THE U NI V ERS IT Y OF MI C H I G A N COLLEGE OF LITERATURE, SCIENCE, AND THE ARTS Department of Physics Technical Report THE NEUTRAL DECAY MODE OF THE LAMBDA HYPERON AS OBSERVED IN A XENON BUBBLE CHAMBER Howard Co >ryant, UMRI Proect 03931 ' e ~. ~.. '~ "' '".. under -contract with~ Uo So ATOMIC ENERGY COMMISSION CONTRACT NO. AT (1-1)-363 CHICAGO OPERATIONS OFFICE ARGONNE, ILLINOIS administered bys THE UNIVERSITY OF MICHIGAN RESEARCH INSTITUTE ANN ARBOR August 1960

This report has also been submitted as a dissertation in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University-of Michigan, 1960

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vii ABSTRACT ix DEFINITIONS OF COMMON OR IMPORTANT SYMBOLS xi I. INTRODUCTION 1 II. EXPERIMENTAL ARRANGEMENT 4 III. DATA ANALYSIS 12 IV. THE NEUTRAL PIONIC BRANCHING RATIO OF THE A 24 V OTHER PROPERTIES OF THE A 48 A. The Asymmetry Parameter of the A 48 B. The Lifetime of the A 52 C. The Mass of the it~ from A Decay 56 APPENDIXES 59 A. The Pionic Decay of the A, V-A Theory, and the IAI = 1/2 Rule 59 Bo The Determination of the Asymmetry Parameter of the Neutral Mode (Calculations) 67 C. The Mass of the Tc from the Decay of the A (Calculations) 74 D. Search for a "Complete" Neutral Decay of the A 79 E. Lists of Events: ABC and ABD 82 BIBLIOGRAPHY 86 iii

LIST OF TABLES Table Page 1 Physical Properties of the A 3 2 Bubble Chamber Properties 6 3 The Computed Results of a Measurement of the Event Shown in Figure 4 19 v

LIST OF FIGURES Figure Page 1 Michigan Xenon -Bubble Chamber, Summer 1958. 5 2 Schematic of Bubble Chcnber Electronics, Summer 1958. 7 3 Typical Double V Event.' 16 4 Points Measured in Figure 5 o 17 5 Single K' with Two Associated Gamma Rayso 18 6 Distribution of 6 for K~'s and for A's. 29 7 Distribution of Difference between Measured G and Predicted G' for A's with Both Sides Stopping. 30 Calculated Energy Distribution for Converted Gamma Pairs. 33 9 The Percentage of A's with Legs Less than 2 mm Versus P Ao 40 10 Distributions of the Number of Tracks Per Picture Versus Number.o' Pictures o 44 11 Distributions of Cos of Cos 45 K0 12 Decay Length Distributions for ABC and ABD with A Distribution for ABD, 53 13 Momentum of Monte Carlo A's, X Distribution, and Distribution of Difference in X for Two Measurements. 57 14 Diagram Defining Vectors. 61 15 Plot of Possible Isotopic-Spin Mixtures. 64 16 Diagram Defining Terms in the io Decay. 70 17 Diagram Defining Neutral Decay Coordinate Systems. 72 18 Diagram Defining X and a, 74 vii

LIST OF FIGURES (concluded) Figures Page 19 Diagram Defining G* and. G 75 Jf 75 20 Photograph of "Complete" Neutral Decay. 78 21 Diagram of "Complete" Neutral Decay. 79 22 Diagram Defining Terms Used in Neutral Decay. 80 viii

ABSTRACT The decay of the lambda hyperon into a neutral pion and a neutron has long been suspected and indeed has been indirectly observed electronically and in a bubble chamber. For, about half of such neutral decays that occur in a xenon bubble chamber both gamma rays from the decay of the neutral pion convert into electron-positron pairs, This high conversion probability mnakes possible a rather clear-cut identification of spch events. In an exposure of The University of Michigan xenon bubble chamber to a beam of negative pions of about one billion electron volts kinetic energy, thirty-two events of the above described type were found in association with charged decays of the neutral theta meson in pictures of high visibility. On the basis of these events and ninetyy-six events of the charged-pionic decay mode of the lambda, with the same conditions as were applied to the neutral events, the rate of neutral decay to all pionic decays for the lambda hyperon is 0.35 + 0.05. The ratio of the neutral mode asymmetry parameter to the charged mode asymmetry parameter is found to be 1.16 + 0.97, and the mass (in terms of its energy equivalent) of the neutral piOn from the lambda decay is found to be 126 + 7 million electron volts. ix

DEFINITIONS OF COMMON OR IMPORTANT SYMBOLS MAg Mgo Mn Mass of the A, T~C neutron in Mev. PA Momentum of the A in Mev/c. LA Distance of decay of A from point of production in cm. V V-shaped bubble-track configurations which could be due to the decay of a neutral particle into two charged particles. 6 "Coplanarity angle," the angle between the plane of the V and the line joining its apex to the presumed origin. G The angle between the two legs of a V. GL 0G2 The angle between leg 1, 2 of a V and the line joining the apex and the presumed origin. ("r" or "p" can be substituted for "1" or "2" to indicate knowledge of type of particle involved. ) 9G, 9G Angle in the CM made by leg 1, 2 of a V and the line of flight of the particle which decayed into the V. Rl, R2 The range of leg 1, 2 in the xenon chamber. A The distance of closest approach between two gamma rays as predicted from the electron pairs which they produce. Ak The distance one must move the 2nd point of the direction measurement of the kth electron pair in order that the gamma ray k appears to come from an arbitrary point of origin. a) "Production angle," the angle -the line of flight of a particle makes with the direction of the beam track from which it was produced. ABC, ABD Used to indicate the category of events which satisfy criteria A, B and C, D given in chapter 4, or the number in the category ABC, ABD. ok The correction factor in the kth bias enumerated in chapter 4 used in computing the neutral branching ratio. xi

DEFINITIONS OF COMMON OR IMPORTANT SYMBOLS (concluded) R The ratio of the rate of A;- it~ + n to the rate of A ~- - + p. BA The neutral branching ratio defined as R/1 + Ro The angle between the directions of two associated gamma rays as determined by their electron pairs. LAB The laboratory coordinate system. RMS Root mean square. CM The center-of-mass coordinate system. xii

I. INTRODUCTION Since the first convincing proof for the existence of the A hyperon was presented i 1951 (1), much work has been done to determine its physical properties, the latest values for which are given in Table I. Although for several years the only observations of the particle were through the decay mode, A -> x + p, it was expected that the mode, A -> + n, should.also occur. The first attempts to observe this mode were done with counters using an "extended source" technique (1). This method involves measuring the apparent size of a gama source consisting of a target in a beam of protons. Since the lifetime of the go meson is less than 0 15 seconds, the i ts produced directly will not increase the apparent size. of the source. However, if relatively long-10 lived particles, say of lifetimes of the order of 10 seconds, which decay into gamnas either directly or through a g~ intermediary, are produced, the apparent size of the source as observed with counter-telescopes will appear to increase to a size depending on the velocity distributions and lifetimes of the parent particles. Moreover, as one lowers the energy of the proton beam below the thresholds for production of the parent particles, one should observe a disappearance of the extended source, This method indeed yielded strong, but indirect, evidence for the existence of the neutral mode of the A. Next Eisler et al (2) in a propane bubble ehamber looked for electron pairs in association with K0 mesons from the reaction + p -A + K~o They found 5. such gamma-produced pairsa, which, making use of the prodiuction kinematics and the measured momentum of the K{, they were able to show were consistent with coming from the decay of the ~0 from A ~- ~0 + nj but not l... -.....

-2 consistent with a scheme such as A -> single gamma + neutron. In 1955 Donald Glaser pointed out the usefulness of a heavy-liguid bubble chamber for the study of particle decay modes involving a rays (3), and in 1956 the operation of the first liquid xenon chamber was reported by the Michigan bubble chamber group (4). Shortly after, work was begun on a 21-liter chamber which was completed in the' Spring of 1958 and taken to the Bevatron at Berkeley. During the summer of 1958 an exposure was mde to -r mesons of about 1.1 Bev kinetic energy and about 160,000 pictures were taken (5). The study of the neutral pionic decay mode of the A as observed in these pictures is the subject of this thesis.

- 3 -Table 1. The Physical Properties of the A. Mass = 115138 + 0,13 Mev (6) Spin = 1/2 (7) Mean Life (20505 + 086) x 10 1seconds (8) Decay modes: A ' i + proton A -~t0 + neutron A * nucleon + lepton + neutrino (9) Pionic charged mode branching ratio: w(A~3" 4- p ) ~ +~ ) p.627 +.031 (10) w(A - all modes) Asymmetry parameter of charged mode, absolute value: _1> 0.73 + o1 (11) Ratio of asymmety parameters of two pionic modes: 06 - Properties determined in this thesis: Neutral pionic branching ratio: w(A-*w + n) ~3 -. 5 5 page 47 w(A-+ + n) + w(A. + p) QLP (charged mode) = 32 o11 page 50 loP (neutral mode) = 37.,28 page 51 / neutral ~- ~r = -1.1 6 097 page 51 ( _charged +148 -1o Mean Life (from charged mode) = ( 2.77.34 ) x 10 seconds page 52 Mass of the g~ from the A decay = 126 + 6 Mev page 58

IIo EXPERIMENTAL ARRANGEENT The Bbbl.e Chamber Exposure A schematic diagram of the xnon ubble chamber as it s during the summer of 1958 when this experiment was done ca be seen in Fig. lo Table 2 suDmaarizes the important properties of the chamber In late Jt ue, 1,958, the xenon butbble chamber was placed. in a conerete blok house on the Bevatron floor at Berkeleyo Using a bending magnet and a quadripole faoussirng magnet a beam passing through a H2 target being used by Cool et al (13) was made to pass through the center of the bubble chamber. Since the Cool experiment was a counter experiment whice reaired the beam to be spread over a time inxterval of about one hundred milliseconds in order to avoid gppileaup P and since for uiform b ble size in a bubble chamber the beam shrld be ess than a millisecond in duration, it was convenient to use the "'Rapid Beam Ejector" REB, modelled after a design by D r David Rahm of Brookhaven, by means of which about five percent of the total r beam could be delayed and formed into a spike about fifteen milliseconds after the main beam had passed through the apparatus The timingf the o ansi f the bubble chamber was adjusted so that the chamber was sensitive only to the particles occurring in the spile. A schematic diagram of the electronics associated wit the chamber and a profile of the pressure pulse during an expansion of the chamber cn be seen i Fign 2. The beam intensity at tae chamber was monitored by means of a plastic. scinti,1ator placed in front of the beam window of the bubble chamber and gated with a two millisecond gate centered on the RBE pulse, and the counts displayed on a scaler The signal from the ounter was also displayed in the control room of the Bevatron where by uts of the 'tbem shper d ch patience the operating erew as able;to clean ip the stray beam particles occurrling in te sensitive regiorn of the pressre pulse, thus improing greatly the quality of the pictres -II

5 -Water tight sheet metal ' housing for flash tube P l c s Film magazine circuit 1condensor Camera lens s I Brass j~t~Sth I I /Dry Nitrogen Cooling plate dap - ' Dw oXenon flash Film take-up tube ft 230 magazine ' Beam - Safety Helium at windo widow 140 psig rig 'Front silvered z Ixz Front silvered mirror I mirr orirror Camera side L' — J i __view Glass window.Heliumat Xenon vapor 140 psig prcess. 370 psi Cooling plate - Rubber diaphragm Ei /\ Ali Bellevi lie springs ~~~~~Camera top i \ " \ i \ " ~ Pressure pick-up Kistler SLM PZ 14 view ' \- Perforated hardened steel plate i ~ _^ ~ ^, _j~ ii^4 ~ l^ Dow Corning Silicone oil Rubber bumper ~~~~~~,Film take-up r~ ~-Hardened steel magazine Film magazine -- Hollow Al piston top view top view X BRubber bumper Compressed air -hin steel shell Barksdale Exhaus valves(2 Automobile Exh not showr, muffler ~ EhuExhaust Expansion surge Flexible hose -, ~. chamber From air compressor Michigan Xenon Bubble Chamber Summer 1958 Side view Cross secfion Fig. 1. Michigan Xenon Bubble Chamber, Summer 1958.

