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the prediction of many grand unified theories , that nucleon decay occurs at accessible lifetimes , remains unverified but continues to motivate experimental searches . this expectation was foreshadowed in part by sakharov s early suggestion that the simultaneous effects of baryon number violation , c and cp violation , and departure from thermal equilibrium could produce the baryon - antibaryon asymmetry observed in the universe.@xcite it is interesting and suggestive that no fundamental symmetry is known which implies the conservation of baryon number . currently , nucleon decay as a consequence of the minimal su(5 ) gut model is considered to be ruled out experimentally@xcite . however , other unification models , both with and without supersymmetry , predict baryon number violating processes . amplitudes for these processes involve the exchange of new particles with unknown masses so that precise nucleon lifetimes are not predicted . the expectation that these masses will be in the range between the gut scale of @xmath5  gev and the planck mass of @xmath6  gev leads to proton lifetimes in the range @xmath7 years@xcite . decay modes with strange particles such as @xmath0 , are usually favored in models which incorporate supersymmetry@xcite . previous searches for @xmath0 have been reported by the imb , kamiokande and frejus collaborations@xcite . the @xmath1 track can be imaged in ionization calorimeters such as soudan  2 and frejus , but is usually below cherenkov threshold in water . imb searched for an excess of events in a region of anisotropy and energy with a large background@xcite . kamiokande looked for an excess of single ring mu - like events between 215 and 255 mev / c with a muon decay , and also for three - ring events compatible with an invisible , stopped @xmath8 decay@xcite . frejus used two - track events with ranges consistent with the @xmath1 and the @xmath9@xcite .    in the soudan  2 analysis , we use both the visibility of the @xmath1 in a fine grained tracking calorimeter and the visibility of the decay electron from a stopped @xmath9 to reduce backgrounds from atmospheric neutrino interactions . we searched for the proton decay mode @xmath0 using two @xmath1 decay channels , @xmath10 and @xmath8 . the soudan  2 detector is a time projection , modular iron tracking calorimeter with a total mass of 974 metric tons and fiducial mass of 770 tons . details of module construction and performance may be found in references @xcite . the detector is assembled as a close - packed rectangular stack of 224 modules ; each module is made from 1.6  mm thick sheets of corrugated steel , stacked in a hexagonal  honeycomb " structure . the average density is 1.58  g/@xmath11 . on the walls of the underground cavern surrounding the detector , there is an active  veto " shield comprised of double - layer , hexagonal cell , aluminum proportional tubes@xcite . two million hytrel plastic drift tubes ( 1.0 m long by 15 mm in diameter ) fill the spaces in the honeycomb stacks . ionization electrons deposited in an ar / co@xmath12 gas mixture drift toward either end of the tube in a 180 volt / cm electric field with a velocity 0.8 cm/@xmath13sec . upon reaching the tube end , the electrons are detected by vertical anode wires and horizontal cathode strips . each crossing of a tube by an ionizing particle can create an anode / cathode signal at a common drift time which we call a  hit " . the pulse area , which is proportional to the integrated charge deposited in the tube , and the drift time for each hit are recorded by both the anode and cathode electronics . the primary trigger requires at least 7 hits , separated by at least 600  ns , in a group of 16 anode channels or at least 8 hits in a group of 16 cathode channels within a @xmath14  @xmath13sec window . the trigger efficiency for proton decay final states considered here is @xmath15 85% . the complete detector triggers at a rate of @xmath16 0.5 hz from naturally occurring radioactivity and cosmic ray muons . every 240 seconds a pulser " trigger provides a snapshot of the random background levels in the main detector . these are used as underlying events to add detector noise to monte carlo events . the data analysis proceeds in three stages . first we identify  contained events " . event prongs are defined by scanning as track - like ( @xmath17 , @xmath13 or p ) or shower - like ( e or @xmath18 ) . contained events are defined as having no hits on tracks or the main body of showers which are less than 20 cm from the outside surface of the detector and the prongs do not start or end between modules . this is the same contained event selection as was used for our atmospheric neutrino analysis @xcite . studies in reference @xcite showed that the efficiency for correct identification was 98% for tracks and 94% for showers . an absence of shield activity was required . second , the events are required to have a topology consistent with the proton decay channel under study , based on counting the