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
![Page 1: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/1.jpg)
ISOSPIN-MIXED HYPERNUCLEAR STATES
AND (K,K) REACTIONS
Dmitry LanskoyInstitute of Nuclear Physics
Moscow State University
INPC2007, Tokyo, June 6
![Page 2: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/2.jpg)
*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)
![Page 3: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/3.jpg)
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
![Page 4: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/4.jpg)
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)
![Page 5: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/5.jpg)
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
![Page 6: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/6.jpg)
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
![Page 7: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/7.jpg)
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
![Page 8: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/8.jpg)
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
![Page 9: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/9.jpg)
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→
![Page 10: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/10.jpg)
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+-)
![Page 11: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/11.jpg)
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
![Page 12: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/12.jpg)
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
![Page 13: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/13.jpg)
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
![Page 14: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/14.jpg)
Results for the K-p→K+reaction
Differential cross sections at various cm energies
Integral cross sectionversus cm energy
![Page 15: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/15.jpg)
Results for the K-p→K0reaction
Integral cross sectionversus cm energy
Differential cross sections at various cm energies
![Page 16: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/16.jpg)
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
![Page 17: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/17.jpg)
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.
![Page 18: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/18.jpg)
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!
![Page 19: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/19.jpg)
Backup slides
![Page 20: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/20.jpg)
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
![Page 21: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/21.jpg)
Results for the K-n→K0reaction
Integral cross sectionversus cm energy
Differential cross sections at various cm energies
![Page 22: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/22.jpg)
)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
![Page 23: ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS](https://reader035.vdocuments.us/reader035/viewer/2022062423/56814901550346895db6312a/html5/thumbnails/23.jpg)
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