Lightest Kaonic Nuclear Clust
DOI:
https://doi.org/10.26577/phst-2016-1-94Keywords:
three-kaonic cluster, four-body kaonic cluster, hyperspherical harmonicsAbstract
We present our study of kaonic three-body KNN , KNN and KKK and four-body KNNN , and KKNN clusters within the framework of a potential model using the method of hyperspherical functions in momentum representation. To perform a numerical calculations for the bound state energy of the light kaonic system, we use a set of different potentials for the nucleon-nucleon and KN interactions, as well as for the kaon-kaon interaction. The calculations show that a quasibound state energy is not sensitive to the NN interaction, and it shows very strong dependence on the KN potential. We also compare our results with those obtained using different theoretical approaches. The theoretical discrepancies in the binding energy and width for the lightest kaonic system related to the different NN and KN interactions are addressed.
References
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[nucl-th].
[29] N. Barnea. A. Gal. and E. Z. Liverts. Three-body calculations for the K−pp system within potential models // Phys. Lett. B. – 2012. – Vol. 712. – P. 132.
[30] . R. Ya. Kezerashvili and Sh. M. Tsiklauri. Investigation of the structure of the few body kaonic nuclei using the method of hyperspherical functions in momentum space // EPJ Web Conf. – 2014. – Vol. 81. – P.02022.
[31] M. Agnello. G. Beer. L. Benussi et al.Evidence for a Kaon-Bound State K−pp Produced in K− Absorption Reactions at Rest // Phys. Rev. Lett. – 2005. – Vol. 94. – P.212303.
[32] -PARC E15 Collaboration: T. Hashimoto. S. Ajimura. G. Beer. et al. Search for the deeply bound K–pp state from the semi-inclusive forward-neutron spectrum in the in-flight K– reaction on helium-3 // Prog. Theor. Exp. Phys. – 2015. – P. 061D01.
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[38] D. Jido and Y. Kanada-Enyo. KK-N molecule state with I=1/2 and JP=1/2+ studied with a three-body calculation // Phys. Rev C. – 2008. – Vol. 78. – P. 035203.
[39] Y. Kanada-Enyo. and D. Jido. K-K-N molecular state in a three-body calculation // Phys. Rev. C. – 2008. – Vol. 78. – P. 025212.
[40] T. Hyodo. S. I. Nam. D. Jido. and A. Hosaka. Flavor SU(3) breaking effects in the chiral unitary model for meson-baryon scatterings // Phys. Rev. C. – 2003. – Vol.68. – P. 018201; Detailed Analysis of the Chiral Unitary Model for Meson-BaryonScattering with Flavor SU(3) Breaking Effects // Prog. Theor. Phys. – 2004. – Vol. 112.– P.73-97.
[41] R.B. Wiringa. R. A. Smith. and T.L. Ainsworth. Nucleon-nucleon potentials with and without Δ(1232) degrees of freedom // Phys. Rev. C. – 1984. – Vol. 29. – P.1207.
[42] R. B. Wiringa. V. G. J. Stoks. and R. Schiavilla. Accurate nucleon-nucleon potential with charge-independence breaking // Phys. Rev. C. – 1995. – Vol. 51. – P. 38.
[43] R. A. Malfliet and J. A. Tjon. Solution of the Faddeev equations for the triton problem using local two-particle interactions // Nucl. Phys. A. – 1969. – Vol.127. – P. 161.
[44] R. Tamagaki. Superfluid State in Neutron Star Matter. IGeneralizedBogoliubov Transformation and Existence of 3P2 Gap at High Density // Prog. Theor. Phys. – 1970. – Vol. 44. – P. 905.
[45] D. R. Thompson. M. LeMere. Y. C. Tang. Systematic investigation of scattering problems with the resonating-group method // Nucl. Phys. A. – 1977. – Vol.286. – P. 53.
[46] R. I. Jibuti and N. B. Krupennikova. Method of hyperspherical functions for few-body systems. (in Russian) Metsniereba. Tbilisi.– 1984.
[47] J. Avery. Hyperspherical Harmonics. Kluwer Academic. Dordrecht.– 1989.
