Transcript BARYON 2002, TJNAF, March

Miami, FL
Feb 2003
Looking at close nucleons in nuclei
by
high momentum transfer reactions
<1 fm
1
Eli Piasetzky
Tel Aviv University, ISRAEL
Very Weird Universe
• Universe flat
Significant vacuum energy
Cosmology:
Most matter/energy density
not baryonic
The Composition of Our Universe
Baryons
Cosmological
Constant
Dark Matter
5-10%
~30%
60-65%
2
Miami
Miami
Near us more than ~ 99.95% (1-me/mp)
of
the mass is nuclear matter
These nuclei exist because of
strong interaction
3
the
At distances of a few fm the strong force is
attractive- creating the nuclear bound system.
At sub fm distances the strong force is
repulsive - preventing the nuclei to collapse to a point
V(rNN )
?
1.5 - 2 fm
rNN
4
R=5-10 fm
ATOMIC
NUCLEUS
A=4-200
CARBON :
R=3 fm, A=12
12
3


0
.
1
fm
4 / 3 33
24
1
.
710
3
14 gr
  0.1 fm  0.1 13 3  0.1 13 3  10
(10 )
(10 )
cm3
mp
5
d 3 1
0.17
~ 1  2 fm
ATOMIC
NUCLEUS
 0  0.17 fm 3
16O
R  R0 A
6
1 3
109Ag
208Pb
The nucleons are moving in a potential well that
describe the interaction of each nucleon with all the
other nucleons in the nuclei.
Using uncertainty principle we can
estimate a typical momentum of a bound
nucleon in nuclei.
xp ~ h
x ~ R ~ 5 fm
2 197
p 
~ 200 MeV
c
5
7
Fermi gas model:
p < KF ~ 250 MeV/c
Nucleons in nuclei :
Typical distance between neighbors : 1-2 fm
Typical momentum :~200 MeV/c
In this talk we will focus on nucleons
which are closer than that and with
larger momenta.
<1 fm
1 fm ~ Nucleon radius <
Distance between nucleon centers
In nuclei we call these pairs
short - range correlated pairs
8
2N SRC
Why should we care about 2N
in close proximity ???
NUCLEON
 The repulsive core of the nucleon and nuclear medium
modification.
NUCLEUS
 Properties of nuclei beyond the scope of effective
mean-field.
MASSIVE DENSE SYSTEMS
 Relevance to the center of neutron stars.
9
The Independent – Particle Shell Model (IPSM) is
based upon the assumption that each nucleon
moves independently in an average potential
(mean field) induced by the surrounding nucleons.
SPECTROSCOPIC STRENGTH
The (e, e’ p) data for knockout of protons from valance and deeply - bound
orbits in nuclei are 60-70% of the value predicted by the IPSM
10
IPSM
A
Where is the missing strength ?
The IPSM ignores the NN correlations which go beyond
the mean field level:
* The long range NN correlations.
* The short – range (scalar) correlations that reflect the
remnant of the hard - core part of the NN force.
* The intermediate distance, 1-2 fm, (tensor) correlations.
* Spin - isospin, spin – orbit correlations.
* “more than 2 - nucleon” correlations.
The individual roles of the different correlation
types was not established experimentally.
This research focuses on a direct measurement of
11 the short - range NN correlation in nuclei.
2N SRC assumed to be responsible for the large
momentum components in the nucleus.
The purpose is to find the fraction of 2N short - range
correlation in the tail.
How much is due to pp nn and np pairs
Etc.
12
In atomic nuclei gravitation is negligible
A neutron star is a HUGE NUCLEUS . In its center the
gravitational pressure is not negligible and the density is
5-10 times larger than in the center of atomic nuclei.
R ~ km
A ~ MS/Mp~1030/10-27~1057
What happens to compressed
cold nuclear matter?
13
Neutron Star Structure and the Equation of State
J. M. Lattimer and M. Prakash
The Astrophysical Journal, 550:426-442, 2001 March 20
14
Stars containing
nucleons (hyperons)
Stars containing exotic
components
This physics is relevant to the center of
neutron stars
  (5 10)0
*
( / 0 ) K f  (400 500)MeV / c
*
1/ 3
Is the equation of state hard or soft ?
What are the minimal masses for neutron stars
15
and black holes ?
What happens to compressed cold nuclear matter?
The answer depends on the behavior
of the strong force at short distances.
We therefore will return to study the
basic system of a nucleon pair at close
proximity
<1 fm
16
“ 2N SRC ” in momentum space
K1
K1  K2
K 1 > KF ,
K 2 > KF
17
K2
18
LOCAL NEWS BREAK
26
A-
E-01020
W.
Boeglin*
M. Jones
A. Klein
J. Mitchell
P. Ulmer*
E. Voutier
FIU
U of
Maryland
ODU
JLab
ODU
ISN
PR-01-007 and PR-01-008
Combined
D
19
p
p
p
BNL
TJNAF
e
e
20