-6 -Table 2. Bubble Chamber Properties Chamber Dimensions Active volume: 10" deep; 12" diameter; 21 liters Glass windows: 5" thick; 15" diameter Distance between camera lenses: 14 3/8" Distance from lens of camera to center of the chamber: 26" Cylinder diameter: 3.9940 +.0005" Piston travel distance: 3 31/32" Displacement: 0.82 liters Expansion System Diaphragm: Raybestus-Manhattan 2-ply nylon in buma "n" 683, 1/8" thick Supporting fluid: Dqw-Corning "-200" Silicone Oil Barksdale valves: 4 of them, inside diameter 3/4" Compressor pressure: 420-430 p.s.i.g. Free volume: 2.7-3, 0 Pressure pickups: SIM PZ-14, Kistler Instrument Co. (Quartz-piezoelectric) Cooling System Coolant: 50-50 mixture of ethylene glycol and water Refrigerator: 2-ton G.E. designed by Mr. Hugh J. Scullen of Detroit Optical System Light source: General Electric FT 230 (operating voltage about 1500 volts d.c. and capacitance of about 45 microfarads) Duration of light pulse: 100 microseconds Light delay after beam: about 1.5 milliseconds Chamber illumination optics: dark field Collimation lens: 18" focal length; 12" diameter Mirrors: front-silvered Camera: F stop f/45 Film: Kodak Linagraph Panchromatic 70 mm. (blue-gray acetate with resolving power of 70 lines per i. ) Xenon Parameters at Operating Conditions T = (-215+ 0.1)C Density = 2.17 grams/cm.3 Vapor pressure = 370 ps0i^og. Radiation length 3*9 cm.

-7 -Tme Delay Barksdale I pip from Time Dely Firing Circuit Bevatron.. I Control Room RBE Pulse Top Film Mag. PusCoincidence Camera Wind Counter Pulse Circuit Circuit - Bottom Film Mag. Time Deight Time Delay Firing Circuit 4501 Pressure pickup pulse from silicone 312 psi Counter \ 174 pulse PRBE. 5millisec/division t --- Counter Pulse RBE Pulse Light Source Monitor Silicone Pressure Tech tronix Pickup ~ Scope 535 Dual Trace Schematic of Bubble Chamber Elecfronics Summer 1958 Fig. 2. Schematic of Bubble Chamber Electronics, Summer 1958.

from this mn. By monitoring the beam in this way he nmber of usable pictures due to too many tracks (sixteen or more) was kept a't a mini The light as fired by a pulse delayed about 1.5 milliseconds after te RBE e light was monitored, with a phototub in order that its inte$nsity co "ld be kept constanrt The duration of 'the light flash was about, 100 se conds. We foand 'that tUe number of tracks coiud also be vmonitored visually by lookinrg tlough a pe1p1o1 +t hadbeen built iinto ite chm 'in order to abs vrie the xenon. level ae temperatLet OP the in d of t bbble ciamber was reg.lated. 'to -(21o,5 Ol') degrees centi..gradee and. since the operation and timing e rather precse one expects that there were no appreciable fluctuations in the density of 'the xenon from picture to picture. As th.e e.eperiment pirogrssed it as fod, th t te xenon gr.ad'.aily betmes cloudy due to opaque residue from the rubber diaphragm. The xenon was removed and replaced 'twice during 'te ran; this process involves distillation wnch eawvs ~mch of th residue n the storage tankso The., konetie energy tof athe be ws ety t Cool. expriment and vas abot 1,0 Bev for the first 60,000 frames and o Bev for the rest until 160 000, except or frames bttween the numbers 104,037 and. 106,606 for which the beam energy dropped to 0.8 Bev for a background check for Cool. lDring the bout + 1000 frame s of A meesons were also ltsen; these will not be discussed in this paper. e did not independently measure the moment-m of the beo during the eperiment. The purity of the beam was not measured. Data Handling After the film ws developed by the photog3raphic lab at the awenc,adiation Labor.atory it ws ct uRp into 100 foot rolls of 400 frmes each and sent to t High Ergy Lab at ithe ntversity of Michigaw for scanning, meas ilng

- 9 and analysiso The scaning of the pictures as done in a quonset hut located on East University in four specially constructed seanning boothso The scanning booths were constructed, so that the two views of each frame couLd be projected completely independent of each other onto a white table top in front of the observer. The images were a little larger than life sizeo Because of this independent motion of the two views of the same exposure one could easily deterpmine the parallax of a point in the chamber and thus roughly detezmine its position quite easily, We found that a good scanner could look through about 100 frames an hour. Sketches were made of all events that were of interesto A more detailed discussion of the scanning as it is related to this _theRis ll be given in the next chapter.o.' After the scannin, of a roll as completed, the roll with its sketch3es of interesting events was returned to room 3071 Randall Laboratory here the events noted as being of interest were projected on one of the two "Green Screens" (precision measuring devices, so called because of the green coating on the projection glass), and if the evnt was deemed "real" by the measurer, the event was measured. The definition of "real varied as the measuring progressed due to experience as noted in the next chapter. An event was real a s far as this thesis is concerned if it did notclearly violate any of the criteria for scanners and measurers as. given in the next chaptero The Measuring Devices The Green Screens were equipped with two sets of interchangeable lenses, one set giving a magnification of about 1.75 life size and the other set giving a magnification of about k times life 'size. The Green Screens enabled one to get a nuch better look at the events noted by the scanners, and events found to be not real were rejected at this stage.

-10 - The twso Green Screens differed in partcualars but their main featr were the same9 A coding seystem was set up so that each pint of any parti.eallr event could be designated. by a three-digit nmbero Th sage s we.e digitized. so that their positions could be pnched directly onBM cardso Tn orer to measure the spatial coordinates of a particl.ar point in the ha ber,7 one moved the stage of the Green Screen so that the imige of the point in ttt es viws e nererd on a fiducial cro shaLr tne s ren; te onre seat t he poirts coded. designation on a dial and. phed. tihe rea-out rLstton., al,., to 3ticqally7 rc.a,d both the coord nates of th2 stage and thre point d.esignti n i RepetitLion of this procedure for the other stereo iew of tVe point comp1lted the measurement In-t this ma r an event co d be mesu i abot 15 min'tes (abou4 t.1.6 points)0 C~heecks were frequenrtly r d.e for encoder errors~ Comps.ta, ions e me'thod of h.an ni ng the data cards evolved consid erIy dTwgrn the osse ci of anlyss of t lese pictires, going frto a rather nbzro e t pxr9aedwl!"e rig the TBM 6)50 to* e verey con-ven.i.ent one sing V.e LB - 74 V. t Ws rnn io.tusnteIB 04a on te Mchigan ampu in the F1all of 1 959. Oe final IBM progr,' ltped by Mro R.lc..otard Hartug compated first the spatial coordinates of the mesre points in the biubbe chember.nd then all the geometfric l propertc es 0 t2.. array of ponts as ca.led fo by their code numsbers. Te n4en s+tep was thie &naysis of the measurements and the c itsed2 quant+tiies. By mean of range-energy curves and kinematics graphs th events were@ ckheed for consistency and identified and classified Details of thls p t ess as related to P e sject of this thesis willt also e giv i n e net chaptero Flinally, if any qessti3s emained abt t f e cjas casf t

event, it was rescanned on a Green Screen, and perhaps remeasuredo At this point the data was available for various studies of which this thesis is but one of four~

III. DAT ANALYSIS Data selection and assumptions: Thue principal quantity to be determined about the new tral mod.e o the A in this thesis is 'the neutral pionic bra-nching ratio lefined a B W(A__ 3tlW(A c+ n) PA W' (A ~ + D.) + W(A p where W(x) is the rate of process x. In determining this ratio we elect to use those A's from te reaction + xen ules A + eno n e A +resi.duals or tC + xenon nucle.us — ) + + + resid.al s (Zo Y + A) for which K the K decays into 'two charged pion$s iae. K -~)> u + g By restricting ourselves to th even:t-types described aLJove e ignore a lairge fraction of the A's in thea xenon chamber for which the rchged. mode does not oceur. The reasons for making this restriction are i. To avoid possible scanning bias due to th e quitl different appearances of the two A modes A ---- + n (two electron pairs) and A~ ----> +' p (a "V") - 12 -

- 13 iil To positively identify the A, especially the neutral mode* We assume that electron pairs from converted gamma rays point to the position of the A decay, i.e. the "" occurring in the neutral mode of the A decay is the same one as observed in the reaction -t + p -> A ~ + n (s- absorption of hydrogen) and thus has a lifetime of about 10 seconds (14)o Scanning: Definitions T"Vs" are defined as bubble-track configurations in which there is a discontinuity (known as the apex) in direction or bubble density, "Legs of the V" are defined as the continuous segments of the V separated by the discontinuity, "V origins" are defined to be beam-pion interactions such that the lines joining the interactions and the V-discontinuity pass between the two legs of the V in both stereo views. "Associated electron pairs" are electron pairs that are consistent with having been produced by rays which do not appear to come from beam or secondary interactions which are not V origins, but which occur in frames containing V so Instructions to scanners: Scanners -were intrxS cted to look for VTs with origins and to look for associated pairs. They were instructed to trace on a sheet of paper one view of any such event and to record a) the view (top or bottom camera), b) the frame number, c) the apparent bubble density of all tracks participating in the event (light, medium, or heavy), d) the apparent fate of each particle participating in the event (stops, interacts, or leaves the chamber), e) the number of beam tracks in the frame (lightly ionizing tracks less than 15~ in direction from the "x-axs" efined below), f) the scanner's Initials.

