A universal charge-radius relation for spherical objects

Transcription

1 A universal charge-radius relation for spherical objects + preliminary results of a Lunar Soil Strangelet Search Jes Madsen (Aarhus University) 1

2 What is the maximal charge of a sphere? Madsen, PRL100, (2008) Z = 2m e R/α = 0.71R fm (400fm < R < 10 4 fm) Z = 7x10-5 R fm 2 = 7x10 31 R km 2 (R > 10 4 fm) For nuclear matter density: Z = 0.7A 1/3 (10 8 < A < ) Z = 7x10-5 A 2/3 (A > ) 2

3 Where is such a limit relevant? Superheavy nuclei may have Z>137 (limit for electron-positron pair creation for point charge). Strangelet models have Z=0.1A, Z=8A 1/3, or Z=0.3A 2/3 and A up to Other exotica with high charge (e.g. Q- balls) exist at least in the theoretical literature. 3

4 Where is such a limit relevant? Neutron stars have Z < A (electrostatic repulsion < gravitation). Strange (and other self-bound) stars have Z < A 2/ (electrostatic repulsion < binding). Extensive literature on black holes with Z of order A (but Damour and Ruffini, PRL 35, 463 (1975) find GR black hole constraint similar to my non-gr result). 4

5 Rate of pair creation in supercritical electric field: Critical field E critical = m e2 /e = 1.3x10 16 V/cm The rate for pair creation is the first term in the Schwinger [PR 82, 664 (1951)] formula for the vacuum decay rate: 5

6 Thomas-Fermi model n e = p 3 F 3π 2 [ ] 3 / 2 = µ 2 2 e m e 3π 2 = θ ( µ e m e ) [( µ eff e + eφ) 2 2 m ] 3 / 2 e 3π 2 θ ( µ eff e + eφ m e ) Positive core Electrons Classical Thomas-Fermi model (neutral atom): Relativistic Thomas-Fermi model for maximal charge: Müller and Rafelski, PRL 34, 349 (1975) 6

7 Relativistic Thomas-Fermi model (1) n e = [( eφ ) 2 2m e eφ] 3 / 2 3π 2 θ( eφ 2m e ) Poisson s equation (outside positive core additional term inside): 7

8 Relativistic Thomas-Fermi model (2) But also [Madsen, PRL 100, (2008)] : R Z CORE Width of screening electron layer (inner parts neutral): r 2 8

9 Relativistic Thomas-Fermi model (3) Maximal net charge of sphere (R > 400 fm): R Z CORE r 2 Nuclear matter density: 9

10 Convergence for Z CORE =0.3A 2/3 Z CORE Z MAX Z =2m e R/α m e R 10

11 Rate of pair creation in supercritical electric field: Critical field E critical = m e2 /e = 1.3x10 16 V/cm The rate for pair creation is the first term in the Schwinger [PR 82, 664 (1951)] formula for the vacuum decay rate: 11

12 Electron production rate W in surface region 12

13 Charge equilibration time scale τ WV = -dz/dt V = 4πR 2 ΔR = 4πR 2 /m e dz/z = -dt/τ (charge producing volume) Fixed time scale means constant x, so Z~R 2 For 1 second: Z 7x10-5 R fm 2 7x10-5 A 2/3 Prefactor varies only by factor of 2 from weak interaction to age of the Universe! 13

14 What is the maximal charge of a sphere? Madsen, PRL100, (2008) Z = 2m e R/α = 0.71R fm (400fm < R < 10 4 fm) Z = 7x10-5 R fm 2 = 7x10 31 R km 2 (R > 10 4 fm) For nuclear matter density: Z = 0.7A 1/3 (10 8 < A < ) Z = 7x10-5 A 2/3 (A > ) 14

15 Can a Van de Graaff work above 1MV? The maximal charge for a static system Z MAX 2m e R/α corresponds to a surface potential Φ 2m e /e 1MV! Accelerator physics is saved by the time required to form the screening electrons from pair creation, so for radii above 10 4 fm Φ MAX 11.2m e2 Rα/e 10-4 MV R fm. 15

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18 arxiv: [hep-ph] LATER WITHDRAWN 18

19 arxiv: [hep-ph] 19

20 Lunar Soil Strangelet Search 20

21 Wright Nuclear Structure Lab Yale Lunar Soil Strangelet Search Collaboration: Han, Ashenfelter, Chikanian, Emmet, Finch, Heinz, Majka, Parker, Sandweiss (Yale) Monreal (MIT) Madsen (Århus) 21

22 Interesting events Two events from AMS He: Z = 2, A~16 in ~10 6 Z = 2 cosmic ray events 54 O: Z = 8, A = 54+8( 6) event in ~10 5 events with Z > 2. Balloon-borne detectors events 4 events from 3 different experiments All consistent with strangelet characteristics, but none can be seen as definite evidence. SQM2008, Oct 9, Beijing

23 NASA gave us 15 g lunar dust from Apollo 11 23

24 Our project Search for strangelets at 2σ range of the AMS-01 event. Confirm or rule out AMS-01 event: this requires a lunar soil search with sensitivity. SQM2008, Oct 9, Beijing

25 Strangelet detection Smaller Z/A longer stopping range Strangelets are isolated on the E de plot. Without foil With foil SQM2008, Oct 9, Beijing

26 Strangelet detection Smaller Z/A longer stopping range Strangelets are isolated on the E de plot. Without Foil With Foil 56 Fe SQM2008, Oct 9, Beijing

27 Experiment setup Yale tandem Van-de-Graaff accelerator at WNSL. Inflector Magnet Mass acceptance 0.3amu Step size 0.25amu Analyzing Magnet V T =17MV, charge +5 E total =102MeV SQM2008, Oct 9, Beijing

28 Search sensitivity Single event sensitivity (SES) with respect to oxygen atom is determined by particles out of ion source per unit time run time per mass setting transmission efficiency. strangelet stripping prob. to charge +n. We get as high as per second (16 ua). We run 2 hours About 8% For n=5 ( 54 O), P n =0.4±0.1 SQM2008, Oct 9, Beijing

29 Limits SQM2008, Oct 9, Beijing

30 Limits Carbon and Fluorine SQM2008, Oct 9, Beijing

31 Summary We searched for strangelet event with mass range 42 to 70 amu at about SES level. No strangelet signal was found. This may rule out the AMS-01 event pending evaluation of our full systematic errors. AMS-02 experiment will be 100 times more sensitive, and it covers the whole mass range. SQM2008, Oct 9, Beijing