Nonmesonic decay of the Lambda hyperon in nuclear matter - implications on the weak Lambda-N interaction

21 Pages·0.32 MB·English

by  W. Cassing

EPJ manuscript No.
(will be inserted by the editor)
Lifetime of heavy hypernuclei and its implications on the weak
ΛN interaction
3
0 W. Cassing1, L. Jarczyk2, B. Kamys2, P.Kulessa3,4, H. Ohm3, K. Pysz3,4, Z. Rudy2,3, O.W.B. Schult3, and H.
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2
Stro¨her3

n
a
J 1 Institut fu¨r Theoretische Physik, Justus Liebig Universit¨at Giessen, D-35392 Giessen, Germany

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2 M. Smoluchowski Instituteof Physics, Jagellonian University,PL-30059 Cracow, Poland

4
v 3 Institut fu¨r Kernphysik,Forschungszentrum Ju¨lich, D-52425 Ju¨lich, Germany
2
1 4 H.Niewodniczan´ski Instituteof NuclearPhysics, PL-31342 Cracow, Poland
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9
0
Received: date/ Revised version: date
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/
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Abstract. The lifetime of the Λ–hyperon in heavy hypernuclei – as measured by the COSY–13 Collabo-
e
-
cl ration in proton – Au, Bi and U collisions at COSY–Ju¨lich – has been analyzed to yield τΛ =(145±11)
u
n ps. This value for τΛ is compatible with the lifetime extracted from antiproton annihilation on Bi and
:
v
U targets, however, much more accurate. Theoretical models based on the meson exchange picture and
i
X
assumingthevalidityofthephenomenological∆I=1/2rulepredictthelifetimeofheavyhypernucleitobe
r
a
significantlylarger(2–3standarddeviations).Suchlargedifferencesmayindicatethattheassumptionsof
thesemodelsarenotfulfilled.Amuchbetterreproductionofthelifetimesofheavyhypernucleiisachieved
in thephase space model, if the ∆I=1/2 rule is discarded in thenonmesonic Λdecay.
PACS. 13.30.-a Decaysofbaryons –13.75.Ev Hyperon-nucleoninteraction–21.80 Hypernuclei–25.80.Pw
Hyperon-inducedreactions
1 Introduction process, Λ → π +N, with an energy release of about 38
MeV, whereas collisions with nucleons lead to the non-
mesonic decay, e.g. N + Λ → N + N, with an energy
The Λ hyperon decay can be studied for free hyperons as
release of (∼ 180 MeV).
wellas forhyperonscollidingwithnucleonsinside the nu-
clearmedium.Inthefirstcaseitproceedsviathemesonic
2 W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction
The mesonic decay also occurs for hyperons bound in amplitudes dominate by far the | ∆S |= 1 non-leptonic
hypernuclei, but it is strongly inhibited for all but the weak interactions [15]. This suppression of the ∆I = 3/2
lightest hypernuclei due to Pauli blocking of the nucleon amplitudewasexplainedbyMiura–Minanikawa[16]and
final states. The nonmesonic decay, on the other hand, Pati – Woo [17] in terms of the colour symmetry of the
can be studied only in hypernuclei because neither Λ hy- valence quarksin the baryon.Thus,one is tempted to as-
peronbeamsnortargetsareavailable.Duetotheimmense sume a dominance of ∆I = 1/2 transitions also in the
difficulty in producing Λ hypernuclei and of subsequently nonmesonic decay of the Λ - hyperon. It was, however,
detecting their decay the available experimental data on observed that theoretical calculations involving this as-
the nonmesonic process are scarce and have large uncer- sumption – i.e. only ∆I = 1/2 transitions – systemati-
tainties. cally underpredict the ratio Γ /Γ of nonmesonic decay
n p
rates induced by neutrons (n+Λ → n+n) to the decay
Most of the measurements for the decay of hypernu-
ratesinduced by protons(p+Λ→p+n) [18].Severalat-
clei have been based on limited statistics and been pre-
tempts have been made to reconcile this discrepancy e.g.
dominantly performed for light hypernuclei (see e.g. the
in Refs. [19,20,21,22,23,24], but none of them has solved
reviews [1,2,3] or refs. [4,5,6,7,8,50,10]). Even the total
this problem in a convincing way.