Beubble c be camber coord.nate system As seen in Fig. the active volume of the chanber is a cylinder 10" long ad 12" in difameter, boundeda on the ends by two large lylindr.ical nwidows. winow through which the cameras "look" we call.: ' front" window and the indow throuh which -thZe illumination system hines we call the tack" window. Both front and back windows ar scrzbed. with g'rid Marks (see Fig. 3) in a suare array with spacing of 2 cm. and parallel to 'the stereo axis (the line joining the two camera lenses)o Tlhe cernt'zr grl. mark of 'the frornt window we take as the origin of a right-hande Cartesia coordinate system wit. the x ais running parallel to the plan of te.a front window and perpendicTlar to the stereo axis and witt the same sense and approximate dietion of the bramete z axis -s take as n to the front window with sense such 'that the z coordinate i creases as one goes from front to backo Measuring: The measuring and analysis was done in two parts. The f rst par (1I) consisted o'f the pictaures up to frame number 86,000 and t e seond) pa (II) dealt with the pict.res f rom8 86,000 'to 140I000. Part I was done first and the procedure as a little more involved and ausualy more tedious than that of part II for wich we were able to take advantage of the experience gained in part I. The results of part I have already been reported (5B) For part I each event with one or two Vsa with or wthout associated. electron pairs was measured. For part II only those events having eiter two Vs or One V and two or more associated electron pairs were measure although all events found by the scanners were care fly checked to asune that nothing had been missed (Gaa pairs caa easily be ovrlookedo )

- 15 - A typical double V event (charged lambda and 8 KI decays) and a rather good single KI with associated gamma pairs can be seen in Fig. 3 and Fig. 5. Fig. 4 shows the points that were measured on the neutral event shown in Fig. 5. The center grid mark (1) and the four corner grid marks (13, 14, 15, 16) were routinely measured to determine the absolute positions of the other points, to check on film shrinkage, and to check for rotation of the two views with respect to each other. Then all possible origins (2) for the V's were measuried, and a second point (3) taken along the track to determine the beam direction. The apex point (4) was measured and points at appropriate points along each leg (5, 6, 7, 8), including the point at which the leg either stops or leaves the chamber. Each electron pair was measured at its apex (9, 11) and usually near the point where the two electron tracks appear to separate (10, 12). (One can show that the optimum point to measure for determination of the direction of the pair is near the separation point, although electron pairs at this energy, 20 to 200 Mev, suffer from rather violent statistical fluctuations.) The quantities pertaining to this paper computed by our final program are given in Table 3. Examination of the compated spatial coordinates of several duplicate measurements of typical points in the chamber show that the BIf error in determining the location of points in the chamber is obout.03 cm. For 22 duplicate measurements the average difference in the x and y coordinates was about.01 cm and in the z,.02 cm. The analysis of V's The pertinent information for the identification and classification of V's is the coplanarity of the V with respect to the origin, a, the opening angle, Q, the angles of the two legs with respect to the line of flight of

-16 -_i$~~~iliiii ~ ~ ~ ~ t L:j::. ~:ji: _i:i:I:::::::::::::": ~ _ - _:::::::::-::::g Y _ _::: — n* _ ~i~-i-j~i:1:::i.: —:::::'::::::::::': -iL~~ri L:::::::::j:: _ Ls::::::::::: _:::::::::::.::::::::-:::1-::~i:::::: * _ __ — I -. —:::- |0 __::::- I |::":j:;: ~::-:-::i::::~ —S::::-::::::::::::: -:r-::-i:::j~i:- rii- - ~-ii:::: i-';ii- -iX~-: j:-:i:: -~~Fg 3. Tyia obeVEe

- 17 - I Fig. 4. Points Measured in Figure 5.

0 I 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(. aD ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~4 H - oH H bD I ' Elt -H _ ~~~~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.- 1* | I *l I * _ Ad~~~~~ 1 is * | l * _ % ' 1 an~~~~~~~~~~~~~~~~~~~~~~~~~~~o CD _l pi ace Ed~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.H ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~PI

19 - Table 3. The Computed Results of a Measurement of the Event Shown in Figure 4 Spatial Coordinates (all measurements are in cm unless otherise indicated) Point x y z Point x y z 1 0,00 0.00 0 00 7 8,26 3.69 8.60 2 - 9.26 3.82 8.05 8 9.17 3.75 24.96 3 -10.53 3.76 8.02 9 4.28 4.20 11.22 4 - 8,80 3.67 7.84 10 - 3,95 436 11-33 5 - 8.21 3.10 6.36 11 5.54 2.76 11.15 6 - 6.10.62 0.09 12 - 5.23 225 11.52 Origin Data Distance between 3 and 2 = 1.3 Direction cosines of the beam = 0.9988, 0.0447, 0.0177 V Data Leg One: Range = 8.76 = 1,69 + 7.07 Chord (distance between 4 and 6) = 8 8 Angle between two segments of leg one = 3,40 Direction cosines of leg one = 0.3534, -0.3359, -0.8731 eg Two: Range 24.85 0.93 + 23.91 Chord = 24.8 Angle = 11.30 Direction cosines of leg two = 05820, 0.0266, 0.8128 Opening Angle (angle between the two legs of the V), Q = 120.9 Errors in 0 due to motion of the dependent coordinates by 100 microns 4) 3.90, 1.6,~ 1o0 5) 1.5~ 0.3~ 0 70 7) 2*.3~ lol' 1.6~ V Origin Data Direction cosines of the V = 0.8733, -0*2957, -0.3872 Decay Length = 0.53 Potential path = 15.61 Production angle = 31e5~ Direction cosines of normal to the production plane = -0.0230, 0.7687, -0.6391

Table 3. V Origin Data (con't) Angle between leg one n e Vd the T direction, l 7 79,30 Errors in @ due to motion of the coordinates by 100 micronsi 2) 2,5, 0.5a 4,70 4) 0,3, 110, 6,80 7) 2.3", 1.9o0 1.6 Coplanarity anile, 8 = 4,20 Errors in due to motion of coordinates by 100 microns: 2) 1,40, 5o00 1,o1 4) 2.5", 9,20, 2.30 5) 0,5" 1,8, 0,50 7) 0070 220, 0,60 Gamma Ray Data Distance one must move coordinates of 12) if gama one were to come from origin = 0 22, 0.36, 0.07 Distance one must move coordinates of 10) if gamma two were to come from origin = -0.01, -0.13, 0o09 Length of nose of gamma one (distance between 11 and 12) = 0.71 Length of nose of gamma two (distance between 9 and 10) = 0 37 Coordinates of best origin point: -5~95, 3,43, 10o66 Distance of closest approach of the projected paths of the gaas = 0o006 Conversion length of gamma one = 0.92 Conversion length of gamma two = 1,92 Amounts one must add to coordinates of 12) if gamma one were to come from best origin point: 0.000, 0.000, 0 000 Amounts one must add to coordinates of 10) if gamma two were to come from best origin point:.001,.000 o.001 Production angle of parent = 38,00 Decay length = 423 Angle between gammas = 759

the V from the origin, G and 2, and the distances the two legs go in the chamber, R1 and R2 If a track does nt leave the chamber it is not always clear whether it stops or interacts, although bubble density is a clueo This ambigity must always be kept in mind. One starts by making a reasonable assumption about the fate of each leg. 1) If both legs stop in the chamber the V cannot be a 1K (except under rare circumstances)o. Then assuming the V is a lambda one uses the two raes R1 and R2 to determine the predicted opening angle, @, for which there are in general two possibilities depending on which leg is chosen as the proton. By comparing 9 as predicted and 0 as measured one then tentatively decides if the V is a lambda and which leg is the proton, If the V is consistent with being a lambda then the predicted opening angle., 9 and the range of the proton or the range of the pion are usei:. to.pr:tt the angle between the line of flight of the V and the proton or pion, p or 0. If the predicted angles, Op and 0, are consistent with their counterparts, 01 and G2, and the coplanaaity agle ~, is consistent with being zero, then the V is identified as being a real A to origin. If 0 is consistent, but and 1 and 02 are not, then the V is identified as a possible scattered Ao The predicted angles, and 0, are used to determine the momentum and the center of mass p decay angle for the A. If 0 is not consistent, but i is consistent with being zero, one side may not have actually stopped, and one proceeds to 2), 2) If one side stops, say leg 1, and $ is consistent with being zero, one uses R1 and 0 to predict 1 under the assumptions that a) the V is a K:, b) the V is a A ith leg as proton and ) the is a A with leg as Epion If none of these assptions gives a prediction for 0 tat

22 is consistent with its measred value, the one proceeds to 3)o If one or more of these assumptions give a consistent value fr 01 then one uses Q2 = (o - Q1) to predict a range for leg 2. If this predicted range is significantly less than the measured lower limit on the range then one proceeds to 3). If not, one may be able to decide further between the assumptions a), b) or c) if there were any ambiguity One then uses the predicted angles 01 and 02 to determine the momentum and the center of mass decay angle. It is not always possible to differentiate by the above means between a lambda aad a Kj, however. a^nd further information imst be sed such as bubble density and the identit^ of the other particle in the pictZre if there is another particle associated. 3) If neither side stops and the coplanarity is consistent with zero, then one uses the two angles, '1 and 9, to predict the ranges of the two legs. By comparing the predicted ranges with the lower limits on the rnges as measured, R1 and R2, one can eliminate bogas Vs and usually differentiate betAween A's and KlS although this is not always possible0 If the ranges are consistent with the measurements, one uses the two ang1es to determine e themomentum ad the CM decay anle The analysis and computations of associated pairs As described above each electron pair believed to be associated with a suspected KI1 and one or more other such pairs was measured at two pointss one being the apex and the other point the most representative in 'the opinion of the measurer of the most likely direction of the g ray. As pointed out above usually the second point is chosen where the two electron tracks of the ps aea the par appear t diverge fr eac other alth ere are man exceptions for e cases when the energy is very meqpally divided

23 between te thwo electrons or when, as in the case of pairs nearly perpendicular to the beam direction (x-axis), it is more impot that one be assured he is measuring corresponding points, (The difference between the x coordinates o.f two points is- prctiially constant for the two stereo views, but the y difference is not ) Then from the positions and directions of any to electron pairs one c tes the most likely point of origin of their two parent gama rays, this point being defined as the point for which the quantit 2 2 Q=4 + 4 is minimized where A is the distance one must move the second point of the measurement of the kt gama ray in order that the projected path of the gmm ray pass throuh te hypothesized point of origin From the best meeting point one calculates the production le of the A, assuming it is from the same origin as the i;, and also its decay distance, LA One can estimate a lower limit on the energy of each pair by measuring the total length of the electron paths of each pairo This was done by tracing the paths on both Tiews with a "verstmeter", a small roller device used to measure distances on maps, and using a scaling factor given by the calculated distance between two measured points and the same distance as meaured with the verstmetero The energy loss per centimeter by minim ionizing particles is about 279 ev in the bubble chamber. This was taken to be the energy loss of the electrons, neglecting such effects as relativistic rise*

IV.o NEUTL PIONIC BRANCHING RATIO OF TEE A Definitions of the problem As described in the preceeding chapter the rough data for the calculation of the branching ratio, BA, consists of all events of the type o + xenon nucleus — >A + K~ + residuals or ~-_ O + Ko + residuals where Zo ~ + A (lifetime 1019 seconds) for which the A dcecayseither as i. A — ~ + p ii A gt: + n and the K~ appears as a K1 and decays as + + Operationally we can defin te two categories as iL) A V with an origin that satisfies the kinematcs conditions on Kq —> a + t (see analysis of Vss, page 15) and anothr V which satisfies the kinematics conditions on the decay A — - + p and which could have be0en produced at the same interaction from which the K1 appears to comeo iio ) A V with an origin that satisfies the kinematics condition= on K- =+ + ~, and ea least two associated electron pairos From these two categories of rough data two fin data c ategories - 24 -

