Spectrum of kaonic atom and kaon-nucleus interaction revisited - PowerPoint PPT Presentation

Spectrum of kaonic atom and kaon-nucleus interaction revisited 2018.11.11-12 ”Hadron structure and interaction in dense matter” @KEK Tokai campus Yutaro IIZAWA 1 , 2 Daisuke JIDO 2 , 1 Natsumi IKENO 3 Junko YAMAGATA-SEKIHARA 4 Satoru HIRENZAKI 5 1 Tokyo Metropolitan Univ. 2 Tokyo Tech 3 Tottori Univ. 4 Kyoto Sangyo Univ. 5 Nara Women’s Univ.

1.Kaonic atom and Strong interaction Motivation • the fundamental information of hadron physics 1 / 24 K − -nucleus interaction is ( K is one of NG bosons) Kaonic atom spectrum → K − -nucleus interaction

Kaonic atom Coulomb interaction • The strong interaction provides energy shift from pure Coulomb spectrum 2 / 24 • Kaonic atom is a bound system of K − and nucleus mainly by i.e. The orbital electron is replaced by K − • K − interacts strongly with nucleus → EM + strong • Nuclear absorption provides decay width ↑Width ←Energy Shift ↑Energy Spectrum by Pure Coulomb

Phenomenological potential by Friedman, Gal and Batty 1 • global fjt with all data 1 E. Friedman, A. Gal, C.J. Batty, Nucl. Phys. A579(1994)518-538 3 / 24 • 4 model ( t eff ρ , Infm., Comp, Nominal) • t eff ρ model is linear in nuclear density : V opt ( r ) = − 4 π µ 2 µ (1 + m N )(0 . 69 + 0 . 94 i ) ρ ( r ) Re V opt (0) ∼ − 80 MeV , Im V opt (0) ∼ − 110 MeV • Nominal model is famous ” deep ” potential including non-linear term : � � � ρ ( r ) � 0 . 21 � � V opt ( r ) = − 4 π µ 1 + ( − 0 . 15 + 0 . 62 i ) + (1 . 63 − 0 . 01 i ) ρ ( r ) 2 µ ρ (0) m N Re V opt (0) ∼ − 180 MeV , Im V opt (0) ∼ − 70 MeV

Aim of this study • Puzzle : • The energy shift is found to be repulsive in all kaonic atoms • Possible solutions of this puzzle : It repels the atomic states upwards ( level repulsion ) • Purpose : Which solution is realized in actual kaonic atom ? 4 / 24 • But the K − N interaction is known to be attractive • How do we understand the inconsistency between K − A and K − N ? 1. Attractive strong interaction provides Bound state (nuclear state) . 2. Large imaginary part of optical potential works as repulsively .

2.Formulation Klein-Gordon equation 5 / 24 � � 2 � − d 2 � d r 2 + l ( l + 1) µ − B.E. − i + µ 2 + 2 µV opt ( r ) 2 Γ − V c ( r ) rR ( r ) = 0 − r 2 V c ( r ) : fjnite Coulomb potential → EM interaction 2 µV opt ( r ) : self energy → Strong interaction

6 / 24 K − A strong interaction linear potential V opt ( r ) = ( V 0 + iW 0 ) ρ N ( r ) 1 = ( V 0 + iW 0 ) � r − R B � ρ 0 1 + exp a V 0 , W 0 : parameters fjtted by datum for each kaonic atom W 0 < 0 because of nuclear absorption assume : potential is proportional to ρ N and V 0 < 0 because K − N interaction is attractive

Our approach We study strong potential in the following 2 steps : kaonic atoms 2. confjrm whether these potentials describe the data of other 7 / 24 experimental datum for each kaonic atom 1. determine potential parameters so as to reproduce one input output Datum ( ∆ E, Γ ) → Parameter( V 0 , W 0 ) − − − − − − − − → − − − − each nucleus KG eq check universality : potential fjtted by Cu → Co, Ni

1 : determine potential parameters 8 / 24

Potential is not determined uniquely. 3 How about wave functions of kaonic atom using these potentials ? 28.5 199.5 pot 3 20.0 78.5 pot 2 114.5 79.5 pot 1 Cu feature potential nucleus Potentials for kaonic Cu atom (last orbit : 4f) These potentials have different features from each other. MeV) 9 / 24 → We fjnd 3 potentials which provide same datum (0< − V 0 , − W 0 <500 using datum ( ∆ E, Γ ) = (0.240 keV, 1.65 keV) ℓ − V 0 [MeV] − W 0 [MeV] large Im V opt small Im V opt deep Re V opt , small Im V opt

Wave function of kaonic atom 10 / 24 pot 1 pot 2 pot 3 0 20 40 60 80 100 r [fm] (atomic range) Figure 1: wave functions of Cu kaonic atom Wave functions are similar to one another in atomic range ( r = 10 ∼ 100 fm )

Wave function of kaonic atom The number of nodes(nuclear states) is different 11 / 24 pot 1 pot 2 pot 3 0 2 4 6 8 10 r [fm] (nuclear range) Figure 2: wave functions of Cu kaonic atom Wave functions are different in nuclear range ( r = 0 ∼ 10 fm )

12 / 24 Nuclear state which has same angular momentum (Cu, l = 3 ) • Potential 1 provides no nuclear states ( l = 3 ) • Potential 2 provides a nuclear state ( l = 3 ): − B.E. − i Γ / 2 = ( − 5 . 8 − i 22 . 4 / 2) MeV → level repulsion • Potential 3 provides 2 nuclear states ( l = 3 ): − B.E. − i Γ / 2 = ( − 102 . 5 − i 57 . 0 / 2) MeV (ground state) − B.E. − i Γ / 2 = ( − 17 . 65 − i 32 . 0 / 2) MeV → level repulsion