[48] R. I. Jibuti. K. V. Shitikova. Method of hyperspherical functions in atomic and nuclear physics. (in Russian) Energoatomizdat. Moscow.– 1993.
[49] R. I. Jibuti. N. B. Krupennikova. V. Yu. Tomchinsky. Hyperspherical basis for the continuum spectrum// Nucl. Phys. A. – 1977. – Vol. 276. – P. 421.
[50] R. I. Jibuti. R. Ya. Kezerashvili. Double-charge-exchange reactions of π-mesons on three-and four-particle nuclei // Nucl. Phys. A. – 1985. – Vol.437. – P. 687.
[51] J. Raynal and J. Révai.Transformation coefficients in the hyperspherical approach to the three-body problem // NuovoCimento. – 1970. – Vol.68A. – P. 612.
[52] A. Gal. Recent studies of kaonic atoms and nuclear clusters // Nucl. Phys. A. – 2013. – Vol.914. – P.270.
[53] A. Doté. T. Inoue. and T. Myo.Application of a coupled-channel complex scaling method with Feshbach projection to the K–pp system // Prog. Theor. Exp. Phys.– 2015.– P. 043D02.
[54] A. Doté. T. Inoue. and T. Myo.Essential bar K cluster "K?pp" studied with a coupled-channel Complex Scaling Method + Feshbach method // J. Phys: Conf. Ser. – 2014. – Vol. 569. – P. 012084.
[55] A. Martnez Torres. K. – P.Khemchandani. and E. Oset // Phys. Rev. C. – 2009. – Vol. 79. – P. 065207.
[56] A. Martnez Torres. K. – P.Khemchandani. D. Jido. Y. Kanada-Enyo. and E. Oset // Nucl. Phys. A. – 2013. – Vol. 914. – P. 280.
[57] A. Martnez Torres and D. Jido. Solution to Faddeev equations with two-body experimental amplitudes as input and application to JP=1/2+, S=0 baryon resonance // Phys. Rev. C. – 2010. – Vol. 82. – P.038202.
[58] S. R. Beane. et al.K+K+ scattering length from lattice QCD // Phys. Rev. D. – 2008. – Vol. 77. – P.094507.
[59] A. Martnez Torres. D. Jido. and Y. Kanada-Enyo. Theoretical study of the KKK¯¯¯ system and dynamical generation of the K(1460) resonance // Phys. Rev. C. – 2011. – Vol. 83. – P. 065205.
[60] Y. Akaishi. K. S. Myint. and T. Yamazaki. Kaonic nuclear systems KbarN and KbarNN as decaying states // Proc. Jpn. Acad. Ser. B. – 2008. – Vol. 84. – P. 2
[61] E. Hiyama. Y. Funaki. N. Kaiser. and W. Weise.Alpha-clustered hypernuclei and chiral SU(3) dynamics // Prog. Theor. Exp. Phys.– 2014.– P. 013D01.
[2] C.H. Lee. Kaon condensation in dense stellar matter// Phys. Rep. – 1996. – Vol. 275. – P. 255.
[3] O.L. Berman. R.Ya. Kezerashvili. G.V. Kolmakov. and Yu.E. Lozovik. Turbulence in a Bose-Einstein condensate of dipolar excitons in coupled quantum wells // Phys. Rev. B. – 2012. – Vol. 86. – P.045108.
[4] O. L. Berman. R. Ya. Kezerashvili. K. Ziegler. Superfluidity and collective properties of excitoni-cpolaritons in gapped graphene in a microcavity // Phys. Rev. B. – 2012. – Vol.86. – P. 235404.
[5] Y. Akaishi and T. Yamazaki.Nuclear K¯ bound states in light nuclei // Phys. Rev. C. – 2002. – Vol. 65. – P.044005.
[6] T. Yamazaki and Y. Akaishi. (K−,π−) production of nuclear K̄ bound states in proton-rich systems via Λ∗ doorways // Phys. Lett. B. – 2002. – Vol. 535. – P. 70.
[7] T. Yamazaki. A. Doté. and Y. Akaishi. Invariant-mass spectroscopy for condensed single- and double-K̄ nuclear clusters to be formed as residues in relativistic heavy-ion collisions // Phys. Lett. B. – 2004. – Vol. 587. – P. 167.