decay rate (or inverse lifetime) of heavy hypernuclei was
uptoveryrecentlyknownonlywithalargeerror[11].The This leads to the conclusion that the contribution of
experimental knowledge of the partial decay rates is also the ∆I = 3/2 transition to the nonmesonic decay of the
not satisfactory, e.g. the experimental studies devoted to Λ hyperon might not be negligible, i.e. the ∆I = 1/2
light (A ≤ 28)[4,5,6,7,10] and medium heavy (40 < A < rule should be violated [25,26,27,28,29]. The arguments
100) hypernuclei [12,13,14] report different values for the presentedin favorof this hypothesis in refs.[25,26,27,29]
neutron and proton induced Γ /Γ decay rates. The re- have been based essentially on the observed nonmesonic
n p
sultsforlighthypernucleiareclosetounitywhereasthose decaywidths ofthelightesthypernuclei.However,theex-
for heavy hypernuclei vary between 1.5 and 9.0. The ex- perimentaluncertaintiesaretoolargetoallowforanydef-
perimental situation – together with uncertainties in the initeconclusion.Itisthusnecessarytogetinformationon
theoretical description – show that the nonmesonic pro- the (possible) violation of the ∆I = 1/2 rule from other
cess is barely understood so far. properties of hypernuclei, e.g. from the mass dependence
of the lifetime of hypernuclei as addressed in ref. [28].
WerecallthatintheStandardModeltheweak|∆S |=
1 transitions can proceed with both ∆I = 1/2 and ∆I = As far as experiments are concerned it can be stated
3/2amplitudes.However,it wasfoundexperimentally (in from the inspection of Table 1, that the data - with ex-
−
the decaysoffree kaonsandhyperons)thatthe∆I =1/2 ception of the experiment performed with an e beam
W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction 3
in Kharkov [30] - agree within the limits of errors. In ref. theΛ lifetime isgiveninsection4.Insection5wediscuss
[32]ithasbeenshown,thatahypernucleusfractiondecay- the implication of the latter results for the selection rule
ing on a timescale of 2700 ps (as quoted in [30]) must be ∆I = 1/2 in the ΛN → NN transition. A discussion of
smaller by orders of magnitude compared to the fraction open problems and a summary are presented in sections
of hypernucleidecayingontimescales of 200ps. However, 6 and 7, respectively.
the errors for τ in the measurements from [31,11] are so
Λ
large, that no severe constraints could be imposed on the
2 Heavy hypernuclei formation in p+A
various theoretical models for the nonmesonic decay.
reactions and their decays
Table 1. The lifetimes of heavy hypernuclei from e− and p¯
Incaseofheavyhypernucleithe applicationofdirecttim-
induced reactions from refs. [30,31,11]. The numbers given in
ing methods - as adopted for light hypernuclei - is not
parenthesis represent the systematic errors.
feasibleduetothelargebackgroundoflightparticlespro-
Target τΛ / ps Ref. Comment
duced. This problem is circumvented by detecting heavy
& projectile
fragmentsfromthefissionprocesses,whichareinducedby
Bi + e 2700 ± 500 [30]
theΛ–hyperondecayinheavyhypernuclei.Thetechnique
Bi + p 250+250 [31]
−100
used is the recoil shadow method originally suggested by
Bi + p 180± 40 (± 60) [11] Reanalysis
Metag et al. for the measurement of fission isomers [33].
of data from [31]
It has also been employed by Armstrong et al. [11] in the
U + p 130 ± 30 (± 30) [11]
lifetime measurements with antiprotons.
A novel approach to produce heavy hypernuclei for
In order to improve the situation, experiments with lifetime measurements – as performed by the COSY–13
Au,BiandU targetshavebeenperformedduringthelast Collaboration – is to use proton collisions on heavy tar-
years at the Forschungszentrum Ju¨lich using the internal gets like U,Bi or Au. The possibility to vary the beam
proton beam of the COSY accelerator by the COSY–13 energy allows to measure the background(at a low beam
Collaboration. We briefly describe the different stages of energy, e.g. of 1 GeV) concurrently with the effect (e.g.
theproton-nucleusreactions–leadingtohypernucleusfor- at 1.9 GeV) by operating COSY in a supercycle, which
mation and their delayed fission due to the ΛN → NN has not been possible in the p¯ induced reactions in [11].
