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Variational Calculation on A = 3 and 4 Nuclei with Non-Local Potentials

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Abstract.

The application of the hyperspherical harmonic approach to the case of non-local two-body potentials is described. Given the properties of the hyperspherical harmonic functions, there are no difficulties in considering the approach in both coordinate and momentum space. The binding energies and other ground-state properties of A = 3 and 4 nuclei are calculated using the CD Bonn 2000 and N3LO two-body potentials. The results are shown to be in excellent agreement with corresponding ones obtained by other accurate techniques.

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References

  • R. B. Wiringa V. G. J. Stoks R. Schiavilla (1995) Phys. Rev. C51 38 Occurrence Handle1995PhRvC..51...38W

    ADS  Google Scholar 

  • V. G. J. Stoks et al. (1994) Phys. Rev. C49 2950 Occurrence Handle1994PhRvC..49.2950S

    ADS  Google Scholar 

  • R. Machleidt (2001) Phys. Rev. C63 024001 Occurrence Handle2001PhRvC..63b4001M

    ADS  Google Scholar 

  • W. Glöckle et al. (1996) Phys. Rep. 274 107 Occurrence Handle10.1016/0370-1573(95)00085-2 Occurrence Handle1996PhR...274..107G

    Article  ADS  Google Scholar 

  • J. Carlson R. Schiavilla (1998) Rev. Mod. Phys. 70 743 Occurrence Handle10.1103/RevModPhys.70.743 Occurrence Handle1998RvMP...70..743C

    Article  ADS  Google Scholar 

  • W. Glöckle (1983) The Quantum Mechanical Few-Body Problem Springer Berlin Heidelberg New York

    Google Scholar 

  • A. Nogga H. Kamada W. Glöckle (2000) Phys. Rev. Lett. 85 944 Occurrence Handle10.1103/PhysRevLett.85.944 Occurrence Handle2000PhRvL..85..944N

    Article  ADS  Google Scholar 

  • A. Nogga et al. (2002) Phys. Rev. C65 054003 Occurrence Handle2002PhRvC..65e4003N

    ADS  Google Scholar 

  • F. Ciesielski J. Carbonell C. Gignoux (1999) Phys. Lett. B447 199 Occurrence Handle1999PhLB..447..199C

    ADS  Google Scholar 

  • A. Deltuva R. Machleidt P. U. Sauer (2003) Phys. Rev. C68 024005 Occurrence Handle2003PhRvC..68b4005D

    ADS  Google Scholar 

  • A. Deltuva A. C. Fonseca P. U. Sauer (2005) Phys. Rev. C71 054005 Occurrence Handle2005PhRvC..71e4005D

    ADS  Google Scholar 

  • B. S. Pudliner V. R. Pandharipande J. Carlson R. B. Wiringa (1995) Phys. Rev. Lett. 74 4396 Occurrence Handle10.1103/PhysRevLett.74.4396 Occurrence Handle1995PhRvL..74.4396P

    Article  ADS  Google Scholar 

  • B. S. Pudliner V. R. Pandharipande J. Carlson S. C. Pieper R. B. Wiringa (1997) Phys. Rev. C56 1720 Occurrence Handle1997PhRvC..56.1720P

    ADS  Google Scholar 

  • A. Kievsky S. Rosati M. Viviani (1993) Nucl. Phys. A551 241 Occurrence Handle1993NuPhA.551..241K

    ADS  Google Scholar 

  • A. Kievsky S. Rosati M. Viviani (1994) Nucl. Phys. A577 511 Occurrence Handle1994NuPhA.577..511K

    ADS  Google Scholar 

  • A. Kievsky L. E. Marcucci S. Rosati M. Viviani (1997) Few-Body Systems 22 1 Occurrence Handle10.1007/s006010050049 Occurrence Handle1997FBS....22....1K

