ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS

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


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


>

->

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



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



)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


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


NHCD1 model

Lower stateUpper state 20 nb/sr 8 nb/sr


NHCD2 model

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ISOSPIN-MIXED X HYPERNUCLEAR STATES AND (K,K) REACTIONS