Zero range three-particle equations. [Karlsson-Zeiger equations] Page: 1 of 7
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lrJatlntduiY+ 1000U f tt. u w L0 .'a
ZERO RANGE THREf-PARTICLE EUT~fItfli
.. "err. Ales
Eoriqoe NS. beigot
toaefort Linear Accelerator Coer
Stooford Ifoivotofty. Stanford, Colifornia 945
Is order Co oerote rthe attire effect of to-particle a1
ring:.n tohreo-parricle system fIroe the effects of hidden
of froode (off-shell effects and threto-body foceo) .. take
limit of the Kolaonoo-flerorquotetnu. Although the Toddo
ambiguous go thio limit. the KZ eqution. eait Cell diteted
too-particle phase shifts, indieg orren, and seduced ogdt
range oqatioo uniquely predict the three-particle obsevale
cur in the abseoce of hfddo seoofte degree of freedom,
oplfitdoo poase all reoquisite phyteul oyeotry properftes
picwd oe ho uoitsy if trh specator bais .l ocothooaal so
Poenlit ooteoof co of the sems fo the onalysis of thea-np
atotea, to c0e a0e fotupaaticle eorentios, and to calori
rag eqlureod.iulypeitte he-atcl bavb
(Sohmftted for puolftiton in the Prceedigao of the eo
Few-Body Problem9 in Nuclear Physics. Triesto, Italy,
Work performed under the auspices of the fleperaent of Energy
(T/E) Ever tan e Wick li shoved that the finite range of nuclear forces in
Yukava's oason theory 2 aries naturally from the coupling of the uncertainty
principle with special relativity, and more particularly since the experimo-
teal discovery of the pion, we have known that nuclei sut, in v0" senes, fe-
Wein pion, os well ao protons end neutrons. Yet sot of nuclear physic. he
been developed using phenomenologici nuclear potentials which do not take
explicit account of these mesni degrees of freedom. The main counter-
example 'g the study of the too nucleon problem, ohero ah effort has Roes
into the construction of the so-toled "sewn-theoretio pote lss" sing in -
sct eses either a combination of field theory sad dispetion thery or oe
bosn exchange models roughly correlated with the eirial homeamoe spec-
true. Although sch model can, after conidehble effort and a peers oa
of espfrftfl paramtera, provide a reasonably quantitative diocriptio of tan
nucleon elastic scattering, this 1. ne goorontse that those models provide a
correct description oven of the cleaonie degrees of freedom at short ditaseso,
doe to the fat that there are always an infinite number of ways to dscrihe
this short range behavior which lead to identical elastie scataring aplitedes.
TTh the first stringent test of tha nuclear fora Models tma foem
t onfrontlag them with three nuclen do"a. a.". us w hawe kne fee mama
time, the tes fai.. The "reatiscic potentials" sederbld the teieon by 1
5 to 1.5 NOV. and predict etactrwstatia form fetters with a first 01.1w i at
higher energy and s second maximum of such smaller magnitude than given by
the experimental results of a-Hal elastic -cttmring. Thus the mesanic degrees
of Freedom do matter in a quantitative acte, whether don to the fact that
thay give alert range behavior quit. different from (thrush phase equivalent
tam) the "realistic paeenciale"-in the ]argon of the trade theme ate called
n-shelf stet- "off-.hell affetaar due to the face that they give rise to abort tungs
smsonic degree. three-body tortes, or most likely bath.
the sero range When I started work on the three body problem in 1965 theme htnral
equations are considerations led m to anticipate that it would be lmpormant to .,panht
SUsing only the long rang. or ou-shell effects which aria. I. the region hern 911. pr-
he, these zero- titles ate outside the range of forces from the sore nomplicated sheet raspe
es which would effects. By 1969 I had sont m6d Is making a formal Th mrrll ..g n neio etuP u tl i aesufficint toee de
,and ten he standing of earn of the subtleties In the threm-body problem to reduce this
d complete. farmilis to a practical aalytic tool.
lot syet.-s The key to the successful solution of the probe rase fom quite other
coide-atiaea connected with the Interpretative of qtw(es oat", .e 1
dlatesed in my talk on "'Ihse.-Body PorceX" at OCL.A in 19721 . If w rorm-
late the scattering problem directly In terma of the as-shall scatteflsge
rlkahop on betsae. free Particle, e amp be doe consistently in a descriptive sense ,
13-16 North 1918) then we can for example introduce msonic off""t into the three nu l""
problem by assuming that this system cms-..s of three nation"e and a pie.
and solving this four-body problem. The .chare 2 cowlectured which weuld
make this passible was general in that I anvionged that it would be posslblo
co discuss any n-partIll system In terms of the n-1 partlcl e n-sboll muat-
tering. and an intrinsic n-parrlclo process to be dmtermined eplsically.
The basic difficulty Is that in this type of sero range theory, which he* Mo
Interaction Hamiltonian. the task of guaranteeing uniterity to haft to the
, form of the aquatione themelves, and nuac be investigated sparstely for
By 1975 1 thought I had abstracted a viable, eMhougM1 a~d hat, aet of thmae-
body equation. from the Faddeev equations. I presented these on-shell equa-
tions nt Llblice, Mb only to have them shot down by Losbrecht Kok. One basic
PnriTTerryr "r T'e T-e i'-,,T 79 iin lrM g TE i
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Noyes, H.P. & Zeiger, E.M. Zero range three-particle equations. [Karlsson-Zeiger equations], report, April 1, 1978; California. (https://digital.library.unt.edu/ark:/67531/metadc1192674/m1/1/: accessed March 18, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.