number of visible tracks and showers . finally , kinematic selections which characterize a particular proton decay mode are applied to the data and also to event samples which monitor background processes . the analysis procedure involves finding efficient selection criteria using our proton decay monte carlo program , while minimizing the backgrounds from atmospheric neutrinos and atmospheric muons . the former backgrounds are calculated using the atmospheric neutrino monte carlo program described in reference @xcite , which incorporates the flux predictions of barr , gaisser and stanev@xcite . backgrounds from atmospheric muons may result when muons inelastically scatter in the rock outside the active shield . we use the term  rock " event to describe the interactions of a resulting secondary such as a neutron or @xmath19 which goes into the soudan  2 calorimeter and causes a contained vertex event . most rock events have hits in the soudan  2 shield which are time - coincident with the contained event in the calorimeter . these shield - tagged events are used to estimate any background from rock events without shield tags . a detailed analysis of the penetration depth distributions of events with and without shield hits has led to the conclusion that @xmath20 of all rock events have shield tags . [ sec : pdepth ]    our monte carlo simulation program tracks the decay products through the detector geometry and generates electronic hits in the same format as real data . the generator starts with a parent ( or target ) nucleon within a nucleus . the nucleon is considered to have a fermi momentum chosen from the bodek and ritchie parameterization@xcite . the spatial location and the atomic number of the parent nucleus is chosen according to the composition and mass distribution of the detector . the rescattering of pions within a parent nucleus is generated according to a phenomenological model@xcite . parameters of the model have been set to reproduce pion production by low energy neutrinos in @xmath21-ne and @xmath21-deuteron reactions@xcite . inelastic intranuclear rescattering for @xmath1 mesons is not expected to be significant due to the absence of low - lying @xmath22 resonances and is not simulated . the detector response used in this monte carlo program was verified against calibration data from the isis facility using @xmath17 , e , @xmath13 and p beams at a variety of angles and energies@xcite .      to choose the selection criteria and determine efficiencies we generated a large sample of @xmath10 monte carlo events from proton decay . features of the typical monte carlo event shown in figure  [ fig : pnk ] include a highly ionizing @xmath1 which ( usually ) comes to rest , and emits a 236 mev / c @xmath9 . the @xmath9 has an average range of 42 cm in the soudan  2 detector . at the end of its range , the @xmath24 of the muon is rising . the @xmath9 comes to rest and decays into an @xmath25 , which gives an average of 3 hits . the results of the analysis for the proton decay simulation , the neutrino simulation , the data , and the shield - tagged rock background are given in table  [ tab : effpnk ] . the simulated events are generated in the entire mass of the soudan  2 detector . efficiencies within the fiducial mass are calculated by dividing the fraction of events which pass a set of cuts by the ratio of the fiducial mass to the total mass ( 0.79 ) . the monte carlo events were first subjected to a simulated trigger , which 81 events failed . both monte carlo and data events were processed through a filter program which applied containment criteria , reducing cosmic ray muons by a factor of more than @xmath26 . 114 mc events , essentially all with hits outside the containment volume , were rejected . the remaining events were then scanned by physicists to remove the remaining non - contained events , mostly events starting or ending on module boundaries . at this stage , 204 @xmath23 events remained , compared with 367 data events without shield hits , 1008 shield - tagged rock events , and 1923 events from the atmospheric neutrino monte carlo . the data corresponds to 3.56 fiducial kiloton - years of exposure , compared to 20.24 kiloton - years for the atmospheric neutrino mc . the required topology is two charged tracks with a common vertex . events in which both tracks appear to be protons based on ionization and straightness are not included . these topology features were exhibited by 95 of the remaining 204 events from the mc . we also require that the @xmath1 candidate , which is usually the shorter track , has a length less than 50 cm . the muon track length distributions for all four event samples at this stage of the analysis are shown in figure  [ fig : muran ] . the range of muons from the @xmath27 decay is peaked at 43  cm whereas the background distributions are relatively flat . the muon range was therefore required to lie between 29 and 58 cm . our final cut requires a visible muon decay electron having two or more hits . this requirement discriminates strongly against neutrino