25 were chosen according to the criteria stated below~ We shall denote these two final categories as ABC (corresponding to i) and ABD (corresponding to ii)o The criteria were chosen to insure high scanring efficiency and to cut dow on bacground events Before the mbers of events found to be in the two categories ABC and ABD can be compred several corrections must be made. These corrections are listed elow with their corresponding correction factors, a. It is important to note at this point that no biases affecting the branching ratio are introduced by the criteria on q since the is simply used as a "signature" for the presence of a A. We define the ratio of neutral to charged events to be Rwit A -x~ +n) R = + w A. r + P and experimentally aaa ABD R 12 t a.ea5a6ABC where ABD and ABC are taken to stand for the number of events found in the correspondincg categories, and where a is the correction for the fact that not all occurrences of neutral decay have both gamas converting in the chambero a is the correction for events that satisfy ABD but are really cases in which only one gamma from the io converts, the other g ama coming from the decay of a ~O, a3 is the correction for background in the ABD category a4 is the correction for the bias lntroduced by restriction C3 below (cutoff) o a. is the correction for the bias introduced by restriction C5

26 below (one -legged V T) a6 is the correction for the relative scanning efficiency for the ABC events compared to the ABD events. The branching ratio as defined above then wil be given by BCriteria A. General 1o The picture must have less than 16 beam tracks. A beam track is defined as any lightly ionized traek entering the chamber at projected angle on either view less than 15' with respect to the x (beam) axis. 2 The picture must have no background of bubbles or electron shower which could possibly obscure an electron pair, or less likely, a Vo 30 The picture may not be torn, badly developed or d A i n an wayo 4 The presed origin for the associated particles satisfyg 'the criteria below ust not have a prong tat leaves the chambro (This requirement was used in part II to eltminate many useless lmeasurements of bogs Vts but vey few good ones.) B. Restrictions on the K1.:There must be a V in the picture that fits the kinematics cures for the twoody decay of the K within the expected errors, and for which the predicted ranges are in agreement with their observed bubble densities. 2 The measured eoplanarity of they aV from the first measuemnt mst be less tn o to five dlegrees, independent of the

27 estimated errors invlved& (Since K1 ith wide opening angle hve in general larger errors thSn with small opening angles, wideoangle K are discriminated against here. This discrimination is desirble here because the wide angle V's are difficult to recognize and hence their detection depends on the detection of the lambdao ) 3o The deay dist t be at least 5 mill/m0etrs 4, The apex of the V must fll within the fidacial volume defined by R! ll centimeters (R x2 '+ y); 2 cm. 4- z 24 cm Co Requirements on the charged mode 1. In addtion to the K, there must be a V in the pictur that fits the kinenatics curves of the lambda within the expeted error and for which theb bbe densities are consistent with the predicted 2o The V, although it may have scattered, must be conistent with having been produced. at te same origin as the V satisfying criterit, B above4 30 The decy d$istce must be at least 5 millmeters 40 The apex must fall within the f e iducial volume defined in B3 above0 5 Both legs of the V mut be greater than 2 millimeters in lengtho D. Requirements on the neutral mode 1. There must be t least two electron pairs in the picture that ar consistent with having been produced by ga having a common origin0 2. Neither of the pairs st atppea to hae eoe from an Interaction, excluding the production reaction 3o Each pair mst have at least 3 centimeters of electron tracko

28 4. The apex of each patr mst fall inside the fiduacival vole deiine in B3 above, Uncorrected:result s Events satisfying ABC in part I, 51. In part II, 45. Events satisfying ABD in part I, 15 In part II, Jo Events satisfying ABCD in part I, l In part. II, 0o The distribution in I for the K~ s in the ABC ad ABD categories and for the A 's in the ABC category can be seen i.n Fig 6 eThe d fferenee between the measur opnin, nd t pedit opening nuglee ap, openg (based on the ranges of the two legs) for all ABC A's for which both legs stop in the chamber ithout sutffering any apparent inelastic collisions can be seen in Fig0 7. (Of the 96 ABC A's, 51 have oth legs stop, 33 have only one leg stop, and 12 have neither leg stop.) Othe per properties of nterest of ABC and ABD events are tabulated in Appendix E Corrections A o The neutral mode lo The conversion probability for both g s from the o is the lgest ~correction mde nd was based on a Monte Carlo calc lation c In effect this calculation computed the averge probability for conversion for a sample of r( os having tihe same momenta and positions as a group of - Is from labdas occurring in dodble V events The events chosen w.re required to pass A3 and Ak4 and B and C, except C3 and C5. The calculation was perfomed, on the IBM 704~ The Input aita for each event were i) the size of the iedca volue as defined Bn B4, ii) the location of the lambda apex, iii) the nergy of the pion as tobtained from its measured or calculated range, iv) the dire tion cosines of the piono The calcblation went as follows: The pion was alswed

- 29 - 14 2 ABC A PART I S1 t PART II 1 2 3 4 5 6 7 8 9 10 11 SCAT DEGREES 22 - 20 18 ABC K0 16 14 12 - 3 4 5 2 3 4 5 1o 8 DEGREES 8 DEGREES Fig. 6. Distribution of for K and for Fig. 6. Distribution of 5 for Ko's and for A's.

- 30 - ABC -30 -20 -10 0 10 20 30 8-e' DEGREES Fig. 7. Distribution of Difference between Measured G and Predicted 9' for A's with Both Sides Stopping.

-31 - to deca using five different sets of center-of-ss decay g es based on 10 random numbers generated by a computer subroutine For each of the resulting hypothetical gaa rays a potential path was computed and the probability that the gmwould convert within the potential path was computed using a elion between mean conversion distance and eergy discussed below0 Then usin the results for the five trials the probabilities of one and two gas convertig in the chamber wre compted. The average conversion probability for the sampl was then obtained0 The-results of this calcultion gave the follkring 4here the errors ted are statistical-: Probability that both gams convert (denote P(2)) Part I P(2) = 48 + ~02 Par II P( 42) = 51 i02 Probability that only one of the gammas convert (dnote P(l)) Part I P(O) = G43 Q01 Part II P(l) = o0 - 01 The correction factor, a1, defined on page for conversion probability is then a1 2=.02 004 The relation between mean onversion length, in centimeters,:nd the gama energy, E in Mev used in te Monte Carlo calculatieon wa g = - 5.0~9 + 2 E 0 Eg Eg This fotea wBs got by empirialy fitting the esults of a' nfmercl 1 integrationl on the Bethe-Heiltler fo a with corrections for screening, se of the Bo approximtion and prodiaction Inte electronst fitli (15)o

The density of xenon ws taken to be 20167 /gmo/no. The results which the fomla is taken to represent are below, E (Me,) (cm.) 10 19 o10 30 9.868 50 8l165 70 7.391 100 6o8%6 200 6o042 500 5.627 oo 5 5090 One can show from the calculated energy distribution for converted gama pairs by the Monte Carlo method given in Fig0 8 that the use of the above empirically fit formula give an estimate of the conversion efficiency which is about.1% tooo igh0 This effect has been neglected, 2. Correction for ZE even ts Certain of the events satisfying criteria.ABD were not really cases in which both gamms from the it converted., but rat he cases in which only one gama from the on converted and the gama from a E~ alao convertedo Since ga s from Z~ occur in bout; 10% of the dovb V events, 10 of theo cass here ly onl y one from the A converts appear as 2ngama events0 In -some cases these eve ts are consistent idti identification as bona fide neutral decay events., ioeo they aV'tisfy D, The correction for this effect was made as follows. All events that satisfied ABD an. which had three associated ga: rayr pairs were examined carefullyo Let us denote the three pairs as, b, and co If allr three of combS tis ab, ac, and e culd, be misataken for as a from the la.mbda then te event is ass$Igned the n 1.br If only two of

48 40 32 24 16 20 40 60 80 100 120 140 160 180 200 220 ENERGY OF GAMMA mev Fig. 8. Calculated Energy Distribution for Converted Gamma Pairs.

34 the combinations could be mistaken for the gams from the leambda then the event' i assigned the number 1/2a If on ey o of the combinations could be real, then the event is not counted Then one expects tat the numer of bogus two-gaa events in sampe ill b h s he e of the ssigned n ers multiplied by the ratio of the probability of one ga converting to the probabil ty for two sg s converting o In part I two such three a events were found each th weight 1. In part II two such events were found, each with eight l/2. The total correction will then be -4,3 4,0 o _ 1 + 1 - 2o.6 events. The correction factor then for ABD events will be = 0.93 ^04 where the error is statistictal. 3. Background. In the 96 events satisfying, AC, one event was found that also satisfied critria D. This means that the backgroun d of events satisfying D is about 1%, or a3 99 0010 o4 Correction for electron pairs for which the electron track length is less than 3 cmo., i eo those that.fail D3o RR.o Wilsoon (16 Caro cacultio on the range and straggling of electrons in leado His results wee tated in terms of radiation lengths and should apply in generalo He finds the following equations describe his Tesults

-35 -R(E) = 1 2n 2 In (E/ 2 in 2 + 1) where R(E) is the range in centimeters of an electron of energy E in Mev, 1 is the radiation length in centimeters, 3 is the energy r lost by an electron going one radiation length (minimum ionizing) in Mev. For xenon 1r 3.9 cm. and B = 10.88 Mev. The percentage straggling (RMS) is given by S/R(E) where s/R(E) = (1 - n(E)/l ) (In 2 lr/R(E))1/2 These results do not take into account multiple scattering. As an estimate of the ranges of electrons occurring in pairs in the xenon chamber we took the average range of the two etremes, namey when the energy of the gama, is equally divided between the two electrons and when one electron takes all the energy of the ganmma The probability for any particular ratio of energies is roughly independent of the ratio. That is we took as the range of the pair R pair. 2 where E is the energy of the gamma producing the pair. The straggling was taken as s pair 2 The results of this are

20 Mev 4~03 cmx. lo 0 cmao 20 30 5o. 1. 62 9.0 40 5o99 1 96 65 50 6.69 2.25 >0 60 7.28 2 0o 4, 80 380 2 2o88 35 100 9,o06 3 0o 3o 120 9(65 3~42 2.5 160 0-o 67 3 80 2.0 200 1,1.61 4 09 2 0 From the ene y tIstrIbtion of Mosnte Carlo ggi emas;gvn In Figo 8, one finds tat about 35,:,% of the gmas waonuld, be L.es than 3 co i.,n length. This relt dsu~lt shoa'.d be regarded as an upper limit beca;ua it neglects secondya1, t electrons, which in practice cadnnot be spacated, from the prii~'xB4e No. o;ec tion ias made the rfore fr pairs fJ alling below 3 cm. in lengtho This:r.r.equtm, rment ts resps to' for tue rmje'.tion of t 1least one evt f scts.f. ied te ABD condtions othervt se0 1. measured length of t e rejected electron pair was 1:,2 cm. This;requ>iemenlot of tin t ck 1 ngt a wa..eftul In irIP. t,.itst 'l iio'%A the ne cessity tort cons ~21. ne, th ume ous shot backg, d1. e.L.ceetotn tIckts that occur in Pte xOn tber B. The charged, mode 1o Correction for amias decaying less thhan 5..o from their origins There is no restriction corresponding to the 5 omm cd eay length cut-off (C3) for te charged mode placed on thte neutral mod In order. to correct or ths we mst calu1te theo -rt*i of deCays occurrYinf from 0 to 5 mmo compared to the number o r1ring from 5 mmo to the potential. paths o We

