Er, der Melnitchouk, untersucht vor 2 Jahren in Virginia mal schnell das Deuterium

17/11/2012 - 23:45 von Gamma Funktion | Report spam
Leider ist mir nicht klargeworden, was er eigentlich gemessen hat.

Er sagt, er würde gar das p und das n getrennt behandeln - krass.


Ich hab die betreffende TV Vorlesung zwar gehört, aber
statt der ewigen Q Quadrats sollte er mal da das Quadrupolmoment klar rausarbeiten :


Nuclear effects in deuterium


Because the deuteron is a very weakly bound nucleus, most analyses have assumed
that it can be treated as a sum of a free proton and neutron. On the other hand, it has long
been known from experiments on nuclei that a nontrivial x dependence exists for ratios
of nuclear to deuteron structure functions. These effects include nuclear shadowing at
small values of x [7], anti-shadowing at intermediate x values, x 0.1, a reduction in
the structure function ratio below unity for 0.3 . x . 0.7, known as the European Muon
Collaboration (EMC) effect, and a rapid rise as x!1 due to Fermi motion.
The conventional approach to describing nuclear structure functions in the
intermediate- and large-x regions is the nuclear impulse approximation, in which
the virtual photon scatters incoherently from the individual bound nucleons in the
nucleus [8]. Furthermore, since quarks at large momentum fractions x are most likely
to originate in nucleons carrying large momenta themselves, the effects of relativity
will be ever more important as x!1. A relativistic description of the process therefore
required the development of a formalism for DIS from bound, off-shell nucleons, which
was pioneered in Ref. [6]. (Actually, the original motivation for that study was the quest
for a consistent description of pion cloud corrections to nucleon PDFs, in particular the
d¯/u¯ ratio, through the coupling of the photon to an off-shell nucleon dressed by a pion
[9].)
The off-shell DIS analysis [6] identified the conditions under which usual convolution
model [8] of nuclear structure functions holds, and found that in general these are
not satisfied within a relativistic framework. In a follow-up study [10] (referred to as
"MST"), it was found that one can however isolate a convolution component from
the total deuteron structure function, together with calculable off-shell corrections. The
general expression for the deuteron F2 structure function can then be written as [10]
Fd
2 (x,Q2) = å
N=p,nZ dy fN/d(y,g ) FN
2 x
y
,Q2 + d (off)Fd
2 (x,Q2) (1)
where FN
2 is the nucleon structure function, and fN/d gives the relativistic light-cone
momentum distribution of nucleons in the deuteron (also referred to as the nucleon
"smearing function"). The scaling variable y = (Md/M)(p · q/pd · q) is the deuteron's
momentum fraction carried by the struck nucleon, where q is the virtual photon momentum,
and p(pd) and M(Md) are the nucleon (deuteron) four-momentum and mass.
In the Bjorken limit the distribution function fN/d is a function of y only and is limited
to y Md/M. At finite Q2, however, it depends in addition on the ratio g = |q|/q0 p1+4x2M2/Q2 [11], which can have significant consequences when fitting large-x
deuterium data [12]. Furthermore, at finite Q2 the lower limit of the y integration is
given by ymin = x(1-2Med/Q2), where ed is the deuteron binding energy, while the
upper limit is in principle unbounded [13].
The relativistic nucleon momentum distribution derived by MST [10] (written here
for simplicity in the g !1 limit) is given by
fN/d(y) Md
32p2 yZ dp2
(Md/Ep-1)
|Yd(p)|2 q (p0) , (2)
where Ep = pM2+ p2 and p0 = Md - Ep are the recoil and struck nucleon energies,
respectively, and p2 = p20
- p2 the struck nucleon's virtuality. The deuteron
wave function Yd(p) contains the usual nonrelativistic S- and D-states, as well as the
small P-state contributions in relativistic treatments, and is normalized according to
R d3p|Yd(p)|2 /(2p)3 = 1.
Since the deuteron binding energy ed = -2.2 MeV is 0.1% of its mass and the
typical nucleon momentum in the deuteron is |p| 130 MeV, the average nucleon
virtuality p2 will be 4% smaller than the free nucleon mass. For x not too close to 1
one can therefore expanded the deuteron scattering amplitude in powers of p/M, using
the so-called weak binding approximation (WBA) [11, 12, 14]. To order O(p2/M2) one
can then show explicitly that the relativistic smearing function in Eq. (2) reduces to the
nonrelativisticWBA smearing function [11, 12],
fN/d(y)
O(p2/M2)
-! Z d3p
(2p)3 1+
pz
N |YD(p)|d y-1-
e + pz
M fWBA
N/d (y) , (3)
where e = Md -M -Ep ed - p2/2M. The resulting distribution function is sharply
peaked around y 1, with the width determined by the amount of binding (in the limit of
zero binding it would be a d -function at y = 1). At finite Q2 (or g ) the function becomes
somewhat broader, effectively giving rise to more smearing for larger x or lower Q2.
Finally, the convolution-breaking, off-shell correction d (off)Fd
2 in Eq. (1) receives contributions
from explicit p2 dependence in the quark-nucleon correlation functions, and
from the relativistic P-state components of the deuteron wave function. This correction
was estimated within a simple quark-spectator model [10], with the parameters fitted to
proton and deuteron F2 data, and leads to a reduction in Fd
2 of 1 - 2% compared to the
on-shell approximation.
The overall effect on the ratio Fd
2 /FN
2 is a 2 - 3% depletion relative to the free
case at intermediate x (x 0.5), with a steep rise at larger x (x & 0.6 - 0.7) due to Fermi
motion, as illustrated in Fig. 1 for Q2 =5 GeV2. Here the result for theWBA distribution
(3), with relativistic kinematics, is shown with and without the off-shell correction from
Ref. [10], and including finite-Q2 target mass corrections (TMCs) [15]. In both cases
the EMC effect is larger than that obtained within a light-cone approach [16], in which
one assumes on-shell kinematics and no binding. The depletion at large x is smaller,
however, than that predicted by the nuclear density extrapolation model [17], in which
the Fd
2 /FN
2 ratio is taken to scale with nuclear density.
 

