be substituted into the Q valueexpression for the 12C(7Li,p)A+B reaction,Q = EA + EQ3D +p2B2mB− Ebeam, (3)where the energy of particle B has been related to its momentum by EB =p2B2mB. Rearranging this to be in the formy = mx + c gives the following expression,Ebeam − EA − EQ3D =p2B2mB− Q, (4)which allows the calculated value of p2B2 to be plotted against the measured value of Ebeam − EA − EQ3D, generatinga locus with a gradient of 1/mB and a y-intercept of −Q if the correct assumption has been made regarding the massof the particle in Equation 2. If a detected particle does not have the same mass as the one assumed, the associatedlocus will not lie on the line described by this gradient and y-intercept. Such a diagram is known as a Catania plot,and FIGURE 2 shows a labeled example.020037-3(a) (b)FIGURE 2: A comparison of experimental (a) and simulated (b) data plotted on a Catania plot. The simulated datawere produced using Resolution8.1 [9][10], an in-house Monte Carlo simulation package, and contain 2 types ofbreak-up: 12C(7Li,p)α+14C (Q = +2.173 MeV) and 12C(7Li,p)n+17O (Q = +0.355 MeV). The momenta for all parti-cles detected in the DSSD were calculated assuming they were 14C, allowing correct events to lie on the locus definedby the red line with y-intercept = −Q = −2.173 MeV and gradient = 1mα . Incorrect assumption of the particle masscause the other visible loci to arise, but these are still distinct from one another and allow for particle identificationwhen compared with simulation.(a) (b)FIGURE 3: A comparison of simulated data (a) and experimental data (b), scaled to show low reconstructed energyevents, which demonstrates the agreement between the simulation of the 7.115 MeV 4+ state in 18O decaying to the6.404 MeV 3− state and the 7.969 MeV state 3+/4− photon decaying to the 6.880 MeV 0− state (both highlighted inblack ellipses). The simulation includes the decay modes mentioned in FIGURE 2, which are labelled in both (a) and(b) and can be seen to be in good agreement.Photon EventsStates that have a significant γ decay branch, such as unnatural parity states below the n decay threshold (8.045 MeV),will also be present on a Catania plot, but due to the small amount of momentum taken by the photon the loci formedby γ decay events will contaminate other loci from massive particle decay with a large variability depending on the γ-ray energy of the associated decay. As one of the excitation regimes investigated in this analysis was centered around020037-4(a) (b)FIGURE 4: Two-dimensional plots showing the number of events hitting each pixel of the detector, with eventssmeared randomly across the area of the pixel (9 mm2). Experimental data are shown in (a) while simulated data areshown in (b). The region in the center of the Gaussian profiles with the largest number of counts is largely formedby the focused nature of the 18O distribution, which is confirmed using the simulation to identify features. The pixelcenters of the detectors of the detectors are shown by the grid of points for both experimental and simulated data.7500 keV, several states might be expected to decay via photon emission. An example of this contamination can beseen in FIGURE 3, along with simulation comparisons using two states (7.115 MeV and 7.969 MeV) which matchwell to the observed features in the data.As the γ events prevent gating on the loci formed due to massive particles, they must be removed in order toestablish branching ratios for the various decay modes. This can be achieved through plotting the in-plane and out-of-plane Cartesian angles for detections in the DSSD array on a 2D histogram and observing the Gaussian distributionsdue to each particle, as shown in FIGURE 4. The momentum of an 18O nucleus detected in the DSSD array is largelydefined by the momentum of the proton detected at the focal plane (as the photon takes very little), which resultsin a very small Gaussian distribution for 18O relative to other similar particles which share momentum with massivedecay products, such as 17O with the n. Thus, by putting a gate around the possible 18O detection region, which wasconfirmed through comparison with Monte Carlo simulation, γ events were removed from the Catania