37 - take the probability for decay at a distance x from th origin in an interval.x as P(x)dx = (1/) exp (-x/f) dx where 7 is the mean decay length ad is given by h = pTC/m hCere p is thne tmmenmtn of the lebda in /c, is e rest ener. r in Mev (1115 o2), T is th, if etime in seconds 10 )0 and 2c i s t Ihe velocity of light in cmo/seC.o Then for N evwnt..'.d to fit the cuiteria one eec the nber missed from 0 to 5 mo will be n where 1 e1.T^ ep - ef 5/AI where 1i is lthe poten t;al path of the lambda in event io Tb.e qwantity /N was computed usg the 864 ABC events BCtth origins inside the fid.ial volwme (asee page 27 ) ad -s found to be n/N o14. o Qll, where te or i statisticalo The correction for ABC events sthen 4 l o.214 o.011 20 Correction for one legged Aso One legged A's are those cases of the charged mode in which one of the two legs is too short to be sts be overlooked and, if foed, are difficult to identif positively the requirmentthat eboet legs hve aes lone ta2 a n B o (C5) mpased on.e ABC evn

and a correction made for those failing this resuirement: Let Ep, p* and P* be the total energy in the LA, total energ in the A CM nd m mentam in the A CM, respetiely, of the proton, and Ey, E* and P* be the corresponding quantities for the to Thn E (s* + PR Cos *) P p and I (1* - PP cos 0 ) where 3 = v/c r is +t: e velocity of t he A and 8 - (1 -2-J2 and, O* is the angle between the proton and the A line,-of -fl'ight i.n t e A CMO Putting in nu emnial values aid letting the enX lergiesg of VSe i p corresponding to range of 2 mmn, be,(a mn.) arId BE (2 n) resp)ctLveaJy one can show -that it is possible for Ep <Ep(a mm. ) only for the A mometum, P A' se th san 308..e/c and EB ES (2 x..a ) for 400o < PA oo0 Mev/c o Let us designatee e % of Ais with both legs ggreater th an 2 mm. by F(PA), a function of te A momentum ~ Then for PA <67 Mev/c, F(P^) = O For 67 < PA (308 M/c, F(PA)= ~ TW

- 39 where E @2*() -m2 and Ep(2 mmo) = 9512 Mev; Ep = 943)5; P* = 99~4 Mev/c. p P For 308<PA <40 Mev/c, F(PA) 100l% cos Q*(2 mo) = 3.. where E* = 171-7 4ev; B (2 mm.) = 146 Mewr P* 994 Mev/c. For P^ 1200 Mew/c, F(PA) = 100o A plot Of F(PA) as a function of PA is givn n Fig 9~ The corction factor then, as defined. on page is N where Pe is the momentnm of te ih Ao Using 94 ABC events (the two Aas tht clearly scattered were omitted) c5 - 1o069 + 011, where the error is statistiCalo Co Scannit efficiency 1. The direct method for detening sannng efficiency is 'to scan some number of frames ticeF, sy by Iscaners i a d 2, Let n3 be the n. er of events found by bth anners, n1 b'ethe number found eb 1 alone and n2 be the nber found be scaaner 2 aloneO Th then" t he "tru e" nber of nts i he $ape ^h be

- 40 - 100 SHORT PIONS 90 F (PA) SHORT PROTONS 80 60 40 20 200 400 600 800 1000 1200 1400 PA mev/c Fig. 9. The Percentage of A's with Legs Less than 2 mm Versus PA.

n1 + n2 + n here x is the scanning efficiency of 1 and y is the sc-aning efficiency of 2, and assuming x and y are independento So 3 y n3 + n2 x anId Y - 3 -Splving for N we get (n + n%) (n + nl):n3 The reslts of rescanning criteria satisfied. n3 nn x N ABC 5 O 0 1 Z Part I ABD 2 1 0 5/6 1 6 AB only |4 0 -, '.,....,..~..._ CPar 14 0 0 1 1 4 Part I I MABD 6 o o 1 1 6 ABC 19 0 0 1 1 19 TOTAL TOTl AB only and.AD 12 1 0 12/13 1 13 From this d ^ata we estimate the relative scannin efficiency for ABD events compared to ABC events is o096 + O0074

- 42 - 2. Another estimate of the relative scEani efficiency of the ABD events compaed. to ABC events can be made b assuming i. The g a rays do not aid in the findin of ABD eventso iig After an event has been locaed by the scanner he does not look for additional V's in the picturee iii. The meas ring and addititonal film-hanu.ing always turn up all V's on frames designated by the scanners as containing events of interest. Then the relative scannin efficiency can be obtained from the number of events in the ABC category that were originally id.entified, as AC events, ioe. the K1 was not seen by the scanero There were two such events out of the 51. in part I and 2 out of 45 in part II. The relative scanaing efficiency is therefore on this basis 92/96 or 0,96 0o02o Since this estimte 'mkes somae unjustified assumptions about the psychology of scamning, it should be taken only vt.h reservationso 3o One expects that the mjor scanning biases, if there are ay., should appear when distriTbutions of the events in the variables that influence the visibility of the e'ents are studied, One might expect that the two most accessible variables to affect the scanning efficiency would be io The number of beam tracks per picture, since the amount of backgrou. d in the picture should be roughly proportional, to the number of bem tracks, and ii. The center-.of-mass decay angle of the K{ since the opening

43 angle of the KO as well as the distribution of momenta between the two legs should affect te visibility of the ~ and theae two characteristics depend on the center-of.mass decay angle The decay of the should be isotropic in the center-of-mass decay anle ie sethee K has no spin0 Let us see then if any useful information can be obtained from looking at the distributions in these two variables~ i.o The nuber of tracks per picture Let us take the relative scanning efficiency fo ABD events with respect to ABC cvents as being linearly dependent on th number of tracks per picture, and being unity when there are no beam tracks per pictureo That is, we take e(x) 1 -ax where e(x) is the relative scanning efficiency as a funtction of x, the number of tracks per picture0 The average s nning efficiency for ABD events compared to ABC events is then X3C X where Xo is the averae of x over the AD sample and x and x are over the ABC sample. These two distributions are shown in Fig. 10 We find a- 1.15 0 o55. This method is therefore much too naccurate to be of use iio The center-of-mass decay angle. let the cosine of this ane be given by y Assume that the

- 44 - ABD 2 4 6 8 10 12 14 ABC 12 I0 I2 3 4 5 6 7 8 9 10 12 13 14 15 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 TRACKS PER PICTURE Fig. 10. Distributions of the Number of Tracks Per Picture Versus Number of Pictures.

oe sod jo suoT:q. nq-F:TJ:ST 'TT -'T lO soo 0'1 8' 9' ' Z 0 01 oN 01V )IQ-S >18 Soo 0_1' 8' 9' 27 O _^^^~ i.

-46 dependence on y of the scanning efficiency is given by e(x) 1 -by b is then given by b =qL~ The distribution of y in the two categories is given in Fig. 11. We find a = ' 1 24, where the statistical error due to yo alone is - 024. Thus this method also is too imprecise to be of use. Conclusion: The relative scanning efficiency will be taken as that given by the direct rescan, namely 6 = 0,96 - 0.07 Results of the calculations: As the result of the foregoing considerations we have the following values for the constituents of the equation 1R; 2 A3BD a4R 56 ABC ABD/ABC 35/96.364 + 072 a = 2 02.0 4= 1214. 011 2r =.93 -.04 a = 1.069.Oll 3 = 99 -.01 6 =.96 -07

-47 - So R.54 +.12 and -R ~+ BA 1 + R5 It is of interest to compare this number with (10) w(A p) 627 0 + 31 w(A all modes) = 27.031. The fraction of A's decaying via pionic modes is then (1 + R) A-al966 -.089

V. OTHER PROPERTIES OF THE A A. The Asymmetry Parameter of the A. In the A CM the angular distribution of the t is given by ( see Appendix A) dI I~ t JFc0%0 dc 4T1 L i ^' S ^ where 5 is the angle between the pion and the direction of polarization of e P te e e polaiat f the the polarizatio of t e (aveged over all production angles), and0 is given by ( see Appendix A ) z Re SP S S t P P where S and P are the the amplitudes of the L =0 and I I 1 orbital angular momentum states occurring in the pionic decay of the A, These two states have even and odd parity, respectively. tc therefore arises from the interference of two states of opposite parity. The charged mode. Because the A CM decay angle,6n, of the A can be determined for the charged mode of the A ( see page ), it is possible to obtain the distribution of the i in the A CM from the observed distribution in the LAB. Since we assume parity conservation in the production of the A ( see Appendix A ), the polarization of the A is taken normal to the production plane. In this case is related simply to the in LAB by the formula cost coS g5 COS where~ is the LAB angle between the direction of polarization and the i- line-of-.flight,0 is the LAB angle between the A line-of- 48 -

flight and that of the A, and is the CM angle between the A line-offlight and that of the t ( or the proton). The statistical estimate of dP is got by using the distribution function f( x, a ) ( 1 +ax) 2 where we set a =dP and x = cos. From f(x,a) we construct the Bartlett "S-function" ( 17 ) which is given below N S)a. A n Z f (XKfVi dygo) where -I th Xr is the value of cos4r o r th event and N is the number of.'. v f (al a cevaosni The most likely value of a ( call it a ) and the standard devations on the plus and minus sides of ao, Aa and La,, can be found from a graphical solution of the equations S( ao) 0 an + + + S(:a ) - 1 - A A sample of A's -was chosen from parts I and II to satisfy the following criteria: 1. The measurements of the A be in reasonable agreement with the kinematics graphs for the charged decay.