decay – in section 2. The experimental setup used to dis- Furthermore,avariationoftheprojectileenergyinproton
tinguish prompt and delayed fission events is sketched in inducedreactionspermitstofindoutwhetheranordinary
section 3 and an overview of the experimental results for fissionisomermightfakethedecayofahypernucleus.Such
4 W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction
a test is also not possible in antiproton–nucleus interac- time [s]
tions since the center-of-mass energy is fixed for stopped V (r)
N
p A E
F
antiprotonsandalwaysabovethresholdforΛproduction. 50 MeV
-23
10
Furthermore,inp+Areactionsalargepartofthe proton
Λ
Λ
momentum is transferred to the hypernucleus such that associated VΛ (r)
strangeness
+
production K
30 MeV
the surviving hypernuclei move faster than in p¯ induced
reactions;thisincreasesthesensitivityoftherecoilshadow
Λ
Ν
method for lifetime measurements accordingly. elastic VΛ (r)
scattering Λ Λ
N
Ν
ForillustrationweshowinFig.1thevariousstagesand
-10
10
Ν
timescalesinvolvedinthep+Areactionfromi)theinitial Λ
N
weak interaction VN , Λ (r) Ν
configuration to ii) the associated hyperon production in ΛN NN N N Ν
Λ
the target nucleus by pN inelastic scattering (∼ 10−23s),
iii) Λ hyperon capture in the residual nucleus via elastic
A Z
ΛN scattering(∼10−22s),iv)theΛN →NN reactionon 1 1 VN (r) VN (r)
EF EF
A Z
thetimescaleof200psleadingtov)delayedfissionofthe 2 2
fission
hypernucleus.Therightpartshowsthenucleonpotentials
during the various phases. Fig. 1. Time evolution of a proton-nucleus collision from i)
the initial configuration up to v) the delayed fission of a hy-
Due to the complexity of these reactions the various
pernucleus: ii) associated strangeness production; iii) elastic
stagesillustratedinFig.1havebeensimulatedbycoupled-
ΛN scattering; iv) decay of a Λ hyperon via the ΛN → NN
channelBoltzmann-Uehling-Uhlenbeck(CBUU)transport
process leading v) to fission of the excited nucleus. The right
calculations for the fast nonequilibrium phase [34,35,36,
part shows thenucleon potentials duringthe various phases.
37] followed by Hauser-Feshbach calculations for the sta-
tistical evaporation phase [38]. The transport model em- the properties of the hypernuclei produced – i.e. primary
ployed has been used for a variety of hadron-nucleus and mass, charge, excitation energy, linear momentum, angu-
nucleus-nucleus reactions from low to relativistic bom- larmomentumetc.– ina givenreaction.The latterinfor-
bardingenergiesandbeentestedwithrespecttotheover- mation from the CBUU calculation then is used to evalu-
allreactiondynamics as wellas the productionofstrange ate (within Hauser-Feshbach calculations) for each event
andnonstrangehadrons(forreviewsseerefs.[39,40]).The the subsequent statistical decay as well as the probabil-
CBUU calculations provide information on i) the forma- ity P of a heavy hypernucleus to survive in competition
s
tion cross section of ’hot’ hypernuclei as well as on ii) with prompt fission [37]. Thus, the final distribution in
W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction 5
mass and charge of the ’cold’ hypernuclei – reached after 1.50 b
0.25 b
∼ 10−18s (see below) – is evaluated together with their PROMPT FISSION
0.10 b
U
individual (A,Z dependent) velocity distribution in the SPALLATION
p + Bi
laboratoryframe.TheprobabilityfordelayedfissionP –
fΛ
Au PROMPT FISSION
ΛFORMATION SPALLATION
asinducedbytheΛN →NN reactionforahyperonfrom
theS-stateintheindividualhypernucleionatimescaleof 345100µµbb 12 % 85 % ΛD IENLDAUYCEEDD 42 µb
200 ps – is calculated again within the Hauser-Feshbach 330µb 80 % 9 % FISSION 25 µb
99 % 5 % 16 µb
formalism [37]. The kinematics of the fission fragments,
P P
s
fΛ
furthermore, is simulated according to the Viola system-
atics [41] assuming isotropic angular distributions for the Fig. 2. Schematic representation of contributions from dif-
fission fragments in the rest frame of the decaying hyper- ferent competing processes in p+Au, p+Bi, p+U reactions at
nucleus.Fordetails we referthe readerto refs.[36,37,42]. Tp=1.9GeVaccordingtotheCBUU+Hauser-Feshbachcalcu-
lations (see text). The experimental cross sections for prompt
fission havebeen taken from Refs. [43,44].