n
e
p
*
e
n

p
*
p
Relevant publications :
J. Aclander et al. Phys. Lett. B453 (1999) 211.
A. Malki et al. Phys. Rev. C65 (2001) 015207.
21
A. Tang Phys. Rev. Lett. 90 ,042301
(2003) .
The EVA spectrometer and the n-counters:
22
23
Exclusive large-momentum-transfer
scattering
• Dimensional counting rule:
For incoming momenta above a few GeV/c
and cm angles above 400 , the differential
cross section scales as:
d s
( n
+n +n
+n
2)
dt
AB  CD
 S
A
B
C
D
t
f ( )
s
Where nA, nB, nC, and nD are the number of
valence quarks inside the hardons A, B, C, and D.
24
For p-p elastic scattering:
ds
dt
25
pp  pp
~ S
10
For quasi-elastic p-p scattering near 900 c.m.,
there is a very strong preference for reacting
with protons in the nucleus moving in the
beam direction.
p
p
This reduced s and preferentially
selects high momentum protons !
26
Pin = 6 GeV/c, PF = 0,
S0 = 13.16 (GeV/c)2
Pin = 6 GeV/c, PF = 0.4 GeV/c,
S = 9.3 (GeV/c) 2
(S / S 0 )10 = 32
27
The light - cone variable
The momentum of a nucleon is described in
light cone formalism by Pt and a , where
E  PZ
PZ
a
1 
m
m
For example :
Incident proton
Proton in the nucleus
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0.2 GeV/c
a  0.8
a 1
a
a 1
DATA:
0.2 GeV/c
a 0.8
QE (p,2p),
6 GeV/c,
exp 850, BNL
Calculations:
Farrar et al. PRL 62
(1989) 1095.
Yaron, Sargsian,
Frankfurt,
Piasetzky,Strikman
29
no s- dependence of
the pp cross section
Investigation of the high momentum components of the nuclear
wave function using hard quasielastic A(p,2p)X reactions
I. Yaron, PiasetzkyE. nd L. Frankfurta
School of Physics and Astronomy, Sackler Faculty of Exact
Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
M. Sargsian
Department of Physics, Florida International University,
Miami, Florida 33199
M. Strikman
Department of Physics, Pennsylvania State University,
University Park, Pennsylvania 16802
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Phys. Rev. C 66, 024601 (2002)
beam
n-array
beam
n-array
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Directional correlation
Pn>220 MeV/c
øpn
Pn<220 MeV/c
32
Cos øpn =Pp•Pn / |Pp|•| Pn|
33
The longitudinal CM momentum
of the correlated pair
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cm
P z
= 105 ± 20 MeV/c
The partner’s longitudinal
relative momentum
rel
35
P
z
= 300 ± 100 MeV/c
A typical broken pair
Z
~100 MeV/c
36
“Triples” vs. “Doubles”
# ( p, 2 p + n)
1
2


