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Mapping the proton drip line
ELSEVIER
Nuclear Physics A7 19 (2003) 209c-2 12c www.elsevier.com/locate/npe
Mapping
the proton
G. ,4. L,alazissis”,
drip line
D. Vretenarb
and P. RingC
aPhysics Department, Aristotle University Thessaloniki GR-54124, Greece
of Thessaloniki,
b Physics Department, 10 000 Zagreb, Croatia
University
‘Physik-Department D-85748 Garching,
Faculty
of Science,
der Technischen Germany
Universitat
of Zagreb,
Miinchen,
The relativistic Hartree-Bogoliubov (RHB) model is employed in the mapping of the proton drip line for medium-heavy, heavy and superheavy elements. The RHB prediction for the last bound isotope of each element is compared with experimental data on the location of the proton drip line. 1. RHB
CALCULATION
OF
THE
PROTON
DRIP
LINE
Models based on the relativistic mean-field approximation have been very successfully applied in the description of a variety of nuclear structure phenomena, not only in nuclei along the valley of P-stability, but also in exotic nuclei with extreme isospin values and close to the particle drip lines. For weakly bound nuclei at the drip lines, in particular, the Relativistic Hartree-Bogoliubov (RHB) model, based on the relativistic mean-field theory and on the Hartree-Fock-Bogoliubov framework, provides a unified description of mean-field and pairing correlations. In proton rich nuclei the RHB model has been used to map the drip line from 2 = 31 to Z = 73, and to investigate the phenomenon of ground-state proton radioactivity [l-4]. The location of the proton drip-line, the groundstate quadrupole deformations and one-proton separation energies at and beyond the drip-line, the deformed single-particle orbitals occupied by the odd valence proton, and the corresponding spectroscopic factors have been compared with available experimental data. The structure of nuclei at the proton drip line in the mass region 60 < A < 100 is important for the process of nucleosynthesis during explosive hydrogen burning. The exact location of the proton drip line determines a possible path of rapid proton capture The path of the rp-process lies between the line of ,&stability and the drip process. line, and it is a very complicated function of the physical conditions, temperature and density, governing the explosion. In addition to its importance for astrophysical processes, the information about the exact location of the drip line, as well as the proton separation energies beyond the drip line, are essential for studies of ground state proton radioactivity. 0375-9474/03/$ - see front matter 0 2003 Elsevier Science B.V doi: lO.l016/SO375-9474(03)00919-9
All rights reserved
21oc
G.A. Lalazissis et al. /Nuclear Physics A719 (2003) 209c-212~ 50 Proton
drip
line
RHBINL3 30
40
50
N Figure
1. Map of the proton
drip line in the region
31 < Z 5 49.
In Fig. 1 we display the results of the relativistic Hartree- Bogoliubov calculation for the proton drip line in the region 31 < Z 5 49 [4]. The NL3 effective interaction [5] is used for the mean-field Lagrangian, and pairing correlations are described by the pairing part of the finite range Gogny interaction DlS [6]. This particular combination of effective forces in the ph and pp channels has been used in most of our recent applications of the RHB theory. The RHB (NL3+DlS) calculation predicts the last bound isotopes for each element. Nuclei to the left are proton unstable. For odd-Z nuclei the proton drip line can be compared with available experimental data. For 2 = 31 and 2 = 33 the calculated drip line nuclei “lGa and 65As, respectively, are in agreement with experimental data reported in Refs. [7,9]. These two nuclei are on the rp-process path proposed by Champagne and Wiescher [lo]. In Ref. [ll] evidence was reported for the existence of ‘joGa, but of course the observation of an isotope does not necessarily imply that the nucleus is proton bound, but. rather that its half-life is longer than the flight time through the fragment analyzer. For 2 = 35 the RHB calculation predicts that the last proton bound isotope is 70Br. The isotope 6gBr is calculated to be proton unbound in most mass models. Experimental evidence for 6gBr was reported in Ref. [7], but no evidence for this isotope was found in the experiment of Ref. ill], and it was deduced that 6gBr is proton unbound with a half-life shorter than about 100 ns. For 2 = 37 the experiments of Refs. [7,8] confirms that 74Rb is the last proton bound nucleus, in agreement with the result of the present calculation. For 2 = 39,41,43 the lightest isotopes observed in the experiment of Ref. [12] are 78Y 82Nb and 86T~, respectively. While for Nb and Tc these results correspond to the drip line as calculated in the present work, for Y the RHB model predicts that the last proton bound nucleus is 77Y This isotope would then be the heaviest T, = -$ nucleus, in contrast to the suggestion of Ref. [7] that ‘jgBr is most likely the highest observable odd-Z T, = -i nucleus. The calculated odd-Z drip line nuclei “Rh and “Ag were observed in
G.A. Lalazissis et al. /Nuclear Physics A719 (2003) 209c-212c
Proton nuclei
211c
2’4Pc
drip line for odd 2 with E-71
*‘*ACT *02Fr 7 ‘g6AtPlgoBlrd
80
‘7’1r/
IX
0 RHB/NLB predictions X GSI Novikov et al N.P. A697 92 (2002)
‘66Ra ‘=TCIr
120
100 *
N
Figure
2. The proton
drip line in the region
73 5 2 < 91.
