EXPERIMENTS TO MEASURE THE FORCE OF GRAVITY ON POSITRONS

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617 EXPERIMENTS TO MEASURE THE FORCE OF GRAVITY ON POSITRONS William M. Fairbank Department Physics Stanford University Stanford CA 9435 USA Fred C.

1 617 EXPERIMENTS TO MEASURE THE FORCE OF GRAVITY ON POSITRONS William M. Fairbank Department Physics Stanford University Stanford CA 9435 USA Fred C. Wittebom NASA Ames Research Center N245-6 Mfet Field USA Presented by William M. Fairbank Abstract An experiment described to measure force gravity on positrons. experiment a modification a previous experiment used to measure force gravity on electrons. Recent techniques for rmalizing positrons by reflection from copper surfaces make such an experiment feasible. Such an experiment could in principle check for a scalar fifth force coupling to leptons.

2 618 For many years we have been involved in measurement force gravity on electrons with ultimate objective measuring force gravity on positrons( 1-4) experiments on positrons assumed increased importance with suggestion Nieto, Goldman and Hughes including talk at th conference by Hughes that antimatter would behave differently to a scalar and a vector force than ordinary matter, vector force being attractive for antimatter interacting with ordinary matter but repulsive for ordinary matter interacting with ordinary matter. y have stimulated present efforts to measure force gravity on antiprotons(6). A measurement on positron as well as antiproton would differentiate between forces on leptons and on baryons. It now appears possible to make a slow positron source sufficiently well rmalized to make experiment we performed on electrons possible for positrons(7-9). Figure 1 shows apparatus used to measure force gravity on electrons. It consts a pulsed electron source, two copper cylindrical tubes each 1 meter long and 2 inches in diameter, placed in a 4 inch diameter copper tube. Th 4 inch tube serves as a. vacuum jacket and alignment fixture for a high homogeneity vertical superconducting solenoid. Pulses electrons emitted from bottom traverse ax clrift tube guided by magnetic field and ir time flight determined with aid an electron multiplier detector at top second tube. Two methods have been used to measure forces on electrons. In one method second tube electrically removed from time flight by applying a small positive voltage and time flight measured as a function various axial electric fields by running a current axially along walls lower tube. A variety techniques are employed to eliminate non uniformities in axial electric and magnetic fields. se are described elsewhere(l-4 ). A very important technique involves use ground state electrons in which only electrons are employed which are in magnetic ground state making vertical magnetic force on electrons smaller than gravitational force on electrons. results th method for electrons figure 2 and 3. are shown in In figure 2 time flight dtributions for three different electric fields along tube are shown. Figure 3 summarizes results a series experiments which showed reduced force determined from a variety fields plotted against field(l-2). From se data it was determined that re was no force: on electron to within ±1% mg for an electron 1to within one standard deviation. Th was interpreted to mean that free electrons had same gravitational mass as electrons on surface tube. Indeed success first experiment in whiclh patch effect field was shielded at low temperatures still a oretical puzzle( IO-

3 619 LEA S T S Q U A R E S F I T S F O R T H R E E D I F F E R E N T A P P LI E D F O R C E S --- E E - E : CATHODE MAGNET CATHODE Fig. Schematic apparatus current for supply at a negative chamber. electrons. I1 regulated maintains both tubes relative to vacuum biased only tubes. movable in so current I 3 produces that In >z w ;: C> t; :!; >- >- Z ww,...., o > "- >w z "' "' 1 - electrons stationary tube. uniform electric field a _ forces. 1. E iii E :J c.,.2.:: 1 56.I 11 1 _ 11 1 _ IEJ, APPL I E D ELECTRIC FIELD (VOLT S / M E T E R } Measured determined force vertical from flight dtribution value deliberately s was Fig. 3. solid - N'(t) v s TOF for three different moved 8 force. TIME OF FLIGHT Fig. 2. first tube in stationary tube. 5 o 1s o.""'=. i-,oj :-'-= so o.-= free controls relative potential two positively diagram voltage I2 experiment slowly t 6 x v;m 1 6 S>---'Vw--rnr-, 4µ.f 1s STATIONARY DRIFT TUBE fall 27. x 1o ll Vim 13. x 1 1 l Vim value analys absolute line b T e force time horizontal magnitude electric field. 4. Data experiments., curves. diagonal versus Fig represents F=I e E a l for a particle having electron's inertial mass. movable vertical tn { 1 1 ev) from potential and ax movable horizontal difference stationary ax tube between tubes. ratio number electrons with flight time between 25 and 5 25 ms to number with flight times between and ms., Each ratio requires 1 to 1 5 h o f data accumulation., separation = 3 1 cm. Separation = 1 cm;

