A Measurement of Atomic X-ray Yields in Exotic Atoms and Implications for an Antideuteron-Based Dark Matter Search
T. Aramaki, S. K. Chan, W. W. Craig, L. Fabris, F. Gahbauer, C. J. Hailey, J. E. Koglin, N. Madden, K. Mori, H. T. Yu, K. P. Ziock
AA Measurement of Atomic X-ray Yields in Exotic Atoms and Implications for anAntideuteron-Based Dark Matter Search
T. Aramaki a , S. K. Chan a , W. W. Craig b , L. Fabris b , F. Gahbauer a , C. J. Hailey a , J. E. Koglin a , N. Madden b , K.Mori a , H. T. Yu a , K. P. Ziock b a Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA b Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
Abstract
The General AntiParticle Spectrometer (GAPS) is a novel approach for the indirect dark matter search that exploitscosmic antideuterons. GAPS utilizes a distinctive detection method using atomic X-rays and charged particles fromthe exotic atom as well as the timing, stopping range and dE / dX energy deposit of the incoming particle, whichprovides excellent antideuteron identification. In anticipation of a future balloon experiment, an accelerator test wasconducted in 2004 and 2005 at KEK, Japan, in order to prove the concept and to precisely measure the X-ray yieldsof antiprotonic exotic atoms formed with di ff erent target materials [1]. The X-ray yields of the exotic atoms withAl and S targets were obtained as ∼ / ISAS balloon facility in Hokkaido, Japan in summer 2012 [4, 5] and a proposed GAPSscience flight is to fly from Antarctica in the austral summer of 2017-2018.
Keywords:
Dark Matter; Antiparticle; antideuteron; Exotic atom; GAPS
1. Introduction
The General AntiParticle Spectrometer (GAPS) is anovel approach for an indirect dark matter search thatexploits cosmic antideuterons. Since the GAPS projectutilizes atomic X-rays of exotic atoms to identify an-tideuterons (see Section 1.4), an accelerator test wasconducted in 2004 and 2005 at KEK, Japan, in orderto prove the concept and to precisely measure the X-rayyields of antiprotonic exotic atoms formed with di ff er-ent target materials [1]. This paper describes not onlythe detailed analysis for the X-ray yields for antipro-tonic exotic atoms (Section 3), but also the developmentof a comprehensive cascade model for the exotic atom Email address: [email protected] (T. Aramaki) (Section 2). The cascade model was compared and val-idated with other experimental data and cascade modelsfor muonic and antiprotonic exotic atoms. The resultsfor the accelerator test were used to estimate the X-ray yields for antideuteronic exotic atoms in the GAPSflight experiment. The subsequent GAPS antideuteronsensitivity [3] indicates that the GAPS project has astrong potential to detect antideuterons as a dark mat-ter signature.
The recent result by the Planck experiment [6] showsthat 68% of our universe is composed of dark energy,and 27% is dark matter ( ∼
5% for baryonic matter). Thenature and origin of these phenomena, however, are stillunknown, and thus are the great cosmological problemsof the 21st century. Unlike dark energy, dark matter iswell-motivated by many theoretical models, and many
Preprint submitted to Astroparticle Physics September 26, 2018 a r X i v : . [ a s t r o - ph . I M ] A ug xperiments are currently being conducted to determinethe origin of dark matter.The existence of dark matter was postulated by FritzZwicky in 1933 from the observation of the rotationalspeed of galaxies. The recent observations of gravita-tional lensing in the Bullet Cluster (two colliding clus-ters of galaxies), also indicate the existence of dark mat-ter [7].Since dark matter has never been directly observed,it is considered to interact with the Standard Modelparticles only by the weak force and the gravitationalforce as seen in rotational curves and gravitational lens-ing. The small density fluctuations seen in the cos-mic microwave background (CMB) [8] and the largescale structure of the present universe indicate that darkmatter should be a non-relativistic and massive parti-cle (called cold dark matter). Moreover, it should bestable on a cosmological time scale to be observed inthe present universe. Weakly interacting massive parti-cles (WIMPs) are the theoretically best-motivated can-didates among the variety of dark matter candidates.Neutralinos, the lightest supersymmetric partner (LSP)in supersymmetric theories, and Kaluza-Klein particles(LKP) and right-handed neutrinos (LZP) in extra di-mension theories are examples of popular WIMP can-didates. There are dozens of experiments designed to searchfor particles associated with various manifestations ofWIMP dark matter categorized into three types, parti-cle collider, direct search, and indirect search. The di-rect and indirect searches will measure the relic WIMPs,while the particle collider will try to create WIMPs.The direct search measures the recoil energy of a tar-get atom in the detector induced by the interactionwith the WIMP, while the indirect search focuses onWIMP-WIMP annihilation products such as electrons,positrons, gamma rays, antiprotons and antideuterons.The detection methods and the background models foreach search are di ff erent, but also complementary, help-ing to illuminate the nature of dark matter.Antideuteron production in WIMP-WIMP annihila-tions was proposed by Donato et al., in 2000 [9, 10].The antideuteron flux due to WIMP-WIMP annihila-tion (called primary flux) can be estimated based on thedark matter density profile of the galaxy, the WIMP-WIMP annihilation channel, the hadronization and co-alescence model, and the propagation model. The pri-mary antideuteron flux at the top of the atmosphere dueto the WIMP-WIMP annihilation is shown in Figure1 (solid purple line: LSP with m χ ∼
100 GeV, dashed green line: LKP with m χ ∼
500 GeV, dashed blue line:LZP with m χ ∼