    Article  ADS  Google Scholar 

  • M Viviani A. Kievsky S. Rosati (2005) Phys. Rev. C71 024006 Occurrence Handle2005PhRvC..71b4006V

    ADS  Google Scholar 

  • N. Barnea W. Leidemann G. Orlandini (2000) Phys. Rev. C61 054001 Occurrence Handle2000PhRvC..61e4001B

    ADS  Google Scholar 

  • P. Navrátil B. R. Barrett (1999) Phys. Rev. C59 1906 Occurrence Handle1999PhRvC..59.1906N

    ADS  Google Scholar 

  • Navrátil, P., Caurier, E.: Phys. Rev. C69, 014311 (2004); C73, 021302(R) (2006)

  • H. Kameyama M. Kamimura Y Fukushima (1989) Phys. Rev. C40 974 Occurrence Handle1989PhRvC..40..974K

    ADS  Google Scholar 

  • Y. Suzuki K. Varga (1998) Stochastic Variational Approach to Quantum Mechanical Few-Body Problems Springer Berlin Heidelberg New York Occurrence Handle0997.81509

    MATH  Google Scholar 

  • H. Kamada et al. (2001) Phys. Rev. C64 044001 Occurrence Handle2001PhRvC..64d4001K

    ADS  Google Scholar 

  • A. Kievsky M. Viviani L. E. Marcucci (2004) Phys. Rev. C69 014002 Occurrence Handle2004PhRvC..69a4002K

    ADS  Google Scholar 

  • A. Kievsky J. L. Friar G. L. Payne S. Rosati M. Viviani (2001) Phys. Rev. C63 064004 Occurrence Handle2001PhRvC..63f4004K

    ADS  Google Scholar 

  • A. Kievsky S. Rosati M. Viviani (2001) Phys. Rev. C64 024002 Occurrence Handle2001PhRvC..64b4002K

    ADS  Google Scholar 

  • A. Deltuva et al. (2005) Phys. Rev. C71 064003 Occurrence Handle2005PhRvC..71f4003D

    ADS  Google Scholar 

  • H. Witała et al. (2001) Phys. Rev. C63 024007 Occurrence Handle2001PhRvC..63b4007W

    ADS  Google Scholar 

  • K. Ermisch et al. (2005) Phys. Rev. C71 064004 Occurrence Handle2005PhRvC..71f4004E

    ADS  Google Scholar 

  • Y. Koike J. Haidenbauer (1987) Nucl. Phys. A463 365c Occurrence Handle1987NuPhA.463..365K

    ADS  Google Scholar 

  • H. Witała W. Glöckle T. Cornelius (1988) Nucl. Phys. A491 157 Occurrence Handle1989NuPhA.491..157W

    ADS  Google Scholar 

  • A. Kievsky et al. (1996) Nucl. Phys. A607 402 Occurrence Handle1996NuPhA.607..402K

    ADS  Google Scholar 

  • M. Viviani et al. (2001) Phys. Rev. Lett. 86 3739 Occurrence Handle10.1103/PhysRevLett.86.3739 Occurrence Handle2001PhRvL..86.3739V

    Article  ADS  Google Scholar 

  • B. Pfitzinger H. M. Hofmann G. M. Hale (2001) Phys. Rev. C64 044003 Occurrence Handle2001PhRvC..64d4003P

    ADS  Google Scholar 

  • D. Hüber J. L. Friar (1998) Phys. Rev. C58 674 Occurrence Handle1998PhRvC..58..674H

    ADS  Google Scholar 

  • T. Tornow W. Tornow (1999) Few-Body Systems 26 1 Occurrence Handle10.1007/s006010050103 Occurrence Handle1999FBS....26....1T

    Article  ADS  Google Scholar 

  • D. R. Entem R. Machleidt H. Witała (2002) Phys. Rev. C65 064005 Occurrence Handle2002PhRvC..65f4005E