4 62 12) John Bardeen( l 3) and John Madey ( l 4) have each suggested that a surface state electrons produce shielding. second method( l -2) does not depend on fortuitous shielding a patch field. In second method potentials two tubes are adjusted until y preciely equal. are Th equality determined by repeatedly performing time flight experiments as a function potential to second tube until fraction slow moving electrons maximized. Figure 4 shows results in an experiment for tubes figure I using electrons. By determining equality for two different heights for second tube, difference in potential due to height between two tubes can be determined. In electron experiment gravitational potential difference mgh cancelled by gravitationally induced electric potential from electrons on walls. For positrons th electric field would exert a force in opposite direction. refore in pure gravity one would measure for electrons and mgh for for positrons. If in addition re a scalar or vector fifth and sixth force on electron, we measure for positron twice sum gravitational force mg and scalar force. vector force cancels out. If we calibrate electric field by measuring force gravity on proton we can determine also vector force if we know total forces on proton. It now possible to obtain slow positrons by reflection from a metallic surface(7-9). fact that positron work function repulsive enables one to retrieve rmalized positrons before y are annihilated in metallic surface. y would n be measured in an experiment similar to that which was done for electrons. Such an experiment for positrons shown in figure 5. A pulsed beam positrons created with aid an electron accelerator and rmalized with a spread about I volt, are reaccelerated to about 1 kilovolt and caused to impinge on a single crystal copper surface in a high vacuum. positrons penetrate a short dtance iinto metal and are m1alized. Since work function for a metal negative for a positive particle, positrons, when y are rmalized are reflected out metal. A few percent positrons escape annihilation in metal and are rmalized to temperature metal If copper surface in a high magnetic field, say 5 kilogauss, n most reflected positrons will be in magnetic ground state. se rmalized positrons are n guided down axes apparatus with a guide magnetic field until y reach upper three tubes. Since positrons arrive at th tube in a short time pulse it possible to use tube as a velocity selector, fastest positrons arriving at end tube first. If a retarding voltage which varies with 1time between first and 2nd tubes spread in energy positrons can be furr reduced.

5 621 Rerrnalizer Copper Crystal _.---- rmalized Positrons Guide Magnet #1 (-3 G) Top LHe Dewar Guide Magnet #2 (-3 G) Velocity Selector Tube Upper (Fixed) Drift Tube --- Lower (Movable) Drift Tube Test Region Magnet (-4 G) Fig. 5 Schematic diagram apparatus for measuring force gravity on positrons. Using one se two methods one has at entrance to second tube a dtribution slow positrons mostly in magnetic ground state that contains some very slow positrons, in sufficient numbers to perform experiment to determine force gravity on individual positrons. At th point positrons would be introduced to 2nd tube and simultaneously to a very much smaller magnetic field. Th reduces magnetic energy for all electrons except those in magnetic ground state. Since energy conserved for positrons all positrons except those in magnetic ground state are accelerated arriving at or end lower tubes in a time short compared with one millecond. Only ground state positrons remain. In a series pulses arrival times very slow positrons are determined After measurements for enough time to determine dtribution slow positrons voltage between lower two tubes changed. As a function voltage between two tubes number slow positrons arriving per unit time determined. From our experience with electrons(l-2) th should peak with a spread in peak a small percentage force gravity on electron. space between tubes n changed and voltage maximum time flight again determined. If re a gravitational plus fifth force acting on positron energy with which a positron arrives at second tube will change, causing maximum in slow positrons to occur at a

6 622 slightly different balancing voltage. From th we can in principle determining change in potential energy positron in going through a height h between tubes. dtance between two tubes can be measured very accurately to determine force gravity on positrons to highest possible accuracy. If one to determine strength a fifth or sixth force on positrons or antiprotons it willl be necessary to make extremely accurate measurements since it not expected that correction for fifth or sixth force on positrons and antiprotons will be very large. Still th may be only way that one can uniquely determine force on electron and proton and will represent first measurement gravity on antimatter. antiproton has advantage that conventional force gravity on anti proton 2 times larger than on positron and refor in many ways easier to measure. However, if fifth force equal on positron and antiproton, n as a percent gravity, positron 2 times easier to measure. If fifth force turns out to have short range it seems to have, n it would be possible to perform positron and antiproton experiments with tube horizontal near a large mountain since guide magnetic field will be very little affected by gravity. References 1. F. C. Witteborn and W. M. Fairbank, Rev. Sci. Instrum. il, 1 (1977) 2. F. C. Witteborn and W. M. Fairbank, Nature 22, 436 (1968) 3. J. M. Lockhart, F. C. Witterborn and W. M. Fairbank, Phys. Rev. Lett,.3_8., 122 (1977) 4. Ph.D. s Stanford Universiy : F. C. Witteborn(1965), J. M. J. Madey(1971), J. M. Lockhart( 1971), G. A. Westenskow(1982), J. R. Henderson(1987) 5. T. Goldman, R. J. Hughes, and M. M. Nieto, Phs, Lett. II l (1986) 6. N. Beverini et al, LANL report LA-UR (1986) 7. B. L. Brown, W. S. Crane, and A. P. Mills Jr., Appl. Phy s. Lett (1968) 8. R. H. Howell, M. J. Fluss, I. J. Rosenberg, and P. Meyer, Nucl, Instr. and Methods B l.qlll, 373 (1985) 9. R. Rich, private communication. 1. L. I. Schiff and M. V. Barnhill, Phys. Rev. Ll.l. 167 (1966) 11. A. J. Dessler, F. C. Michel, H. E. Rorschach, and G. T. Trammel, Phys. Rev (1968) 12. C. Herring, Phys. Rev. l (1968) 13. J. Bardeen, "Comments on Shielding by Surface States", to be publhed in Near Zero 14. R. S. Hanni and J. M. J. Madey, Phys. Rev. B 11.,1976 (1978)

PHYSICS 12 NAME: Electrostatics Review

PHYSICS 12 NAME: Electrostatics Review NAME: Electrostatics Review 1. The diagram below shows two positive charges of magnitude Q and 2Q. Which vector best represents the direction of the electric field at point P, which is equidistant from