40 GeV) [11]. The relatively flat peakis located at E ∼ / n. The antideuteron fluxdue to the cosmic-ray interactions with the interstel-lar medium (secondary / tertiary flux, red dashed line) isalso shown in Figure 1 [12, 13, 14]. Unlike primaryantideuterons, collision kinematics suppress the forma-tion of low-energy secondary antideuterons. Moreover,the interaction rate is drastically decreased at high en-ergy since the flux of the cosmic-ray protons followsthe power law, F p ∼ E − . . Therefore, the primary an-tideuteron flux is two orders of magnitude larger thanthe secondary / tertiary antideuteron flux at low energy,and we can clearly distinguish them. LDB+ ! Secondary/Tertiary LZP (m χ = 40 GeV) ! LSP (m χ = 100 GeV) ! LKP (m χ = 500 GeV) ! Kinetic Energy per Nucleon [GeV/n] ! ! ! ! ! -7 ! -5 -3 -10 ! -8 ! -6 -4 -9 ! A n ti d e u t e r on F l ux [ m - s - s r - ( G e V / n ) - ] ! AMS AMS BESS limit ! LDB ! GAPS ! Figure 1: Antideuteron flux at the top of the atmosphere, comparedwith the BESS upper limit [15], and GAPS and AMS sensitivity [3].The flight altitude for GAPS and BESS is ∼ / tertiary flux due to the cosmic-ray interactions [12, 13,14]. The GAPS and AMS (5 year flight) sensitivities [3],and the current upper limit for the antideuteron flux ob-tained by the BESS experiment [15] are also shown inFigure 1. The flight altitude for GAPS and BESS is ∼ ∼ / cm atmospheric depth), while AMSis on the International Space Station (ISS). As seen inthe figure, the GAPS experiment is more than two or-der of magnitude more sensitive than the BESS upperlimit and 1.5 times more sensitive than the AMS satel-lite mission. (The sensitivity for a GAPS 210 day flightprogram (LDB + ) is also shown in the figure.) Thus,GAPS has a strong potential to detect antideuterons asthe dark matter signature. In the following section, thedetails of the GAPS project are introduced including the2etection concept and the instrumental design. The GAPS project was first proposed in 2002 andwas originally named the Gaseous AntiParticle Spec-trometer [2, 17]. The original GAPS was designed touse a gaseous target, but with further studies, includ-ing the KEK (high energy accelerator research organiza-tion) beam test in Japan described below, we concludedthat a solid target was more e ffi cient and e ff ective for theflight experiment. GAPS is a balloon-borne experiment(flight altitude ∼
35 km), and there are constraints onthe size and mass of the payload. Therefore, the solidtarget can greatly simplify the setup of the GAPS flightmodule by removing the bulky gas handling system andallowing more complex designs, such as a multi-layertracker geometry. The higher density of the solid tar-get can also easily slow down and stop more incomingantiparticles, which provides a larger detectable energyrange. A GAPS prototype flight (pGAPS) was launchedsuccessfully from the JAXA / ISAS balloon facility inHokkaido, Japan in the summer of 2012 [4, 5], and aproposed GAPS science flight is to fly from Antarcticain the austral summer of 2017-2018.
The GAPS detection method involves capturing an-tiparticles into a target material with the subsequentformation of an excited exotic atom. A time-of-flight(TOF) system measures the velocity (energy) and di-rection of an incoming antiparticle. It slows down bythe dE / dX energy loss and stops in the target material,forming an excited exotic atom. The exotic atom de-excites in a complex process involving Auger ionizationand electron refilling at high quantum number states,followed by the emission of X-rays at the lower quan-tum states (see Section 2). With known atomic num-ber of the target, the Bohr formula for the X-ray energyuniquely determines the mass of the captured antiparti-cle [2]. Ultimately, the antiparticle is captured by thenucleus in the atom, where it is annihilated with theemission of pions and protons. The number of pionsand protons produced by the nuclear annihilation is ap-proximately proportional to the number of antinucleons,which provides an additional discriminant to identifythe incoming antiparticle. The concept of the detectiontechnique has been verified through the accelerator test-ing at KEK in 2004 and 2005, as described in Section3. + "π , " π , " π , "π + "p" p" π , "π + "π , " 107"keV"58"keV"35"keV"p" d"_" p"_" Si(Li)"Layer" θ" θ" ! " " Si " " " _"d "Exo6c"Atom" Si(Li)"Detector" Figure 2: The schematic view of the GAPS detector and the detec-tion method. An antiparticle slows down and stops in the Si(Li) tar-get forming an exotic atom. The atomic X-rays will be emitted as itde-excites followed by the pion and proton emission in the nuclearannihilation. The antideuteron identification method from antiprotonsis also shown in the schematic view.
Antiprotons are the major background in this exper-iment, since they can also form exotic atoms and pro-duce atomic X-rays and charged particles. However,the atomic X-rays and the number of pions and pro-tons emitted from the exotic atom uniquely identify themass of the original antiparticle, as do the depth sensing(stopping range of the incoming particle) and the dE / dXenergy loss in each Si(Li) detector, once the velocityof the incoming antiparticle is determined by the TOFsystem. The three highest antideuteronic X-rays witha Si target in the GAPS detectable energy range are 67keV, 44 keV and 30 keV, while antiprotonic X-rays are107 keV, 58 keV, and 35 keV. The number of chargedparticles produced by the nuclear annihilation for theantideuteronic exotic atom is approximately twice aslarge as the one for the antiprotonic exotic atom. Ad-ditionally, antideuterons with the same speed have alonger stopping range and can go deeper into the detec-tor than antiprotons. Thus, antideuterons with the samestopping range will have a smaller velocity and depositmore energy at each layer than antiprotons, since thedE / dX energy loss is inversely proportional to the ve-locity squared at low energy. As a result, these detectionmethods provide an excellent antideuteron identification[3]. The detection concept and the particle identificationmethod in the GAPS project are shown in Figure 2.3 .4.3. Instrumental Design The GAPS balloon flight instrument will have a verylarge, pixellated Si(Li) detector surrounded by a verylarge TOF system without a pressure vessel as shownin Figure 2. There will be 10 layers of detectors sur-rounded by TOF plastic scintillators, with each layercomposed of 4 inch diameter, 2.5 mm thick Si(Li) de-tectors. Each Si(Li) detector will be segmented into4 strips, and adjacent tracking layers will have theirstrips positioned orthogonally, providing modest three-dimensional particle tracking. The tracking geometrycan count the number of particles produced in the nu-clear annihilation and separately identify atomic X-raysfrom particle tracks. It also permits direct measurementof particle stopping depth and naturally conforms to themulti-detector geometry. Since each strip is relativelysmall, ∼ ∼
20 cm,X-rays and charged particles (pions / protons) can be de-tected separately in the di ff erent strips / channels [18].Each Si(Li) layer also works as a degrader and a tar-get material to slow down the incoming antiparticle andto form an exotic atom. Note that since KEK accelera-tor test focused on the X-ray yields for the antiprotonicexotic atoms, the instrumental setup was di ff erent fromthe one in the GAPS flight instrument as described inSection 3.