induced background , since the predominant background is @xmath28 and in our iron detector most @xmath29 are absorbed rather than decay after stopping . after all cuts , our efficiency for accepting @xmath23 events in the fiducial volume is 14% . two atmospheric @xmath30 monte carlo events pass all of the cuts and represent an expected background of 0.21 events , taking into account that we found the atmospheric neutrino flavor ratio ( @xmath31 ) to be only 0.61 of the expected value@xcite . the rock event background in the zero shield hit sample is calculated to be 0.19 events . this was found based on the penetration depth analysis mentioned above , which found background in the track data equal to 9.5% of the shield - tagged track sample . as shown in table  [ tab : effpnk ] , one event in the data survives our cuts . = 6.0 in    .numbers of mc and data candidate events for @xmath23 which survive the triggering , containment , topology , and kinematic cuts of this analysis . events are generated in the full detector , while efficiencies in table 3 are quoted for the fiducial volume . [ cols="<,>,>,>,>",options="header " , ]     . the kamiokande collaboration@xcite has reported a limit for @xmath0 of @xmath32 years with 9 candidate events and an estimated background of 7.3 events . their unsubtracted limit is @xmath33 years . imb has reported a limit without background subtraction of @xmath34 years with 6 candidate events and an estimated background of 4.7 . more recently , they report @xmath35 years without a background subtraction based on 14 candidates@xcite . with background subtraction of 21.4 events , they calculated their limit to be @xmath36 years . frejus has reported a background subtracted limit of @xmath37 years with 1 candidate and an estimated background of 1.8 . in all experiments , the largest contribution to the estimated background comes from @xmath21 quasielastic scattering . the existence of the atmospheric neutrino @xmath21 deficit then calls into question the reliability of background estimates in all of these experiments . it is not clear that rescaling the total @xmath21 rate to the observed rate leads to a correct estimate of the background for proton decay in this channel , since whatever is causing the atmospheric @xmath21 deficit may be energy dependent or different for @xmath21 and @xmath38 . we note the possibility of such differences by comparing plots 2b and 2c . we would assign a resulting systematic error of as much as 100% to the background estimates for this channel . in view of this large systematic error we distrust the background subtraction in this channel and prefer to rely on the unsubtracted limit , which is unaffected by the background uncertainly . we note that the background level in this analysis , and thus the importance of background subtraction , is an order of magnitude lower than in the water cherenkov experiments .    in summary , we have searched for the proton decay mode @xmath0 using two decay modes of the @xmath1 , @xmath10 and @xmath8 . we observe one candidate event for @xmath10 and zero candidates for @xmath8 ; the estimated backgrounds are 0.40 events and 1.14 events respectively . our combined lower lifetime limit at 90% cl is @xmath39 years . our limit with background subtraction is @xmath40 years . this work was undertaken with the support of the u.s . department of energy , the state and university of minnesota and the u.k . particle physics and astronomy research council . we wish to thank the following for their invaluable help with the soudan 2 experiment : the staffs of the collaborating laboratories ; the minnesota department of natural resources for allowing us to use the facilities of the soudan underground mine state park ; the staff of the park , particularly park managers d. logan and p. wannarka , for their day to day support ; and messrs b. anderson , j. beaty , g. benson , d. carlson , j. eininger and j. meier of the soudan mine crew for their work in the installation and running of the experiment . sakharov , zh . pisma 5 ( 1967 ) 32 ( jetp lett . 5 ( 1967 ) hirata et  al . , _ kamiokande collaboration _ , phys . b220 ( 1989 ) 308 . r. becker - szendy et  al . , _ imb collaboration _ , phys . d42 ( 1990 ) 2974 . j. hisano , h. murayama , and t. yanagida , nucl . b402 ( 1993 ) 46 . j. wess and b. zumino , nucl . phys . b70 ( 1974 ) 39 ; phys . b49 ( 1974 ) 52 . nath , a.h . chamseddine , and r. arnowitt , phys . d32 ( 1985 ) 2348 . t. haines et  al . , _ imb collaboration _ , phys . 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we have searched for the proton decay mode @xmath0 using the one - kiloton soudan  2 high resolution calorimeter . contained events obtained from a 3.56 kiloton - year fiducial exposure through june 1997 are examined for occurrence of a visible @xmath1 track which decays at rest into @xmath2 or @xmath3 . 
 we found one candidate event consistent with background , yielding a limit , @xmath4 years at 90% cl with no background subtraction . 
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