Lesen sie die antworten

#1 Gamma Funktion
17/11/2012 - 23:49 | Warnen spam
Am Samstag, 17. November 2012 23:45:46 UTC+1 schrieb Gamma Funktion:
Leider ist mir nicht klargeworden, was er eigentlich gemessen hat.



Er sagt, er würde gar das p und das n getrennt behandeln - krass.





Ich hab die betreffende TV Vorlesung zwar gehört, aber

statt der ewigen Q Quadrats sollte er mal da das Quadrupolmoment klar rausarbeiten :





Nuclear effects in deuterium





Because the deuteron is a very weakly bound nucleus, most analyses have assumed

that it can be treated as a sum of a free proton and neutron. On the other hand, it has long

been known from experiments on nuclei that a nontrivial x dependence exists for ratios

of nuclear to deuteron structure functions. These effects include nuclear shadowing at

small values of x [7], anti-shadowing at intermediate x values, x 0.1, a reduction in

the structure function ratio below unity for 0.3 . x . 0.7, known as the European Muon

Collaboration (EMC) effect, and a rapid rise as x!1 due to Fermi motion.

The conventional approach to describing nuclear structure functions in the

intermediate- and large-x regions is the nuclear impulse approximation, in which

the virtual photon scatters incoherently from the individual bound nucleons in the

nucleus [8]. Furthermore, since quarks at large momentum fractions x are most likely

to originate in nucleons carrying large momenta themselves, the effects of relativity

will be ever more important as x!1. A relativistic description of the process therefore

required the development of a formalism for DIS from bound, off-shell nucleons, which

was pioneered in Ref. [6]. (Actually, the original motivation for that study was the quest

for a consistent description of pion cloud corrections to nucleon PDFs, in particular the

d¯/u¯ ratio, through the coupling of the photon to an off-shell nucleon dressed by a pion

[9].)