2. Cascade Model for Exotic Atoms
As seen in the previous section, X-ray yields of ex-otic atoms play an important role in the GAPS an-tideuteron detection. The energy of the atomic X-rayis unique to the exotic atom, allowing us to di ff eren-tiate antideuterons from other particles, including an-tiprotons. Therefore, it is crucial to develop a compre-hensive cascade model to estimate the X-ray yields forany kind of exotic atom (any negatively charged cascad-ing particles with any target materials) that can form inthe GAPS instrument.Cascade models for exotic atoms were widely devel-oped after the existence of the exotic atom was predictedin the 1940s. Since the GAPS project focuses on the an-tiprotonic and antideuteronic exotic atoms formed witha variety of target materials, we have developed a gen-eralized and extendable cascade model. Additionally,since the GAPS detector is designed for X-rays withan energy higher than 10 keV, a very simple cascademodel with a few parameters has been developed, fo-cusing on the low n state transitions (E >
10 keV). The parameters were optimized by the measurement of an-tiprotonic exotic atoms with Al and S targets at KEKin Japan 2005. The extended cascade model was usedto estimate the X-ray yields of the antiprotonic and an-tideuteronic exotic atom with a Si target and other ma-terials in the GAPS instrument to derive the ultimateantideuteron sensitivity (see Section 3).
A negatively charged particle ( µ − , π − , K − , ¯ p , ¯ d , etc.,called ”cascader” hereafter) will be captured into a tar-get atom at the radius of its outermost electrons after itslows down and its kinetic energy becomes comparableto the binding energy of an electron [19, 20]. The ini-tial principal quantum number for the exotic atom canbe estimated as follows: n ∼ n e (cid:112) M ∗ / m ∗ e . Here, n e is the principal quantum number of the out-ermost electron shell of the target atom, m ∗ e is the re-duced mass of the electron in the target atom and M ∗ isthe reduced mass of the cascader. The cascade modelis designed to calculate the probability for the cascaderto be in the ( n , l ) state, where l is the orbital angularmomentum, and to estimate the X-ray yields of the ex-otic atom as it decays. The cascade model starts at theelectron K shell ( n e =
1) and the orbital angular mo-mentum l is assumed to have a statistical distribution, P l ∝ (2 l + e al . There are (2 l +
1) magnetic quantumnumbers, m = − l + , − l + ... ... l − , l −
1, for each l , and e al is a correction factor due to the de-excitationat the outer shell, n e > a ∼ . n in the cascade model is about 14 for µ − , 16 for π − , 31 for K − , 42 for ¯ p , and 58 for ¯ d .The three leading de-excitation processes, Augertransition (emission of an Auger electron), radiativetransition (emission of an atomic X-ray), and nuclearcapture (interaction with the nucleus), dominate the cas-cade model for atoms with Z >
2, as shown in Figure 3.Auger transitions dominate at the beginning of the cas-cade, followed by radiative transitions. The nuclear cap-ture takes place in a very low n state. Since the exoticatom can be assumed to be hydrogen-like, the Augerand the radiative transitions with ∆ l = ± In a high n state, an Auger electron is emitted as soonas the energy di ff erence of the initial state ( n , l ) andthe final state ( n , l ) exceeds the ionization energy. The4 =42n=41n=40n=11n=10n=9n=8n=7n=6n=5n=4n=3n=2n=1 l=0 l=1 l=2 l=41 Auger TransitionRadiative TransitionNuclear CaptureNucleus
Figure 3: The schematic view of the cascade model of the antiprotonicexotic atom. The Auger transitions dominate in high n states, whilethe radiative transitions dominate in low n states. The nuclear capturetakes place in very low n states. Auger transition rate for the K shell and L shell elec-trons can be estimated by considering the interactionbetween the cascader and the electron as follows [21]. Γ Aug , Kn , l → n , l = πα ca µ (cid:32) Z ∗ Z (cid:33) max( l , l )3(2 l + · y + y exp[ y (4 arctan y − π )]sinh π y I Γ Aug , Ln , l → n , l = πα ca µ (cid:32) Z ∗ Z (cid:33) max( l , l )3(2 l + · y (4 + y )(4 + y )(4 + y ) · exp[ y (4 arctan y − π )]sinh π y I Here, µ , y , and I are defined as follows. µ = M / m e y ≡ Z ∗ α (cid:112) ( T / m e c ) + (2 T / m e c ) T ≡ ∆ E n , n − E ionization I ≡ (cid:90) ∞ dr r R ( n , l ) R ( n , l ) Γ Aug , Kn , l → n , l ( Γ Aug , Ln , l → n , l ) is the Auger transition rate foremitting K (L) shell electrons with the initial state ( n , l ) and the final state ( n , l ), a is the Bohr radius ofhydrogen atom, α is the fine structure constant, Z ∗ is the e ff ective nuclear charge seen from the electron, T is thekinetic energy of the emitted electron, and R ( n , l ) is thenormalized radial function of the exotic atom. The tran-sitions with ∆ l = ± Γ re f and also from the higher shell with thefluorescence rate. The refilling rate can be estimated asfollows: Γ re f = n · σ · v . Here, n is the density of target atoms, σ is the cross-section for charge transfer ( ∼ − cm ), and v is therelative velocity of the exotic atom with respect to otheratoms of the medium ( < cm / s). The typical valueof the refilling