50 - 2. 1he coplanarity of the A, 6, be no greater than 70 3o The decay length of the A, LA, be no less than 5 mm. 4. No origin prongs leave the visible volume of the chamber. 5, A possible K' charged decay occur in the picture which is consistent with having been produced with the A. Any biases that may occur in the above sample are not expected to affect the measurement of the asymmetry. 222 events satisfied the above criteria and gave- a result of c = +.32 11 The chance that an unpolarized sample give rise to this result is about 0.3%. The neutral mode. The most precise method for determining the asymetry of 'the neutral mode is by looking at the distribution of the bisector in the CM of the angle between the two gas from the t ', as discussed in Appendix Bo Since the individual momenta of neutral events cannot be determined, the sample was assumed mono-energetic and transformed into the CM for several different values of the A momentum, PA The sample was chosen to satisfy the criteria 1. No origin prongs leave the visible volume of the chamber. 2. A possible KI charged decay be associated ith the event and be consistent with coming from the origin. 3. There be two gamma-produced electron pairs which are clearly associated with the event and whose directions are measurableo Seventy-one events fell in the sample ( from both parts ) and

51 as shown below the dependence of the result on P was slight ( for the charged mode the average P is about 500 Mev/c ) P /( ev/ ) t/4 WBoP 0 +.25 a.19 300.25.19 400.24 + 19 500.24.19 600.24. 19 700.23 + o18 The factor wB is a "'washout factor" calculated in Appendix B where we show w, 0.82 Therefore,P-= +.37.28 As shown in Appendix A the ratio of asymmetry parameters for the two modes is of particular interest. Our result is not very meaningful, however. We find ile+1.16 +.97 This quantity has been measured muach more precisely by Cronin et al (12) using counters and was found to be d= -+1.10 +.27.

52 B. The lifetime of the A. If the momenta and potential paths of a sample of As is knomw in addition to their decay distances it is possible to estimate the lifetime. If in addition to requirements ABC in Chapter IV we require that 1. the origin be inside the fiducial volume of the two Vs ( see page 27), 2. the A charged mode be unscattered outside the nucleus, we are left with a relatively unbiased sample from which a lifetime estimate can b'e obtained. Using the Bartlett "S-function" corrected for skewness(17) we find for the 84 ABC A's that satisfy the above conditions +.4i8 -10 A Mean Life -2 77 ( ) x 10 seconds where the errors are standard deviations. The 5 mm. cut-off on the A decay distance ( criterion C3 on page 27) has been taken into account. Since the momenta of the neutral mode events cannot be determined no lifetime can be obtained directly for this mode. One can, however, compare the decay length distributions of the two samples, ABC and ABD, which are given in Fig 12 ~ The following biases should be kept in mind: 1. The charged mode A's have a 5 mm. cut-off, 2. The distribution of neutral decays should be distorted by the expected dependence of conversion probability on the position in the chamber and the momentum of the tA 3. MEasuring error should tend to increase the apparent decay

- 5J - 13 PART I ABD 3 PART II 2 3 4 5 6 7 8 11 12 13 14 UNABC 0.5 I 1.5 2 U.D. Acm 2 3 4 5 6 7 8 9 10 II ' 12 13 14 SCATLA cm L ^cm DTERED Fig. 12. Decay Length Distributions for ABC and ABD with A Distribution for ABD.

54 lengths of the neutral decays. An estimate of the size of the errors expected in determining the origin of the two associated gad rays can be got from the distribution of the distance of closest approach, A, for the extensions of the measured paths of two associated gammas, as seen in Fig.12. As a parameter for comparing the two distributions let us choose the average decay length, LA, for each distribution. For the 32 neutral events ( ABD) for which LA could be determined we find A neutral 239 cm Instead of comparing this directly with the average of the ABC events let us rather consider an adjusted average defined in the following manner: Lju = L + o2x.21 A charged, adjusted 121 where L is a weighted average of the ABC A's run in the Monte Carlo calculations described on page 28 and is givtby - 92 L w L, 92 i-=l i i / Z w i=l where wi is an integer from 0 to 5 and is the number of times out of five passes the event was found by the Monte Carlo calculation to have both gammas convert. The term.21x.25 is the correction for the 21% of the ABC type A's that would be expected to decay less than 5 mmo from the origin ( see page 27). The factor 1.21 in the denominator is the proper normalization factor.

- 5 - One finds.A charged, adjusted 309.25 cm This result neglects effects due to measuring errors. Thae chance that these two measurements of what we presume is the same quantity differ by.70 cm or more is about in ten. We can therefore state that the two average decay lengths are not inconsistent with a comnon lifetime for the events satisfying C and those satisfying D. It is reassuring to note that the average potential path for the ABC A's is 13.02 -.52 cm., and that if the neutral decays were random in the chamber we would expect the average "decay length" to be more like half the average potential path, rather than the much smaller number we have stated above.

^56 C. The mass of the t~ from the Ao As shown in Appendix C it is possible to measure the mass of the io from the A decay by looking at the distribution of the opening angle,,C between the two gamma rays from the iOx and the distribution of the momentum., PA of the A population as got from the charged mode events. We see in fac from equations C 1.9 and C 1.11 that ttTT~ - (' ~+ P2 )"- ^_.E(n2 & rAAP — Th "m I+ "/3 2. PM \a\ where P* is the momentum of the '~ in the CM of the A and. is, of course, a fnction of the g~ mass. As an unbiased sample we choose the events used in the Monte Carlo calculation. The momentum distribution of this sample can be see n Fig. 13. We find P = ( 3,23.23 ) x 10 (Mev/c) The sample of it~ s we choose to be 30 of the 35 ABD events for which both gama rays produced well-defined and measureable electron pairs. The distribution forZ for these events is given in Fig. 13. We find cot l'X/2) -.97.1

- 57 - X DEGREES 42 10 20 30 40.6 -40 60 80 100 120 140 160 180 321 28 24 20 16 12 _. 4 20 20 0 40000 80 1800 1000 1200 PA mev/c Fig. 13. Momentum of Monte Carlo A's, X Distribution, and Distribution of Difference in X for Two Measurement.

-58 - This number must be corrected for skewness due to the error in determining as explained in Appendix C2. Using an average square error ( in radians ).=.038 as got from 21 pairs of g pairs that were measured twice in part I ( see Fig.13 ) we find cot2//2 corrected.89.13 eot )/2 corrected where cot4/2 was taken as 1.51 as calculated from the 30 ABD events and was not corrected for skewness. Inserting these numbers into the equations on the preceding page we find M o= 126 - 6 Mev where the error is one standard deviation. This number should be taken as evidence that the neutral mode of the A decay is indeed A - A' + neutron

Appendix A. The Pionic decay of the A, V-A theory, and the II=1/2 rule Al. Channels for the decay If the spin of the A is 1/2 and the final states are not required to be eigenstates of the parity operator, one can describe the final states of the A by four complex numbers Sl =JSjeil S3| S e where S and P correspond respectively to L = and i = 1, where L is the orbital angular momentum of the pion-nucleon system, and where the subscripts I and 3 correspond respectively to 1he two isotopic spin states, I = 1/2 and I = 3/2, possible for a pion-nucleon system in general. If the decay is invariant under time reversal, it can be shown (18) that the relative phases,, 3 are just those expected from t-N scattering at the energy in the CM given by the Q value (about 40 Mev). The experimental values for these phase shifts are (19) = + 80 31= 0 Al.2 LI l = 0 Thus the amplitudes are real to within one percent. We shall - 59 -

60 - neglect the imnaginary parts. A2. Charge distribution With the help of the Clebsch-Gordan coefficients we can relate the two charge states ( + p denote '"-" and ~ + no denote "0") to the isotopic spin statesa Then the ratio of neutral to charged mode is given by A2.3 R ~ or 2( I tD9 >+ t + p where A.3 The angular distributions Assming parity is conserved in the A production process the A can have no component of polarization on the production plane. Let us define "up" as the direction of the production plane normal (the vector product of a unit vector in the beam direction with a unit vector in the A direction). The wave fuxiction for the A with spin up may be written

61 A391 'P,4 syO~(4 /y04Y 3,) and with spin "down" A3-2 9 sO t - ^ ^ ^ ) where 0 and (3 are the spin functions for the nuclear spin up and down, respectively, S and P are either So, P or S,P and the Y's are the first four spherical harmonics: I Yo= -)CosA3.3 'I S +1 ' ~. ~, - where S * and y,* are polar and azimuthal angles of the decay pion in the CM system of the A as shown in Fig. 14. ^ 1 fAroY A dec^ <^ _~ L Bear Cr1 o ( prodotn dm^e) Figure 14 A t,

6 - The angular dstribution of the decay pion from A's tith spin up will be A3 p I + d or /di \ I + oC CosT where we have defined 3Re S-P A3.6; 2. 2 -q +-?P Likewise, /I\ _ I- cosS0 A3.7 Y(?J.i SL-TL Now if we deflne the fractionB of As" with spin up to be F and the fraction down to be F 1 -F down up averaged over all production 1anles (0 ~ see Fig. 14), then the average polarization will be A3.8?P F F up down and therefore for the total sample we will have A3.9 L -( s ) For the charge mode we find A3~lQ 0t 2 + $2 ( )(t 4 Xt 9- 2(lti ) fr(x^^) ' (tz.i)

63 and for the neutral mode A3.11, dOD i 2 i. 2 f where x, y, z are as defined aboveo A4 Predictions of the A = 1/2 Rule Gell-Man and Pais (20) have suggested that there may be a selection rule that te total isotopic spin changes by 1/2 ib. the decay of a strange particle, For the case of the lebda this mea.Xs x y Oo Then BR 1/2 A41o and E1 It is importfant to point out, however, that R =1/2 and /ol/d = 1, are not sufficient conditions that the lA= 1/2 ~le hold. Let us consider thequantities (I+.z) -2-f (x^ i) +2(x+Z2Y ) 2( |+t3) flnli ( tr x) + X+ %2 and:4o3 P~~_2- F=:,,,o f^~r~ / = - 2, X + r + c( ] Eq3ation A402 can be written A^1 -

64 which one ca see is a two-parameter family of ellipses in the x-y plane. If R 1/2 and z I (parity non-conservation is maximum) we have Equation A4.3 can be written A4o6 [ + *. Z~ ( tl — 2~6-(X- )2 - which is a one-parameter family of hyperbolae on the x-y plane. If r = 1/2 A4.7 = From Fig. 15 we see that, if _ 1 and R 1/2, we have restricted ourselves to the region x y 0 (Il: 1/2) or x =y = 2. If z differs from 1, the circle will become an ellipse with axes parallel to the x-y axs and still passing through the points x = y and x = y = 2-.+2+ '" Figure 15

- 65 - A5. Predictions of the V-A Theory Okubo, Marshak, and. Sudarshan (21) have stated that extension of the V-A theory to the A decay gives rather uniquely for the weak interaction producing the decay A5.1 Nw G4) nt(t5a t H.C. where G is the universal weak-coupling constant,%p?, F " are the wave functions for the proton, neutron, and. A, and the as are the well-known Dirac 's. Using the Born approximation the above authors show that their postulated H (A5.1) gives A5.2 x y= 2 -Thus we see from Fig, 15 that V-A theory in lowest approximations also predicts R = 1/2 and =O 1. However the above authors also show that higher approximations lead to slightly different predictions from those of the Born approximation, and, although present experimental results are too imprecise to decide between the V-A theory and the A = 1/2 rule, such a decision in principle could be made on the basis of precisely determined values for R and It is amusing to note then that there is at present no good reason for preferring either one of the two intersection points of the curves In Fig. 15 as indicating roughly the relative abundances of |I | 3/2 to 3 | 1/2 participating in the A decay.