The cross sections for Au,Bi, and U targets at T
lab
= 1.9 GeV – as calculated from the CBUU + evapora-
to unity. We find, furthermore, that also their product
tion calculations – are displayedin Fig. 2, where we show
remains constant within a factor of 2−3.
the predicted cross sections and branching ratios for all
targets. The experimental cross sections quoted in Fig. The comparison of the cross sections for delayed fis-
2 for prompt fission have been taken from refs. [43,44]. sion of hypernuclei and prompt fission of target nuclei in
In contrast to the large differences in the prompt fission Fig. 2 shows that in experiments with Bi and Au targets
cross sections, which amount to a factor of ∼ 15 for U thesamestatisticsfordelayedfissionfragmentscanbeob-
and Au targets, the cross sections for delayed fission (∼ tainedusing2–3timesthebeamtimeforacorresponding
42,25and16µbforU,BiandAu,respectively)arerather uranium experiment. On the other hand, the background
similar.This is due to the fact that the probability to ob- from prompt fission in the Bi or Au experiments is much
servethedelayedfissionofhypernucleiisdeterminedbya smallerbecausetheratiooftheprompttothedelayedfis-
productoftwoprobabilities:thesurvivalprobabilityP of sion cross sections is small compared to a U target. This
s
(’hot’) hypernuclei against prompt fission and the prob- reduces the load on the detectors in the prompt fission
ability P for fission of (’cold’) hypernuclei induced by regionfor Au andBi targetsby aboutanorderof magni-
fΛ
a Λ - hyperon decay. These two probabilities correspond tuderelativetoU.Theseexpectations(calculations)were
to opposite processes; their sum is approximately equal confirmed in the actual experiments at COSY-Ju¨lich us-
6 W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction
ingBi[32],Au[45]andU targets[46],wheresimilarcross equilibriumCBUUcollisionstagebeforetheCoulombbar-
sections could be observed experimentally. rierisformed;afterthattheprotonemissionissuppressed
bythe Coulombbarrierandneutronemissionfills outthe
Anotherimportantingredientforthedataanalysis(to
’valley of stability’.
be discussed later) is the velocity distribution of the hy-
pernucleiinthelaboratory.Thelatterisdominantlydeter-
mined by the nucleon-nucleon and hyperon-nucleon cross 80 Au
section in the initial stage of the reaction as modeled by
70
the CBUU approach. It has been shown in comparison
to independent experimental data from refs. [47,48] that Z 160 170 180 190
the momentum transferto the residualnucleus is wellde- 90
Bi
scribed by the transport approach in p+U reactions for
80
T = 0.5 – 3 GeV [46].
lab
70
During the statistical decay phase the hypernucleus
170 180 190 200
velocity distributions change only moderately, however,a
100
U
very pronounced change in the mass and charge distri-
90
butions is observed [37]. The final charges and masses of
80
’cold’ hypernuclei are correlated to form a valley of sta-
200 210 220 230
bility. The resulting two-dimensional spectra in charge Z
A
and mass A of cold hypernuclei (typically after 10−18 s)
are shown in fig. 3 in terms of cluster plots. These differ- Fig. 3. Two dimensional spectra from CBUU + evaporation
entialdistributionsrepresentCBUU+evaporationmodel calculations in charge Z and mass A of hypernuclei for p +
calculationsforhypernucleiproducedinthereactionsp+ 197Au at Tp=1.7 GeV, p + 209Bi at Tp=1.9 GeV and p +
197Au at T =1.7 GeV, p + 209Bi at T =1.9 GeV, p + 238U at Tp=1.9 GeV. The solid and dashed lines indicate hy-
p p
238U at T =1.9 GeV. It is seen that the two dimensional pernuclei of fissility Z2/A = 34 and 32, respectively. Delayed
p
fissioneventsessentially stemfrom nucleiwithfissility param-
plots are quite similar for the three reactions considered,
eterZ2/A≥34.
but shifted in mass and charge according to the initial
target. It should be noted, that the width of the distri-
bution in charge Z remains rather constant as a function It has to be pointed out that although the distribu-
of mass A. This can be inferred directly from the isospin- tions in mass differ by about 10 to 30 units for the dif-
independent emission of protons and neutrons in the pre- ferent targets, they have some common overlap region in
W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction 7
HISTOGRAM
the tails. Furthermore, the Λ induced fission probability 108
counts
essentially depends on the fissility parameter Z2/A (see
106
Fig.3). The solid and dotted lines in Fig. 3 show hyper-
104
nuclei of Z2/A = 34 and 32, respectively. We recall that
102
only a fraction of the (A,Z) distributions of hypernuclei
createdinp+Ainteractionsleadto actualdelayedfission 1
coordinate along beam axis
events (see P in Fig. 2), i.e. essentially for Z2/A≥ 34.
