References
395
{S n , S 2n , S 3n } > 0. Gamow shell model calculations with the ˆ ¯
Q-box interactions
exclude a direct tetraneutron decay because S 2n < 0, though a sequential emission
of two dineutrons is still possible.
The main configuration in the ground state of 28 O is (ν1s 1/2 ) 2 (ν0d 3/2 ) 4 . The
single-particle resonance ν0d 3/2 is occupied by four neutrons in the neutronunstable ground state of 28 O. The decay width of 28 O is predicted to be several tens
of keV. In order to exhibit the influence of the ν0d 3/2 resonance and the scattering
contours, one did calculation with and without coupling to the continuum (see
Fig. 8.9). The gained binding energy arising from the coupling to the continuum
is about 0.5 MeV for 26 O and 1 MeV for 28 O.
Results for fluorine isotopes obtained with the Gamow shell model and NNLO opt
interaction are shown on the lower panel of Fig. 8.9. Energies are given with respect
to that of the 22 O ground state. One obtains a good description of ground state
energies for the 23–28 F isotopes. While experimentally 31 F is located at the neutron
dripline [150, 151], the Gamow shell model calculation yields the energy of 31 F
lower than that of 30 F. Nevertheless, 31 F remains unbound with respect to 29 F. This
discrepancy originates from the truncations which had to be imposed because of
the rapid increase of Hamiltonian matrix dimensions with the number of valence
nucleons. For example, the matrix dimension in the calculation of 29 F ground state
in (sdpf 7/2 ) valence space without truncations, is ∼1.95×10 10 . Gamow shell model
matrices of this size cannot be handled at present so in the calculations of 29–32 F
isotopes, at most two valence particles in the nonresonant continuum were allowed.
A partial explanation of the difference between positions of driplines for oxygen
and fluorine isotopes can be put forward by analyzing the effective single-particle
energies. At the end of the isotopic chains of oxygen and fluorine, ν0d 3/2 is unbound
in the oxygen isotopes, whereas it is bound in fluorine isotopes where about 1 MeV
of binding energy is gained due to the proton–neutron interaction.
References
1. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)
2. R. Machleidt, Phys. Rev. C 63, 024001 (2001)
3. H. Leutwyler, Ann. Phys. 235, 165 (1994)
4. D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001(R) (2003)
5. R. Skibi´ nski, J. Golak, K. Topolnicki, H. Witała, Y. Volkotrub, H. Kamada, A.M. Shirokov,
R. Okamoto, K. Suzuki, J.P. Vary, Phys. Rev. C 97, 014002 (2018)
6. S.C. Pieper, R.B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001)
7. S. Coon, M. Scadron, P. McNamee, B. Barrett, D. Blatt, B. McKellar, Nucl. Phys. A 317, 242
(1979)
8. U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999)
9. A. Nogga, H. Kamada, W. Glöckle, Phys. Rev. Lett. 85, 944 (2000)
10. P. Navrátil, W.E. Ormand, Phys. Rev. C 68, 034305 (2003)
11. E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Phys. Rev. C 83, 034301 (2011)
12. E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Phys. Rev. Lett. 103, 082501 (2009)
13. R. Roth, J. Langhammer, A. Calci, S. Binder, P. Navrátil, Phys. Rev. Lett. 107, 072501 (2011)
14. S.K. Bogner, R.J. Furnstahl, A. Schwenk, Prog. Part. Nucl. Phys. 65, 94 (2010)
395
{S n , S 2n , S 3n } > 0. Gamow shell model calculations with the ˆ ¯
Q-box interactions
exclude a direct tetraneutron decay because S 2n < 0, though a sequential emission
of two dineutrons is still possible.
The main configuration in the ground state of 28 O is (ν1s 1/2 ) 2 (ν0d 3/2 ) 4 . The
single-particle resonance ν0d 3/2 is occupied by four neutrons in the neutronunstable ground state of 28 O. The decay width of 28 O is predicted to be several tens
of keV. In order to exhibit the influence of the ν0d 3/2 resonance and the scattering
contours, one did calculation with and without coupling to the continuum (see
Fig. 8.9). The gained binding energy arising from the coupling to the continuum
is about 0.5 MeV for 26 O and 1 MeV for 28 O.
Results for fluorine isotopes obtained with the Gamow shell model and NNLO opt
interaction are shown on the lower panel of Fig. 8.9. Energies are given with respect
to that of the 22 O ground state. One obtains a good description of ground state
energies for the 23–28 F isotopes. While experimentally 31 F is located at the neutron
dripline [150, 151], the Gamow shell model calculation yields the energy of 31 F
lower than that of 30 F. Nevertheless, 31 F remains unbound with respect to 29 F. This
discrepancy originates from the truncations which had to be imposed because of
the rapid increase of Hamiltonian matrix dimensions with the number of valence
nucleons. For example, the matrix dimension in the calculation of 29 F ground state
in (sdpf 7/2 ) valence space without truncations, is ∼1.95×10 10 . Gamow shell model
matrices of this size cannot be handled at present so in the calculations of 29–32 F
isotopes, at most two valence particles in the nonresonant continuum were allowed.
A partial explanation of the difference between positions of driplines for oxygen
and fluorine isotopes can be put forward by analyzing the effective single-particle
energies. At the end of the isotopic chains of oxygen and fluorine, ν0d 3/2 is unbound
in the oxygen isotopes, whereas it is bound in fluorine isotopes where about 1 MeV
of binding energy is gained due to the proton–neutron interaction.
References
1. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)
2. R. Machleidt, Phys. Rev. C 63, 024001 (2001)
3. H. Leutwyler, Ann. Phys. 235, 165 (1994)
4. D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001(R) (2003)
5. R. Skibi´ nski, J. Golak, K. Topolnicki, H. Witała, Y. Volkotrub, H. Kamada, A.M. Shirokov,
R. Okamoto, K. Suzuki, J.P. Vary, Phys. Rev. C 97, 014002 (2018)
6. S.C. Pieper, R.B. Wiringa, Annu. Rev. Nucl. Part. Sci. 51, 53 (2001)
7. S. Coon, M. Scadron, P. McNamee, B. Barrett, D. Blatt, B. McKellar, Nucl. Phys. A 317, 242
(1979)
8. U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999)
9. A. Nogga, H. Kamada, W. Glöckle, Phys. Rev. Lett. 85, 944 (2000)
10. P. Navrátil, W.E. Ormand, Phys. Rev. C 68, 034305 (2003)
11. E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Phys. Rev. C 83, 034301 (2011)
12. E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Phys. Rev. Lett. 103, 082501 (2009)
13. R. Roth, J. Langhammer, A. Calci, S. Binder, P. Navrátil, Phys. Rev. Lett. 107, 072501 (2011)
14. S.K. Bogner, R.J. Furnstahl, A. Schwenk, Prog. Part. Nucl. Phys. 65, 94 (2010)