rate is ∼ s − for low pressure gasesand ∼ − s − for solid and metal [19].Since the Auger transition can take place only if anelectron occupies a shell state, the time-dependent fill-ing condition of the electron in each shell and the re-filling rate from outside, including the electron fluores-cence transition (de-excitation) from the outer shell tothe inner shell, Γ f lu , needs to be included for a moreprecise calculation in the cascade model with the timedependent electron population [22]. However, as de-scribed below, this will not a ff ect the X-ray yield in thelow n states since the radiative transition rate dominatesover the Auger transition rate as n becomes smaller andthe radiative transition takes place much faster than theelectron refilling rate. Therefore, we simply estimatethe modified Auger transition rate, including the elec-tron refilling rate and the fluorescence transition rate,as: Γ Aug , K , modn , l → n , l = Γ Aug , Kn , l → n , l + Γ re f + Γ f lu − . The radiative transition rate becomes larger than theAuger process at a relatively low n state. It can be es-timated with a perturbation method and in the dipoleapproximation it follows [21]. Γ Radn , l → n , l = e (cid:126) c (cid:32) a µ Z (cid:33) (cid:0) ∆ E n , n (cid:1) · max( l , l )2 l + I E n , n ≡ hcR y µ Z n − n Here, Γ Radn , l → n , l is the radiative transition rate with theinitial state ( n , l ) and the final state ( n , l ), ∆ E n , n is the energy di ff erence between the initial and finalstate, and R y is the Rydberg constant. As seen in theequation, the radiative transition rate increases as n de-creases ( ∆ E n , n increases), and becomes the main tran-sition process in low n states. The radiative transitionsdominate for n < n < ∆ n since they are proportional to (cid:0) ∆ E n , n (cid:1) , as seen in the equation. However, once thecascader reaches the circular state, ( n , n − ∆ l = ±
1) restricts the transition to ( n , n − → ( n − , n − n states, since the cascader is predominantlyin a circular state at low n . Since the e ff ective Bohr radius for the cascader, a /µ ,is much smaller than the Bohr radius, a , the strong nu-clear force interaction between the cascader and the nu-cleus can become large in low n states. This may termi-nate the de-excitation cascade of the exotic atom beforeit reaches the ground state, since the cascader is cap-tured by the nucleus. In particular, the antiproton andthe antideuteron annihilate with the nucleus due to thenuclear capture and produce pions and protons. The op-tical potential between the cascader and the nucleus canbe estimated as follows [23, 24]: U ( r ) = − π M ∗ (cid:32) + M ∗ m N (cid:33) ¯ a ρ ( r ) ≡ − ( V + iW ) ρ ( r ) ρ (0) ρ ( r ) = ρ (0)1 + e r − cz . Here, M ∗ is the reduced mass of the cascader, m N is themass of the nucleon, ¯ a is the average complex “e ff ec-tive” hadron-nucleon scattering length (experimentallydetermined), and ρ ( r ) is the Fermi distribution with theparameters ρ (0) = .
122 fm − , c = . × A / fm, and z = .
55 fm [23, 24, 25].The nuclear capture rate can be derived with the per-turbation method using the imaginary part of the opticalpotential W , as seen below: Γ Capn , l = (cid:126) (cid:90) Im( U ( r ))( R ( n , l )) r dr = W (cid:126) (cid:90) ( R ( n , l )) r + e r − cz dr . Here, (cid:126) is the reduced Planck constant and W is ∼ Z atoms and negligible com-pared with the energy of the atomic X-rays ( ∆ E n , n ). A Monte Carlo simulation for the cascade model wasdeveloped to estimate the X-ray yields of the exoticatom. The simulation takes into account all the possi-ble Auger transitions including the electron refilling andfluorescence transitions, the radiative transitions, andthe nuclear capture. It starts at n e = l is determined with the modified statistical distri-bution P l ∝ (2 l + e al as discussed above. Cascadersare then allowed to cascade until they are captured bythe nucleus or reach the (1 ,
0) state. The absolute X-rayyields, Y n → n , in the low n states (radiative transitiondominates) were calculated as follows: Y n → n = n − (cid:88) l i = n − (cid:88) l j = N n , l i N all P Radn , l i → n , l j . Here, the initial and final states are ( n , l ) and ( n , l )(no final state for the nuclear capture), N all is the num-ber of antiprotons simulated in the cascade model and N n , l i is the number of antiprotons that cascaded to thestate ( n , l i ).The Monte Carlo simulation was conducted withthree parameters, a for initial angular momentum distri-bution, Γ re f for the electron refilling rate, and W for theoptical potential. (The statistical uncertainty was neg-ligible compared to the systematic uncertainty.) Table1 shows the X-ray yields of antiprotonic exotic atoms(Al target) with the di ff erent values of Γ re f around theempirical values, Γ re f = s − ( a = .
16 and W =
10 MeV). This indicates, as discussed above, the X-ray yields at low n states were not a ff ected by the elec-tron refilling rate. The results are also consistent withmodels including the time dependent electron popula-tion . Table 2 shows the X-ray yields of antiprotonicexotic atoms (Al target) with the di ff erent values of W ( a = .
