isospin-mixed x hypernuclear states and (k,k) reactions
DESCRIPTION
ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS. Dmitry Lanskoy Institute of Nuclear Physics Moscow State University. INPC2007, Tokyo, June 6. - PowerPoint PPT PresentationTRANSCRIPT
ISOSPIN-MIXED HYPERNUCLEAR STATES
AND (K,K) REACTIONS
Dmitry LanskoyInstitute of Nuclear Physics
Moscow State University
INPC2007, Tokyo, June 6
*Isospin mixing in hypernuclei and Lane potentialwith Y.Yamamoto (Tsuru Univ)
*The (K-,K0) versus (K-,K+) reaction on nuclei*Phenomenological model for the elementary processes with V.Korotkikh, D.Sharov (Moscow Univ)
Pure charge states
M(-)- )=6.48±0.24 MeV
AZ+
A(Z+1)+-
V
0+V
1(T)
Pure isospin states
HYPERNUCLEI AZ with Z=(A-1)/2 (mirror cores)
0n--p coupling
Pure charge states
M(-)- )=6.48±0.24 MeV
AZ+
A(Z+1)+-
V
0+V
1(T)
Pure isospin states
HYPERNUCLEI AZ with Z=(A-1)/2 (mirror cores)
4H 10Be 12B 14C 16N 20F 28Al 40K
5 5 5 4 3.5 3 3 2.5
, MeV (without Lane potential V1)
Pure charge states
M(-)- )=6.48±0.24 MeV
AZ+
A(Z+1)+-
V
0+V
1(T)
Isospin-mixed states
HYPERNUCLEI AZ with Z=(A-1)/2 (mirror cores)
>
->
4H 10Be 12B 14C 16N 20F 28Al 40K
5 5 5 4 3.5 3 3 2.5
, MeV
Calculational scheme
Single-channel wave functions are calculated by a folding procedure with G-matrix interactions obtained from various meson-exchange (mostly Nijmegen) potentials core wave functions from a Skyrme-Hartree-Fock calculationDensity dependence of the N interaction is takeninto account within LDA; nonlocality is treated inthe effective mass approximation
Lane potential arises from the n--p coupling or,equivalently, from the isospin dependence of the Ninteraction
Results for the ESC04d model(strong Lane potential)s
MeV
MeV
p(T=0)=8%
p11B+
threshold
11C+-
threshold
K(1s
MeV
p(T=0)=21%
p
MeV
Results for the ESC04d model(strong Lane potential)s
MeV
MeV
p(T=0)=8%
p11B+
threshold
11C+-
threshold
K(1s
MeV
p(T=0)=21%
p
MeV
Results for various potential models (the lower state)
p(T=0pure charge
state)
p(pure isospin
state)
NHCD58%
Ehime53%
ESC04c81%
ESC04d92%
p
NHCD56%
Ehime51%
ESC04c72%
ESC04d79%
p
hypernuclei with Z=(A-1)/2 can be produced in the
(K-,K0)(not in the (K-,K+)) reaction from Z=N targets
The reaction is more complicated both forexperiment (neutral particle detection is needed) and fortheory: hyperon can be produced on protons as well ason neutrons
p→K+- p→
n→
reaction
dd =
dd
p→K+-) ·Zeff
reaction
dd =
dddd p→K00)·Z
eff·cos2+
ddn→K0-)·N
eff·sin2
|A(Z-2)>=|(A-1)(Z-1)+->
)>=cos|(sin|(A-1)Z+
f(Kp→K00)f*(K-n→K0-)+c.c.)(Zeff
Neff
)½cos ·sin
From isospin algebra
fp→fn→c.c dd
p→K00)
dd
n→K0-) dd
p→K+-)
Effective numbers of protons and neutrons
pK=1.8 GeV/c, forward angle
ESC04d model
C(K-,K0)12B 40Ca(K-K
Zeff
1.7·10-3 1.9·10-4
Neff
2.0·10-3 2.8·10-4
DWIA + eikonal approximation
Effective numbers of protons and neutrons
pK=1.8 GeV/c, forward angle
ESC04d model
C(K-,K0)12B 40Ca(K-K
Zeff
1.7·10-3 1.9·10-4
Neff
2.0·10-3 2.8·10-4
But empirical data on the elementary reactions are too poor,especially on the K-n→K0- reaction
Therefore, we need a theoretical model