the experiment reported in Ref. [13], and experimental evidence for “In was reported in Ref. [14]. For even-Z nuclei in this region, it is not possible to compare the calculated proton drip line with experimental data. While for the odd-Z elements most of the last proton bound nuclei lie on the N = 2 line, with just few T, = -$ nuclei, the proton drip line for even-Z elements is calculated to be at T, = -3, or even at T, = -f. The only exception is the drip line nucleus 84R~ with T, = -2. Nuclei with such extreme values of T, are virtually impossible to produce in experiments, and since they lie so far away from the rp-process path, the even-Z proton drip line nuclei in this mass region do not play any role in the process of nucleosynthesis during explosive hydrogen burning. The phenomenon of ground-state proton radioactivity in the region 53 < Z < 7’3 has been the subject of numerous experiments and theoretical analyses in the last decade. An important issue in future experimental studies of heavy proton rich nuclei is the possible observation of ground state proton emission in the suburanium region. A detailed knowledge of the proton drip-line is important in planning experiments on proton radioactivity. In Fig. 2 we display the map of the proton drip-line for odd-Z nuclei with 73 5 2 < 91, calculated in the RHB framework with the NL3+DlS combination of effective interactions. The RHB prediction for the last proton-bound isotope of each element is compared with recent experimental data on the proton drip-1:ne [15]. An excellent agreement between theory and experiment is found. Only for Ta and Ir the RHB model prediction differs by one unit from the experimental position of the proton drip-line. Model predictions of the location of the proton drip line are also very important for
212c
GA. Lalazissis et al. /Nuclear Physics A719 (2003) 209c-212~ Proton drip line for odd Z Superheavy Nuclei
I RHWNLB predictions IZI Discovered isotopes
Figure
3. The proton
drip line in the region
93 5 2 5 119.
All the experimental studies of the synthesis and stability of the heaviest elements. recently discovered isotopes of the superheavy elements, in particular, belong to very proton rich systems. In Fig. 3 we display the section of the chart of the nuclides along the proton drip line in the region 93 I: 2 5 119. The RHB (NLS+DlS) prediction for the last bound isotope of each odd-Z element is shown together with the experimentallyknown superheavy nuclei (2 > 103). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
D. Vretenar, G.,4. Lalazissis, and P. Ring, Phys. Rev. Lett. 82 (1997) 4595. G.X. Lalazissis, D. Vretenar, and P. Ring, Nucl. Phys. A 650 (1999) 133. GA. Lalazissis, D. Vretenar, and P. Ring, Phys. Rev. C 60 (1999) 051302. GA. Lalazissis, D. Vretenar, and P. Ring, Nucl. Phys. A 679 (2001) 481. GA. Lalazissis, J. Konig, and P. Ring, Phys. Rev. C 55 (1997) 540. J. F. Berger, M. Girod and D. Gogny, Nucl. Phys. A 428 (1984) 32. M.F. Mohar et al., Phys. Rev. Lett. 66 (1991) 1571. A. Jokinen et al.; Z. Phys. A 355 (1996) 227. J.A. Winger et al., Phys. Lett. B 299 (1993) 214. A.E. Champagne and M. Wiescher, Annu. Rev. Nucl. Part. Sci. 42 (1992) 39. B. Blank et al., Phys. Rev. Lett. 74 (1995) 4611. S.J. Yennello et al.; Phys. Rev. C 46 (1992) 2620. M. Hencheck et al., Phys. Rev. C 50 (1994) 2219. K. Rykaczewski et al., Phys. Rev. C 52 (1995) R2310. Yu.N. Novikov et al., Nucl. Phys. A 697 (2002) 92.
