1. Tel Aviv University, ISRAEL
Miami, FL Feb 2003
Looking at close nucleons in nuclei by
high momentum transfer reactions
<1 fm
Eli Piasetzky
Tel Aviv University, ISRAEL

2. Significant vacuum energy
Very Weird Universe
Universe flat
Cosmology:
Significant vacuum energy
Most matter/energy density
not baryonic

3. Near us more than ~ 99.95% (1-me/mp) of the mass is nuclear matter
Miami
Miami
Near us more than ~ 99.95% (1-me/mp)
of the mass is nuclear matter
These nuclei exist because of the
strong interaction

4. 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 ) fm
rNN

5. R=5-10 fm
ATOMIC NUCLEUS
A=4-200
CARBON : R=3 fm, A=12

6. ATOMIC NUCLEUS
208Pb
109Ag
16O

7. p < KF ~ 250 MeV/c Fermi gas model:
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.
p < KF ~ 250 MeV/c Fermi gas model:

8. < Nucleon radius~ 1 fm <1 fm Distance between nucleon centers
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.
< Nucleon radius~ 1 fm
<1 fm
Distance between nucleon centers
In nuclei we call these pairs short - range correlated pairs
2N SRC

9. 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.

10. SPECTROSCOPIC STRENGTH
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.
The (e, e’ p) data for knockout of protons from valance and deeply - bound orbits in nuclei are % of the value predicted by the IPSM
IPSM
SPECTROSCOPIC STRENGTH A

11. 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 the short - range NN correlation in nuclei.

12. How much is due to pp nn and np pairs
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.

13. 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 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?

14. Neutron Star Structure and the Equation of State
J. M. Lattimer and M. Prakash
The Astrophysical Journal, 550: , 2001 March 20
Stars containing nucleons (hyperons)
Stars containing exotic components

15. This physics is relevant to the center of neutron stars
Is the equation of state hard or soft ?
What are the minimal masses for neutron stars
and black holes ?

16. 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

17. “ 2N SRC ” in momentum space
K 1
K 1
K 2
K 1 > KF ,
K 2 > KF
K 2

19. LOCAL NEWS BREAK A- 26
PR and PR Combined
FIU U of Maryland ODU JLab ODU ISN
W. Boeglin* M. Jones A. Klein J. Mitchell P. Ulmer* E. Voutier E D

20. p n p
BNL
TJNAF e p e p e p n

21. Relevant publications : Aclander et al. Phys. Lett. B453 (1999) 211.
Malki et al. Phys. Rev. C65 (2001)
A. Tang Phys. Rev. Lett. 90 , (2003) .

22. The EVA spectrometer and the n-counters:

24. Exclusive large-momentum-transfer scattering
Dimensional counting rule:
For incoming momenta above a few GeV/c
and cm angles above , the differential
cross section scales as:
Where nA, nB, nC, and nD are the number of valence quarks inside the hardons A, B, C, and D. d s t S - ( n + n + n + n - 2 ) f ( ) A B C D dt s AB CD

25. For p-p elastic scattering:d s - ~ S 10 dt pp pp

26. This reduced s and preferentially selects high momentum protons !
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 !

27. Pin = 6 GeV/c, PF = 0,
S0 = (GeV/c)2
Pin = 6 GeV/c, PF = 0.4 GeV/c,
S = 9.3 (GeV/c) 2
(S / S 0 )10 = 32

28. The light - cone variable
The momentum of a nucleon is described in light cone formalism by Pt and a , where m P E Z - = 1 a
For example :
Incident proton
0.2 GeV/c 8 . a
Proton in the nucleus

29. 8 . » a Calculations: 0.2 GeV/c DATA: QE (p,2p), 6 GeV/c, exp 850, BNLa
0.2 GeV/c
DATA:
QE (p,2p),
6 GeV/c,
exp 850, BNL
Calculations:
Farrar et al. PRL 62 (1989) 1095.
Yaron, Sargsian, Frankfurt, Piasetzky,Strikman
no s- dependence of the pp cross section

30. Investigation of the high momentum components of the nuclear
wave function using hard quasielastic A(p,2p)X reactions -
nd L. Frankfurta PiasetzkyE. I. Yaron,
School of Physics and Astronomy, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
Sargsian M.
Department of Physics, Florida International University, Miami, Florida 33199
Strikman M.
Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802
Phys. Rev. C 66, (2002)

31. fully correlated protons
uncorrelated protons
beam
n-array
fully correlated protons
beam
n-array

32. Directional correlation
Pn>220 MeV/c
øpn
Pn<220 MeV/c
Cos øpn =Pp•Pn / |Pp|•| Pn|

34. The longitudinal CM momentum of the correlated pair
Pcmz = 105 ± 20 MeV/c

35. The partner’s longitudinal relative momentum
Prelz = 300 ± 100 MeV/c

36. A typical broken pair
MeV/c Z p n
MeV/c
~100 MeV/c

37. “Triples” vs. “Doubles”
For Pp>PF, Pn>PF
( 49 ± 12 ) % • • =
For Pp<PF, Pn>PF

38. QE

39. C EXP 850 / BNL Projectile (p) Pin = 5.9 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
EXP / BNL
Measured ( 90° - 130° ) : ( 29.9 ± 2.4 ) %
Extrapolated out to 180° : ( 46.5 ± 3.7 ) %
Projectile (p)
Pin = 5.9 GeV/c
Pt > 0.6 GeV/c C

40. Inclusive measurements with
Beams of hadrons, electrons, photons, neutrinos, and antineutrinos
A universal probability for backward particle emission < 10 % for Carbon.

41. 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.

42. A large component of 2N SRC in nuclei.
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.

43. P
FIU

44. PF
NN = pp or pn

45. Q2 = 2 (GeV/c)2,
X>1,
pm= MeV/c

46. We optimized kinematics to minimize the competing processes
XXXL
We optimized kinematics to minimize the competing processes
HIGH ENERGY
LARGE Q2
LARGE X
LARGE Em, Pm, Pmz

48. A A

49. Experimental setup
HRS
HRS
EXP p
n array p e n e
Big Bite

54. Summary
The large-momentum-transfer hadronic reactions naturally select large nuclear momenta because of “s-weighting”

55. 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.

56. 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.

57. 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.

61. For QE (p,2p) events Phys. Lett. B453 (1999)211 + 1998 data.
Vertical proton momentum
Neutron momentum

62. Number of coincident detected neutrons42 37 46 2
Pn>220 MeV
Pn<220 MeV/c