16 and Γ re f = s − ). This also indicates that private communication with Dr. Takahisa Koike (RIKEN Japan) a ff ects only one transition, the lowest n , as expected.Table 3 shows the X-ray yields of antiprotonic exoticatoms (Al target) with the di ff erent values of a ( W = Γ re f = s − ). As seen in the tables, theX-ray yields are driven mainly by a , the initial angu-lar momentum distribution, except the last transition isstrongly a ff ected by W , the nuclear potential. Γ re f [s − ] 10
92 keV (5 →
4) 72% 68% 67% 67%50 keV (6 →
5) 91% 84% 82% 81%30 keV (7 →
6) 83% 71% 69% 68%
Table 1: X-ray yields of the antiprotonic exotic atom (Al target) withdi ff erent values of Γ ( a = . W =
10 MeV). W [MeV] 0 10 30 50 10092 keV (5 →
4) 89% 67% 46% 35% 22%50 keV (6 →
5) 82% 82% 82% 81% 82%30 keV (7 →
6) 69% 69% 69% 68% 69%
Table 2: X-ray yields of the antiprotonic exotic atom (Al target) withdi ff erent values of W ( a = . Γ ref = s − ). a →
4) 41% 58% 67% 71%50 keV (6 →
5) 46% 69% 82% 88%30 keV (7 →
6) 37% 56% 69% 75%
Table 3: X-ray yields of the antiprotonic exotic atom (Al target) withdi ff erent values of a ( W =
10 MeV, Γ ref = s − ). Additionally, our cascade model was compared withthe data for muonic exotic atoms, which are widelymeasured in experiments [26]. The nuclear absorptionsare not seen in the muonic exotic atoms (except for highZ targets) and therefore, there is only one parameter, a , to control the X-ray yields at low n states. Table 4shows the comparison with the experimental data anda cascade model developed by Vogel and Hartmann forthe muonic exotic atoms [26, 27, 28]. The parametersused here were W = Γ re f = s − , and a = n states in our cas-cade model are in good agreement with both experimen-tal data (muonic exotic atoms) and other cascade models(both muonic and antiprotonic exotic atoms) with a timedependent electron population. Transition exp our model model in [27, 28]Al (2 →
1) 80% 78% 80%(3 →
2) 63% 60% 60%(4 →
3) 34% 38% 42%Fe (2 →
1) 72% 71% 74%(3 →
2) 44% 49% 45%(4 →
3) 33% 33% 33%Au (2 →
1) 90% 94% 95%(3 →
2) 80% 85% 84%(4 →
3) 76% 75% 76%
Table 4: Experimental data and cascade models for X-ray yields ofthe muonic exotic atoms with Al, Fe and Au targets
3. Accelerator Test at KEK
The KEK facility is located north of Tokyo, inTsukuba, Japan. During the course of the experimentsthe proton synchrotron produced an 8 GeV (up to 12GeV) proton beam in the main ring. The H − ion sourcegenerated in the plasma chamber was injected into thepre-injector, followed by the linac, booster synchrotronand main ring and accelerated to 750 keV, 40 MeV, 500MeV and 8 GeV, respectively. Our experiment was per-formed at the π .The beam test was conducted at KEK in 2004 and2005 to verify the GAPS original concept described in[2] and measure the X-ray yields of the antiprotonic ex-otic atom with several di ff erent target materials. Theresults constrained the parameters in the cascade modeldescribed in Section 2. This also allowed us to extendthe cascade model to any exotic atoms and estimate theX-ray yield of the antiprotonic and antideuteronic exoticatoms in the GAPS experiment. The experimental setup in the KEK test was com-posed of a TOF, degraders (lead brick and sheets),shower counters, a target and X-ray detectors. The an-tiprotons in the beam were first identified by the TOFsystem, since antiprotons are slower than the other par-ticles in the beam. The degrader slowed down antipro-tons and stopped them in the target material where theyformed an excited antiprotonic exotic atom. Atomic X-rays and charged particles are emitted in the decay of KEK PS experiment [http: // / kekps / index.html] "ray&detector&Plas/c&Scin/llator& Degrader& Figure 4: KEK experimental setup. the exotic atom as discussed in the previous chapter. ASodium Iodide doped with Thallium, Nal(Tl), detectorarray was installed around the target material and de-tected the atomic X-rays and pions. The shower coun-ters monitored the energy deposited by the particles inthe beam and distinguished antiprotons from other par-ticles, including the in-flight annihilation products.While gaseous targets and a few liquid targets wereused in 2004, liquid and solid targets were tested in2005, since they are simpler to implement in the real-istic design for the balloon experiment. The actual pic-ture and the schematic view of the experimental setup in2005 are shown in Figures 4 and 5. Figure 6 shows anunfolded view of the cylindrical detector module and atypical stopped antiproton event for the Al target. Num-bers are the energy of the stopped X-rays and π ∗ indi-cates a pion hit. MainDegrader X-ray Detector
Target
NaI(Tl)P2P0 ShowerCounterP3SubDegrader VetoCounterP1 P5P4 NaIHousing(S1-S4)
Figure 5: The schematic view of the experimental setup at KEK in2005. It was composed of a TOF system (P0-P5), degraders (leadbrick and sheets), shower counters (S1-S4), a target and X-ray detec-tors. The distance between the P0 and P2 counters is 6.5 m and theoverall length of the X-ray detector is ∼
50 cm. (cid:3)(cid:3)
Beam Direction P1 Time [ns] E [MeV]
P2 S1 S2 S3 S4 P3 P4 P5 Target
NaI Energy [keV] * % π * % Figure 6: A typical antiproton event for the Al target. Numbers arethe energy of the stopped X-rays and π ∗ indicates a pion hit. The momentum of the beam was controlled and fo-cused by dipole and quadrupole magnets, while themomentum spread was controlled by a shutter. Theparticles were delivered in 1.5 s long spills, and eachspill was separated by a 4 s interval. A momentum of1 GeV / c was used in all of the 2005 measurements.Up to several GeV / c the antiproton flux from the π / c was found toprovide the highest rate of antiproton stops in our tar-get during our 2004 measurements. The beam spill witha momentum of 1 GeV / c contained about 20-30 antipro-tons, 10 π − , and a somewhat smaller number of K − ande − , as measured in the 2004 experiment, and these num-bers were consistent with the data sheets provided byKEK.The spatial beam profile at the P0 counter was mea-sured by changing the last dipole magnet, which con-trolled the horizontal direction, and the height of the re-mote controlled table (for the vertical direction). Themeasured beam profiles at P0, P1 and P2 were used asinput in the GEANT4 simulation together with a TUR-TLE beam line optics ray trace to simulate the beamprofile, divergence and momentum bite. GEometry ANd Tracking, a toolkit for the simulation of the pas-sage of particles through matter, developed by CERN. PSI Graphic Turtle Framework by U. Rohrer based on a CERN-SLAC-FERMILAB version by K.L. Brown et al. .2.2. Time of Flight System The TOF system in the KEK 2005 test was composedof 6 scintillation counters, P0-P5. The TOF timing, thetravel time of the incoming particle between the P0 andPi (i =