The off-shell DIS analysis [6] identified the conditions under which usual convolution

model [8] of nuclear structure functions holds, and found that in general these are

not satisfied within a relativistic framework. In a follow-up study [10] (referred to as

"MST"), it was found that one can however isolate a convolution component from

the total deuteron structure function, together with calculable off-shell corrections. The

general expression for the deuteron F2 structure function can then be written as [10]

Fd

2 (x,Q2) = å

N=p,nZ dy fN/d(y,g ) FN

2 x

y

,Q2 + d (off)Fd

2 (x,Q2) (1)

where FN

2 is the nucleon structure function, and fN/d gives the relativistic light-cone

momentum distribution of nucleons in the deuteron (also referred to as the nucleon

"smearing function"). The scaling variable y = (Md/M)(p · q/pd · q) is the deuteron's

momentum fraction carried by the struck nucleon, where q is the virtual photon momentum,

and p(pd) and M(Md) are the nucleon (deuteron) four-momentum and mass.

In the Bjorken limit the distribution function fN/d is a function of y only and is limited

to y Md/M. At finite Q2, however, it depends in addition on the ratio g = |q|/q0 >
p1+4x2M2/Q2 [11], which can have significant consequences when fitting large-x

deuterium data [12]. Furthermore, at finite Q2 the lower limit of the y integration is

given by ymin = x(1-2Med/Q2), where ed is the deuteron binding energy, while the

upper limit is in principle unbounded [13].

The relativistic nucleon momentum distribution derived by MST [10] (written here

for simplicity in the g !1 limit) is given by

fN/d(y) >
Md

32p2 yZ dp2

(Md/Ep-1)

|Yd(p)|2 q (p0) , (2)

where Ep = pM2+ p2 and p0 = Md - Ep are the recoil and struck nucleon energies,

respectively, and p2 = p20

- p2 the struck nucleon's virtuality. The deuteron

wave function Yd(p) contains the usual nonrelativistic S- and D-states, as well as the

small P-state contributions in relativistic treatments, and is normalized according to

R d3p|Yd(p)|2 /(2p)3 = 1.

Since the deuteron binding energy ed = -2.2 MeV is 0.1% of its mass and the

typical nucleon momentum in the deuteron is |p| 130 MeV, the average nucleon

virtuality p2 will be 4% smaller than the free nucleon mass. For x not too close to 1

one can therefore expanded the deuteron scattering amplitude in powers of p/M, using

the so-called weak binding approximation (WBA) [11, 12, 14]. To order O(p2/M2) one

can then show explicitly that the relativistic smearing function in Eq. (2) reduces to the

nonrelativisticWBA smearing function [11, 12],

fN/d(y)

O(p2/M2)

-! Z d3p

(2p)3 1+

pz

N |YD(p)|d y-1-

e + pz

M fWBA

N/d (y) , (3)

where e = Md -M -Ep ed - p2/2M. The resulting distribution function is sharply

peaked around y 1, with the width determined by the amount of binding (in the limit of

zero binding it would be a d -function at y = 1). At finite Q2 (or g ) the function becomes

somewhat broader, effectively giving rise to more smearing for larger x or lower Q2.

Finally, the convolution-breaking, off-shell correction d (off)Fd

2 in Eq. (1) receives contributions

from explicit p2 dependence in the quark-nucleon correlation functions, and

from the relativistic P-state components of the deuteron wave function. This correction

was estimated within a simple quark-spectator model [10], with the parameters fitted to

proton and deuteron F2 data, and leads to a reduction in Fd

2 of 1 - 2% compared to the

on-shell approximation.

The overall effect on the ratio Fd

2 /FN

2 is a 2 - 3% depletion relative to the free

case at intermediate x (x 0.5), with a steep rise at larger x (x & 0.6 - 0.7) due to Fermi

motion, as illustrated in Fig. 1 for Q2 =5 GeV2. Here the result for theWBA distribution

(3), with relativistic kinematics, is shown with and without the off-shell correction from

Ref. [10], and including finite-Q2 target mass corrections (TMCs) [15]. In both cases

the EMC effect is larger than that obtained within a light-cone approach [16], in which

one assumes on-shell kinematics and no binding. The depletion at large x is smaller,

however, than that predicted by the nuclear density extrapolation model [17], in which

the Fd

2 /FN

2 ratio is taken to scale with nuclear density.



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Übrigens :

Für mich besteht das n aus ddu und 5 i.

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