Nuclear Physics A7 19 (2003) 209c-2 12c www.elsevier.com/locate/npe
Mapping
the proton
G. ,4. L,alazissis”,
drip line
D. Vretenarb
and P. RingC
aPhysics Department, Aristotle University Thessaloniki GR-54124, Greece
of Thessaloniki,
b Physics Department, 10 000 Zagreb, Croatia
University
‘Physik-Department D-85748 Garching,
Faculty
of Science,
der Technischen Germany
Universitat
of Zagreb,
Miinchen,
The relativistic Hartree-Bogoliubov (RHB) model is employed in the mapping of the proton drip line for medium-heavy, heavy and superheavy elements. The RHB prediction for the last bound isotope of each element is compared with experimental data on the location of the proton drip line. 1. RHB
CALCULATION
OF
THE
PROTON
DRIP
LINE
Models based on the relativistic mean-field approximation have been very successfully applied in the description of a variety of nuclear structure phenomena, not only in nuclei along the valley of P-stability, but also in exotic nuclei with extreme isospin values and close to the particle drip lines. For weakly bound nuclei at the drip lines, in particular, the Relativistic Hartree-Bogoliubov (RHB) model, based on the relativistic mean-field theory and on the Hartree-Fock-Bogoliubov framework, provides a unified description of mean-field and pairing correlations. In proton rich nuclei the RHB model has been used to map the drip line from 2 = 31 to Z = 73, and to investigate the phenomenon of ground-state proton radioactivity [l-4]. The location of the proton drip-line, the groundstate quadrupole deformations and one-proton separation energies at and beyond the drip-line, the deformed single-particle orbitals occupied by the odd valence proton, and the corresponding spectroscopic factors have been compared with available experimental data. The structure of nuclei at the proton drip line in the mass region 60 < A < 100 is important for the process of nucleosynthesis during explosive hydrogen burning. The exact location of the proton drip line determines a possible path of rapid proton capture The path of the rp-process lies between the line of ,&stability and the drip process. line, and it is a very complicated function of the physical conditions, temperature and density, governing the explosion. In addition to its importance for astrophysical processes, the information about the exact location of the drip line, as well as the proton separation energies beyond the drip line, are essential for studies of ground state proton radioactivity. 0375-9474/03/$ - see front matter 0 2003 Elsevier Science B.V doi: lO.l016/SO375-9474(03)00919-9
All rights reserved
21oc
G.A. Lalazissis et al. /Nuclear Physics A719 (2003) 209c-212~ 50 Proton
drip
line
RHBINL3 30
40
50
N Figure
1. Map of the proton
drip line in the region
31 < Z 5 49.
In Fig. 1 we display the results of the relativistic Hartree- Bogoliubov calculation for the proton drip line in the region 31 < Z 5 49 [4]. The NL3 effective interaction [5] is used for the mean-field Lagrangian, and pairing correlations are described by the pairing part of the finite range Gogny interaction DlS [6]. This particular combination of effective forces in the ph and pp channels has been used in most of our recent applications of the RHB theory. The RHB (NL3+DlS) calculation predicts the last bound isotopes for each element. Nuclei to the left are proton unstable. For odd-Z nuclei the proton drip line can be compared with available experimental data. For 2 = 31 and 2 = 33 the calculated drip line nuclei “lGa and 65As, respectively, are in agreement with experimental data reported in Refs. [7,9]. These two nuclei are on the rp-process path proposed by Champagne and Wiescher [lo]. In Ref. [ll] evidence was reported for the existence of ‘joGa, but of course the observation of an isotope does not necessarily imply that the nucleus is proton bound, but. rather that its half-life is longer than the flight time through the fragment analyzer. For 2 = 35 the RHB calculation predicts that the last proton bound isotope is 70Br. The isotope 6gBr is calculated to be proton unbound in most mass models. Experimental evidence for 6gBr was reported in Ref. [7], but no evidence for this isotope was found in the experiment of Ref. ill], and it was deduced that 6gBr is proton unbound with a half-life shorter than about 100 ns. For 2 = 37 the experiments of Refs. [7,8] confirms that 74Rb is the last proton bound nucleus, in agreement with the result of the present calculation. For 2 = 39,41,43 the lightest isotopes observed in the experiment of Ref. [12] are 78Y 82Nb and 86T~, respectively. While for Nb and Tc these results correspond to the drip line as calculated in the present work, for Y the RHB model predicts that the last proton bound nucleus is 77Y This isotope would then be the heaviest T, = -$ nucleus, in contrast to the suggestion of Ref. [7] that ‘jgBr is most likely the highest observable odd-Z T, = -i nucleus. The calculated odd-Z drip line nuclei “Rh and “Ag were observed in
G.A. Lalazissis et al. /Nuclear Physics A719 (2003) 209c-212c
Proton nuclei
211c
2’4Pc
drip line for odd 2 with E-71
*‘*ACT *02Fr 7 ‘g6AtPlgoBlrd
80
‘7’1r/
IX
0 RHB/NLB predictions X GSI Novikov et al N.P. A697 92 (2002)
‘66Ra ‘=TCIr
120
100 *
N
Figure
2. The proton
drip line in the region
73 5 2 < 91.