fΛ
shadowed region bright region
When averaging over the experimental results for all tar-
Multi Wire
gets one thus obtains a value for τ that corresponds to
Λ Þ Proportional
Þ
Chambers
an average over all nuclei with masses A ≥ 180.
target holder
3 Experimental setup and data analysis
Þ delayed
fission
fragments
Hypernuclei produced in proton-nucleus collisions, which á á
proton beam target A Þ
Λ
survive the prompt fission stage, leave the target with a
recoil velocity v . They subsequently decay at some dis-
R
tance from the target proportional to the lifetime τ of
Λ
Fig.4. Schematicviewoftheexperimentalsetupandillustra-
the Λ–hyperon and to the velocity v . Thus prompt and
R
tionoftherecoildistancemethod(seetext).Thedimensionof
delayedfissionevents canbe separatedby the spatialdis-
thetargetholderandtargetinthelowerpartareincreased by
tribution of their decays. The problem, however, is that
a factor ≈ 30 relative to the MWPC’s.
the prompt fission events are more frequent than the de-
layed fission processes by factors of ∼ 105 (cf. Fig. 2) – Aschematicviewofthedetectionscheme[49]isshown
which corresponds to the ratio of prompt to delayed fis- inFig.4,wherethedimensionsofthetargetanditsholder
sioncrosssections–andthespatialdistributionofdelayed –servingas a diaphragm– areincreasedby a factor ≈ 30
events has to be measured with high accuracy. The par- in comparison to the dimensions of the low pressure mul-
ticular solution to this problem is provided by the recoil tiwireproportionalchambers(MWPC)placed30cmfrom
shadow method [33], which allows to analyse the spatial the target in a direction perpendicular to the target. The
distributionofdelayeddecayswithrespecttotheproduct multiwire chambersare sensitive to fissionfragments,but
τ ·v in the presence of a huge backgroundcomparedto not sensitive to protons and other lighter particles.These
Λ R
the investigated effect. detectors were partly screened by the target holder such
8 W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction
that the prompt fission fragments - originating from the Thefragments,thathittheshadowed(left)partofthe
target - could not hit the shadowed (left) part of the de- detector, thus originate either from the delayed fission of
tector.Thiswas,however,possibleforfragmentsfromthe hypernuclei (or hyperfragments) or they are emitted in
delayed fission of hypernuclei A escaping from the tar- prompt fission from the target and due to scattering on
Λ
get downstreamthe beam and fissioning in some distance the shadow edge (part of the targetholder) have changed
fromthetarget.Aschematiceventdistribution-projected their initial trajectories. Therefore, scattering creates a
on to the beam axis - is shown in the upper part of Fig. background in the shadow region with an intensity pro-
4, which is characterizedby anexponentialfall-off for the portional to the prompt fission cross section. In order
delayed fission events in the shadowed (left) region and to determine the background distribution of hits in the
a constant (prompt) yield in the bright (right) region of shadowed part of the detector measurements have been
the detector.Forfurtherdetailswereferthereadertoref. performedat a much lower protonenergy (T =1.0 GeV),
p
[49]. wherethe crosssectionforhypernucleusproductionisex-
pectedtobenegligiblysmall(about4ordersofmagnitude
In order to check whether the events detected in the
smallerthanat1.9GeV),whereasthepromptfissionyield
′
shadow region are not light particles or even γ s, the fol-
is about the same.
lowing tests have been performed:
It has been shown by Monte Carlo simulations that
hyperfragments from prompt fission of hypernuclei, that
– The MWPC were irradiated with minimum ionizing
− havechangedtheirdirectionduetotherecoilinducedbya
particles(γ’sande );itwasshownthatthe detection
efficiency for such particles is below 10−11. subsequentΛ-hyperondecay,canhit the shadowedregion
of the detectors only in a very narrow region of 1-2 mm
– A pure carbon foil was used as a target in p+A mea-
close to the edge of the shadow region and, thus, do not
surements, leaving the detection system unchanged.
contribute to the distribution that was actually used for
The measuredspectra in the shadowedpartofthe de-
the extraction of the lifetime of hypernuclei (see below).
tectors were found to contain no events.