[8] A. Doté. H. Horiuchi. Y. Akaishi. and T. Ya-mazaki. Invariant-mass spectroscopy for condensed single- and double-K̄ nuclear clusters to be formed as residues in relativistic heavy-ion collisions // Phys. Lett. B. – 2004. – Vol. 590. – P. 51.
[9] A. Doté. H. Horiuchi. Y. Akaishi. and T. Yamazaki. Kaonic nuclei studied based on a new framework of antisymmetrized molecular dynamic // Phys. Rev. C. – 2004. – Vol. 70. – P. 044313.
[10] T. Yamazaki and Y. Akaishi. Basic K- nuclear cluster, K−pp, and its enhanced formation in the p+p→K++X reaction // Phys. Rev. C. – 2007. – Vol. 76. – P. 045201.
[11] A. Doté. H. Horiuchi. Y. Akaishi. and T. Ya-mazaki.The Study of Deeply Bound Kaonic Nuclei with Antisymmetrized Molecular Dynamics// Prog. Theor. Phys. Suppl. – 2002. – Vol. 146. – P. 508.
[12] A. Doté and W. Weise.Study of Light Kaonic Nuclei with a Chiral SU(3)-Based KN Interaction // Prog. Theor. Phys. Suppl. – 2007. – Vol. 168. – P. 593.
[13] A. Doté. T. Hyodo. and W. Weise. K−pp system with chiral SU(3) effective interaction // Nucl. Phys. A 804. – 2008. – Vol. – P. 197.
[14] A. Doté. T. Hyodo. and W. Weise. Variational calculation of the ppK− system based on chiral SU(3) dynamics // Phys. Rev. C. – 2009. – Vol. 79. – P. 014003.
[15] S. Wycech and A. M. Green. Variational calculations for K-–few-nucleon systems // Phys. Rev. C. – 2009. – Vol. 79. – P. 014001.
[16] N. V. Shevchenko. A. Gal. J. Mareš. Faddeev Calculation of a K−pp Quasibound State // Phys. Rev. Lett. – 2007. – Vol. 98. – P. 082301.
[17] N. V. Shevchenko. A. Gal. and J. Mareš. and J. Révai. K–NN quasibound state and the K–N interaction: Coupled-channels Faddeev calculations of the K–NN–πΣN system // Phys. Rev. C. – 2007. – Vol. 76. – P.044004.
[18] Y. Ikeda and T. Sato. Strange dibaryon resonance in the K–NN-πYN system // Phys. Rev. C. – 2007. – Vol. 76. – P. 035203.
[19] Y. Ikeda and T. Sato. Resonance energy of the K–NN−πYN system // Phys. Rev. C. – 2009. – Vol. 79. – P. 035201.
[20] A. Martnez Torres. K. P. Khemchandani. and E. Oset. Solution to Faddeev equations with two-body experimental amplitudes as input and application to JP=1/2+, S=0 baryon resonances // Phys. Rev. C. – 2009. – Vol. 79. 065207.
[21] Y. Ikeda. H. Kamano. and T. Sato. Energy Dependence of K̅ N Interactions and Resonance Pole of Strange Dibaryons // Prog. Theor. Phys. – 2010. – Vol.124. 533.
[22] M. Bayar. J. Yamagata-Sekihara. and E. Oset. K–NN system with chiral dynamics // Phys. Rev. C. – 2011. – Vol. 84. – P. 015209.
[23] E. Oset. D. Jido. T. Sekihara. A. Martnez Torres. K.P. Khemchandani. M. Bayar and J. Yamagata-Sekihara. A new perspective on the Faddeev equations and the system from chiral dynamics and unitarity in coupledK–NN channels // Nucl. Phys. A. – 2012. – Vol.881. – P. 127.
[24] M. Bayar and E. Oset. Improved fixed center approximation of the Faddeev equations for the the K–NN system with S=0 // Nucl. Phys. A. – 2012. – Vol. 883. – P.57.
[25] M. Bayar and E. Oset. The K–NN system revisited including absorption // Nucl. Phys. A. – 2013. – Vol. 914. – P. 349.