the experiment reported in Ref. [13], and experimental evidence for “In was reported in Ref. [14]. For even-Z nuclei in this region, it is not possible to compare the calculated proton drip line with experimental data. While for the odd-Z elements most of the last proton bound nuclei lie on the N = 2 line, with just few T, = -$ nuclei, the proton drip line for even-Z elements is calculated to be at T, = -3, or even at T, = -f. The only exception is the drip line nucleus 84R~ with T, = -2. Nuclei with such extreme values of T, are virtually impossible to produce in experiments, and since they lie so far away from the rp-process path, the even-Z proton drip line nuclei in this mass region do not play any role in the process of nucleosynthesis during explosive hydrogen burning. The phenomenon of ground-state proton radioactivity in the region 53 < Z < 7’3 has been the subject of numerous experiments and theoretical analyses in the last decade. An important issue in future experimental studies of heavy proton rich nuclei is the possible observation of ground state proton emission in the suburanium region. A detailed knowledge of the proton drip-line is important in planning experiments on proton radioactivity. In Fig. 2 we display the map of the proton drip-line for odd-Z nuclei with 73 5 2 < 91, calculated in the RHB framework with the NL3+DlS combination of effective interactions. The RHB prediction for the last proton-bound isotope of each element is compared with recent experimental data on the proton drip-1:ne [15]. An excellent agreement between theory and experiment is found. Only for Ta and Ir the RHB model prediction differs by one unit from the experimental position of the proton drip-line. Model predictions of the location of the proton drip line are also very important for
212c
GA. Lalazissis et al. /Nuclear Physics A719 (2003) 209c-212~ Proton drip line for odd Z Superheavy Nuclei
I RHWNLB predictions IZI Discovered isotopes
Figure
3. The proton
drip line in the region
93 5 2 5 119.
All the experimental studies of the synthesis and stability of the heaviest elements. recently discovered isotopes of the superheavy elements, in particular, belong to very proton rich systems. In Fig. 3 we display the section of the chart of the nuclides along the proton drip line in the region 93 I: 2 5 119. The RHB (NLS+DlS) prediction for the last bound isotope of each odd-Z element is shown together with the experimentallyknown superheavy nuclei (2 > 103). REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.
D. Vretenar, G.,4. Lalazissis, and P. Ring, Phys. Rev. Lett. 82 (1997) 4595. G.X. Lalazissis, D. Vretenar, and P. Ring, Nucl. Phys. A 650 (1999) 133. GA. Lalazissis, D. Vretenar, and P. Ring, Phys. Rev. C 60 (1999) 051302. GA. Lalazissis, D. Vretenar, and P. Ring, Nucl. Phys. A 679 (2001) 481. GA. Lalazissis, J. Konig, and P. Ring, Phys. Rev. C 55 (1997) 540. J. F. Berger, M. Girod and D. Gogny, Nucl. Phys. A 428 (1984) 32. M.F. Mohar et al., Phys. Rev. Lett. 66 (1991) 1571. A. Jokinen et al.; Z. Phys. A 355 (1996) 227. J.A. Winger et al., Phys. Lett. B 299 (1993) 214. A.E. Champagne and M. Wiescher, Annu. Rev. Nucl. Part. Sci. 42 (1992) 39. B. Blank et al., Phys. Rev. Lett. 74 (1995) 4611. S.J. Yennello et al.; Phys. Rev. C 46 (1992) 2620. M. Hencheck et al., Phys. Rev. C 50 (1994) 2219. K. Rykaczewski et al., Phys. Rev. C 52 (1995) R2310. Yu.N. Novikov et al., Nucl. Phys. A 697 (2002) 92.