    ADS  Google Scholar 

  • Epelbaum, E., Glöckle, W., Meissner, U.-G.: Nucl. Phys. A637, 107 (1998); A671, 295 (2000); A747, 362 (2005)

  • Epelbaum, E.: [nucl-th/0509032]

  • Kaiser, N.: Phys. Rev. C64, 057001 (2001); C65, 017001 (2002)

    Google Scholar 

  • D. R. Entem R. Machleidt (2003) Phys. Rev. C68 041001 Occurrence Handle2003PhRvC..68d1001E

    ADS  Google Scholar 

  • J. L. Friar D. Hüber U. van Kolck (1999) Phys. Rev. C59 53 Occurrence Handle1999PhRvC..59...53F

    ADS  Google Scholar 

  • U. van Kolck (1994) Phys. Rev. C49 2932 Occurrence Handle1994PhRvC..49.2932V

    ADS  Google Scholar 

  • E. Epelbaum et al. (2002) Phys. Rev. C66 064001 Occurrence Handle2002PhRvC..66f4001E

    ADS  Google Scholar 

  • J. L. Friar G. L. Payne U. van Kolck (2005) Phys. Rev. C71 024003 Occurrence Handle2005PhRvC..71b4003F

    ADS  Google Scholar 

  • E. Epelbaum U.-G. Meissner J. E. Palomar (2005) Phys. Rev. C71 024001 Occurrence Handle2005PhRvC..71b4001E

    ADS  Google Scholar 

  • S. K. Bogner T. T. S. Kuo A. Schwenk (2003) Phys. Rep. 386 1 Occurrence Handle10.1016/j.physrep.2003.07.001 Occurrence Handle2003PhR...386....1B

    Article  ADS  Google Scholar 

  • L. Coraggio A. Covello A. Gargano N. Itaco T. T. S. Kuo R. Machleidt (2005) Phys. Rev. C71 014307 Occurrence Handle2005PhRvC..71a4307C

    ADS  Google Scholar 

  • M. Viviani A. Kievsky S. Rosati (1995) Few-Body Systems 18 25 Occurrence Handle10.1007/s006010050002 Occurrence Handle1995FBS....18...25V

    Article  ADS  Google Scholar 

  • A. Kievsky M. Viviani S. Rosati (1995) Phys. Rev. C52 R15 Occurrence Handle1995PhRvC..52...15K

    ADS  Google Scholar 

  • M. Viviani S. Rosati A. Kievsky (1998) Phys. Rev. Lett. 81 1580 Occurrence Handle10.1103/PhysRevLett.81.1580 Occurrence Handle1998PhRvL..81.1580V

    Article  ADS  Google Scholar 

  • R. Lazauskas J. Carbonell A. C. Fonseca M. Viviani A. Kievsky S. Rosati (2005) Phys. Rev. C71 034004 Occurrence Handle2005PhRvC..71c4004L

    ADS  Google Scholar 

  • Rosati, S.: Series of Advances in Quantum Many-Body Theory, Vol. 7 (Fabrocini, A., Fantoni, S., Krotscheck, E., eds.), p. 339. Singapore: World Scientific 2002

  • M. Fabre de la Ripelle (1983) Ann. Phys. 147 281 Occurrence Handle0559.35068 Occurrence Handle708968 Occurrence Handle10.1016/0003-4916(83)90212-9 Occurrence Handle1983AnPhy.147..281F

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • J. Raynal J. Revai (1970) Nuovo Cim. 68 612 Occurrence Handle267848

    MathSciNet  Google Scholar 

  • See, for example, Barnea, N., Mandelzweig, V. B.: Phys. Rev. A41, 5209 (1990) and references therein

  • L. Deng D. Li Y. Wang C. Deng (1995) Phys. Rev. C51 163 Occurrence Handle1995PhRvA..51..163D

    ADS  Google Scholar 

  • Novoselsky, A., Katriel, J.: Phys. Rev. A49, 833 (1994); Ann. Phys. 256, 192 (1997)