=
# ( p, 2 p )
T 
• •
For Pp>PF, Pn>PF
( 49 ± 12 ) %
For Pp<PF, Pn>PF
0
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QE
38
EXP 850 / BNL
C
Projectile (p)
Pin = 5.9 GeV/c
Pt > 0.6 GeV/c
Pt > 0.6 GeV/c
The probabilities for a backward emitted
high – energy (E > 52 MeV/c, p > 320 MeV/c) neutron
are
39
Measured ( 90° - 130° ) : ( 29.9 ± 2.4 ) %
Extrapolated out to 180° : ( 46.5 ± 3.7 ) %
Inclusive measurements with
Beams of hadrons, electrons, photons,
neutrinos, and antineutrinos
40
A universal probability for backward
particle emission < 10 % for Carbon.
The reason for the large high-energy backward
neutron yield is the strong total center of mass (s)
dependence of the hard reaction cross section and its
sensitivity to the short range nucleon correlations in
nuclei.
The strong s-dependence of the hard reaction
selects the high momentum protons in the nuclei
(small s)
These protons, most likely, have a correlated
partner at short range which are the
backward going neutrons.
41
Consequences :
A strong s - dependence to a much broader class of
hard processes than just the elastic scattering.
A large component of 2N SRC in nuclei.
42
P 01-015
FIU
43
PF
NN = pp or pn
44
Q2 = 2 (GeV/c)2,
X>1,
pm=300-500 MeV/c
45
XXXL
We optimized kinematics to minimize
the competing processes
HIGH ENERGY
LARGE Q2
LARGE
X
LARGE Em, Pm, Pmz
46
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A
A
48
Experimental setup
HRS
HRS
EXP 01-015
p
p
n array
e
n
e
49
Big Bite
50
51
52
53
Summary
The large-momentum-transfer hadronic
reactions naturally select large nuclear
momenta because of “s-weighting”
a 1
DATA:
0.2 GeV/c
a 0.8
QE (p,2p),
6 GeV/c,
exp 850, BNL
Calculations:
Farrar et al. PRL 62
(1989) 1095.
Yaron, Sargsian,
Frankfurt,
Piasetzky,Strikman
4
54
no s- dependence of
the pp cross section
The longitudinal CM momentum distribution
of the correlated pair is a Gaussian with a
width of a 105±20MeV/c.The longitudinal
relative momentum is 300±100 MeV/c.
The longitudinal CM momentum
of the correlated pair
1
55
cm
P z
The partner’s longitudinal
relative momentum
rel
= 105 ± 20 MeV/c
8
P
z
= 300 ± 100 MeV/c
In about half of the hard scattering exclusive
and inclusive events with two high pt
particles, there is also, at least one, backward
emitted neutron with momentum greater than
0.32 GeV/c.
“Triples” vs. “Doubles”
EXP 850 / BNL
# ( p,2 p + n )
1
2


=
# ( p,2 p )
T 
• •
C
Projectile (p)
Pin = 5.9 GeV/c
Pt > 0.6 GeV/c
Pt > 0.6 GeV/c
56
Measured ( 90° - 130° ) : ( 29.9 ± 2.4 ) %
Extrapolated out to 180° : ( 46.5 ± 3.7 ) %
( 49 ± 12 ) %
For Pp<PF, Pn<PF
0
The probabilities for a backward emitted
high – energy (E > 52 MeV/c, p > 320 MeV/c) neutron
are
11
For Pp>PF, Pn>PF
10
The leptonic reactions will allow to study both
pp and np pairs.
An experiment is scheduled to start by
the end of this year at TJNAF.
Experimental setup
HRS
HRS
EXP 01-015
p
p
n array
e
n
e
57
15
Big Bite
58
59
60
For QE (p,2p) events
Phys. Lett. B453 (1999)211 + 1998
61
Neutron momentum
data.
Number of coincident detected neutrons
Pn<220 MeV/c
62
Pn>220 MeV
42
37
46
2
63
64
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