Strangeness in Nuclear Physics

J. Mares,P.Bydzovsky, A. Cieply, D. Gazda, V. Krejcirık, L. Majling, N. Shevchenko, M. Sotona

Nuclear Physics Institute, Rez

NuPECC Meeting – Villa Lanna, Prague, 17 June, 2011

Hypernuclei

Why to study hypernuclei?

Hyperon X Nucleon → no Pauli blocking

Hyperon can penetrate deep into the nuclear interior and probe the nuclear interior.

Test models of baryon-baryon and meson-baryon interactions(meson exchange models, quark models, chiral models, ...)

Test nuclear models(RMF,EDF, shell model,...)

Test models of hadrons(SU(3)symmetry, quark models ...)

Hypernuclear production – test reaction mechanisms

Hypernuclear decays → study of weak interaction

Implications for:

astrophysics (compact stars)

HI collisions (strangeness production, medium modification od hadrons)

Λ hypernuclei

> 30 Λ-hypernuclei:

Λ hypernuclei

(K−, π−) reaction (emulsions,

CERN, BNL, KEK, Frascati, JParc)

(π+,K+) reaction (BNL, KEK)

Textbook example of single-particle structure

Λ hyperon bound by ∼ 28 MeV in nuclear matter

Negligible spin-orbit splitting ≤ 0.3 MeV

Λ hypernuclei

RMF calculations (J.M., B.K. Jennings, PRC (1994):

(+ quark model + Yω tensor coupling fωY2MY

ΨY σµν∂νVµΨY )

Λ hypernuclei

(K−stop, π−) reaction

(FINUDA, PLB 622 (2005) 35):

Λ binding energy spectrum in 12Λ C

(e, e ′K ) reaction(JLab, PRL 99 (2007) 052501):

12Λ B excitation spectrum

Λ hypernuclei

γ spectroscopy (BNL, KEK)⇒ spin dependence of the effective ΛN interaction in the nuclear p shell

Λ hypernuclei

Electroproduction of strangeness (Bydzovsky, Sotona)

e + A → e ′ + K+ + H∗

Provides information about:

effective ΛN interaction

elementary-production operator

Electroproduction of Λ hypernuclei

Results for p-shell hypernuclei: Spectrum of 12BΛ

Theoretical prediction: elementary operator – Saclay-Lyon A model

(dashed line) ΛN interaction from γ -ray spectra of 7LiΛ

data: E94-107, JLab Hall A, Iodice et al, PRL 99 (2007) 052501

s1 /2 Λ

p1/2Λ , p3/2Λ

1-, 2-

1-

1-, 2-

1+, 2+, 3+

Larger model space?

Electroproduction of Λ hypernuclei

Spectrum of 16NΛ

Theoretical prediction: elementary operator – Saclay-Lyon A model

(dashed line) ΛN interaction fitted to 16OΛ and 15NΛ spectra

data: E94-107, JLab Hall A, Cusanno et al, PRL 103 (2009) 202501

different splitting

sΛ

pΛ

Larger model space?

(1hω calculations)

0-,1-

1-,2-2+,1+

2+,3+

Σ hypernuclei

Σ-nucleus interaction:(J.M., Friedman, Gal, Jennings, NPA (1995))

Σ hyperons are not bound in nuclei except for 4ΣHe

Sawafta et al, PRL 83 (1999) 25; Noumi et al, PRL 89 (2002) 072301

DWIA calculations (Harada & Hirabayashi, NPA 759 (2005) 143)

Ξ hypernuclei

Ξ-nucleus interaction:

no established yet QBS12C(K−,K+) spectra (KEK -E224, BNL-E885) → VΞ ≈ 14 MeVSpectroscopic study of Ξ hypernucleus 12

Ξ B ... (T. Nagae),A ’Day-1’ experiment E05 at J-Parc

Multi-strange baryonic systems

Multiply strange nuclear systems (N, Λ, Σ, Ξ)

of interest for astrophysics (neutron stars)of interest for HI collisionstheir study = source of information about B − B interactions

Unfortunately, only ΛΛ hypernuclei known (4ΛΛH (?), 6ΛΛHe, 10

ΛΛBe, 13ΛΛB)

RMF calculations:

predict bound systems with appreciable number of hyperonsfor some critical number of Λ’s:ΛΛ → ΞN energetically favorable due to Pauli blocking of Λ’s⇒ It is necessary to include Ξ !! (Ξ-nucleus potential ?)