    Google Scholar 

  • V. D. Efros (1995) Few-Body Systems 19 167 Occurrence Handle10.1007/s006010050024 Occurrence Handle1995FBS....19..167E

    Article  ADS  Google Scholar 

  • M. Viviani (1998) Few-Body Systems 25 177 Occurrence Handle10.1007/s006010050101 Occurrence Handle1998FBS....25..177V

    Article  ADS  Google Scholar 

  • A. Kievsky (1997) Nucl. Phys. A624 125 Occurrence Handle1997NuPhA.624..125K

    ADS  Google Scholar 

  • M Abramowitz I. A. Stegun (Eds) (1972) Handbook of Mathematical Functions Dover New York

    Google Scholar 

  • S. A. Coon et al. (1979) Nucl. Phys. A317 242 Occurrence Handle1979NuPhA.317..242C

    ADS  Google Scholar 

  • M. R. Robilotta H. T. Coelho (1986) Nucl. Phys. A460 645 Occurrence Handle1986NuPhA.460..645R

    ADS  Google Scholar 

  • P. Doleschall I. Borbély (2000) Phys. Rev. C62 054004 Occurrence Handle2000PhRvC..62e4004D

    ADS  Google Scholar 

  • P. Doleschall et al. (2003) Phys. Rev. C67 064005 Occurrence Handle2003PhRvC..67f4005D

    ADS  Google Scholar 

  • A. Nogga et al. (2003) Phys. Rev. C67 034004 Occurrence Handle2003PhRvC..67c4004N

    ADS  Google Scholar 

  • Nogga, A.: Private communications

  • Deltuva, A.: Private communications

  • Navrátil, P.: Private communications

  • R. Lazauskas J. Carbonell (2004) Phys. Rev. C70 044002 Occurrence Handle2004PhRvC..70d4002L

    ADS  Google Scholar 

  • Machleidt, R.: Private communications

  • D. H. Beck R. D. McKeown (2001) Ann. Rev. Nucl. Part. Sci. 51 189 Occurrence Handle10.1146/annurev.nucl.51.101701.132312 Occurrence Handle2001ARNPS..51..189B

    Article  ADS  Google Scholar 

  • Armstrong, D. S., Michaels, R. [HAPPEX Collaboration]: Parity Violation from 4He at Low Q 2: A Clean Measurement of ρs (Jefferson Lab. Proposal E00-114), (accepted by PAC 18) [http://hallaweb.jlab.org/experiment/HAPPEX/]

  • S. Ramavataram E. Hadjimichael T. W. Donnelly (1994) Phys. Rev. C50 1175 Occurrence Handle1994PhRvC..50.1175R

    ADS  Google Scholar 

  • E. J. Stephenson et al. (2003) Phys. Rev. Lett. 91 142302 Occurrence Handle10.1103/PhysRevLett.91.142302 Occurrence Handle2003PhRvL..91n2302S

    Article  ADS  Google Scholar 

  • A. Gardestig et al. (2004) Phys. Rev. C69 044606 Occurrence Handle2004PhRvC..69d4606G

    ADS  Google Scholar 

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Authors and Affiliations

  1. INFN, Sezione di Pisa, I-56127, Pisa, Italy

    M. Viviani, L. E. Marcucci, S. Rosati & A. Kievsky

  2. Department of Physics “E. Fermi”, University of Pisa, I-56127, Pisa, Italy

    M. Viviani, L. E. Marcucci, S. Rosati, A. Kievsky & L. Girlanda

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  1. M. Viviani
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  2. L. E. Marcucci
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  3. S. Rosati
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  4. A. Kievsky
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  5. L. Girlanda
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Viviani, M., Marcucci, L., Rosati, S. et al. Variational Calculation on A = 3 and 4 Nuclei with Non-Local Potentials. Few-Body Systems 39, 159–176 (2006). https://doi.org/10.1007/s00601-006-0158-y

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