Zero range three-particle equations. [Karlsson-Zeiger equations] Page: 6 of 7
This report is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to Digital Library by the UNT Libraries Government Documents Department.
The following text was automatically extracted from the image on this page using optical character recognition software:
to the successes already achieved by separable models, once we include enough
two-nucleon states. A careful error analysis will then reveal where in the
Inceasingly detailed three-nuelecon data there is evidence for genuine
moonie effect, or where we ran scasre two nucleon phases Which are poorly
known from two-naueleo clastic scattering experiments (c.1P1 and el) in
amplitude. where other uncertainties ace small. A alternative approach
Would be wo Investigate our limit at finite range and include the odifiea-
tiono of the kernel and driving terms arising fren the vanishing of the two-
partiCle wave functions inside C. Judging From the success of Brayhe's
boundary condition approach ) we can bope that this will still provide os
with one-variable equations. and can adjust R to fit al and the triton binding
energy. If this still does not give good electromagnetic form factors, at the
eost of going to to-variable interior equations, we could alo pontulae
nucleanic structure Inside R and investigate phenomenologically what is re-
quired to fit the electromagnetic properties.
VA can hardly expect all three-hadron systems to be as inwensitive to
hidden degree of freedom as the three-nucilon system. Therefore we will
seed a nystaeatic way to introduce phenoeonological parencters into the scheme
which can be used to anatyze the three particle final staten relative to on
assumed act of phase shifts for nhe to-particle subsysems. Ono way to do
this would he to go from e 3x3 to a 4.4 component description by including a
direct threoe-particle teen range scattering procers. If the new components
are then eliminated to get back to a 3.3 description the three-paretile phoen
shifts will appear oxylicitly in the modified kernels and driving terms.
whishee the rcnulting equations will .till retain their on -variable atruturo
is not nampletly clear, but for sore parametrteatiens thin should be possible
to achieve. Then we could use the scheme to determine genuine three-particle
parameters directly fro experiment. This should prove to be particularly
useful in the kinematic regions where there are broad overlapping two-porticle
resonances in che seubnytem. since cheae could be included without approxi-
Another important problm is th extenaion of the oche.. to four-particle
nyates. mne we hacwsrnderocd in detail the rolatiosip beenween a direct
on-shell thee-particle serttering description and cbe more detailed aetteals-
lin of nhn arsplitsdoo is ters of the Faddeer channel deccampoition, it sighs
he pooiblo to construct an on-shell four-particle theory using only 2+1 and
2+2 olonten (i.., a pay channel description). whether or not thi proves
no be pontible, we can with same effort surely construct a two-variable but
on-$hell 1810 component four-particle theory-
Mother gmneralieation that is almot lamediate is the corresponding
fovarint three-particle theory. ue keew this beejuse of Braynhaw's nucees
with the tovaelant boundary condition approach. [1 In the current sehene we
was hope to replace the boundary condition by invoking directly the inelasticity
parameter which oncure in the cwo-particle plastic amplitudes due to the
opening up of particle production chacocis. we also an now use sodelo~with
left-hand cuts representing particle eehange n crossed channel, cad thus
cOme closer tha Brayohaw to conventional elementary particle theories.
Once a four-particle cvariant theory exists we can look at the aln
system belo production threshold for the pion, and compare it with NMI
cluster. in the NShi system similarly restricted. In both cases we can define
uhat we might call a two-nucleon off-shell t-matrix. To the extent chat they
are the -ae we could then justify using this similarity so define a
Here’s what’s next.
This report can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Report.
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/m1/6/: accessed April 22, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.