plot to facilitateaccurate measurement of the branching ratios for each decay mode. FIGURE 5 shows the comparison of the totalexcitation spectrum to that formed when looking at Q3D events coincident with a hit in the DSSD array inside the 18Ogate.The 18O gate also contained events from the other decay modes which needed to be accounted for in the branchingratio determination. Considering a single excitation and a single decay mode, the fraction of events outside of the 18Ogate was calculated from the Monte Carlo simulations using the relationshipf =Nsimtot − NsimgateNsimtot, (5)where Nsimtot is the total number of simulated events and Nsimgate is the number of these events in 18O the gate.Using this fraction, the total number of erroneous events in the 18O gate, Ngate, belonging to this decay mode wasdetermined from the number of events in the γ-removed Catania plot, Ncat, byNgate =Ncatf− Ncat. (6)Hence, Ngate was hence subtracted for each state in the 18O-gated excitation spectrum, leaving only true γ decay eventsonce this process was done for all decay modes. The γ decay branching ratio was then established for each state.020037-5Excitation Energy (keV)6500 7000 7500 8000 8500 9000Counts/20 keV050100150200250300350+7155 keV 4_7619 keV 1_7702 keV 2_7855 keV 5) +/4 _7969 keV (3 +8214 keV 2_8284 keV 38508 keV+7796 keV 0(a)Excitation energy (keV)6500 7000 7500 8000 8500 9000Counts/20 keV020406080100120140160+7155 keV 4_7619 keV 1_7702 keV 2) +/4 _7969 keV (3_7855 keV 5 +8214 keV 2_8284 keV 38508 keV(b)FIGURE 5: A comparison of the total excitation spectrum produced centered at 7500 keV (a) with the excitationspectrum produced when gating on DSSD array hits in the 18O gate (b). States that are likely to γ decay are shown inred, due to low barrier penetrability in the case of the 7.115 MeV state and the unnatural parity of the 7.770 MeV and7.969 MeV states, which are below the n threshold of 8.045 MeV. Enhancements of these states relative to the stateslabelled in blue can be observed in (b).CONCLUSIONThe experimental method for measuring the branching ratios of excited states in 18O has been discussed, includinga technique that allows for the measurement of the γ decay branching ratio through the use of a DSSD array solelydetecting charged particles. States which are expected to γ decay due to their spin-parity and excitation energy relativeto decay thresholds have been investigated through use of Monte Carlo simulations and found to match observedfeatures in experimental data Catania plots, which can then be removed and hence accurate determination of bothmassive particle decay and γ decay branching ratios achieved.ACKNOWLEDGMENTSThe authors would like to thank Andy Bergmaier for his help loaning equipment during the set-up of the experiment, aswell as the operators of the tandem Van de Graaff accelerator at the Maier-Leibnitz Laboratory in Munich for providingand maintaining the 7Li beam. This work was funded by the UK Science and Technology Facilities Council (STFC)under Grant No. ST/L005751/1 and from the European Unions Horizon 2020 research and innovation programmeunder the Marie Skłodowska-Curie Grant Agreement No. 65F9744.REFERENCES[1] M. Freer, Rep. Prog. Phys 70, 2149–2210 (2007).[2] B. Fulton, Contemp. Phys 40(5), 299–311 (1999).[3] W. von Oertzen et al., Eur. Phys. J. A 11, 403–411 (2001).[4] J. Hiura et al., Progr. Theor. Phys 42, 555–580 (1969).[5] W. von Oertzen et al., Eur. Phys. J. A 43, 17–33 (2010).[6] H.-F. Wirth, Ph.D. thesis, Technischen Universita¨t, Mu¨nchen 2001.[7] H.-F. Wirth et al., Beschleuniger Laboratorium Munchen, Annual Report (unpublished), p. 71 (2000).[8] C. Wheldon et al., Phys. Rev. C 83, 2503–2504 (2011).[9] N. Curtis et al., Phys. Rev. C 51, 1554–1557 (1995).[10] N. Curtis et al., Phys. Rev. C 53, 1804–1810 (1996).[11] N. Curtis et al., Phys. Rev. C 66, 024315:1–10 (2002).[12] H. Fortune, Phys. Rev. C 18, p. 1053 (1978).[13] K. Artemov, Sov. J. Nucl. Phys. 37, p. 805 (1983).[14] G. Morgan, Nucl. Phys. A 148, p. 480 (1970).020037-6

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A method to determine γ branching ratios using charged particle detectors for states in 18O

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