1, 2, 3, 4, 5) counters, allowed us to identifythe incoming particle, since all the particles in the beamhad a fixed momentum and the antiprotons were muchslower than the other lighter particles (see below). TheP0, P2, P3 and P4 counters had a dimension of 12 cm ×
12 cm and a thickness of 1.0 cm, while the P1 and P5counters had a thickness of 0.2 cm. The paddles werecoupled to the light guide and then to the 2 inch fastphotomultiplier tube (Photonis XP2020). A high volt-age of ∼ -1800V was applied to the PMT base (PhotonisS5632).The P0, P1, and P2 counters were used for tim-ing only, while the P3, P4 and P5 counters were usedfor both timing and energy deposition. The timing ateach counter was measured relative to the acceleratorbeam structure by passing the signal from the last diodethrough a fast timing preamplifier (Ortec VT120b), fol-lowed by a constant fraction discriminator. The timeof flight (TOF) between the P0 counter and the P1-P5counters were measured using time- to-analog convert-ers (TAC, Canberra 2020). The dE / dX energy depositwas characterized using the signal from the PMT an-ode passed through a preamplifier (Camberra 2005) fol-lowed by a spectroscopy amplifier (Ortec 452). The four shower counters, S1-S4, were installed be-hind the main degrader in 2005 (see Figure 5), and eachof them had a dimension of 12 cm ×
12 cm × / dX energy loss, since non-relativistic slow antiprotons deposit more energy thanrelativistic particles such as π − .The veto counters (6 cm wide, 1 mm thick ribbonscintillation fibers, coupled to a Hamamatsu R1942A 1inch PMT) were installed between the target and theX-ray detectors. They were designed to monitor theo ff -axis antiprotons hitting the detector and the framewithout stopping in the target material. However, sincethe energy resolution of these counters was relativelycoarse, it was di ffi cult to uniquely identify potential o ff -axis antiproton interactions from annihilation productsproduced in the target. The X-ray detectors were 128 NaI(TI) crystals (1 inch × × ∼ / keV. Since the NaI(Tl) is a relatively high Zmaterial, up to 300 keV X-rays (20 keV threshold) canbe photo-absorbed in the 5 mm thick crystal. Each crys-tal is coupled to a Hamamatsu 1 inch PMT (R1924A)on the back surface. The wavelength of the scintilla-tion light is ∼
410 nm, where the quantum e ffi ciency ofthe PMT has a peak. Every 8 crystals and PMTs, sep-arated from each other by 1.5 inch, are mounted in atightly sealed steel housing with a 0.125 mm Al win-dow. Each PMT is connected to the custom made PMTbase and ∼ -800V HV was applied. The preamplifierwas mounted inside the housing and the gain for eachdetector was controlled externally. Sixteen sets of de-tectors were mounted around the target as seen in Figure6. In 2005, four target materials were chosen based onthe energy of the atomic X-rays in their antiprotonicexotic atom, which needed to be in the useful energyrange of the X-ray detector, 25 keV < E <
300 keV.The detectable antiprotonic atomic X-rays for each tar-get tested in KEK are shown in Table 5.
Table 5: Antiprotonic atomic X-rays for each target (25 keV < E <
300 keV)
Target X X X X X X Al 92 keV 50 keV 30 keV - - -S 139 keV 76 keV 46 keV 30 keV - -Cl 86 keV 52 keV 34 keV 23 keV - -Br 145 keV 99 keV 71 keV 52 keV 41 keV 31 keV
Al (Aluminum wool), S (Sulfur), CBr (Tetrabro-momethane) and CCl (Carbon tetrachloride) targetswere tested in 2005 and we will focus on the Al (Z =
13) and S (Z =
16) targets in this paper to estimate theX-ray yields for the Si (Z =
14) target for the GAPS bal-loon experiment. It is also more challenging to analyzethe data for the CBr and CCl targets since they arecompounds and many atomic X-rays can be producedin the small energy region. The Al wool was filled intotwo 1 mm thick plastic bottles, each with a diameter of12 cm and 22 cm in length, and the average density was ∼ / cm . The target holder for the Sulfur powderwas framed with Al pipes of diameter 12 cm cut at a 45degree angle, and both openings were covered with 19m thick plastic sheets (see Figure 7). This is the mostfavorable geometry for X-rays to escape in the cylindri-cal geometry. The holders were placed onto two guidedrails to minimize the blockage of X-rays from the target. Figure 7: Sulfur target geometry
Since antiprotons in the beam were too energetic tostop in the target, a combination of active and passivedegraders were used to slow down the antiprotons be-fore they entered the GAPS target region (see Figure5). The optimized total thickness of degrader was es-timated by measuring the number of events at the P4counter (just before the target) with di ff erent thicknessesof degrader. Since the number of antiprotons in thebeam was very small, in order to have better statisticswe used positively charged beam (protons and π + ) withthe same magnet settings for the beam except for thepolarity. Figure 8 shows the number of protons at eachcounter, normalized with the number of protons at theP2 counter. The GEANT4 simulation result at the P4counter is also shown in the figure, taking into accountthe uncertainty on the thickness and density for each degrader thickness [cm]5 6 7 8 9 10 11 12 c oun t s no r m a li z e d w i t h P c oun t s S1S2S3S4P3P4P5GEANT4 (P4)
Figure 8: Number of hits at each counter vs. degrader thickness (cm).The counts were normalized to the counts at the P2 counter. lead brick and sheet ( ∼ ∼ Since the momentum of the beam was set as 1 GeV / cby the dipole and quadrupole magnets, the antiprotonsin the beam can be distinguished from other particlesby the velocity, β . The TOF timing and energy depositin the plastic scintillator for antiprotons are larger thanother particles in the beam (mainly pions) since β forantiprotons is smaller and dE / dx energy loss is propor-tional to ∼ β − . p""_"" π (cid:1) T A C % [ n s ] % TAC1%[ns]%
TOF [ns]5 10 15 20 25 30 35 40 nu m b e r o f eve n t s (cid:61) TAC1TAC2TAC3TAC4
TAC1%[ns]% T A C % [ n s ] % Figure 9: TOF timing at TAC1 (red), TAC2 (green), TAC3 (blue),TAC4 (purple), and TAC1 vs. TAC2 (bottom).