Large Im part (Potential 1) 79.0 142.0 last orbit : 4f pot 1 nucleus(Z,A) Co 28.5 91.0 Ni 164.0 We fjnd that potentials of other kaonic atoms have similar feature Cu 79.5 114.5 Cu2 2 23.5 134.0 Potentials 1 have large imaginary part. 2 another experimental datum of Cu 79.0 Cl 142.0 79.0 last orbit : 3d pot 1 nucleus(Z,A) Mg 24.5 79.0 Al 46.0 126.0 Si 61.5 120.5 P 67.0 142.0 S 13 / 24 − V 0 [MeV] − W 0 [MeV] − V 0 [MeV] − W 0 [MeV]

Small Im part (Potential 2) Ni 26.5 last orbit : 4f pot 2 nucleus(Z,A) Co 93.5 17.5 82.5 We fjnd that potentials of other kaonic atoms have similar feature 16.0 Cu 78.5 20.0 Cu2 82.5 14.5 Potentials 2 have small imaginary part. 84.0 Cl 27.0 93.0 last orbit : 3d pot 2 nucleus(Z,A) Mg 128.5 24.0 Al 126.0 28.0 Si 116.5 31.0 P 100.5 26.5 S 14 / 24 − V 0 [MeV] − W 0 [MeV] − V 0 [MeV] − W 0 [MeV]

Deep Re part, small Im part(Potential 3) Ni 38.5 last orbit : 4f pot 3 nucleus(Z,A) Co 215.5 19.5 203.5 We fjnd that potentials of other kaonic atoms have similar feature 27.0 Cu 199.5 28.5 Cu2 197.0 20.0 Potentials 3 have deep real part and small imaginary part. 231.0 Cl 38.5 258.0 last orbit : 3d pot 3 nucleus(Z,A) Mg 305.0 24.5 Al 316.0 32.5 Si 301.0 35.5 P 270.0 36.5 S 15 / 24 − V 0 [MeV] − W 0 [MeV] − V 0 [MeV] − W 0 [MeV]

2 : confjrm universality of potentials 16 / 24

Potentials fjtted by Si Pot 3 It seems that potential 1 is best of 3 potentials. 17 / 24 Pot 2 Pot 1 datum (E shift, Γ ) = (0.130 keV, 0.800 keV) ( − V 0 [MeV], − W 0 [MeV]) = (61.5, 120.5), (116.5, 31.0), (301.0, 35.5) 1.5 pot 1 for Si Energy shift[keV] pot 2 for Si 1 pot 3 for Si 3ddata 0.5 0 -0.5 -1 10 11 12 13 14 15 16 17 18 Mg Mg Mg Mg Mg Al Al Al Al Al Si Si Si Si Si P P P P P S S S S S Cl Cl Cl Cl Cl Atomic number → How about potentials fjtted by other kaonic atoms ?

Large Im part (Potential 1) and provides repulsive shifts in all kaonic atoms. 18 / 24 2 1.2 Mg Co Energy Shift[keV] Energy shift[keV] Al 1 Ni Si Cu 1.5 P 0.8 Cu2 S 4fdata 0.6 Cl 1 3ddata 0.4 0.2 0.5 0 0 -0.2 10 11 12 13 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 32 Mg Al Si P S Cl Co Co Ni Ni Cu Cu Atomic number Atomic number Potential 1 (large Im V opt ) globally explains the data

Small Im part (Potential 2) It is hard to explain repulsive shifts universally using Potential 2 19 / 24 1.5 Mg Co Energy Shift[keV] Energy Shift[keV] Al 0.4 Ni 1 Si Cu P Cu2 S 4fdata 0.5 0.2 Cl 3ddata 0 0 -0.5 -1 -0.2 10 11 12 13 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 32 Mg Al Si P S Cl Co Co Co Co Co Co Co Ni Ni Ni Ni Ni Ni Ni Cu Cu Cu Cu Cu Cu Cu Atomic number Atomic number (small Im V opt ) .

Deep Re part, small Im part(Potential 3) It is hard to explain repulsive shifts universally using Potential 3 20 / 24 4 0.5 Mg Energy Shift[keV] Energy Shift[keV] Al 3 Si 0 P 2 S Cl 1 -0.5 3ddata 0 Co -1 Ni Cu -1 Cu2 4fdata -2 -1.5 10 11 12 13 14 15 16 17 18 22 23 24 25 26 27 28 29 30 31 32 Mg Al Si P S Cl Co Co Co Co Co Co Co Co Co Co Co Co Co Co Co Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Ni Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Cu Atomic number Atomic number (small Im V opt ) .

Why do not potentials 2 and 3 work well ? Potentials 2 and 3 provide nuclear state (NS) and repulsive shift in repulsive shifts in other kaonic atoms Energy spectrum of NS depends on potential size, which is AS is sensitive to energy spectrum of NS. atomic state (AS) is provided by level repulsion of NS. 21 / 24 repulsive repulsive atomic state atomic state atomic state attractive nuclear state nuclear state no effect of level repulsion proportional to mass number A . → Potential fjtted by one kaonic atom does not necessarily provide

summary - 1 and provides repulsive shifts in all kaonic atoms. It is hard to explain repulsive shifts universally using Potentials 22 / 24 • Potential 1 (large Im V opt ) globally explains the data • large imaginary potential Im V opt works well ! 2 and 3 (small Im V opt ) .