- 66 - A60 Phase space correction Because of the difference in the masses of the decay products for the two pionic decay modes of the A one expects that there should be slightly different amounts of phase space available to the two modes0 Indeed this is so; assuming for instance that the 1l\ =1/2 rule is correct we find that R = 3390 instead of 1/3

Appendix B The Dtermnation of the Asymetry Parameter of the Neutr al de BO As shown in appendix A the angular distribution of the o0 in 'the A CM is given by We h rh dhe (p r o boisF S) We shall approach the problem of determining 3 l Pc first by looking at the diBtribution of the gaas and second by looking at the distribution of the bisector of the angle between the gas Unless otherwise indicated the asterisk will denote the A CM. Blo Angular distribution of the gammas In the following we shall show that the form of the distribution for gamas from the A is the same as that for the i with the asymetric term being multiplied by a 'washout" factor which 'e shall ca<lc.ulateo Let us first consider the general case of a distribution on ie unit sphere given by Fo ( ).where ~ is the polar ngle and there is no dependence on the aztthal angle Now let us introduce a disordering process D($), which is the probability that a point on the unt sphere will be moved to a pwint within an area sinlso 1, a distance away, Loe. a pointat, will be moved to wh ere. 67 -

- 68 - D(0) is independent of and. Then the disordered distribution can be written B12 F(,)= dF )S d 6 0 Blo~3 |DC 1)(Z4)) 51/nA " I O 0 Expand D(0) in terms of the egen:dre plynomials B1.4 D( j- b f Pos ) nO B1.5 rq P I(cosS)p P",c5) (cos )?)C -4) P^5 Sz 2 (- r)C C (osF,) o 5 ) m ( Expand F o( ) in the Legendre polyomials 00oo.1= Then using the ohogonality relations we get B1.7 F-) 1 n t Now we mst find D(0) for the case of ge as from the A In the CM of the Ahe e has a unique veloity, so D(0) is just the probability that a 11w come off at an angle 0 from the line of flight of the o0. Let us denote the velocity of the x in uits of the speed of light as Ao Let P be the momentum of the a and be the angle with respect to the line of flight of the i in the CM of the no0 Let

P* and O* be the corresponding quantities in the CM of the A Then if (1 - 2)o /2 we have from the Lorentz transformation / Posf\ /O 00\ P0s0 Svl 0 1 00Q Bi. po " o oi! j c J 8l.8 O' 00 1-co cs ' B1.9 Co $ -0 Now the dstrlbution s isopic il he Now the gamma distribution is isotropic In -the -o C A if the go has no spin., loeo Bl.ll ~ - =, Therefore B1012 d - (If05 ) co's Now we expand D(O*) in the Legendre polynomials with interest only in the first two terms Blo13 DP^ - IL ( I+3 os,) Inserting this expansion into equation Blo7 we find — ~JU _-^^^ ^

70 where the "washout" factor V/ is given by Bl.15 w_ (MU A( e) ) \5 > For = 0.61, we find = 0.43. B2. Angular distribution of the bisector of the angle between the gammas Analogously to B1 we find for the distribution of the bisector of the angle between the two gamas, B, to be B2. D(X) = -__) cos _____ where 0 is defined by Fig. 16. ^^ 1 Figure 16 Expanding D(0) in Legendre polynomials B2.2 DUO): = I + 3 WrCos $ +I i where B2.3 ^ - (l- P S O) J(| - _~ X~ )

71 - Then d4 4r ( I+ t d CoS 4 B2aA For P 061, VKB = 0.82o B3o We can now decide which of these two approaches yield the most Sinformation Let us look for eample at the fractional error in determining the average vlue of cos 5* One can show A cos; 3%-A B3.1l - B3~S COS S3( w A1N where A = W>P and N is the number of eventsa Taing as a reasonable value for d P as 1/2 one can see the bisector method ia more accuate by a factor of about47 2 It s clear tat the latter method shouldN provide more information ince it takes into accotxt the correlations of the gaas in pairs, whereas the former method treats all g mas independently, B4o The above distributions are given for the A CM and the distributions in the LAB are in general more complicated ince the Lorentz transfomation is not independent of and o Moreover, since in the xenon cham.ber one canot iner the momenti of the A from the gaa rays alone, because teir enrgies cannot be detemined, one camnot transform into the A CM, The projections of four-vectors onto the plane perpendicular to the line-of-flight are however invarient under Lorentz transformations of the veacors in the direction of the line-of-flighto Let us choose a new coordinate system so that the new azimuthal angle,, lies in this plane as shown in Fig. 17

72 -Then still in the CM we can write B44.1 d a1i 4s1 r o 3 and X^ t^. 8 oCos r ) write also for the LAB 34.3 _L -. +O S For the bisectors no such siple relation exists. Indeed the x y', and z axes, respectively, then B4.4 COS --- =' z '..t. o t r The direction eosines transfe o as

73 B45 ( )/(B5 Error in az$uthl -distribution Suppose we sh to deterine A P from N event say n rfo la, B4o3 above, then the "S fenction" (17) is UI, A cosV where J o 3B5,2 A =05 z2Ji lI AL&72Z A Iok I

Appendix C. The Mass of the o from the Decay of the A Cl. Derivation By application of the Lorentz tranformation to a gt whose -momentum and mass are designated by Po and. o respectively, one can show that C1.1 cot)= ^ SW where is the angle between the gamas from the decay of the 'o in LAB and is the to CM decay angle, as shown in Fig. 18. 07-C A C1 *\2 i 9 p * G x the LAB d1 1/ an Oare the LA the m Application of t ite Lorentz transfo ian t t A respec ive as sho-m in Fig. 197 - the LAB and ' ' C -,a)2f/'. %,,,an. @*are the angle:s the 'o makes wwith the A l.ne off ffight in AB 'and A 'CM, respectively, as shown in Fig. 19.

75 - P" Ac (\ A LAB (3 Integztiag over *.e geat70 Figure 19 Then jco 4 P Eoco5O* z cl.3 0 ^ L* 2 ^c One can easily show that equation BO1. can3 be written in the coordinate system in which Q* is the polar angle and * is the azsimthal angle as cl.4 drEl P r iCOs 3 Mo Integrating over we get Cl.5 - - * coi5C o Q Since the oo is presumed spinless we have also 01l.6 ~ Eliminating P o from equations C1.1 and C1.3 and averaging over d, 9* and we get C01.7 3 c. -c 7T = [ 3 IA A. 1 J IA f7\

-76 Noting that C1.8 A(=p A aA\ and.SM where P E ad M are.te momentum, energy, an mass, respectively,of the A; we find then C1.9 (Note that P is a function of ) we can express the mass of the io in terms of measurable quantities Clell M7 D I ( + ) ( z MPHAN) MN is the neut on mss. C02 Skewness correction for cot2//2 In calculating the average alue of cot2 /2 a correction must be made for the error in measuring /. Let us suppose the error in measuring is, then C2.1 / v + g 0 i2.1 " measured To second order in C + 3/9t cotf ) ) 0^~~

- 77 - Averaging over all measurements we expect c2.3 6 and.&6gf co4t X -3/Y cot C2.1 C-)

cj (]) H (]) -) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a, 0 b —~~~~~~ '- D0 I.s l S~~~~~~b 0 4 0 CO a E L I P aa m c; O I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.-. - O 4 0 - l l~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ l ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~bD

Appendix D. Search for "Complete" Neutral Decay of the A No clear cut cases of interactions in the xenon chamber of the neutron from the decay of the A were found in pictures containing a charged K{ mode and two associated gammas (ABD events), although each picture was carefuly sanned. Howeer one event was dicovered, more or less by accident, of the AD type for which the neutron apparently interacted and the K~ decayed neutrally. This as frame number 115,441, shown in Fig. 20. The interpretation of this event is shown in Fig. 21. Figure 21 where the stations denote the following occurrences 1. C (1.1 Bev) + xe -- + KS + residual nucleus Z -> ~ + A~ 2. 6 converts 3. 0..> io + Ao (3 of the 4 resulting g s convert) 4. Ao — > + n 5. and 6. The two gamas from the A convert 7. n + xe.-> p + residual nucleus - 79

- 80 From measurements of the positions of points 1, 4, 5, 6 and 7, and given the masses of the A and the neutron, one can compute the mass of the' ~. This is possible because the direction of the go can be determined by the intersection of the plaue defined by 4, 5, and 6 with the plane defined by 1, 4, and 7. That is the intersection of the decay plane of the n~ with the decay plane of the A. One can show 2 r (62^-5 2 Dll /%V " L ~~ A =4(a2 +)b2 e2 B 4(a2 +1)) - 2 e2 c-b2 c /7 Sn -T -0 b2 2 ps and'where 01 '2', and n are defined in Fig. 22. Figure 22

81 - The two stereo views of this event were measured five times, giving it mass values of 128, 108, 148, 116, ad 133 Mev. The average of these values is 127 6 Tevo Systematic errors were not taken into account.

Appendix E. LISTS OF EVES USED IN THE BRANCHING RATIO ABC events, Part I. Frame P LAPQ L0^ ( LA )A K 0I 9A 1 1K 4348 220 3.94 31.1 61 420 3.74 52.3 27 9029 605 10.50 34-.4 112 620 4,90 26.5 61 9655 290 6o01 93.1 128 440 1.01 18 0 86 10121 260 scattered 41 320 l.I4 147 7 67 10655 1040 4.44 10.4 75 180 0.95 30.4 58 11832 430 3.65 5.-9 57 225 1.32 1014 55 12662 4o00 4.84 54.4 15 250 0o94 67.9 59 13422 450 4.15 44.2 130 500 1.36 25.1 39 15401 540 8,80 - 17.1 136 220 3.41 80.2 43 17538 365 6.41 12.7 127 360 1.45 50.8 47 19737 540 o.68 30.9 110 31b 1.51 6509 85 21006 410 1.98 63.1 84 430 0o53 51,1 72 22215 250 0,94 8.7 56 385 o.69 72,4 72 22533 650 0.86 18.4 ' 35 320 6o09 2009 77 '23364 405 3-74 50,4 104 780 0o59 32.1 51 23432 520 2.24 24.1 64 310 0,57 66o8 70 26311 450 0,92 86.6 115 340 3.01 9.4 76 27324 500 1.94 25.8 86 215 0,57 70,2 86 28556 590 2.64 403 150 400 o064 74.6 70 29333 980 3.20 40 4 29 200 0.83 39 6 80 39660 180. 075 20.9 73 780 2,09 4.5 57 39882 770 3 45 48.5 116 300 o.69 31.7 89 39898 240 1.27 61.0 97 230 0.75 123.7 75 41301 570 3-05 32.8 68 190 1,91 112.4 75 42184 480 2.35 31.7 32 510 1,51 61.2 80 43055 610 1,98 28.4 40 470 4,78 13.2 83 50456 300 2.40 68.3 124 540 1.97 19-6 73 51870 460 2.66 23.7 104 430 3.55 32.1 39 51975 590 2.70 21.1 71 160 1.58 97-3 88 53658 415 scattered 71 260 2.83 22.2 73 55906 355 1,09 18o5 116 460 1.44 63,4 83 57303 610 4.39 31*4 40 580 5.94 15.6 85 59541 840 3.87 18.4 93 410 0.95 50.0 55 59574 250 3.23 61.9 80 280 3.10 46.9 63 60879 870 7.98 10.9 54 410 0.78 33.7 25 61458 590 3.24 28.0 85 580 10.17 24.9 78 62253 230 0.61 92.5 67 340 1,14 30.4 89 64511 510 1.60 19.7 36 580 1.14 12.2 48 66501 520 2.11 12.7 88 650 o.96 18. 66 67634 600 5.16 48.6 88 200 1,06 78.1 73 68417 540 2.45 77 5 102 650 1.41 47.9 73 71029 490 0.90 65.1 31 460 1.14 82.4 83 71469 275 1.76 43.6 110 260 1.84 91,0 61 74985 550 1,21 14,0 100 580 2.75 14.7 90 75718 640 1.69 7.3 81 270 1.58 27.5 62 77638 1090 3.91 32.5 52 500 1.23 36.3 87 81591 230 1.16 33.3 108 750 3*71 16.3 33 -82 -

