Inclusive Scattering and Dynamics in Light Nuclei Page: 4 of 14
This article 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:
The 4He response functions for a variety of single-nucleon couplings are shown
in Fig. 1. The nucleon, proton, isovector, spin-longitudinal, and spin-transverse
couplings are defined, respectively, as:
PN(k) = Zekr,
p,(k) = Zeikrtl+rz(i)
pr(k) = zekrr
For each coupling pa there is an associated response Ea. Note that the spin re-
sponse functions ErL and Err defined here are purely isovector, and that neglecting
isospin-breaking interactions one may replace r+ by rz when calculating E(k, r) for
an isoscalar target. The spin-independent isovector response Er is simply a weighted
average of ErL and E, r.
Most immediately apparent in Fig. 1 is the strong isospin dependence in the
response. This arises naturally in any model incorporating charge exchange. For
example the proton response E,(k, r) measures the propagation of charge in imaginary
time in a nucleus, and can be written as
E,(k,r) = Zfdr;2 jo(kri) E,(ri+,r) ,
where r;; is the distance between the initial position of proton i at time 0 and final
position of proton j at time r, r;, 1 r; - r?. In the limit r -+r 0, the propagator
< R ~e' '>- .(R - R'). As r increases the nucleons move, the imaginary-
time free particle propagator is proportional to exp[-(m/2r)(R - R')2]. In addition,
the charge exchange terms in the interaction shift the charge from one nucleon to
another, substantially reducing the contribution of the incoherent (i = j) terms to
the response. The difference between the nucleon and proton response indicates the
importance of the charge-exchange mechanism in quasi-elastic scattering.
For short imaginary times r, this difference can be described as a decreased effec-
tive mass for probes coupling to the nuclear charge. In a naive independent particle
model, one would naturally be led to ascribe a bigger charge radius to the proton. In
fact, this 'increased radius' is a simple consequence of nuclear dynamics.
Here’s what’s next.
This article 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 Article.
Schiavilla, Rocco. Inclusive Scattering and Dynamics in Light Nuclei, article, May 1, 1993; [Newport News, Virginia]. (https://digital.library.unt.edu/ark:/67531/metadc934151/m1/4/: accessed April 19, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.