DWIA + eikonal approximation
Phenomenological u channel exchange model
Exchanged hyperons: Y=Λ, Λ(1520), Σ, Σ(1385)
p
K‾
K0
p
K‾
K+
n
K‾
K0
fitted parameters: 4 products of the coupling constantsf
KNYf
KY and 4 cut-off parameters
Fit was performed to available data on differential and integralcross sections at E
cm<3.2 GeV
for 374 points
Results for the K-p→K+reaction
Differential cross sections at various cm energies
Integral cross sectionversus cm energy
Results for the K-p→K0reaction
Integral cross sectionversus cm energy
Differential cross sections at various cm energies
Forward differential cross section for hypernuclear production
pK=1.8 GeV/c
C(K-,K0)12B 40Ca(K-KC(K-,K+)12Be
Lower (ground)state
Upper state 5 nb/sr 1 nb/sr
70 nb/sr 37 nb/sr 4 nb/sr
ESC04d model (strong mixing)
Lower (ground)state
Upper state 20 nb/sr 5 nb/sr
23 nb/sr 6 nb/sr
Ehime model (almost pure charge states)
67 nb/sr
Summary
In hypernuclei with Z=(A-1)/2, mixed states appear, which possess neither pure isospin, nor pure charge. Such hypernuclei can be produced in the (K-,K0) reaction from Z=N targets.
Cross sections of the (K-,K0) reaction are of the same order ofmagnitude as those of the (K-,K+) reaction (though somewhatsmaller) and are strongly dependent on the isospin mixing.
A simple phenomenological u channel exchange model of theelementary processes gives fairly good description of availabledata and provides information necessary for hypernuclearcalculations.
Summary
In hypernuclei with Z=(A-1)/2, mixed states appear, which possess neither pure isospin, nor pure charge. Such hypernuclei can be produced in the (K-,K0) reaction from Z=N targets.
Cross sections of the (K-,K0) reaction are of the same order ofmagnitude as those of the (K-,K+) reaction (though somewhatsmaller) and strongly dependent on the isospin mixing.
A simple phenomenological u channel exchange model of theelementary processes gives fairly good description of availabledata and provides information necessary for hypernuclearcalculations.
Thank you!
Backup slides
0 1 2 3 4P ro je c tile m o m e n tu m , G e V /c
0
2 0 0
4 0 0
6 0 0
8 0 0
1 0 0 0
Hyp
eron
mom
entu
m, M
eV/c
K NK N
NKNK
NK
NK
K NK
N N(N K )
Kinematics of hypernuclear production
Results for the K-n→K0reaction
Integral cross sectionversus cm energy
Differential cross sections at various cm energies
)0()21()21( MBB ..5 chm
fL
)0()21()21( MRB ..chm
fL RB
)0()23()21( MRB
)0()23()21( MRB
.., chm
fL RB
..,5 chm
fL RB
Effective Lagrangians
Fitted parametersFormfactors F(q)=e-(q/)2
(1116): fKN
fK
= 809 MeV
(1520): fKN
fK
=1141 MeV
(1190): fKN
fK
= 692 MeV
(1385): fKN
fK
=1261 MeV
Forward differential cross section for hypernuclear production
pK=1.8 GeV/c
C(K-,K0)12B 40Ca(K-KC(K-,K+)12Be
Lower stateUpper state 3 nb/sr 0.2 nb/sr
31 nb/sr 16 nb/sr 1 nb/sr
ESC04d* model
Lower stateUpper state 1 nb/sr 0.01 nb/sr
7 nb/sr 4 nb/sr 0.06 nb/sr
ESC04c model
Lower stateUpper state 35 nb/sr 10 nb/sr
123 nb/sr 45 nb/sr 13 nb/sr
NHCD1 model
Lower stateUpper state 20 nb/sr 8 nb/sr
70 nb/sr 26 nb/sr 10 nb/sr
NHCD2 model