[26] . S. Maeda. Y. Akaishi. and T. Yamazaki.Strong binding and shrinkage of single and double K nuclear systems (K−pp, K−ppn, K−K−p and K−K−pp) predicted by Faddeev-Yakubovsky calculations // Proc. Jpn. Acad. Ser. B. – 2013. – Vol. 89. – P. 418.
[27] J. Révai and N. V. Shevchenko. Faddeev calculations of the K−NN system with a chirally motivated K−N interaction. II. The K−pp quasibound state // Phys. Rev. C. – 2014. – Vol. 90. – P. 034004.
[28] R.Ya. Kezerashvili. Sh.M. Tsiklauri. I.N. Fili-khin. V. M. Suslov. and B. Vlahovic.Benchmark for a quasi-bound state of the K−ppsystem // arXiv. – 2015.– P.1508.07638
[nucl-th].
[29] N. Barnea. A. Gal. and E. Z. Liverts. Three-body calculations for the K−pp system within potential models // Phys. Lett. B. – 2012. – Vol. 712. – P. 132.
[30] . R. Ya. Kezerashvili and Sh. M. Tsiklauri. Investigation of the structure of the few body kaonic nuclei using the method of hyperspherical functions in momentum space // EPJ Web Conf. – 2014. – Vol. 81. – P.02022.
[31] M. Agnello. G. Beer. L. Benussi et al.Evidence for a Kaon-Bound State K−pp Produced in K− Absorption Reactions at Rest // Phys. Rev. Lett. – 2005. – Vol. 94. – P.212303.
[32] -PARC E15 Collaboration: T. Hashimoto. S. Ajimura. G. Beer. et al. Search for the deeply bound K–pp state from the semi-inclusive forward-neutron spectrum in the in-flight K– reaction on helium-3 // Prog. Theor. Exp. Phys. – 2015. – P. 061D01.
[33] J-PARC E27 Collaboration: Y. Ichikawa. et al. Experiment to Search for a Nuclear Kaon Bound State K−pp // Prog. Theor. Exp. Phys. – 2014. – P. 101D03; Y. Ichikawa. et al. Observation of the “K− pp”-like structure in the d(π+, K+) reaction at 1.69 GeV/c // Prog. Theor. Exp. Phys. – 2015. – P. 021D01.
[34] HADES Collaboration: G. Agakishiev. et al. Partial Wave Analysis of the Reaction p(3.5GeV)+p->pK+Λ to Search for the "ppK−" Bound State // Phys. Lett. B. – 2015. – Vol. 742. – P. 242.
[35] T. Yamazaki. et al. Indication of a Deeply Bound and Compact K−pp State Formed in the pp→pΛK+ Reaction at 2.85 GeV // Phys. Rev. Lett. – 2010. – Vol.104. – P. 132502.
[36] T. Hyodoand W. Weise. Effective K−N interaction based on chiral SU(3) dynamics // Phys. Rev. C. – 2008. – Vol. 77. – P. 035204.
[37] W. Weise. Antikaon Interactions with Nucleons and Nuclei // Nucl. Phys. A. – 2010. – Vol. 835. – P. 51.
[38] D. Jido and Y. Kanada-Enyo. KK-N molecule state with I=1/2 and JP=1/2+ studied with a three-body calculation // Phys. Rev C. – 2008. – Vol. 78. – P. 035203.
[39] Y. Kanada-Enyo. and D. Jido. K-K-N molecular state in a three-body calculation // Phys. Rev. C. – 2008. – Vol. 78. – P. 025212.
[40] T. Hyodo. S. I. Nam. D. Jido. and A. Hosaka. Flavor SU(3) breaking effects in the chiral unitary model for meson-baryon scatterings // Phys. Rev. C. – 2003. – Vol.68. – P. 018201; Detailed Analysis of the Chiral Unitary Model for Meson-BaryonScattering with Flavor SU(3) Breaking Effects // Prog. Theor. Phys. – 2004. – Vol. 112.– P.73-97.
[41] R.B. Wiringa. R. A. Smith. and T.L. Ainsworth. Nucleon-nucleon potentials with and without Δ(1232) degrees of freedom // Phys. Rev. C. – 1984. – Vol. 29. – P.1207.