Figure 9 shows the TOF timing at TAC1 (red), TAC2(green), TAC3 (blue) and TAC4 (purple), between the100 and Pi (i =
1, 2, 3, 4) counters. A plot for TAC1vs. TAC2 was also shown below. Two peaks, relativisticpions (pre-scaled) and antiprotons, are seen at each plot.The selected cuts, peak ± ∼
60 cm away from the P4 counter,the cut on the TAC5 was set as “(TAC4 lower limit + > Table 6: Antiproton selection cuts on each TOF timing
Figure 10 shows the dE / dX energy deposit in theshower counters (S1: red, S2: green, S3: blue, S4: pur-ple). Energy was calibrated with the relativistic pions inthe beam and the GEANT4 simulation with the actualbeam profile. Two peaks, relativistic pions (pre-scaled)and antiprotons, are also seen at each plot. The antipro-ton selection cuts were applied for each dE / dX energydeposit. The applied cuts for each dE / dX energy depositare shown in Table 7. Note that we were not able to setthe upper limits on the cuts for the P3 and P4 dE / dX en-ergy deposits since the signals were saturated at E > energy deposit [MeV]0 1 2 3 4 5 6 7 8 9 10 nu m b e r o f eve n t s S1S2S3S4 p""_"" π Figure 10: dE / dX energy deposit in the S1 (red), S2 (green), S3 (blue)and S4 (purple) counters. lower limit upper limitS1 1.8 MeV 3.2 MeVS2 2.2 MeV 4.2 MeVS3 2.2 MeV 4.2 MeVS4 2.6 MeV 5.0 MeVP3 8.0 MeV -P4 8.0 MeV - Table 7: Antiproton selection cuts on each dE / dX energy deposit As described above, the cuts applied to the TOF tim-ing and dE / dX energy deposit provide excellent antipro-ton selection in the original beam (see Fig 14). Thus,the main background is due to the annihilation prod-ucts of the exotic atom, which can develop an electro-magnetic shower in the target and the detector frame.Similarly, most of the antiprotons in the beam were an-nihilated in the degrader and the annihilation productsdeveloped the electromagnetic shower around the de-tector. Therefore, the background spectrum was esti-mated with the experimental data with cuts on the TOFtiming at TAC1 (between the P0 and P1 counters) andTAC2 (between the P0 and P2 counters) to evaluate theelectromagnetic shower generated by the annihilationproducts. Note that the background spectrum was alsomodeled with a GEANT4 simulation and both models(KEK BG, GEANT4 BG) are compared in Figure 11.They are in good agreement except that the GEANT4BG model has a slightly narrower peak around 100 keV.This could be due to the imperfection of the compli-cated physics process on the antiproton annihilation andthe subsequent shower development in the simulation.In order to check the robustness to the deviation of the energy [keV]50 100 150 200 250 c oun t s / V KEK BG GEANT4 BG
Figure 11: The background models for the Al target obtained from theexperimental data (KEK BG) and the GEANT4 simulation (GEANT4BG).
Since antiprotons were not able to be tracked after hit-ting the P4 counter, the GEANT4 simulation was usedto predict the stopped position of the incoming antipro-tons. The simulation was also used to estimate the en-ergy spectrum in the detector for each atomic X-ray, tak-ing into account all the X-ray interactions before reach-ing the detector. Figure 12 shows the expected energyspectra in the detector for each atomic X-ray with the energy deposit [KeV]20 40 60 80 100 120 140 p r ob a b ili t y / V / ex o t i c a t o m Figure 12: Expected energy spectra in the detector for each atomicX-ray with the Al target. The green, blue, and red lines representsimulation results for 30 keV, 50 keV, and 92 keV X-rays, and thesolid lines are the spectra with the detector response. It is normalizedto the counts per exotic atom with 100% X-ray yield. energy deposit [KeV]20 40 60 80 100 120 140 160 180 p r ob a b ili t y / V / ex o t i c a t o m Figure 13: Expected energy spectra in the detector for each atomic X-ray with the S target. The purple, green, blue, and red lines representsimulation results for 30 keV, 46 keV, 76 keV and 139 keV X-rays,and the solid lines are the spectra with the detector response. It isnormalized to the counts per exotic atom with 100% X-ray yield.
Al target. It is normalized to the counts per exotic atomwith 100% X-ray yield, and the green, blue, and redlines represent 30 keV, 50 keV, and 92 keV X-rays. Thedashed lines are the simulation results without the de-tector response and the solid lines are the spectra withthe detector response (7% FWHM at 1 MeV). Figure 13is the same for the S target (30 keV for purple, 46 keVfor green, 76 keV for blue and 139 keV for red lines).