– A252Cfsourcewasplacedatthe targetpositionanda The proton beam (with typically 5 ·1010 protons in
two–dimensionalenergylossversustime-offlightspec- the COSY-ring) has been accelerated up to 1.9 GeV (for
trum(betweenbothMWPC)wasmeasured.Thespec- the observation of hypernucleus production) and to 1.0
trum was populated in line with Monte Carlo calcula- GeV(foranestimationofthebackgroundoriginatingfrom
tionstakingintoaccountthemass,chargeandvelocity scattered fragments from prompt fission of the target nu-
distributions of fragments according to the Viola sys- cleus). The COSY accelerator was operated in the super-
tematics [41] from the fission of californium. cycle mode, i.e. there were three cycles (each of ∼15 s
W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction 9
duration) of beam accelerationand irradiationof the tar- 10 7
get; two of them at the higher energy of 1.9 GeV and one 10 6 p+Au
5
at1.0GeV.Thisallowedtostudytheeffectandtheback- 10
4
ground concurrently for the same shape and thickness of 10
3
the target. 10
2
10
The distribution of hit positions of the fission frag-
10
ments on the surface of the detector then were projected
1
onto the beamdirection. The respective distributions for
30 40 50 60 70
the Au,Bi, and U target are shown in the upper parts of Position along the wire chamber (mm)
Figs.5,6,7atT = 1.9GeV(full dots)togetherwith the
p 3
10
background measured at T = 1.0 GeV (open circles).
p p+Au
2
10
Theseexperimentaldistributionsthenhavebeencom-
pared with simulated distributions, which were evaluated
10
assuming the velocity distribution of the hypernuclei (as
obtainedfromtheCBUU+Hauser-Feshbachcalculations)
1
andalifetimeoftheΛ-hyperoninthehypernuclei,where
the latter was treated as a free parameter in the fit pro-
30 35 40 45 50 55 60 65
cedure. Since the number of events in the position distri- Position along the wire chamber (mm)
butions was not very large in some experiments, a Pois-
Fig. 5. Upperpart:Theposition distributionofhitsoffission
soninsteadofGaussianprobabilitydistribution p(n ) has
i
fragments in the position sensitive detectors for the p+Au
been used to simulate the number of counts n for each
i
experiment (from ref. [45]). The full dots represent the data
position bin (cf. ref. [46]). Then the best lifetime τ was
Λ for Tp=1.9 GeV whereas the open circles show the data for
searched for by the ’maximum likelihood’ method, which
Tp=1.0 GeV renormalized in the bright part of the detectors
allows also for an estimate of the statistical error for τ
Λ to the 1.9 GeV data. Lower part: The position distribution of
(see e.g. ref. [50]). The results of the fits are shownin the hits from the delayed fission fragments of hypernuclei in the
lower partof Figs. 5, 6,7 by the solid lines in the shadow shadowregionobtainedbysubtractingthebackground(renor-
regionin comparisonto the experimentaldata, where the malizeddatatakenat1.0GeV)fromthedatameasuredat1.9
background (measured at T = 1.0 GeV) has been sub- GeV. The solid line shows the result of the simulation with
p
tracted from the 1.9 GeV data. theextractedvalueforthelifetimeaccordingtothemaximum
likelihood method.
10 W. Cassing et al.: Lifetime of heavy hypernucleiand its implications on the weak ΛN interaction
7 7
10 10
6 p+Bi 6 p+U
10 10
5 5
10 10
4 4
10 10
3 3
10 10
2 2
10 10
10 10
1 1
10 20 30 40 50 60 30 40 50 60 70
Position along the wire chamber (mm) Position along the wire chamber (mm)
3
10
p+Bi p+U
2 2
10 10
10 10
1 1
10 20 30 40 50 25 30 35 40 45 50 55 60
Position along the wire chamber (mm) Position along the wire chamber (mm)
Fig. 6. The same distributions as in Fig. 5 for the p+Bi Fig. 7. The same distributions as in Fig. 5 for the p+ U
experiment (from ref. [32]). experiment (taken from ref. [46]).
clei, that lead finally to fission, have practically the same
Thequestionarises,whetherthevelocitydistributions
velocity distribution.
ofhypernucleimightdiffersignificantlywhenvarying(A,Z).
Insuchacasethesimulationofthepositiondistributions,
which is the crucial part in the analysis of the experi- 4 Summary of experimental results and error
mentaldata,shouldbe carriedoutby folding the velocity
analysis
distributionsofhypernucleiwithspecified(A,Z)withthe
fission time distributions of these hypernuclei. However, In this section we summarize the results of the COSY–13
as detailed calculations have shown [42], those hypernu- Collaboration and compare to the lifetimes measured be-