{ N, Λ, Ξ} configurationsρ ≈ (2− 3)ρ0, fs = |S |/A ≈ 1, |Z |/A � 1, EB/A ≈ (10− 20) MeV

Strange hadronic matter

neutron star structure

Schaffner-Bielich, NPA 804 (2008) 309 Glendenning, Schaffner-Bielich,

PRC 60 (1999) 025803

kaon condensation could occur at ρ & 3ρ0, l− → K− + νl (ωK− ≤ 200 MeV)

KN interaction

KN interactionstrongly attractive ⇐ ∃ I = 0 Λ(1405) πΣ resonance, 27 MeV below K−p threshold

Kaonic nuclei

K -nucleus interactionstrongly attractive and absorptive ⇐ kaonic atom level shifts and widths

? optical potential depth:

ReVopt ' (150−200) MeV ← phenomenological models (Friedman, Gal, JM)

ReVopt ' (50−60) MeV ← chiral models (e.g. Cieply, Friedman, Gal, JM)

⇒ ∃ of K -nuclear states

? sufficiently narrow to allow identification by experiment

Motivation

(2N)K , (3N)K , (4N)K , (8N)K , . . . (Akaishi, Yamazaki, Dote et al.)

large polarization effects ρ ' (4− 8) · ρ0

BK & 100 MeV, ΓK ' (20− 35) MeV

Status Quo

K− capture in Li and 12C (FINUDA, PRL (2005)): B = 115± 6± 4 MeV, Γ = 67± 14± 3 MeV

vs.

K−pN → ΛN + FSI (Magas et al., PRC (2006))

?

p annihilation on 4He (Obelix, LEAR) → K−pp : B ' 160 MeV, Γ ' 24 MeV→ K−ppn : B = 121±15 MeV,Γ<60MeV

(Bendiscioli et al., NPA (2007))

?

pp → K+Λp (DISTO) → K−pp : B = 105± 2± 5 MeV, Γ = 118± 8± 10 MeV(T. Yamazaki et al EXA08, PRL2010)

?

K−pp quasibound state

Coupled-channel Faddeev calculations of a KNN − πΣN system(Shevchenko, Gal, JM, PRL (2007), PRC (2007))

KN strongly coupled with πΣ via Λ(1405) ⇒ πΣ channel included

particle channels α: 1 : (KNN) 2 : (πΣN) 3 : (πNΣ)

i = 1 NN ΣN ΣNi = 2 KN πN πΣi = 3 KN πΣ πN

Table: Calculated K−pp binding energies and widths (in MeV)

single channel coupled channel

AY DHW SGM IS WG

B 48 17-23 50-70 60 - 95 40-80Γ 61 40-70 90-110 45-80 40-85

RMF Methodology

Larger K−-nuclear systems(JM, Friedman, Gal, PLB (2005), NPA (2006); + Gazda, PRC (2007), PRC (2008), PRC

(2009), NPA (2010))

RMF model for a system of nucleons , K mesons, and hyperons interacting through theexchange of σ, σ∗, ω, ρ, φ and photon fields:

L = LRMF + LK + LY

where

LRMF = standard relativistic mean field lagrangian density

LK = (DµK)† (DµK)−m2KK†K − gσKmK σK†K − gσ∗KmK σ

∗ K†K ,

LY = ψY [iD/− (mY − gσY σ − gσ∗Y σ∗)]ψY ,

+ Absorption through:

pionic conversion modes

KN → πΣ+90 MeV, πΛ+170 MeV

nonmesonic modes

KNN → YN+240 MeV

Single-K− nuclei

ΓK− follows the dependence sf(BK− )

0 50 100 150 200B

K- (MeV)

0

50

100

150

200Γ K

- (M

eV)

COCaPb

The K− decay widths ΓK− in 12

K−C, 16

K−O, 40

K−Ca, and 208

K−Pb as function of the K− binding energy B

K− .

The dashed line indicates a static nuclear matter calculation.

Single-K− nuclei

0 50 100 150 200BK- (MeV)

0.10

0.12

0.14

0.16

0.18

0.20ρ _ (

fm-3

)

C

Pb

Ca

O

Average nuclear density ρ as function of the K− binding energy.

Multi-K nuclei

1 2 3 4 5 6κ

0

50

100

150

200B

K(M

eV)

K-

K0

16O + κK

The K binding energies as functions of the number κ of antikaons.

saturation observed across the periodic table

BK << mK + mN −mΛ & 320 MeV, far away from kaon condensation

Multi-K hypernuclei

Fig. 17 The K binding energy BK in 208Pb as a function of the number κ of antikaons and η of Λ hyperons.

Summary

Λ hyperon bound by 28 MeV in nuclear matter, spin-orbit splitting → 0p-shell hypernuclei - effective ΛN interaction determined(exp. JLab, FINUDA, planned JParc, HypHI @ GSI (FAIR))

more data on ΛΛ hypernuclei needed → PANDA@GSI

Σ hyperons are not bound in nuclei except for 4ΣHe

Ξ hyperons perhaps bound by ≈ 14 MeV in nuclear matter

(planned exp. JParc)

K nuclei → the issue is far from being resolved

(searches for K−pp are underway in GSI and JParc)

kaon condensation is unlikely to occur in strong-interaction self-bound

strange hadronic matter

Summary

”In spite of its ‘age’ of over 50 years, Strangeness Nuclear Physics has not lost its

charm and beauty. On the contrary, it keeps up to its young spirit in addressing

new challenging problems and questions ...” (P. Bydzovsky, A. Gal, J. Mares, LNP724)