The absolute X-ray yields (probability to emit anatomic X-ray per exotic atom) for antiprotonic exoticatoms, Y , were estimated by fitting the data with thebackground model and the expected energy spectra foreach atomic X-ray in the detector as below. f data = a BG · f BG + (cid:88) a i · f i Y i = a i / N ¯ p stop Here, a ’s are the fit parameters, i is for the i -th atomicX-ray, f ’s are the spectra in the detector as discussedabove, and N ¯ p stop is the number of stopped antiprotonsin the target. The parameter a i also denotes the numberof the atomic X-rays emitted from the exotic atom. Figure 14 shows the fitting result for the Al target.The solid black, blue and red lines represent the ex-perimental data, the background model and the threeatomic X-rays respectively and the green solid line is energy [keV]50 100 150 200 250 c oun t s Experimental dataAl X-rays (30keV, 50keV, 92keV)KEK BGFitting result
Figure 14: The data for the Al target fitted with the background modelobtained from the experimental data (blue) and the expected X-rayspectrum for each antiprotonic X-ray (red). p -Al Transition Yield92 keV 5 → ± → ± → ± χ - 1.07 Table 8: The fitting result for the Al target. the sum of the background model and the X-rays. Ta-ble 8 shows the X-ray yields for each atomic X-ray in-cluding the fitting error and the systematic uncertainty( Y ± ∆ Y ). The systematic uncertainties due to the de-tector response ( ∆ FWHM ∼ ±
1% at 1 MeV) and theo ff set of the energy calibration ( ± ∼ ∼
7% and ∼
4% respectively. High absoluteyields ∼
80% were seen for all three transitions and thenuclear absorptions were not seen in the n = → n = → ±
13% for 30 keV, 85% ±
11% for 50keV and 81% ±
12% for 92 keV (reduced- χ ∼ Since some of the antiprotons may stop in the Al win-dow / frame around the target, seven atomic X-rays (threefrom the exotic atoms with the Al window / frame andfour from the S target) can be produced in the small en-ergy region. Therefore, considering the huge systematicuncertainty, we constrained the three atomic X-rays forthe S target, 30 keV ( n = → n = → energy [keV]50 100 150 200 250 c oun t s Experimental dataS X-rays (30keV, 46keV, 76keV, 139keV)KEK BGFitting result
Figure 15: The data for the S target fitted with the background modelobtained from the experimental data (blue) and the expected X-rayspectrum for each antiprotonic X-ray (red). and 76 keV ( n = →
5) to have the same absoluteyields. This is consistent with theoretical expectationfor the S target and as predicted and measured for theAl target. Additionally, the X-ray yields for the antipro-tons stopped in the Al window / frame are constrainedwith the value obtained for the Al target.¯ p -S Transition Yield139 keV 5 → ± → ± → ± → ± χ - 1.00 Table 9: The fitting result for the S target.
Figure 15 shows the fitted results for the S target.Same as in Fig 14, the solid black, blue and red linesrepresent the experimental data, the background modeland the three atomic X-rays respectively and the greensolid line is the sum of the background model and theX-rays. Table 9 shows the X-ray yields for each atomicX-ray including the fitting error and the systematic un-certainty ( Y ± ∆ Y ) as discussed above. High absoluteyields were also seen in all the transitions except for the n = → As discussed in Section 2, the cascade model hasbeen developed to estimate the X-ray yields of the ex-otic atoms at low n states. The yields are mainly de-termined by the parameter a , initial angular momentumdistribution, while the last transition rate is strongly de-pending on W , nuclear potential (see Section 2). Thecascade model with the parameters, a = . W = Γ re f = s − is quite consistent with the ex-perimental data for the Al target as seen in Table 10. Ta-ble 11 shows the X-ray yields of the experimental dataand the cascade model for the S target, which is also ingood agreement with the experimental data. Parametersused here are, a = . W = Γ re f = s − . ¯ p -Al Experiment Cascade Model92 keV (5 →
4) 90% ±
13% 78%50 keV (6 →
5) 76% ±
10% 84%30 keV (7 →
6) 84% ±
13% 71%
Table 10: The experimental data and the cascade model for X-rayyields of antiprotonic exotic atom with the Al target ( a = . W = Γ ref = s − ). p -S Experiment Cascade Model139 keV (5 →
4) 59% ±
20% 50%76 keV (6 →
5) 72% ±
18% 83%46 keV (7 →
6) 72% ±
18% 78%30 keV (8 →
7) 72% ±
18% 60%
Table 11: The experimental data and the cascade model for X-rayyields of antiprotonic exotic atom with the S target ( a = . W = Γ ref = s − ). The cascade model was extended to the antiprotonicand antideuteronic exotic atom for a Si target and othermaterials in the GAPS instrument to estimate the an-tideuteron sensitivity. Since parameters are not stronglycorrelated with the atomic number, the same parametersare used for the Si (Z =
14) target as used for the Al (Z =
13) and S (Z =
16) targets. Table 12 shows the re-sult for the antiprotonic exotic atom with the Si target( a = . W = Γ re f = s − ). ¯ p -Si Cascade Model Ref. in [2]106 keV (5 →
4) 70% 50%58 keV (6 →
5) 84% 50%35 keV (7 →
6) 73% 50%
Table 12: Cascade model for X-ray yields of the antiprotonic exoticatom with the Si target ( a = . W = Γ ref = s − ). The X-ray yields for the antideuteronic exotic atomwith a Si target were also estimated by simply changingthe optical potential, W ¯ d ∼ W ¯ p =
10 MeV, as shown inTable 13 ( a = . Γ re f = s − ). It was also esti-mated for higher values of W =
20 MeV, however, theresult does not a ff ect the GAPS antideuteron sensitiv-ity since the nuclear capture only takes place at n = ∼
50 % in[2]. ¯ d -Si W =
10 MeV W =
20 MeV Ref. in [2]112 keV (6 →
5) 28% 17% -67 keV (7 →
6) 96% 94% 50%44 keV (8 →
7) 92% 93% 50%30 keV (9 →
8) 80% 80% 50%
Table 13: Cascade model for X-ray yields of antideuteronic exoticatom with the Si target ( a = . Γ ref = s − ).
4. Conclusion
Absolute X-ray yields for the antiprotonic exoticatom with Al and S targets were measured at KEK,Japan in 2005. We obtained high X-ray yields, ∼ n states. The nuclear absorp-tion was seen only in the very low n state for the S tar-get. A simple but comprehensive cascade model hasbeen developed to estimate the X-ray yields of the ex-otic atom. Since it is extendable to any kind of ex-otic atom (any negatively charged cascading particleswith any target materials), the model was evaluated andvalidated with the experimental data and other mod-els for the antiprotonic and muonic exotic atoms. Themodel allows us to estimate the X-ray yields of the an-tiprotonic and antideuteronic exotic atoms formed withany materials in the GAPS instrument and the X-rayyields for antiprotonic and antideuteronic exotic atomswith a Si target were estimated as ∼
5. Acknowledgments
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