-83 Frame PA X PI VA K e P ~ ~ ~ K L LK,K PA LA R e p,A P1( L1(0 WKO 82767 700 5.85 9.4 165 190 0.50 89.9 80 831416 460 2.38 9.3 57 380 427 1271 49 84008 340 3.58 148.4 102 500 2.02 22.9 69 84126 480 1.83 40.7 99 460 2.92 27.7 59

- 84 - ABC events, Part II. Potentialotentia ^P A LA Path A) QA pK LA K! 088319 750 1,31 15021 5.5 98 720 1.62 15.13 2.9 25 088508 740 9.08 11.56 9.8 69 180 2o91 11.72 78.9 76 088509 250 3.90 21.88 12.4 85 300 2.85 23.56 10.6 44 088601 500 2.79 19-07 62.3 87 280 1.32 11,40 70.5 88 089321 250 2.65 16.33 164.2 35 330 0.70 7074 50.8 22 089794 750 6.34 8.16 23.1 120 240 4.97 5.77 108.4 29 092872 1100 13.37 18.73 11.2 107 270 1.17 -2182 44.0 72 096876 270 2.90 10.53 66.7 108 840 5.30 13.94 8.6 57 097063 390 1.43 1207 27.2 112 760 3.54 11,37 18.3 77 097840 550 11 4.41 16.38 60.8 105 360 6.51 11.37 45.9 8 099001 500 4L:26 21034 83.3 83 150 159 23.72 124.6 34 099655 800 5.71 20.71 20.1 16 640 0 22.25 30.7 65 101202 810 8.42 16.76 40.3 43 270 2.50 14 05 41.5 44 102465 370 4.67 13-92 75.6 -7 505 1,44 7.67 35.5 74 103873 660 5.15 26-71 28.2 42 440 3.31 24.05 12.9 82 107774 490 6.15 20.05 47.0 135 520 12,37 18.97 49.2 60 108103 560 4.48 18.56 11,9 56 90 0o-70 9.11 86.8 15 108567 190 1.75 9.60 32.8 69 200 1,39 15.76 89.8 80 108839 440 1.25 15.93 8.2 78 530 1,03 16,82 9.7 88 o11004 590 1.43 5O00 29,0 136 680 3.16 4.54 24.1 40 110852 890 10023 16.52 22,2.78 570 1,32 16.84 23.5 81 111916 375 0.71 16.63 67.4 69 410 2.02 16,05 52.4 28 112059 680 2.41 8.72 9.0 87 450 3.60 8.77 27.6 87 112110 250 1.64 12.14 71.1 45 270 3.06 11.39 45.5 31 112647 280 2.23 14.10 50.2 112 470 5.26 11.17 63.0 76 113887 500 1.12 2.13 25.2 95 730 1.39 1.94 14.4 72 114503 660 7.64 15,49 29.3 105 730 5.25 21o26 42,2 66 115971 530 7.53 19.04 41o6 102 460 2,16 15.68 43.8 20 116580 560 0.55 13.82 40.6 116 620 4.55 17-13 38.1 65 116779 280 4.02 40.78 44.3 87 670 2.89 5069 24.2 75 1118T:- 260 5 69 7-99 43.0 124 530 4.47 9 46' 65.9 70 120258 520 1.80 15.60 29,4 46 634 1.08 11,99 26.9 87 121400 420 1.43 8.26 73,9 85 290 33 183 4 407 36 122063 570 1.47 11,71 3308 77 720 1.07 15.11 30.2 55 124106 200 1.10 17.13 31.6 45 210 1.74 8.67 107,3 85 128182 880 1,18 10.11 17,1 47 440 3.22 11.43 39.2 65 128540 200 0.79 16.84 37.4- 84 810 0.85 13.99 37,3 25 129043 1110 1.50 23.44 7.7 62 210 5,59 16,85 67.4 -50 129228 340 3.76 6.35 51.8 67 650 1,31 5.77 37.3 72 129707 650 2.50 11.68 53o2 110 550 2.28 7,40 39.4 80 130724 630 2.20 11.14 29.9 128 465 2.56 15.26 101.4 74 134718 350 2.97 9.96 150.6 145 700 4.06 13.76 26.5 64 136418 620 6.91 13.14 29.4 72 320 4.12 17.35 22.2 69 137873 740 9.29 19.27 11.5 70 280 2.80 6.52 113.3 42 139599 485 4.67 1565 46.5 73 690 0.86 1609 1o 6 73

- 85 - ABD events, Parts I and. II. re PKLKO(,A) KO8::,KO 2 " 12 LAWA 9707 520 2.97 45 47 1.36:86 1.19 3.97 24.4 4,6 4.46 24 19742 430 3.91 _63 82 0.50 103 1,78 1.83 16.2 13.2 1,14 126 23397 690 2.21 10 61 0.48 77 2.34 3.99 9.9 14-9 0.81 59 36076 340 3,96 66 47 1.07 128 11.66 1,05 12.4 9.7 2,o6 74 40270o ~630 1.41 6 77 0.19 163 0.66 1o25 6.7 13.7 6.80 78 54649 650 1.06 20 80 0.13 76 6.07 8.21 12o7 17-6 6.88 15 59899 310 0.54 50 74 0.o02 90 995 6.4o0 11. 8.5 4.59 49 63285 430 3.47 73 41 0.09 147 1.01 0,19 13.8 7o0 3.70 100 65970 500 1.21 37 46 1.22 86 5,35 5.76 8.1 8.2 3077 85 67994 210 1.O7 33 66 0.60 141 1.77 10.77 615 6.0 0-85 41 72242 220 1.25 16 43 0.61 69 3.98 4.78 10.9 8.5 1o87 10 74291 19f5'0.53 67 40 0.32 106 12,19 0.74 10,9 4.9 1,10 87 * 76644 630 0,81 46 34 1.92 130 5.57 13.90 7.8 4.3 3 93 74 77818 170 1,36 155 52 0.33 69 2.60 0.77 18.9 15.5 2.25 72 83858 380 2,14 44 77 0.32 72 0.54 10.82 14.4 16.9 0o61 9 * 87048 440 1.51 50 48 Dalitz pr. 4.74 0 13.4 9o6 5.52 42 88467 300 2 -79 -74 77 0.01 79 0,55 3.31 8.5 19.6 0,79 49 89784 450 3.65 45 67 1.16 130 9.35 0*07 8.7 13.3 1,40 67 93400 710 3.45 35 27 0.42 109 732 4.55 13.8 7.9 1o54 52 94908 240 1.67 97 52 0.31 100 1.21 '5 51 2 o 0o2 62 99237 Z~450 5.57 1259 0.05 90 1.28 7.54 13.7 11,9 117 36 101239 390 1.40 13 88 0o43 148 5.12 5.45 11.3 6.0 7.43 30 103521 420 156 64 48 0.38 125 3.06 1.63 11,2 19o0 0,99 43 105243 380 248 165 28 0.6 130 6.49 0,62 8.6 55.0 2.03 38 * 108197 20260 2.71 55 65 3 gamas: cannot pair up 108619 310 4.03 121 48 0.46 80 366 2.50 14,.7 17.5 1.2 80 111093 390 0,65 69 79 0.02 90 4,59 5.10 11,6 15.3 0.96 27 * 115228 '820 1.49 16 86 one gamma ill-defined 14.0 4,,8 1.49 40 116671 300 10-Ao 62 15 1.13 111 0.79 13,49 17.8 21.0 2~40 81 127291 790 3.35 2 66 0.04 94 1,51 3.54 11.3 18,9 0o48 Ill 128568 500 1,42 70 72 0.14 59 4.73 8.63 26.4 6.4 0.83 70 129418 300 0.96 60 59 0.23 130 2.57 1,72 20,8 10.6 1.98 101 131526 640 0.94 44 88 o0.01 69 69 6.38 5,71 7.2 8.2 3.67 30 135797 330 1.35 18 66 0.23 87 2.85 5.18 17.3 13.3 1.44 102 * 136620 20730 0.88 86 53 2.19 91 2.41 10,11 7- 7 14.7 329 78 * Not used for O. mass determination 20 ~ Three associated. gammas, believed. to be a case of a neutrally decaying Z~.

BIBULOGRAPHY 1. C. Franzinetti and G. Meo rgo, Supplemento al vol. VI, Serie X del Nuovo cimento 2 chapters 4 and 5 (1957) 2 EBsl, erPano, P o Sami Schwartz, and Steinberger, Nuovo cento 2 1700 (1957)0 3. D. Glaser, Proceedings of the Fifth Annual Rochester Conference on High Energ Physics (Interscience Publihers, Inc, New York (1955)) 4. J. L. Brown, D Glaser, and M Perl Physo Rev. 102, 586 (1956). 50 Bron, Bryant, Burnstein, Glasers,,g Kadyk, Sinclairs Trilling, Vander Velde, and van Putten, A. Phys, Rev. Letters, 51 (1959) B. Phys. Rev, Letters 563 (1959). 6. Mason, Barkas, Dyer,, Heckman, ick, iSmith, t Bul Armer Phys.~ Soc. Washington Meeting ( 1960 ) 7. Crawford, Cresti, Good, Stevenson, and Ticho, PBys Rev, letters 2, 114 (195). 8. High Energy Conference, Kiev (1959) 9 Nordin, Orear, Reed, Rosenfeld, Solmitz, Taft, and Tripp, Phys. Rev. letters 1, 380 (1958) 10. Craford Cresti, Douglass, ood, Kalbfleisch, StevensonB and Ticho, Phys. Rev. Letters 2, 226 (1959). 11. Crawford, Cresti, ood, Gottstein, Lymn, Solmitz, Stevenson, and Ticho, 1958 Annual Conference on Hig Energy Physics at CER, appendix I. 12. Cronin, Cork, Kerth, Wenzel, and Cool, Bul, Amer. Phys. Soc. New York Meeting (1960)o 13, "Asymmetry in the Decay of the Hyperon", Cool, Cork, Cronin, and Wenzel, Phys. Rev. 114, 912 (1959). 14. A O~ of isotopic spin zero has been proposed, but even if this particle were to occur in the A decay rather than the ordinary isotopic spin I msona, therae should be no detectable differene as the lifetimes for the two neutral particles for 2-gamna decay would be expected to be about the same. cfe A. M. Baldin, Nuovo cimento VII, 569 (1958)o - 86

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