[42] R. B. Wiringa. V. G. J. Stoks. and R. Schiavilla. Accurate nucleon-nucleon potential with charge-independence breaking // Phys. Rev. C. – 1995. – Vol. 51. – P. 38.
[43] R. A. Malfliet and J. A. Tjon. Solution of the Faddeev equations for the triton problem using local two-particle interactions // Nucl. Phys. A. – 1969. – Vol.127. – P. 161.
[44] R. Tamagaki. Superfluid State in Neutron Star Matter. IGeneralizedBogoliubov Transformation and Existence of 3P2 Gap at High Density // Prog. Theor. Phys. – 1970. – Vol. 44. – P. 905.
[45] D. R. Thompson. M. LeMere. Y. C. Tang. Systematic investigation of scattering problems with the resonating-group method // Nucl. Phys. A. – 1977. – Vol.286. – P. 53.
[46] R. I. Jibuti and N. B. Krupennikova. Method of hyperspherical functions for few-body systems. (in Russian) Metsniereba. Tbilisi.– 1984.
[47] J. Avery. Hyperspherical Harmonics. Kluwer Academic. Dordrecht.– 1989.
[48] R. I. Jibuti. K. V. Shitikova. Method of hyperspherical functions in atomic and nuclear physics. (in Russian) Energoatomizdat. Moscow.– 1993.
[49] R. I. Jibuti. N. B. Krupennikova. V. Yu. Tomchinsky. Hyperspherical basis for the continuum spectrum// Nucl. Phys. A. – 1977. – Vol. 276. – P. 421.
[50] R. I. Jibuti. R. Ya. Kezerashvili. Double-charge-exchange reactions of π-mesons on three-and four-particle nuclei // Nucl. Phys. A. – 1985. – Vol.437. – P. 687.
[51] J. Raynal and J. Révai.Transformation coefficients in the hyperspherical approach to the three-body problem // NuovoCimento. – 1970. – Vol.68A. – P. 612.
[52] A. Gal. Recent studies of kaonic atoms and nuclear clusters // Nucl. Phys. A. – 2013. – Vol.914. – P.270.
[53] A. Doté. T. Inoue. and T. Myo.Application of a coupled-channel complex scaling method with Feshbach projection to the K–pp system // Prog. Theor. Exp. Phys.– 2015.– P. 043D02.
[54] A. Doté. T. Inoue. and T. Myo.Essential bar K cluster "K?pp" studied with a coupled-channel Complex Scaling Method + Feshbach method // J. Phys: Conf. Ser. – 2014. – Vol. 569. – P. 012084.
[55] A. Martnez Torres. K. – P.Khemchandani. and E. Oset // Phys. Rev. C. – 2009. – Vol. 79. – P. 065207.
[56] A. Martnez Torres. K. – P.Khemchandani. D. Jido. Y. Kanada-Enyo. and E. Oset // Nucl. Phys. A. – 2013. – Vol. 914. – P. 280.
[57] A. Martnez Torres and D. Jido. Solution to Faddeev equations with two-body experimental amplitudes as input and application to JP=1/2+, S=0 baryon resonance // Phys. Rev. C. – 2010. – Vol. 82. – P.038202.
[58] S. R. Beane. et al.K+K+ scattering length from lattice QCD // Phys. Rev. D. – 2008. – Vol. 77. – P.094507.
[59] A. Martnez Torres. D. Jido. and Y. Kanada-Enyo. Theoretical study of the KKK¯¯¯ system and dynamical generation of the K(1460) resonance // Phys. Rev. C. – 2011. – Vol. 83. – P. 065205.
[60] Y. Akaishi. K. S. Myint. and T. Yamazaki. Kaonic nuclear systems KbarN and KbarNN as decaying states // Proc. Jpn. Acad. Ser. B. – 2008. – Vol. 84. – P. 2
[61] E. Hiyama. Y. Funaki. N. Kaiser. and W. Weise.Alpha-clustered hypernuclei and chiral SU(3) dynamics // Prog. Theor. Exp. Phys.– 2014.– P. 013D01.
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2017-03-06
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Nuclear Physics and Related Techology
